MS PACT Sample 2
Note that in addition to the commentaries provided below, links to various video
clips, lesson plans and other instructional materials can be provided upon
request.
Form: "*PACT - Elementary Mathematics - 1. Context
Form v. 2009"
Created with: TaskStream - Advancing Educational Excellence
Author: Danielle Hamel
Date submitted: 04/12/2011 7:10 pm (PDT)
Context for Learning Form
Please provide the requested context information for the class selected for this Teaching
Event.
About the course you are teaching
(REQUIRED) 1. How much time is devoted each day to mathematics instruction in
your classroom?
1 hour
About the students in your class
(REQUIRED) 2. How many students are in the class you are documenting?
20
(REQUIRED) 3a. How many students in the class are English learners?
9
(REQUIRED) 3b. How many students are Redesignated English Learners?
N/A
(REQUIRED) 3c. How many students in the class are Proficient English speakers?
12
(REQUIRED) 4.1.a. How many students are at the Beginning Listening CELDT
level?
4
(REQUIRED) 4.1.b. How many students are at the Early Intermediate Listening
CELDT level?
1
(REQUIRED) 4.1.c. How many students are at the Intermediate Listening CELDT
level?
1
(REQUIRED) 4.1.d. How many students are at the Early Advanced Listening
CELDT level?
3
(REQUIRED) 4.1.e. How many students are at the Advanced Listening CELDT
level?
0
(REQUIRED) 4.2.a. How many students are at the Beginning Speaking CELDT
level?
3
(REQUIRED) 4.2.b. How many students are at the Early Intermediate Speaking
CELDT level?
1
(REQUIRED) 4.2.c. How many students are at the Intermediate Speaking CELDT
level?
2
(REQUIRED) 4.2.d. How many students are at the Early Advanced Speaking
CELDT level?
2
(REQUIRED) 4.2.e. How many students are at the Advanced Speaking CELDT
level?
1
(REQUIRED) 4.3.a. How many students are at the Beginning Reading CELDT
level?
5
(REQUIRED) 4.3.b. How many students are at the Early Intermediate Reading
CELDT level?
3
(REQUIRED) 4.3.c. How many students are at the Intermediate Reading CELDT
level?
0
(REQUIRED) 4.3.d. How many students are at the Early Advanced Reading CELDT
level?
0
(REQUIRED) 4.3.e. How many students are at the Advanced Reading CELDT
level?
1
(REQUIRED) 4.4.a. How many students are at the Beginning Writing CELDT level?
3
(REQUIRED) 4.4.b. How many students are at the Early Intermediate Writing
CELDT level?
2
(REQUIRED) 4.4.c. How many students are at the Intermediate Writing CELDT
level?
2
(REQUIRED) 4.4.d. How many students are at the Early Advanced Writing CELDT
level?
2
(REQUIRED) 4.4.e. How many students are at the Advanced Writing CELDT level?
0
(REQUIRED) 4.5.a. How many students overall are at the Beginning CELDT level?
4
(REQUIRED) 4.5.b. How many students overall are at the Early Intermediate
CELDT level?
0
(REQUIRED) 4.5.c. How many students overall are at the Intermediate CELDT
level?
2
(REQUIRED) 4.5.d. How many students overall are at the Early Advanced CELDT
level?
2
(REQUIRED) 4.5.e. How many students overall are at the Advanced CELDT level?
1
(REQUIRED) 5. How many students have Individualized Education Plans (IEPs) or
504 plans?
1
(REQUIRED) 6. How many students participate in a Gifted and Talented Education
(GATE) program?
0
About the school curriculum and resources
(REQUIRED) 7. Describe any specialized features of your classroom setting, e.g.,
bilingual, Structured English Immersion, team taught with a special education
teacher.
There are no specialized features of the classroom setting. The classroom teacher or I teach
all of the students including EL students in English within the classroom.
(REQUIRED) 8. If there is a particular textbook or instructional program you
primarily use for mathematics instruction, what is it?
(If a textbook, please provide the name, publisher, and date of publication.)
California Math, Houghton Mifflin, 2005
(REQUIRED) 9. What other major resources do you use for instruction in this
class?
California Math textbook and workbook, ten frames, counters, linker cubes, the Elmo and
Promethean board.
Context Commentary
Please address the following prompts.
(REQUIRED) 1. Briefly describe the following:
- Type of school/program in which you teach, (e.g., middle/high school, themed school or
program)
- Kind of class you are teaching (e.g., third grade self-contained, sixth grade core
math/science) and the organization of the subject in the school (e.g., departmentalized,
interdisciplinary teams)
- Degree of ability grouping or tracking, if any
The school in which I teach is a Title 1 public elementary school. The school offers pre-K
through 5th grade instruction. I teach 1st grade in a class comprised of students of varying
academic ability levels. The students in the class receive instruction in all subjects within my
classroom with the exception of leveled reading, PE, music, and art. For leveled reading, the
students go to different classrooms four days a week based on their reading ability levels.
The students go to PE, music, or art, depending on the day, during the teacher’s prep
period. There are two students who go to math tutoring for 20 minutes in the afternoon.
These students are just below grade level in math and are receiving the tutoring to bring
them up to grade level. They go to tutoring during language arts time. For math instruction
within the classroom the students are not grouped by ability level. However, the seating
arrangement is such that the students sit next to students of different ability levels. This
allows for students to support one another in partner and group work. This seating
arrangement is particularly beneficial for the beginning EL students in the classroom
because they are able to get language support from their peers in addition to the teacher.
2.
Describe your class with respect to the features listed below. Focus on key factors that
influence your planning and teaching of this learning segment. Be sure to describe
what your students can do as well as what they are still learning to do.
(REQUIRED) 2a. Academic development
Consider students prior knowledge, key skills, developmental levels, and other special
educational needs. (TPE 8)
The students range in ability levels from proficient, basic, and below basic in
mathematics. Many of the students are able to count, read, and write whole numbers up to
100 with the exception of a few below basic students. These are vital prerequisite skills for
the learning segment that I will be teaching which involves students learning their addition
facts with sums up to 20. The unit that precedes my learning segment focuses on addition
and subtraction facts to 12. In this unit students learned different strategies for solving
addition facts with sums up to 12. These strategies include adding doubles, doubles plus 1,
adding three numbers, and solving missing addends. These strategies are similar to the
strategies in my unit so the students will be very familiar with the content. Keeping this in
mind, I know that the students are familiar with using the tens frames and counters to solve
addition problems. They use them to add, subtract, and to see the relationships between
different quantities. In fact, these manipulatives are also used in the Kindergarten
classrooms. So the students that attended our school the previous year will be particularly
familiar with using them to solve addition problems. Another skill that the students are
developing that is related to my unit is adding doubles. This skill was introduced early on in
the school year. The students have a double’s rap that they sing that help them remember
the facts. So for many of the students, the lesson that will cover adding doubles will be very
familiar.
Beyond the strategies that are directly related to my unit, the students have other
mathematical skills and abilities. The students skip count by 2’s, 5’s, and 10’s to build their
number sense daily. The students do very well while counting aloud as a class but some
seem to struggle when they are told to skip count in writing. Although this is not in my unit,
it is an important skill that can help them with their adding. The students have also been
exposed to adding in horizontal and vertical form, the associative property of addition,
counting on to add (beginning at the greater addend and counting on to find the sum), and
writing number sentences. These are all important skills that the students must have in
order to successfully achieve the objectives of my unit.
Although students have been exposed to some of the strategies being taught in my
lesson, there are a few below basic students who did not master the content taught in the
previous unit. The areas in which they struggled the most were in adding three addends and
missing addends. These students’ common mistakes in adding three numbers were in
forgetting to add the 3rd number. With the missing addends, they struggled to find the
missing addends because the concept is a bit more abstract than simply adding or
subtracting two numbers to find a solution. But beyond those struggles there are students
who cannot add simple numbers such as 3+5. With manipulatives they have more success
but they will need a lot of support during my unit adding greater numbers.
(REQUIRED) 2b. Language development
Consider aspects of language proficiency in relation to the oral and written English required
to participate in classroom learning and assessment tasks. Describe the range in vocabulary
and levels of complexity of language use within your entire class. When describing the
proficiency of your English learners, describe what your English learners can and cannot yet
do in relation to the language demands of tasks in the learning segment. (TPEs 7, 8)
The students in the class range in ability in terms of language development. There are 8
English Learners. Three of which have a beginning CELT score. These students, along with
one intermediate EL struggle the most with the language demands of mathematics. One
student in the class cannot understand simple instructions such as “take out your folder.”
This student relies on looking at peers to see what they are doing and often times copies
their peers’ responses. Other beginning EL students do this for some tasks that involve
more academic language than others. For example, when students compared quantities
using terms such as greater than, less than, and equals to, many of the EL students
struggled with the language and relied on their peers’ responses for the answer. Despite
their struggle with the academic language, they responded well to visuals in conjunction
with the academic terms.
For the learning segment, the students will be exposed to different terms representing
addition such as sum, addend, doubles, and doubles plus 1. These terms may be difficult for
students who are struggling with acquiring academic language. Visuals will be vital for these
students. The class as a whole struggles with mathematical problems that require a lot of
language. For example, simple word problems. The concept of word problems is abstract to
many of the students and they have difficulty relating word problems into numerical
sentences. Generally these problems have to be worked out as a class. Word problems are
particularly difficult due to the students’ emerging reading skills. Most students have more
success when the word problem is read to them orally. The Houghton Mifflin math program
that I will be using exposes students to word problems daily so that they get multiple
opportunities to build their problem solving skills.
The learning segment involves new terms that the students do not know, however,
many of the terms can be represented visually throughout the unit such as the term sum.
This can be shown visually by an arrow pointing to the sum of a number sentence. The
academic language required in the learning segment can also be simplified as a support. For
example, when using the term “addend”I would also say “the numbers we are adding.”
However, it is important that the academic language is still used throughout the lesson for
the more advanced learners who acquire academic language more quickly than others.
(REQUIRED) 2c. Social development
Consider factors such as the students ability and experience in expressing themselves in
constructive ways, negotiating and solving problems, and getting along with others. (TPE 8)
The students’ social development is still emerging. Some students struggle with
expressing themselves appropriately. These students are seated next to students that they
typically would not get into conflict with. The classroom teacher speaks with the class daily
about appropriate ways to get along with others and communicate their feelings. The
students generate responses on how to get along with their peers during class discussions.
