Today, we will…
1. Establish the need for Higher Order
Thinking Questions
2. Relate Higher Order Thinking Questions
to Differentiation and Rigor
3. Explore Higher Order Thinking Questions
4. See PARCC through the lens of Higher
Order Thinking Questions
5. Create Higher Order Thinking Questions
August 11, 2013
Want a Job? Learn to do what a robot can’t.
“Today, work that consists of following clearly
specified directions is increasingly being carried
out by computers and workers in lower-wage
countries. The remaining jobs that pay enough to
support families require a deeper level of
knowledge and the skills to apply it.”
21st Century Job Growth
In the 21st Century
Marketplace, only 30% of job
growth now comes from
algorithmic work. The
remaining 70% comes from
heuristic work.
--Daniel Pink, DRiVE
Characteristics of H.O.T. Questions
• low consensus.
• engage all students.
• require that students understand the
concepts and be able to apply them.
• emphasize critical and creative thinking.
• value all students’ unique backgrounds
and contributions.
Bloom’s Taxonomy
Benjamin Bloom created
the original Taxonomy in
1956 to express qualitatively
different kinds of thinking.
In the 1990’s, Lorin Anderson (a student of
Bloom’s) revisited the taxonomy with a team of
cognitive psychologists. The goal was to
examine its relevance for the 21st century.
Bloom’s Taxonomy
Original
New
Evaluation
Synthesis
Analysis
Application
Comprehension
Knowledge
Creating
Evaluating
Analyzing
Applying
Understanding
Remembering
Active
Verbs!
Revised Bloom’s
Changes in Structure
Categories were ordered in terms of
increased complexity.
Create and Evaluate have been
exchanged, because creating a story is
more complex than evaluating an
existing story.
BLOOM’S REVISED TAXONOMY
Creating
Generating new ideas, products, or ways of viewing things
Designing, constructing, planning, producing, inventing.
Evaluating
Justifying a decision or course of action
Checking, hypothesizing, critiquing, experimenting, judging
Analyzing
Breaking information into parts to explore understandings
and relationships
Comparing, organizing, deconstructing, interrogating, finding
Applying
Using information in another familiar situation
Implementing, carrying out, using, executing
Understanding
Explaining ideas or concepts
Interpreting, summarizing, paraphrasing, classifying, explaining
Remembering
Recalling information
Recognizing, listing, describing, retrieving, naming, finding
Universal Design for Learning
http://www.udlcenter.org/aboutudl/udlguidelines
Provide Multiple Means of
Representation (the “what” of learning)
Learners differ in the ways that they perceive and comprehend
information that is presented to them. For example, those with
sensory disabilities (e.g., blindness or deafness); learning
disabilities (e.g., dyslexia); language or cultural differences, and
so forth may all require different ways of approaching content.
Others may simply grasp information quicker or more efficiently
through visual or auditory means rather than printed text. Also
learning, and transfer of learning, occurs when multiple
representations are used, because it allows students to make
connections within, as well as between, concepts. In short, there
is not one means of representation that will be optimal for all
learners; providing options for representation is essential.
Provide Multiple Means of Action and
Expression (the “how” of learning)
Learners differ in the ways that they can navigate a learning
environment and express what they know. For example,
individuals with significant movement impairments (e.g.,
cerebral palsy), those who struggle with strategic and
organizational abilities (executive function disorders), those who
have language barriers, and so forth approach learning tasks very
differently. Some may be able to express themselves well in
written text but not speech, and vice versa. It should also be
recognized that action and expression require a great deal of
strategy, practice, and organization, and this is another area in
which learners can differ. In reality, there is not one means of
action and expression that will be optimal for all learners;
providing options for action and expression is essential.
Provide Multiple Means of
Engagement (the “why” of learning)
Affect represents a crucial element to learning, and learners
differ markedly in the ways in which they can be engaged or
motivated to learn. There are a variety of sources that can
influence individual variation in affect including neurology,
culture, personal relevance, subjectivity, and background
knowledge, along with a variety of other factors presented in
these guidelines. Some learners are highly engaged by
spontaneity and novelty while other are disengaged, even
frightened, by those aspects, preferring strict routine. Some
learners might like to work alone, while others prefer to work
with their peers. In reality, there is not one means of
engagement that will be optimal for all learners in all contexts;
providing multiple options for engagement is essential.
RIGOR
defined as deep, authentic command of
mathematical concepts.
To help students meet the standards,
educators will need to pursue
(1) conceptual understanding
(2) procedural skills and fluency
(3) application
with equal intensity.
1
RIGOR
The standards call for conceptual understanding
of key concepts, such as place value and ratios.
Students must be able to access concepts from
a number of perspectives in order to see math
as more than a set of mnemonics
or discrete procedures.
2
RIGOR
The standards call for speed and accuracy in
procedural skills and fluency. Students must
practice core functions, such as single-digit
multiplication, for access to more complex
concepts and procedures.
Fluency must be addressed in
the classroom or through
supporting materials, as some
students require more practice
than others.
3
RIGOR
The standards call for students to apply math in
situations requiring mathematical knowledge.
Correct application of mathematical knowledge
depends on students having a
solid conceptual understanding
and procedural fluency.
Is it time
for
metric in
the US?
Types of Questions
Skinny vs. Fat
Skinny: (yes/no)
Do you know the sum of 3 + 7?
Fat: (elaborate answer)
What are some things you know about
finding sums?
Types of Questions
High Consensus vs.
Low Consensus
High Consensus: (one right answer)
What is the sum of 37 + 15?
Low Consensus: (no single right answer)
What are some ways to find the sum
of 37 + 15?
Types of Questions
Review vs. True
Review: (asker knows answer)
How many ones do you need to
regroup to make a ten?
True: (asker doesn’t know answer)
What are some mental math tricks you
use to compute sums?
PARCC is about applying skills within specific contexts.
We have addressed deeply understanding the skills.
What happens when they are applied within a context?
Read problems around your grade level. What are some
ways we can address the application issue of PARCC?
PARCC Grade 3
Tables C and D are combined to make a larger
table. How would you find the area of the
combined table top? Write equations and
explain your thinking.
PARCC Grade 4
Julian makes and sells juice drinks. The juice drinks
are sold in 6-packs and boxes.
• A six-pack has 6 drinks and costs $2.
• A box has 20 drinks and costs $7.
An order was placed for 24 juice drinks packaged in 6packs and 200 juice drinks packaged in boxes.
Complete the order form below.
PARCC Grade 5
An egg farm packages 264 cartons of eggs
monthly. The farm has 3 different carton sizes.
1/6 of the cartons are small. They hold 8 eggs.
2/3 of the cartons are medium. They hold 12 eggs.
The rest of the cartons are large. They hold 18 eggs.
How many of each size carton is needed each
month? How many eggs are needed to fill 264
cartons?
PARCC Grade 6
Dre has a board that is 3/4 foot long. He wants
to cut the board into 1/8-foot pieces. How many
pieces can Dre cut from the board?
Draw a number line and show how it can be
used to find the answer. Explain your reasoning.
PARCC Grade 7
The number of parts produced by 3 different
machines are shown. Only one machine
produces parts