The students typically do not get physical but often times bicker at one another when they
are in disagreement. The classroom teacher generally has to intervene. Seldom are the
students able to solve their problems on their own. The student with the IEP has difficulty
expressing himself appropriately. Asking for a pencil can even be a difficult task. For this
student, a behavior plan is in place and implemented by the classroom teacher and/or
myself.
Although there are a few students that struggle with their social development, most of
the class behaves well and generally follows social cues from their peers. These students
are able to look to their peers to determine the appropriate way to act in class and at
recess. This is particularly helpful when getting the class on task as well as when doing
group and partner work.
(REQUIRED) 2d. Family and community contexts
Consider key factors such as cultural context, knowledge acquired outside of school, socioeconomic background, access to technology, and home/community resources.
The students in the class come from various cultural backgrounds. Each of which bring
something different to the classroom. Many of the EL students are from Spanish speaking
households with the exception of one student who comes from an Arabic speaking
household. The students all come with various levels of knowledge acquired outside of
school. The support level at home from family also varies. Some parents are in the
classroom asking what they can do to help or support their child’s learning. Other parents
are difficult to get a hold of.
The students at the school are predominantly low income with 94.6% of students who
qualify for free and reduced lunch. This statistic may contribute to the students’ limited
access to outside resources. Not all of the students have access to outside resources such
as computers or academic help. However, many of the students go to the Bridges
afterschool program, which provides homework help. The district offers free reading tutoring
in which 6 students in the class utilize. There is no math tutoring outside of school. The only
math tutoring that is available is the 20 minutes a day two students in my class receive
during reading and language arts. There are other resources available to students such as
the Arden/Dimick public library located 5 miles from the school. However, I am not sure
how often this resource is used by my students and their families.
(REQUIRED) 3.
Describe any district, school, or cooperating teacher requirements or expectations that
might impact your planning or delivery of instruction, such as required curricula, pacing, use
of specific instructional strategies, or standardized tests.
The first grade teachers follow a pacing guide for mathematics instruction. It falls in line
with the scope and sequence of the Houghton Mifflin mathematics program. The first grade
teachers follow this guide and assess their students on the same days and are typically on
the same lessons. In addition to the pacing guide, the California mathematics standards are
also followed. Benchmark tests are given throughout the year to see if students are meeting
grade level standards. In terms of requirements my cooperating teacher has, she follows
the format of the Houghton Mifflin teacher’s guide. This involves the lesson beginning with
Circle Time math, followed by a warm up, guided practice, and independent practice. I will
follow this format to maintain consistency and to maximize students’ learning.
Form: "*PACT - Elementary Mathematics - 2. Planning
Commentary Form v. 2009"
Created with: TaskStream - Advancing Educational Excellence
Author: Danielle Hamel
Date submitted: 04/12/2011 7:10 pm (PDT)
Write a commentary that addresses the following prompts.
(REQUIRED) 1.
What is the central focus of the learning segment? Apart from being present in the school
curriculum, student academic content standards, or ELD standards, why is the content of
the learning segment important for your particular students to learn? (TPE 1)
The central focus of the learning segment is to give students strategies to learn their
addition facts with sums up to 20. By giving the students different strategies they are better
able to see the relationship between numbers. As a result, they will better be able to learn
their addition facts with automaticity. For example, the unit begins with teaching students
how to add doubles. This allows the students to quickly see a relationship between numbers
added with the same addends. They can then see a pattern between the sums (the sums
are even). This will eventually lead them to be able to commit the doubles facts to memory
and use these facts as a reference when solving other addition problems. Not only do the
strategies taught in the unit help students see the relationship between numbers to better
help them add, they also help students use a variety of methods to find the sum to addition
problems. This is vital for students because by giving them several strategies, they can use
the ones they feel most comfortable with to find sums. They will then be able to find sums
with greater ease. This is especially beneficial when they move into higher level math. By
giving the students the various strategies to solve addition problems, they are more likely to
find the correct sums.
This learning segment is an important stepping stone for my students because as
they enter into higher level math, addition is almost always present. By giving them the
skills and strategies to solve addition problems with greater ease, they will be more
successful as they progress through their mathematics instruction throughout their
education. Addition mistakes are common even in upper grades. By giving the students
strategies and helping them see the relationships between the addends and the sums, they
will be more equipped to catch simple adding mistakes or avoid them entirely. This learning
segment gives the students a foundation for becoming automatic with adding addends with
sums up to 20. These skills also have useful real world applications due to the frequency of
using addition in everyday life.
(REQUIRED) 2.
Briefly describe the theoretical framework and/or research that inform your instructional
design for developing your students knowledge and abilities in both mathematics and
academic language during the learning segment.
When considering the strategies to use to teach my lessons I first considered the
importance of scaffolding (Bruner, 1960). I structured my lessons in a way in which I can
scaffold the students’ learning by giving a preview/review, followed by an explanation of the
new concept, modeling, guided practice, and then independent practice. This scaffolding
allows the students to begin the lesson by activating prior knowledge, then having full
support followed by gradual independence as they take on the learning task independently.
When considering academic language, I took into account Stephen Krashen’s input
hypothesis. His hypothesis describes comprehensible input in which we best acquire a
language by learning the language that is slightly above our current comprehension level
(Krashen, 1983). I applied this to the development of academic language. For example,
when learning what an addend is, the students must fist have a comprehensible
understanding of what adding numbers means. The term addend must not be too far above
their language understanding in order for them to adequately understand the term. To
ensure that the new vocabulary is comprehensible, I considered this and made sure to
provide visuals and manipulatives to help students acquire the academic language required
in this learning segment.
I also took into account reception learning when structuring my lessons. According to
Lefrancois (1999), children can learn through structured information presented by the
teacher. He describes this as expository teaching in which the teacher presents information
organized by general to the specific. The teacher also gives introductory information that
prepares students for the learning task . Students then learn key concepts, followed by
comparing the new information to previously learned information. I incorporated these ideas
of Lefrancois by having each of my lessons begin with an activity that allows the students to
explore and gets them ready for the continent of the lesson. I then teach the new
vocabulary followed by the new concepts. Lastly, I students will compare what they have
learned to what they are learning in the Doubles Plus One lesson and the Make a 10 to Add
lessons. By utilizing this type of learning, the students will gain a stronger understanding of
the concepts taught in the learning segment.
References
Bruner, J. (1960). The Process of Education: A Landmark in Educational Theory. United
States: Harvard University Press
Krashen, S. (1983). The Natural Approach: Language Acquisition in the Classroom.
Retrieved from http://eric.ed.gov
Lefrancois, G. (1999). Psychology Applied to Teaching (10th Edition).Belmont, CA:
Wadsworth.
(REQUIRED) 3.
How do key learning tasks in your plans build on each other to support students
development of conceptual understanding, computational/procedural fluency, mathematical
reasoning skills, and related academic language? Describe specific strategies that you will
use to build student learning across the learning segment. Reference the instructional
materials you have included, as needed. (TPEs 1, 4, 9)
Each of the learning tasks in the unit are sequenced in a way that builds on the
previously learned skills. The unit in itself builds on from the previous unit which dealt with
addition facts with sums up to 12. This unit’s learning task builds on the previous unit in
that it focuses on addition facts with sums up to 20. The learning tasks in my lessons build
on each other to support students’ development of conceptual understanding by utilizing the
same concepts and procedures to teach different strategies. For example, the first lesson in
my unit focuses on teaching the students how to add doubles. The students learn how to
use a ten frame to add two numbers that are the same addends. The following lesson
focuses on how to add doubles plus one. The students use the same strategy they used in
the previous lesson by using the ten frame and counters. However, this lesson focuses on
the plus one. The students are familiar with the concept due to the previous lesson;
however, they are adding a new concept to it thus building their conceptual understanding.
The students also look at the relationship between the addends in the doubles facts and the
addends in the doubles plus one facts. They are able to see that that the difference in the
addends is that one of the addends is one greater than the other in the doubles plus one
facts. They can then use that same concept to look at the sum and realize that the sum is
one greater than the sum of a doubles fact. By having these two lessons interconnected
with one another, the students are better able to build their conceptual understanding of
adding doubles and doubles plus one.
Similarly, lessons three and four in the unit build on one another. They not only use
the ten fame and counters as a strategy to find sums as in lessons one and two, but they
also both focus on using ten as a strategy to solve addition problems. The concept in lesson
three, Add with 10, and lesson four, Make a 10 to Add, is that 10 can be used as a strategy
to solve addition problems. Lesson three lays down the foundation of adding with 10. In this
lesson, the students use a ten frame and counters to add an addend plus 10. Students are
able to conceptualize adding an addend to 10 by using counters and a ten frame. In
previous lessons they have used these manipulatives to understand addition. As a result of
the consistent use of these manipulatives, the students are better able to use these tools to
conceptualize adding an addend to 10. Lesson four builds on the same concept in that the
students use the 10 frame and counters but in this case, they use it to make an addend into
a 10. For example, the students may have the number sentence 8 + 5. They would then
move 2 counters from the bottom frame which had 5 counters in it, to the top frame which
had 8. As a result, they would have 10 counters in the top frame, and 3 in the bottom
frame. They can then add 10 + 3. This allows the students to use the concept from the
previous lesson and apply it to the new concept of making a 10 to add. The students are
also able to further their understanding of the relationship between numbers by seeing that
the sum of 8 + 5 is the same as the sum of 10 + 3.
Lessons five and six build on concepts the students had learned in the previous
unit. In the previous unit, the students learned how to add three addends with sums of 12
or less. Lesson five builds on this concept in that it teaches students how to add three
addends with sums up to 20. The same procedure is used as what was used in the previous
unit’s lesson. The students are told to choose two numbers to add, then once they add the
two numbers, they add the third number to the sum. The students are reminded of the
associative property of addition in that it doesn’t matter what order they add the addends.
They will still get the same sum. This deepens the students’ conceptual understanding
because it reinforces the strategy they had learned prior and applies it to a slightly higher
level of mathematical computation. This is also true of lesson six which deals with creating
and solving problems. The problems the students create all deal with concepts taught earlier
in the unit. For example, the students create a number sentence dealing with a picture
representing two of the same addends. The students are then able to solve the number
sentence they wrote using the strategies taught in the unit’s lesson. This lesson allows the
students to deepen their conceptual understanding by applying the concepts in a more
expressive way.
The lessons support the students’ computational/procedural fluency and
mathematical reasoning skills by providing consistent strategies across the lessons to
compute the sums. As mentioned before, the lessons each build on one another using
similar strategies. As a result the students are better able to apply the strategies, although
they very slightly from one lesson to the other, to the different concepts they learn
throughout the unit. The students are then able to have better procedural fluency as they
move across the concepts in the unit. The lessons support their mathematical reasoning
skills by allowing the students to look at the relationships between the addends and the
sums across the lessons. For example, when the students compare the sum they get when
they add doubles like 6 + 6 = 12 to the a doubles plus one like 6 + 7 = 13, they are able to
see that the sum of a doubles plus one is one more than the sum of the doubles fact. By
understanding why the sum is one more, they can then use their mathematical reasoning
skills to solve doubles plus one problems with greater ease and understanding.
The learning tasks build on each other to support related academic language by
using consistent academic vocabulary throughout the unit. For example, the main
vocabulary that is repeatedly used throughout the unit is addend, sum, doubles, and
doubles plus one.This vocabulary is used repeatedly throughout each lesson giving students
ample opportunities to hear, see, use and conceptualize it.
(REQUIRED) 4.
4. Given the description of students that you provided in Task 1.Context for Learning, how
do your choices of instructional strategies, materials, technology, and the sequence of
learning tasks reflect your students backgrounds, interests, and needs? Be specific about
how your knowledge of your students informed the lesson plans, such as the choice of text
or materials used in lessons, how groups were formed or structured, using student learning
or experiences (in or out of school) as a resource, or structuring new or deeper learning to
take advantage of specific student strengths. (TPEs 4,6,7,8,9)
As mentioned in Task 1, eight out of the twenty students in the class are EL
students, and one student has an IEP. There are also three students that are below basic in
math. In addition to this, there are four students who consistently finish their independent
practice early with high levels of success. In between these groups is the rest of the class
who are on level in mathematics. All of these factors were taken into account when
planning my instruction for the unit.
When choosing the text and materials to use in my lessons I wanted to be as
consistent as possible with what was already in place with what my Cooperating Teacher
uses. I did this to ensure that the students can build on previous content with greater ease
and success. I decided to use the students’ California Math text book and workbook as well
as the manipulatives that they used in the previous unit that was closely related to the unit
I am teaching. By doing this, the students will be familiar with the procedures for
approaching the various problems so that they can focus on learning the new content.
I also considered the background knowledge of my students. Many of the students
do not receive additional support in mathematics outside of school so I thought it would be
particularly important to provide as much support as possible throughout the lesson. To do
this I created plans for differentiated instruction for the EL students and struggling
students as mentioned in prompt 7 of this learning task and under the differentiated
instruction section of my lesson plans. The seating arrangement of my class was also
considered. The students are seated in a mixed arrangement of varying ability levels. I
utilized this in my planning in that I incorporated think-pair-shares where students can
discuss their responses with students of different academic ability levels. This will allow the
students to hear mathematical reasoning of their peers that they can build upon or learn
from.
In terms of their interests, I took into account that the students enjoy using
manipulatives and talking with their peers. In the lesson the students get ample
opportunities to use manipulatives to solve the various addition problems. The
manipulatives in this unit include counters, ten frames, linking cubes, and numbered cards.
All of which allow students to use their hands to solve in conjunction with their worksheets.
This will not only keep students engaged but will also support their learning. The other
interest that will support their learning is peers. The students enjoy talking with one
another and do not get many opportunities to do so in class. So by utilizing think-pairshares in which the students can share their responses with a peer, they will be more
engaged in the lesson. By considering all of these factors I am able to take advantage of
the students’ specific strengths and build on their deficiencies.
(REQUIRED) 5.
Consider the language demands of the oral and written tasks in which you plan to have
students engage as well as the various levels of English language proficiency related to
classroom tasks as described in the Context Commentary. (TPE 7)
a. Identify words and phrases (if appropriate) that you will emphasize in this learning
segment. Why are these important for students to understand and use in completing
classroom tasks in the learning segment? Which students?
b. What oral and/or written academic language (organizational, stylistic, and/or
grammatical features) will you teach and/or reinforce?
c. Explain how specific features of the learning and assessment tasks in your plan, including
your own use of language, support students in learning to understand and use these words,
phrases (if appropriate), and academic language. How does this build on what your students
are currently able to do and increase their abilities to follow and/or use different types of
text and oral formats?
I would emphasize the following vocabulary and phrases: addend, doubles, doubles plus
1, sum, plus sign, equal sign, and count on.These words and phrases are important for
students to use and understand because they help the students understand the components
of an addition problem as well as how to solve. For example, the terms addend and sum are
components of an addition problem. When telling students to find the sum, they must first
understand what sum means. Likewise, they must know what an addend means because
the term is used throughout the lesson and is also used in further chapters. The terms
doubles, doubles plus 1, plus sign, equal sign, and count on all deal with procedural
concepts. These terms are used to help students solve addition problems. For example,
when using the phrase count on to add 7+3 the students must understand that count on
means to begin counting with 7 and then continue counting from that number 8,9,10 to find
the sum. Without an understanding of these terms and phrases, the students will struggle
with the learning tasks throughout the unit.
I will teach the vocabulary and phrases mention in the above prompt. I will teach and
reinforce the vocabulary by showing visuals, using the terms frequently in context, and by
having the students use the vocabulary and phrases both receptively and expressively. This
will be done by having students display with their fingers the addends, sum, doubles, and
doubles plus 1. Also they will use the vocabulary expressively by discussing with their
partners what the terms mean. This allows them to use the vocabulary in multiple ways
thus reinforcing their learning. Also, I will go over the structure of the worksheets and point
out that on the top of each guided practice page, the definitions of terms are explained and
they can use the pages as a reference when they are unsure of what is being asked. They
also have a page 327 that can be found in the front of their unit packet that defines the
vocabulary found in the unit. The vocabulary page explains the terms both in written and
pictorial form.
In each lesson I introduce and/or review the vocabulary in the preview/review portion of
the lesson. This is done by giving an oral explanation, showing a visual, and by having the
students use and express the vocabulary on their own. The lessons also use the vocabulary
in the directions and give the students brief explanations at the top of the guided practice
pages. The academic language required in this unit is repeated many times throughout the
lesson. In addition to the repetitive use, the academic language builds on each other. For
example, lesson one introduces the term doubles fact and provides multiple exposures to
the term and strategy to solve a doubles fact. Lesson two builds on this term by using the
term doubles plus 1. By already having exposure and practice with the term doubles fact
they are better equipped at learning the new term doubles plus 1 in which the doubles plus
1 fact is one more than a doubles fact. This use of comprehensible input allows for the
students to better acquire the academic language.
I will also use the academic language required in the learning task frequently throughout
the lesson. When using the vocabulary I will reference the visual representation of the
terms as well as relate the terms to more familiar terms they already know. For example,
when having students identify the addends in 6+4=10, I would say “What are the addends,
what are the numbers we add together?” By doing this, the students are still exposed to the
academic language but they are also exposed to the meaning of the term and are still able
to accomplish the learning task. This will be done throughout the lessons. As the students
become more familiar with the academic language, I will scaffold my use of literal
definitions when using the vocabulary by repeating the definitions less frequently until the
vocabulary becomes normal discourse used in the classroom when discussing addition.
(REQUIRED) 6.
Explain how the collection of assessments from your plan allows you to evaluate your
students learning of specific student standards/objectives and provide feedback to students
on their learning. (TPEs 2, 3)
The informal assessments done throughout each lesson allows me to quickly assess
where students are in their learning of the content. For example, in the lessons I have
students hold up their fingers to identify the sums and addends of particular problems. This
allows me to see which students are grasping the concepts, and which students need
additional support. It also allows me to see if I need to speed up or slow down instruction.
From past lessons teaching this group of students, I have found through informal
assessment that I need to move on or stop the guided practice and allow the students to
work independently. Other times I have seen that the students are not grasping the concept
and I need to adjust my lesson in a way that allows the students to better understand the
material. Through this quick informal assessment I am able to adjust my lesson as needed.
In the lessons I also have the students discuss their responses in pairs. I can listen
to the students’ responses as they share to determine if the students are understanding the
concepts much in the same way as when the students show their responses on their fingers.
However, by having the students discuss their solutions with partners, I am able to assess
whether or not they are using the academic language and if they have an understanding of
how they found the solution.
Also, I use the independent practice as an informal assessment on each lesson. By
circulating the classroom and looking at the students’ solutions I am able to see what
students are successfully finding the sums, who uses the manipulatives as a tool and if they
are using them correctly, and where students are making mistakes. I can then determine
which students need small group intervention and which students need enrichment.
Through these informal assessments, I can give feedback to students on what they
are missing and where their mistakes lie. For example, when asking students to hold up
their fingers and show me what the addend is and some students correctly show the addend
while others show me the sum, I know that I need to reinforce what an addend is. At that
point I can go further into identifying addends and give more examples, then assess again.
Similarly, by looking at the students’ independent practice as they work on it, I can look at
how the students came to their solutions and guide students through the steps of finding
the solution if theirs was done incorrectly. For example, if I see that when a student makes
a 10 to add, they are bringing in additional counters as opposed to sliding up the counters
on the bottom frame to fill the ten frame above, I can model for them that we only use the
counters that we already have on the frame. We simply slide the other counters from the
bottom frame to fill the ten frame above.
Lastly, the formal assessment (see Student Assessment and Rubric PDF) at the end
of the unit will give me a stronger sense of what content the students have a grasp on and
what they need more support with. The Chapter 17 test covers finding the sum of doubles,
doubles plus one, adding with a 10, making a 10, adding three addends, and creating and
solving problems. The problems are displayed as number sentences and written story
problems that are in the same format as the guided and independent practice they
completed throughout the unit. The assessment shows what standards each question
addresses making it easier to see if the students are meeting the standards and what
specific standards they need more support with.
(REQUIRED) 7.
7. Describe any teaching strategies you have planned for your students who have identified
educational needs (e.g., English learners, GATE students, students with IEPs). Explain how
these features of your learning and assessment tasks will provide students access to the
curriculum and allow them to demonstrate their learning. (TPEs 9. 12)
For the EL students in the class, their English proficiency levels range from beginning
to advanced so it is important for me to address their varying ability levels. Keeping this in
mind I plan on using the vocabulary in as simple of terms as possible while referencing
visuals that represent the vocabulary. However, I will also use the vocabulary in more
advanced ways to reach the more proficient EL students as well as the rest of the students
in the class. For example, when explaining addends and doubles in reference to 9+9=18 I
would say “This is an addend. What is the other addend? (9) These addends are the same.
They are called doubles.” Later in the lesson I would use the same vocabulary and reference
the visual representation of it; however, I would have the more proficient students tell me
the vocabulary. For example, I would say “For 6+6=12, the 6s are the___ (the students
would fill in addends).” “This type of fact is called a ___(the students would fill in ‘doubles
fact’).” While students are giving me their response, I will point to the addends and doubles
facts to illustrate visually the vocabulary. This allows all levels of EL students, as well as the
varying levels of the students in the rest of the class, to understand the academic language
used in the lessons.
In addition to breaking down the academic language for the varying levels of EL
students, I would also utilize the hands on manipulatives to help aide the students in their
learning. This allows the EL students to solve the addition problems in a more universal way
that doesn’t rely on the language but more so the concept. For example, when making a 10
to add, the EL student does not have to think about the language to solve as they would if
they were simply looking at a number sentence such as 8+6 or asked to explain their
reasoning verbally. They are able to visualize the steps using a method other than through
language.
While manipulatives are especially beneficial for the EL students, verbalizing is also
important in building their academic language. For this reason, I plan on utilizing think-pairshares in which the students think about a solution, discuss it with a partner, and share it
with the class. This is a SDAIE strategy that helps build EL students’ academic language. It
gives the students an opportunity to verbalize their solutions, but it also gives the EL
students an opportunity to hear how other students verbalize their solutions. Also for EL
students, I would utilize small group instruction for the EL students that demonstrate that
they are struggling through the independent practice. I plan on guiding the students
through the lessons much like I did with the guided practice for the whole class. However, I
will reinforce the vocabulary more by referencing what the vocabulary means through
visuals such as pointing to the addend and sum when saying the corresponding terms.
For the struggling students and student with an IEP, I plan on taking a similar
approach as I would for the EL students. I will reinforce the vocabulary and present it at
varying levels as I will with the EL students. I will also utilize the manipulatives and small
group instruction similarly as I would for the EL students. However, for my student with an
IEP, he does well grasping concepts, however he needs support with staying engaged and
on task. For him I plan on calling on him often when he has a solution, or having him come
up to show how he found a solution. This will keep him engaged and help him complete his
work at the same pace as the rest of the class.
For my advanced students/early finishers I plan on asking higher level questions
throughout the lesson. These include more expressive questioning that elicits a deeper
response. For example, I will ask “9+3+1 what two addends would you add first and why?”
The students would have an opportunity to verbalize their mathematical reasoning and give
a deeper response.
Also I plan on having enrichment activities for them to complete once they have
completed their independent practice. The students will have the option to work in pairs so
they can discuss their reasoning with their classmates.
Form: "*PACT - Elementary Mathematics - 3.
Instruction Form v. 2009"
Created with: TaskStream - Advancing Educational Excellence
Author: Danielle Hamel
Date submitted: 04/12/2011 7:10 pm (PDT)
Video Label Form
Candidate ID #
210516762
Elementary Mathematics Clip(s)
(REQUIRED) Lesson from which clip(s) came: Lesson #
Day 3-Add With 10
(REQUIRED) If Electronic, Video Format of Clip(s): (check one)
•
Windows Media Player
Instruction Commentary
Write a commentary that addresses the following prompts.
(REQUIRED) 1.
Other than what is stated in the lesson plan(s), what occurred immediately prior to and
after the video clip(s) that is important to know in order to understand and interpret the
interactions between and among you and your students? Please provide any other
information needed to interpret the events and interactions in the video clip(s).
Prior to the video clip, as a class we completed circle time worksheet 17.3. The
worksheet was broken up into four sections; Problem of the Day, Patterns Review, Calendar
Activity, and Facts Practice. For the Problem of the Day, the students circled the doubles
plus one facts and solved independently. This portion was a review of lesson 1 and 2, which
dealt with doubles and doubles plus ones. For Patterns Review, as a class the students
chorally continued the pattern. I checked for understanding by listening to which students
were able to respond chorally. For Calendar Activity, we looked at the day’s date. Then I
took individual students’ responses for how they can show the day’s number. Only a few
students raised their hands. I gave additional ways to show the day’s number. For Facts
Practice, we found the differences to each problem as a class by using the number line
displayed on the wall and counted back. Students chorally counted back and stated the
difference as a class. Counting back is a subtraction strategy the students use with their
number line. The students start at the greater number and count back down the number
line toward zero to find the difference. We do this also for addition but we call it counting on
in which the students start at the greater number and count up the number line to find the
sum.
After completing Circle Time worksheet 17.3, the students practiced counting on
since this was a strategy they would be using in the lesson. I picked a number and had
students count on from it as a class. We did this a few times until I was sure I had all the
students accurately counting on. Next, I passed out the students’ ten frames and counters.
I then put the students into pairs for the partner activity. This is where the video clip began.
After the video clip we continued on to complete the guided practice. After the
students worked on number 3 with their partners, I called on a pair of students to tell me
their solution and how they found it. I then had the students complete numbers 4 and 5
independently. As the students completed numbers 4 and 5, I circulated the room to see if
the students were setting up their ten frames correctly and if they were writing the correct
number sentences and sums. I noticed that some students did not understand how to set up
their ten frames so after about a minute, I set up my ten frame for number 4. As I set up
my tens frame I thought aloud my steps. I said “I need to show 10 and 1 more. So I will fill
up my top ten frame with counters. Now I will place 1 counter in my bottom frame to show
10 and 1 more.” I then had the class chorally tell me the number sentence and sum they
found. I also did this for number 5. Then I had the students do number 6 in pairs. The
problem was as follows; How is adding 10=5 like showing 15 with 1 ten and 5 ones? As I
walked around the room I noticed the students were not answering correctly. I decided to
complete this problem as a class. I reread the problem and asked if anyone knew the
solution. I still did not get the proper response so I showed the problem visually by drawing
a 1 tens block and 5 ones. I then asked what my tens block and 5 ones displayed. Some of
the students responded “15.” I then pointed to 10+5 and the 1 ten and 5 ones to show the
students the relationship between the two. I then asked “Does 10+5=15?” Students
responded “yes.” Then I asked “Is 1 ten and 5 ones also 15?” The students responded
“yes.” Then I told students “If they both show 15 then they are both equal.”
As a closure I had the students discuss with a partner how they would show 10+6. I
then had them find the sum. The students used their tens frames and counters to show
10+6. Many of the students found the sum with success. Some students were still unsure
how to display the number sentence on their tens frames. After most of the students found
the sums I asked how they found their sums. The students discussed how with their
partners. I walked around and listened to the students responses. Many of the students
responded that they put 10 counters on the top frame and 6 on the bottom. They then
counted on 6 from 10 to find their sums. I was able to see that most of the students were
ready for independent practice.
For the independent practice I read the directions for each section. As I read the
directions I checked for understanding by asking the students to repeat the direction I had
given after each section. The students then began to work independently. As the students
worked independently, I went around the room to see which students were struggling. I
noticed six students ranging from my below basic students to my beginning EL students
who needed additional support. I called these students to the back of the room where we
began completing the independent practice as a group. I guided the students through the
worksheet as if it were guided practice. We did not finish the guided practice but the
students began showing independence as we worked through it. For the students who
finished the colored practice page, I had them complete the black and white workbook page
168 and for the students who finished that page, I gave them enrichment page 17.3.
The video was cut after the warm up activity because the students had to go to
music class which falls in between math time. We continued on with lesson once they
returned which is where the second clip in the video begins.
(REQUIRED) 2.
Describe any routines or working structures of the class (e.g., group work roles, class
discussion norms) that were operating in the learning task(s) seen on the video clip(s). If
specific routines or working structures are new to the students, how did you prepare
students for them? (TPE 10)
One of the working structures seen in the video was having the students work in
pairs. The students have not had much practice with this prior to the video. Generally they
answer independently or chorally when answering questions. I had the students work in
pairs in the previous two lessons so I knew that they were able to work in pairs effectively
and with minimal to no conflict. The students knew that they are to work with the person
next to them. If there was no one next to them they were to join another partnership or
pair up with another student without a partner. Generally I have to help the students pair
up when they have no partner since they are still learning this skill. Once students are
paired, they discuss their responses with one another and I call on a pair of students to give
their response. This is one way in which I get students responses in class.
Another way I get student responses is by having them respond chorally. When I
want students to do this I say something along the lines of “Everyone, what is the sum?”
They also respond by raising their hands in which I will say “With a quiet hand, who can tell
me ___?” Students also show their responses on their fingers by holding them up so I can
see and check for understanding. All of these methods for getting student responses are
familiar working structures in our classroom.
Using the ten frame and counters was another routine working structure for the
students. Many of the students had used the ten frames and counters in Kindergarten so
they were very familiar with how they are used and how they can represent addition. The
counters are passed out by me and collected by a student. The ten frames are also passed
out by me prior to the start of the lesson. The students’ worksheets are located in a green
math folder in each students’ desk. They have two math packets. One we call the “colored
paper” and the other we call the “black and white” paper. The “colored paper” packet
contains the guided practice and independent practice that is from the Houghton Mifflin text
book. The text book is perforated so before the start of each unit the cooperating teacher
and I pull out the pages for the chapter to create their packets. The same is done for the
black and white pages which contain the Circle Time worksheets and the second part of the
independent practice.
(REQUIRED) 3.
In the instruction seen in the clip(s), how did you further the students knowledge and skills
and engage them intellectually in understanding mathematical concepts and participating in
mathematical discourse? Provide examples of both general strategies to address the needs
of all of your students and strategies to address specific individual needs. (TPEs 1, 2, 4, 5,
7, 11)
To further students’ knowledge and skills and engage them intellectually I used
multiple strategies. I had students utilize manipulatives which also served as visuals, the
students participated in think-pair-shares in order to engage in mathematical discourse, and
I had the students elaborate on their responses by asking why and how as well as building
on limited or incorrect responses.
The first strategy I used was having students use manipulatives to represent
addition. This allowed students to conceptualize addition rather than only seeing it in
numeric form. For example, during the warm up seen at the beginning of the video, the
students had to show 13 by using their ten frames and counters. The students were able to
see 10 counters in the top frame and 3 in the bottom. This not only gave them a visual
representation of 13 but they were also able to see that 13 is also 10 and 3 more. They
were then asked to discuss what number sentence is represented on their ten frames. By
doing this they were able to conceptualize 13 visually, and as a number sentence 10+3=13.
This prepared them for the rest of the lesson in which they had to show 10 plus other
quantities to find sums. The manipulatives not only were a tool for helping students find
sums, but they also demonstrated that addition is one quantity plus another which results in
a higher quantity. Many of the students in the class already understand this concept, but for
some of my below basic students, when asked to add, they give a sum that is less than
what they are adding thus showing that they don’t understand the concept of addition.
Therefore using the manipulatives is an important strategy that not only helps all of the
students conceptualize adding quantities to 10, but it also helps the below basic students
have a better understanding of the concept of addition.
Another strategy I used was think-pair-shares. This strategy served two purposes.
One was to have students engage in mathematical discourse and the other was to have
students explain how they found their solutions rather than simply giving an answer. I felt it
was important for the students to engage in mathematical discourse in order to build their
academic language and enhance their reasoning skills. In the clip I had students discuss
with a partner how they knew there were 13 counters on their ten frames. I heard some
students say there are 10 on top and 3 on the bottom and I heard other students say
because they counted. As I listened to partners share I noticed a difference in the use of
academic language between ability levels. Most of the students who are proficient in
mathematics used more language. While others used less. Although there was a difference
in responses, all of the students were still using mathematical discourse. The students also
used their reasoning skills during each think-pair-share since they had to find a solution
and/or share how they found it. This goes into my next strategy of having students
elaborate on their responses by asking how and why.
It is important for students to not only find a solution, but for them to have a deep
understanding of how they found their solution and why they used the strategies they used.
For example, in the clip I asked why there are 10 counters in the top ten frame for 10+4.
The students struggled with the why, but after rewording my question and pointing to the
visuals a few students were able to raise their hand to explain why. The student that gave
her explanation was able to express why there were ten counters in the tens frame thus
showing that she had a conceptual understanding of 10+4 and its visual representation.
Later throughout the lesson, the students were asked to share how they found their
solutions. This furthered students’ knowledge of the process of addition. Also to further
students’ knowledge I asked students to elaborate on limited responses. For example, when
I called on a student to tell me how they knew they had 13 counters he responded by
saying “I counted.” Since we use the strategy of counting on to add, I wanted him to
explain how he counted to see if he was utilizing this strategy. He then responded he
counted “by 10 then I counted on.” By expanding on student responses, I not only built
academic language, but I engaged the students intellectually thus building their
mathematical knowledge and skills.
(REQUIRED) 4.
Given the language abilities of your students as described in Task 1. Context for Learning,
provide examples of language supports seen in the clips that help your students understand
the content and/or academic language central to the lesson. (TPEs 4, 7)
As a language support I utilized the ten frame and counters as a visual representation of
the tasks, had students think-pair-share, built on students responses, and I referenced the
visual manipulatives as I used academic language.
The vocabulary used in the lesson included counting on, and sum. The vocabulary was
basic but I still wanted students to have many opportunities to use it in academic
discourse.The activity at the beginning of the clip allowed the students with limited language
ability to display their solutions. This allowed all the students, even those who struggle with
the language, to participate. Since the beginning activity was simple, the students at lower
mathematical and language abilities had an opportunity to be successful at finding a
solution by using the manipulatives. Since all of the EL students can count, they were able
to successfully show 13 on their ten frames. The manipulatives served as a visual
representation of the tasks asked in the written directions. This was beneficial for the
students that needed more language supports. For students with higher language abilities,
they were able to use the manipulatives to help them give their reasoning. The ten frames
and counters were used throughout the lesson and students were asked to use language to
explain what they did with their manipulatives.
Also in the beginning activity seen in the first part of the clip, I asked the students to
think-pair-share how they knew they had 13 counters. Think-pair-share is a SDAIE strategy
that allows EL students to have opportunities to use the English language in academic
discourse which varies significantly from everyday discourse. Although the EL students did
not use as much academic language when sharing with their partners, they were able to use
some language as well as hear the language used by their peers. This prepared them for the
language demands later in the lesson. The think-pair-shares also were a language support
because I was able to listen to the academic discourse of the class and hear what academic
language the students were using and what language they were lacking and needed to be
emphasized or built upon.
Building on students’ responses was another language support I used. By building on
students responses I modeled how to use academic discourse to give an explanation. Not
only did I elaborate on students’ responses, I had them elaborate if they gave me an
incomplete response. This demonstrated to students that they must think deeper when
solving thus enhancing their mathematical reasoning and language skills. In pairs, the
students elaborated on their responses by answering “why” or “how” questions. This
required them to use more language which builds on their academic language skills.
Lastly, I referenced visuals when giving explanations and using academic language. For
example, when I reiterated how a student said he “counted on”, I pointed to the counters
and demonstrated counting on. Similarly I pointed to the counters on the ten frame when
reading the problems. For example, for number 1 on the guided practice, I read the problem
“Show 10. Show 2 more.” As I did that, I showed 10 and 2 more on my ten frame and
referenced the visual. The students were able to see what showing 10 and 2 more looked
like visually thus bettering their understanding of the language used in the exercise. I did
this throughout the lesson to support not only the EL students, but to support all of the
students in understanding what showing 10 and another quantity means.
(REQUIRED) 5.
Describe the strategies you used to monitor student learning during the learning task shown
on the video clip(s). Cite one or two examples of what students said and/or did in the video
clip(s) or in assessments related to the lesson that indicated their progress toward
accomplishing the lessons learning objectives. (TPEs 2, 3)
To monitor students’ learning I used a variety of strategies. I had the students show
their responses on their fingers and discuss with partners. At the start of the lesson I asked
students why there are 4 counters in the bottom ten frame. At first, none of the students
raised their hands so I rephrased the question. Still, no one responded. After a few more
seconds one of the advanced students gave me a correct response and explanation. I knew
from the lack of student response that I needed to explain further. So for the next guided
practice problem I explained my reasoning verbally as I completed the problem. After
showing the students I checked for understanding throughout working on number 2. For
example, when showing 10 and 6 more, I had the students hold up their fingers to show
how many counters they needed on the bottom frame. Several students, with the exception
of a few held up their fingers to show 6. I was able to quickly assess how many students
knew how to set up the tens frame based on the information given in the problem. This
showed me that I could give less support on the next problem as I scaffold their learning for
them to gain independence. While this type of informal assessment is easy for students to
do, often times students copy the responses of their peers so it is not the most accurate
way of assessing students understanding.
Because of this, I also had students discuss their solutions with their partners. This was
an effective way to informally assess students because I was able to hear their reasoning.
This let me know where the gaps in their learning were and gave me an idea of what portion
of the lesson needed reinforcing and what portion the students were grasping.
Form: "*PACT - Elementary Mathematics - 4.
Assessment Commentary Form v. 2009"
Created with: TaskStream - Advancing Educational Excellence
Author: Danielle Hamel
Date submitted: 04/12/2011 7:10 pm (PDT)
Write a commentary that addresses the following prompts.
(REQUIRED) 1.
Identify the specific standards/objectives measured by the assessment chosen for analysis.
You may just cite the appropriate lesson(s) if you are assessing all of the
standards/objectives listed.
The standards addressed in the assessment are as follows:
NS 2.1-Know addition facts (sums to 20) and the corresponding subtraction facts and
commit them to memory.
NS 2.5-Show the meaning of addition (putting together, increasing) and subtraction (taking
away, comparing, finding the difference).
NS 2.7- Find the sum of three one-digit numbers.
MR 1.2-Use tools, such as manipulatives or sketches, to model problems.
AF 1.1-Write and solve number sentences from problem situations that express
relationships involving addition and subtraction.
The objectives measured by the assessment are the objectives of each of the six lessons
that can be found on the lesson plans.
(REQUIRED) 2.
Create a summary of student learning across the whole class relative to your evaluative
criteria (or rubric). Summarize the results in narrative and/or graphic form (e.g., table or
chart). Attach your rubric or evaluative criteria, and note any changes from what was
planned as described in Planning commentary, prompt 6. (You may use the optional chart
provided following the Assessment Commentary prompts to provide the evaluative criteria,
including descriptions of student performance at different levels.) (TPEs 3, 5)
To evaluate the classes’ performance as a whole I created five evaluative criteria that
address the objectives of each lesson (see Assessment and Rubric attachment). The
evaluative criteria is as follows; computation of doubles and doubles plus one addition
problems, computation of an addend plus 10, making a 10 to add two addends,
computation of adding three addends, and translating a word problem into a number
sentence and solving with accuracy. Students scored either proficient, basic, below basic, or
far below basic based on the number correct they had under each evaluative criteria.
The first evaluative criteria, computation of doubles and doubles plus one addition
problems, measured students’ performance on problem numbers 1-6 of the assessment.
Thirty five percent of the students scored proficient (5/6-6/6 correct) on this portion of the
test. These students demonstrated that they had a strong understanding of the doubles
facts. It is not measurable from the test whether or not they had the facts committed to
memory or if they used manipulative. Manipulatives were available for the students’ use
throughout the assessment. These students also demonstrated that they had a strong
understanding of the doubles plus one facts. Eighteen percent of the class scored basic (4/6
correct) on this portion of the test. These students demonstrated that they have a basic
understanding of how to solve doubles and doubles plus one addition problems. Twelve
percent of the class scored below basic (2/6-3/6 correct). These students showed that they
are below the level of basic understanding. These students have not committed the doubles
and doubles plus one facts to memory and do not demonstrate that they can use the
manipulatives to help them solve the addition problems. Thirty five percent of the class
scored far below basic (0/6-1/6 correct) on this portion of the test. These students do not
have the doubles and doubles plus one facts committed to memory nor can they have an
understanding of how to use the manipulatives to help them solve.
The next evaluative criteria, computation of an addend plus 10, measured students’
performance on problem numbers 7 and 8 of the assessment. Since there were only two
problems under this criteria, the measure of the classes’ performance in this area is not a
complete picture. Rather it gives a basic idea of the students’ performance. Forty one of the
class scored proficient (2/2 correct). These students were able to accurately write a number
sentence that showed 10 more than a given quantity which includes using the correct
operation (addition). They were also able to solve with accuracy. Twenty four percent of the
class scored basic (1/2 correct). These students were able to accurately write a number
sentence and solve 1 out of the 2 problems. Thirty five percent of the students scored below
basic (0/2 correct). These students were unable to make a number sentence and solve with
accuracy 10 plus another quantity.
Making a 10 to add was the next evaluative criteria and was measured by problem
numbers 9-13 on the assessment. Twenty nine percent of the class scored proficient (5/5
correct). These students were able to accurately solve using the make a 10 to add strategy
with their ten frames and counters, however, since using counters cannot be measured on
the test, some students may have used other strategies to solve. Twelve percent of the
class scored basic (3/5-4/5 correct). These students were able to solve the addition
problems under the criteria with few errors. Twelve percent of the class scored below basic
(2/5 correct). These students solved with less than fifty percent accuracy and showed that
they are below the basic level of understanding how to solve using the make a 10 to add
strategy. Forty seven percent of the class scored far below basic (0/5-1/5 correct). These
students show that they are unable to use the make a 10 to add strategy to solve addition
problems.
Computation of adding three addends was another criteria that measured students’
performance on problem numbers 14-17. Thirty five percent of the class scored proficient
(4/4 correct). These students demonstrated that they understand the strategy of choosing
to addends to add then adding the third addend. Twelve percent of the class scored basic
(3/4 correct). These students showed they had a basic understanding of how to add three
addends using the strategy learned in the lesson. Twelve percent of the class scored below
basic (2/4 correct). These students were slightly below having a basic understanding of
how to solve three addend addition problems. Forty one percent of the class scored far
below basic (0/4-1/4 correct). Students who cored far below basic were unable to use the
strategy for solving three addend addition problems with success.
The last evaluative criteria was translating a word problem into a number sentence and
solving with accuracy. There was only one problem on the test that fell under this criteria so
the measure of students performance in this area is not accurate. However, I decided to
score the students as proficient (1/1 correct) or below basic (0/1 correct). Fifty three
percent of the class scored proficient while Forty one percent of the class scored below
basic. The students who scored proficient were able to demonstrate that they can accurately
create a number sentence from information given in a word problem. They were also able to
solve the problem with accuracy. The students who scored below basic were unable to
create a number sentence and solve based on information given in the word problem.
The overall performance of the class was scored using percentages. Students who
scored 75%-100% were proficient, 50%-74% were scored as basic, 25%-49% were scored
as below basic, and a score of 24% or below was far below basic. I chose these percentage
ranges because there were only a few number of questions on the test and I wanted a more
accurate representation of the students’ overall performance. The students’ overall
performance on the test was as follows; 35% proficient, 18% basic, 12% below basic, and
35% far below basic.
(REQUIRED) 3.
Discuss what most students appear to understand well, and, if relevant, any
misunderstandings, confusions, or needs (including a need for greater challenge) that were
apparent for some or most students. Cite evidence to support your analysis from the three
student work samples you selected. (TPE 3)
The students’ scores on the assessment varied greatly in range of understanding. Some
students had a strong understanding of the skills measured on the assessment while others
struggled in particular areas or on the entire test as a whole. The students demonstrated
their understanding, misunderstandings and needs in a variety of ways on the test.
Beginning with students’ understanding, based on the scores under the double and
doubles plus one category of the rubric, the class was divided with half of the class being
proficient and basic, while the other half of the class was below basic and far below basic.
Although the student’ performance on this portion of the assessment was split, the students
who scored basic and proficient demonstrated a strong understanding of the doubles and
doubles plus one facts. Although it is hard to measure, these students may have the
doubles facts committed to memory or used manipulatives to help them solve. Most of the
students who answered incorrectly on this portion of the test made simple mistakes such as
have an answer that was one more or one less than the correct answer. This indicates that
the students are either miscounting when using their manipulatives or they are adding a
one to the wrong doubles facts for the doubles plus one strategy. For example, on student
sample 1 on problem numbers 1 and 2 the student’s answers were close to the doubles plus
one fact however they failed to add the plus one correctly. (Doubles plus one is when the
students think of a closely related doubles fact and add one. 7+6 is a doubles plus one fact
of 6+6.) This was a common mistake among the students who made errors in this portion
of the test. These students would benefit greatly from practicing their doubles facts to
commit them to memory as well as get additional practice in recognizing and solving
doubles plus one facts. This can be done as a whole class review to reinforce the skills
taught in lessons one and two. Other students simply wrote far off answers such as in
student sample 3 in which the student’s answers were far from the correct response. For
example, for problem number 5 the student said 8+9=91. For the students who scored in
the far below basic range, this was common. This demonstrates that they have limited
number sense and may not fully understand the concept and/or procedures of addition.
These students will benefit from a review of chapter 5 in which the students use doubles to
add, however the addends are much less. These students do not have sufficient prerequisite
skills and need to focus on smaller addends before moving on to the doubles and doubles
plus one facts covered in this unit.
For computation of an addend plus 10, there were only two problems that addressed this
area. Because of the limited number of questions, I wasn’t able to get an accurate
measurement of students’ understanding, but I was able to see what types of mistakes
students were making. Most of the class had an understanding of how to show 10 plus
another quantity. These students either got 1/2 or 2/2 of these questions correct. Their
understanding showed that they understood how to write a number sentence that reflects
10 and however more of another quantity. It also showed that they know how to find the
sum of 10 plus another quantity. This was a strength amongst most of the students. For the
students who struggled, their misunderstandings varied from being able to write the correct
number sentence but finding the wrong sum to not writing the correct number sentence
thus resulting in an incorrect sum. For the students whose mistakes were in writing the
correct number sentence but wrong sum, they demonstrate that they may not be using
their manipulatives correctly to find the sum. A review on how to use the ten frame and
counters will be beneficial for these students. For the students who wrote incorrect number
sentences, they do not understand how to translate the written information into a number
sentence. Their needs can be met by reteaching the lesson.
Most of the class struggled with making a 10 to add. The directions on the test do not
instruct students to do so but I reminded the students as I read the directions to make a 10
to add using their counters to help them solve the problems. Since I am unable to formally
measure whether or not the students utilized the manipulatives other than reflecting back to
what I observed while the students took the test, I cannot determine if this strategy lead to
the students’ success for those who did well on this portion of the test. I can however see
the types of mistakes the students made. For the students who had incorrect responses,
many of their answers were close to the correct response. This demonstrates that the
students may be making errors in counting with their manipulatives. This can be addressed
by revisiting how to use the manipulatives to make a 10. Also the students can benefit from
the counting on strategy in which the student starts at the greater number and counts on to
add the other quantity. For example, for problem number 9, 9+7=, students can count the
manipulatives by starting at 9 then counting 10, 11, 12, 13, 14, 15, and 16. This can reduce
students’ errors in counting resulting in less simple mistakes and more accurate responses.
The class also struggled with adding three addends. The most common mistake was
forgetting to add the third addend after they added the other two addends as in student
sample 2’s answer to problem numbers 14, 15, and 17. This student forgot to add the third
addend resulting in an incorrect response. This common error can be addressed by
reteaching the steps to solving three addend addition problems and by giving the students
additional practice. The last step will need to be emphasized which is adding the third
addend to the two addends that were added.
Translating word problems into a number sentence was also difficult to measure since
there was only one problem on the test that addressed this area. Fifty three percent of the
class were able to create a number sentence and solve it correctly while 41% of the class
was not. Common mistakes were made in creating the number sentence. Many students
used numbers that were not found in the word problem. This indicates that these students
do not understand how to use information in a word problem and apply it to a number
sentence. These students need reteaching in identifying the information needed and putting
it into a number sentence. Other students correctly made number sentences but made
mistakes in finding the sum. For example, in student sample 3 the student circled the
relevant information, the 9s, and put it into an addition number sentence. However, the
sum he wrote was incorrect and he also wrote a plus where an equals sign should have
been. The students whose errors fell in finding the correct sum, will benefit from more
addition practice and by utilizing manipulatives such as a tens frame and counters as well as
a number line.
(REQUIRED) 4.
From the three students whose work samples were selected, choose two students, at least
one of which is an English Learner. For these two students, describe their prior knowledge of
the content and their individual learning strengths and challenges (e.g., academic
development, language proficiency, special needs). What did you conclude about their
learning during the learning segment? Cite specific evidence from the work samples and
from other classroom assessments relevant to the same evaluative criteria (or rubric). (TPE
3)
I chose Student 2 and Student 3 to analyze for this prompt. Student 2 is an EL student
and scored below basic on the assessment. Student 3 scored far below basic on the
assessment. Each student has their own learning strengths and challenges that need to be
built upon and addressed.
Prior to taking the assessment, student 2 demonstrated knowledge of doubles and
doubles plus one facts and adding with 10 by actively participating in class to give
responses as well as by showing understanding in these areas on her independent practice
work. These strengths are reflected on the assessment. Student 2 answered the doubles
and doubles plus one problems with 100% success. They also demonstrated an
understanding of how to make a number sentence that shows 10 plus more of a specific
quantity as in problem numbers 7 and 8 on the assessment. However, this student added
10+5 incorrectly on problem number 7. This is where student 2’s weaknesses are.
Student 2 enjoys participating in class during instruction, however, when left to do
independent practice, Student 2 often asks for help. Even after support is given, student 2
say she still don’t understand and gets frustrated. Student 2 is an EL student. She does
particularly well with visuals and manipulatives to aid in her learning. On the assessment
however, the students were allowed to use manipulatives yet she still struggled with making
a 10 to add and adding three addends. For problem numbers 9, 10, 11, and 13, Student 2
subtracted instead of added. This is a mistake that is common amongst first graders. She
may not have understood the directions, or she may not have paid attention to the + sign
as she worked through the problems. Since she made this mistake, it is difficult for me to
assess whether or not she has an understanding of how to make a 10 to add. I did look at
her independent practice and I was able to see that she got all of the problems correct.
Based on that, she does not need re-teaching but will benefit from reminders to check to
see if the problems are addition or subtraction before completing them. Adding three
addends was one of Student 2’s major challenges. Even prior to the assessment and in the
previous unit, this student would make the same mistake. Her common mistake was
forgetting to add the third addend which can be seen on problem numbers 14-17 of her
assessment. She added the two addends successfully; however, by forgetting to add the
third addend, she received 0/4 on this portion of the test.
Although Student 2 is an EL student, she did well on problem number 18 of the
assessment which is a word problem. She was able to create a number sentence based on
the information in the word problem. However, she got this problem wrong because she
inverted 18 making 81. She makes this mistake often in her work. I address this known
problem by asking the class to tell me how to write numbers as I write them on the board
during class.
Although, Student 2 scored below basic on the assessment, the errors that she made
can easily be addressed. She needs to pay attention to the operation in math problems,
remember to add the third addend to the other two addends when solving three addend
problems, and practice writing her numbers so that she does not switch the digits. Based on
her class participation, she was able to meet the language demands of the unit. She
participated often in class and discussed her answers using academic language. There were
times when she did not know the correct terms to use which are due to her still developing
the English language. This can be addressed by giving her more opportunities to use the
academic language by doing think-pair-shares as well as by helping her expand upon her
individual responses in class. I feel Student 2 is at the borderline in reaching basic based on
the types of errors she made as well as the successes she had on the assessment.
Prior to the assessment, Student 3 struggled greatly in math as well as in other
subjects. This student goes to math tutoring for 20 minutes to build his number sense and
mathematical reasoning skills. Often times this student writes random responses to math
problems. He needs to be reminded to think about his answer before he responds. I also
model one-on-one with him how to solve particular problems after I have taught a lesson.
At times he is successful after, other times he gives responses that are far off from the
correct response. His parents and staff are considering having him repeat the first grade
due to his struggles with math and language arts.
On the first portion of the test you can see that his responses to problem numbers 2, 3,
5, and 6 are far off from the correct response. For example, for problem number 2, he
answered 6+5=91. This shows that he did not use any strategies to solve the problem
including utilizing the manipulatives that were available. He was able to answer 6+6
correctly, although it is unclear if he used manipulatives or had this doubles fact committed
to memory due to the doubles rap we often sing as a class. Regardless, he needs support
with addition and understanding what different quantities represent.
He did show some success with adding a number to 10. His number sentences were
correct for both problem numbers 7 and 8, although he had the incorrect sum for problem
number 7. This shows that he does know how to take written information and translate into
a number sentence. Problem number 18 also demonstrates this strength although again he
had an incorrect sum. He also wrote a + where an = should have gone. He also struggled
with problem numbers 9-13 in which students were told to use their manipulatives to make
a 10 to add. He did add problem number 10 correctly but missed the others. Again he had
an implausible answer, 7+8=45. He needs additional support with adding quantities using
the make a 10 to add strategy.
Overall, Student 3 scored far below basic on the assessment. He did not meet the
objectives of the unit and needs re-teaching in doubles, doubles plus one, making a 10 to
add, and adding three addends. However, he not only needs re-teaching in these areas, he
needs to continue with his tutoring to build his number sense and mathematical reasoning
skills so that he can complete the learning tasks of the class with more success and better
understanding.
(REQUIRED) 5.
What oral and/or written feedback was provided to individual students and/or the group as
a whole (refer the reviewer to any feedback written directly on submitted student work
samples)? How and why do your approaches to feedback support students further learning?
In what ways does your feedback address individual students needs and learning goals? Cite
specific examples of oral or written feedback, and reference the three student work samples
to support your explanation.
I gave feedback to the students in two ways. I gave feedback directly on the
assessments and I gave feedback to the class as a whole. As seen on the student
assessment samples I addressed their mistakes by telling them what type of mistake they
made or by reminding them of the procedure for solving the particular problems. For
example, on student sample 2, I pointed out that the student subtracted instead of added
by writing “Oops! You subtracted. Make a 10 to add.” I also reminded her of the last step in
solving three addend addition problems by writing “don’t forget to add the third number.”
Similar types of feedback were given on each assessment that contained errors.
In addition to giving written feedback on the assessments, I gave oral feedback to the
whole class as I went over each problem a few days after the assessment. I gave oral
feedback for each portion of the test. For problem numbers 1-6, I had the students sing the
doubles rap. I then asked them if there are any doubles in problems numbers 1-6. The
students responded by telling me all the doubles as I circled them. I then informed students
that if they don’t have their doubles facts memorized they can use counters to find the
sums. We worked out the doubles using counters as a class. Then I asked the students if
they see any doubles plus one facts. I drew boxes around the doubles plus one facts as they
called them out. I reminded them that a doubles plus one fact has a sum that is one more
than its related doubles fact. I pointed out the related doubles fact for each doubles plus
one problem. I pointed out to the students that many of the students are choosing the
wrong doubles fact to help them with their doubles plus one. For example, instead of
thinking about 7+7=14 to help them solve 7+8= 15, some students use 8+8=16 and
adding one making 7+8=17. I told the students to be sure to use the doubles fact of the
lesser number.
For problem numbers 7 and 8, I told students that many students had trouble making a
number sentence. We worked problem number 7 out as a class. I used arrows to show how
we bring the information in, “Show 10. Show 5 more” down into the blanks to create a
number sentence. I then had students tell me if I needed a plus or a minus. Many of the
students were able to tell me we needed to add. They also informed me that I needed an =.
We added as a class by using counters and a ten frame. I reminded students that if they
come across this type of problem again to use their ten frames and counters to help them
solve.
Since so many students struggled with problem numbers 9-13, I wanted to give multiple
examples of how to solve these types of problems so we worked out each problem as a
class. I began by reminding students how to make a 10 by modeling how to solve problem
number 9. We then solved problem numbers 10-13 as a class. For problem numbers 14-17,
I displayed the steps to adding three addends (can be found in the day 5 lesson plan). We
read the steps as a class. I then told students that many of the students are forgetting to
add the third addend. I highlighted this step in yellow. We then worked out problem
numbers 14 and 15 as we said each step making sure to emphasize adding the third
addend.
Lastly, for problem number 18, I told students that some of the students were not using
the information from the word problem to make their number sentence. I explained that
some students used numbers that were not even in the word problem. I reminded the
students the steps for solving word problems as we worked out problem number 18 as a
class. I circled the numbers I needed for my number sentence and I underlined the words
“more” and “how many” which helped me know that I needed to add. We then translated
that information into a number sentence and used counters to find the sum.
By going over each section, explaining common mistakes, and working out problems as
a class I was able to address each students’ needs as well as support students’ further
learning. The proficient students got a review that would strengthen their skills. The basic
students were able to reinforce what they already knew while addressing where they may
have had confusion. For the below basic students, they were able to get feedback on
common mistakes as well as have a brief re-teaching of the strategies taught in the unit.
And for the far below basic students, they were also able to get a brief re-teaching of the
strategies, however they will need additional support in developing an understanding of the
concepts covered on the assessment and the unit as a whole (addressed in prompt 6).
(REQUIRED) 6.
Based on the student performance on this assessment, describe the next steps for
instruction for your students. If different, describe any individualized next steps for the two
students whose individual learning you analyzed. These next steps may include a specific
instructional activity or other forms of re-teaching to support or extend continued learning
of objectives, standards, central focus, and/or relevant academic language for the learning
segment. In your description, be sure to explain how these next steps follow from your
analysis of the student performances. (TPEs 2, 3, 4, 13)
Based on the students’ performance on the assessment, there are different areas of the
unit that need to be re-taught, reinforced or built upon for some students in the class which
include the below basic and far below basic students. For the students who scored basic
and proficient, they can benefit from extension activities.
Slightly less than half of the class scored either below basic or far below basic on the
assessment. Since this trend was consistent along each criteria of the assessment, these
students will benefit from me re-teaching the strategies taught in the unit. However, as I
mentioned with Student 3, the far below basic students are not ready for adding sums up to
20 such as what was taught in the lesson. These students will benefit from learning the
same strategies but with smaller numbers. For example, for re-teaching the doubles and
doubles plus one facts, I would need to go back to chapter 5 and teach the same facts but
with smaller numbers such as 2+2=4 and its related doubles plus one fact, 2+3=5. The
below basic students may benefit from this as well but may also benefit from simply reteaching the strategies taught in my learning segment. In addition to re-teaching these
concepts, it would also be of particular importance to reinforce the vocabulary doubles,
doubles plus one, sum, and counting on. Creating a math vocabulary wall for students to
reference, along with visuals, will be a useful support for all of the below basic, far below
basic, and EL students.
For the students who scored proficient and basic, I can build on their understanding by
providing them extension activities. For example, Student 1 only missed 3 problems and
does not need re-teaching, however, she can build her understanding of the concepts
taught in the unit by doing additional enrichment activities. Based on how each student
performed in the different areas of the test, enrichment/extension activities for the basic
and proficient students can include, figuring out what doubles facts go with a given sum. For
example, I can give students the number 16 and have them figure out what doubles fact
goes with it (8+8). I can also do this for doubles plus one facts. This builds on the students’
understanding and enriches their learning. For computing an addend plus 10, I can give
them story problems that utilize this skill as well as have them create story problems for
their peers to solve. This activity can address both adding with 10 as well as translating
word problems into number sentence. For making a 10 to add, I can have the students find
missing addends to figure out how many is needed to make a 10 with a given quantity. For
example, I can give the students the number 7 and have them figure out how many needs
to be added to 7 to make 10. I can have students do this without manipulatives in order to
enrich their learning and build their automaticity in recognizing what numbers make 10. To
build upon the students’ understanding of adding three addends, I would put the addends in
word problems and have them write their own number sentences. I would have students
solve in horizontal form since they have only had exposure to adding three addends in
vertical form. Lastly, to build students’ automaticity in adding, I would have students do
timed addition tests that progress to higher quantities as they successfully finish each timed
test. For example, the first timed test would be an addend plus zero such as, 0+0, 0+1,
0+2…up to 0+10. If students are able to complete the test with 100% accuracy in one
minute, they can take the +1 test and so on. This would build students’ automaticity and
help them meet standard NS 2.1.
All of these strategies will help address students’ individual needs based on their
performance on the assessment. While some students’ need more support than others, it is
important for the students to have a deep understanding of the concepts before moving on
to the next chapter which address subtraction from 13 through 20. The far below basic may
not be ready for the next chapter. These students will need small group intervention and
will benefit from using the alternative approach worksheets provided by Houghton Mifflin to
meet their instructional needs.
Form: "*PACT - Elementary Mathematics - 5.
Reflection Commentary Form v. 2009"
Created with: TaskStream - Advancing Educational Excellence
Author: Danielle Hamel
Date submitted: 04/12/2011 7:10 pm (PDT)
Write a commentary that addresses the following prompts.
(REQUIRED) 1.
When you consider the content learning of your students and the development of their
academic language, what do you think explains the learning or differences in learning that
you observed during the learning segment? Cite relevant research or theory that explains
what you observed. (See Planning Commentary, prompt # 2.) (TPEs 7, 8, 13)
I feel there are three factors that explain the differences in learning among the
students in my learning segment. The students’ prerequisite skills and their varying ability
levels prior to the learning segment, the use of supports such as visuals and hands on
manipulatives to help students understand the concepts and academic language, and the
scaffolding of each lesson to help students gain gradual independence were all factors that
explain the differences among the students’ learning.
A common trend was seen amongst the class in relation to their performance in my
learning segment and their overall mathematical performance in the class. After looking
over past classroom assessment data, the students who consistently perform at far below
and below basic levels in math in the class overall, also performed at this level in my
learning segment. The same applies to the basic and proficient students with slight
variability amongst a few students. Since much of the content prior to the learning segment
dealt with addition, the students who struggled with addition prior to the lesson had the
same difficulties. These students struggled with adding greater numbers due to their
deficiencies in not having adequate addition skills. Although scaffolding was used in the
lesson, the struggling students did not have sufficient prerequisite skills and as a result the
supports I gave were not enough. The struggling students needed the prerequisite skills to
connect the new content to. As a result, they were unable to meet the objectives and will
need additional support. The students who were at basic and proficient levels did well with
meeting the objectives of the lessons, however, some students still struggled and performed
a bit lower than they normally do in the class overall. This is where the variability came in.
This may have been due to my scaffolding.
After the first lesson I realized the students needed more scaffolding (Bruner, 1960)
in order to successfully complete the learning task. As I taught day 2’s lesson, I realized
that some students still needed support in using the manipulatives and counting them to
find the sums. As a result, I spent a bit more time modeling how to solve the problems
before I let the students work independently. Despite doing this, some students still
struggled. This included students that typically perform at basic levels. Some of these basic
students ended up performing at below basic levels on the unit test. After reflecting back,
my scaffolding of the concepts in each lesson should have included more teacher modeling.
This would have allowed the students to have gained a better understanding of the
strategies presented in the lesson.
Lastly, the use of visuals and hands on manipulatives helped lessen the differences
between students who grasped the academic language used in the unit and those who did
not. By taking into account Stephen Krashen’s input hypothesis (1983), I was able to teach
the students the academic language that was at their comprehensible input level. I did this
by referencing the manipulatives as well as visuals when presenting and using the academic
language. The students also used the academic language during think-pair-shares and/or as
they responded to my questions individually. By listening to the students’ use of the
academic language and by their responses as I checked for understanding, it appeared that
most of the students understood the academic language used in the lesson.
References
Bruner, J. (1960). The Process of Education: A Landmark in Educational Theory. United
States: Harvard University Press
Krashen, S. (1983). The Natural Approach: Language Acquisition in the Classroom.
Retrieved from http://eric.ed.gov
(REQUIRED) 2.
Based on your experience teaching this learning segment, what did you learn about your
students as mathematics learners (e.g., easy/difficult concepts and skills, easy/difficult
learning tasks, easy/difficult features of academic language, common misunderstandings)?
Please cite specific evidence from previous Teaching Event tasks as well as specific
research and theories that inform your analysis. (TPE 13)
After reflecting back on my experience teaching my learning segment I learned that my
students need strong, clear, and explicit modeling of concepts before they work
independently, they enjoy and do well with exploring concepts prior to the start of the
lesson, it is difficult for them to solve problems with multiple steps, and that word problems
are a challenge.
I quickly found that the students did better when the initial teacher modeling of
how to solve the problems was very clear and explicit. For example, in my first lesson,
Adding Doubles, I asked several questions as I modeled the first problem of how to solve a
doubles fact. This interrupted the instruction and left some students unsure of the steps to
solve. It would have been more beneficial if I had modeled the first problem on my own
without checking for understanding. Once I had modeled the problem in its entirety, I
should have then checked for understanding. As I realized this I decided to model the first
problems with minimal to no interruptions in the subsequent lessons. This allowed the
students to get a clear understanding of the steps to solving the various addition problems
in the lessons. This experience showed me how important teacher modeling is and also
reinforced the importance of scaffolding (Bruner, 1960). The scaffolding should be done in
such a way that the students have enough supports to gain independence in the leaning
task. For me, the students were more successful with clear and explicit instruction prior to
gradually gaining independence.
I also found that the students enjoyed exploring the concepts prior to the start of
the lesson by doing activities that prepared them for the learning tasks. This type of
exploration falls in line with discovery learning. Discovery learning involves structured
activities in which students can explore materials that can lead them to discover important
ideas and concepts (Schunk, 2000). For example, in the Adding Doubles lesson the students
began by working with a partner to find doubles facts using counters and numbered cards.
The students enjoyed using the manipulatives, working with their peers, and having the
opportunity to explore. Many of the students were able to find doubles facts and write
number sentences based on the doubles facts they found using the counters. All of this was
done without me giving them any supports other than reiterating the directions. I was also
able to refer back to the activity as we went through the lesson to build on their learning.
For example, in the Adding Doubles lesson I asked students to think back about some of the
doubles facts they found with their partner as a way to connect the new concepts with what
they discovered at the start of the lesson. This was beneficial for many of the students. I
used this strategy in all of my lessons with the exception of the Doubles Plus One lesson.
Through teaching the unit, I also found that word problems are very difficult for my
students. Although the lesson involved the students creating their own word problems
through a series of steps, they still had trouble with the language demands of the lesson.
This included using the correct words to represent addition as well as figuring out how to
use the numbers from their number sentence into a story. This lesson required a lot of
teacher directions. Students will need constant practice with this concept since it was a
challenge even for the proficient students. It was more so a challenge for the EL students
and the students who struggle with reading and writing in general. A lot of teacher directed
support was needed for this learning task. Another issue with creating word problems was
that it had several steps that went into it.
The students struggled with solving problems that had more than two steps. For
example, in the Make a 10 to Add lesson, if given 8+5 for example, the students had to first
place 8 counters on the top frame and 5 counters on the bottom. Second, they had to move
two counters up to the top frame resulting in 10 in the top frame and 3 in the bottom.
Third, they had to solve. Many of the students omitted the second step and as a result, did
not properly learn the strategy of making a 10 to add. The multiple step struggle was also
an issue in the Add Three Numbers lesson. The students frequently forgot to add the third
addend resulting in incorrect sums. After realizing that solving problems with multiple steps
can be difficult for my students, I now know how important it is to make each step clear and
check for understanding of the steps to solving math problems in the future.
References
Bruner, J. (1960). The Process of Education: A Landmark in Educational Theory. United
States: Harvard University Press
Schunk, D. (2000). Learning theories: An educational perspective (3rd Ed) Upper
Saddle river, NJ: Prentice-Hall.
(REQUIRED) 3.
If you could go back and teach this learning segment again to the same group of students,
what would you do differently in relation to planning, instruction, and assessment? How
would the changes improve the learning of students with different needs and
characteristics? (TPE 13)
If I could go back and teach this learning segment to the same group of students I
would group the students differently, use different strategies to differentiate instruction,
utilize discovery activities prior to the start of each lesson, model the strategies more
clearly, and create an assessment that gives a clearer measurement of their performance
on the unit.
Beginning with the grouping of the class, I would arrange the classroom into groups
comprised of groups of students of homogenous ability levels. This would allow me to get a
better understanding of what the students are grasping when checking for understanding.
For example, when I taught my learning segment the students were not grouped
homogenously and as a result, when I checked for understanding it was difficult for me to
see if there was a trend in the students understanding or lack thereof amongst the different
ability levels. By grouping the students homogenously I would better be able to see the
levels of student understanding and adjust my teaching accordingly.
Based on the homogenous grouping of the class I would be able differentiate my
instruction more sufficiently. For example, when checking for understanding, I would be
able to quickly see that the proficient students need a challenge, and the struggling
students need further support. I could then allow the proficient students to work
independently while I continue the lesson for the struggling groups or provide support to
individual groups. This would allow the proficient students to move forward with the content
and prevent boredom. At this time the proficient group could work on enrichment activities
such as worksheets or hands on discovery activities. In the mean time I would be providing
additional support to struggling groups.
Another part of my learning segment I would change is the type of support I give to
my struggling students. In my learning segment I pulled the struggling students as well as
the struggling EL students into groups and basically re-taught the lesson. I am now realizing
that it would have been more effective if I used the strategic intervention worksheets that
are found in the Houghton Mifflin Strategic Intervention workbooks. These worksheets deal
with similar concepts of the lessons, however, they are simplified in such a way that
struggling students would have more success with them. They feature more visuals, less
language, and more examples. If I were to teach this learning segment again, this resource
would be greatly beneficial.
Another part of my learning segment I would do differently is to provide more
discovery activities prior to the start of each lesson. While I did include discovery activities
on a few of my lessons, they were either too brief or did not allow the students to explore
deep enough. I would create activities in which the students could spend sufficient time
drawing their own conclusions or even discovering their own method of solving the various
math problems that they would be encountering in the lesson. This would allow all of the
students to get a deeper understanding of the concepts as well as give me an opportunity to
build on their discoveries. While students discuss their findings, I would be able to support
their explanations using the vocabulary that would be later introduced to in the lesson. This
would prepare the students to meet the objectives of the lesson. The students would also
enjoy the lesson much more and feel more connected to the content.
As mentioned in the previous prompt, I would also make my modeling more clear
and explicit. For example when first teaching a concept, I would model the steps for solving
clearly and uninterrupted. This teacher modeling would be in the form of a think-aloud. I
would think aloud my steps for solving the problem so that students would get a clear
understanding of the concepts and know what to do when they later work independently.
After I do the think-aloud, I would then gradually scaffold my instruction as I let students
answer how to solve the subsequent problems.
Lastly, I would create an assessment that provided a clearer picture of the students
performance on the unit. The assessment I used had several problems from the Adding
Doubles and Doubles Plus One lessons, but only two problems from the Add With 10 lesson
and one problem from the Create and Solve lesson. Because of this I was unable to get a
clear picture of the students overall performance on the unit. If I were to give an
assessment on the unit again, I would have an equal number of problems from each lesson.
I would also ensure there are multiple problems from each lesson so that I can get a better
understanding of the type of mistakes students are making and how I can address them.
Other than that, I think the assessment I gave had questions that directly reflected what
was covered in the unit and I would use the same types of questions.
These are all parts of my learning segment I would change so that I could see
greater success amongst my students and hopefully have no students at far below and
below basic levels.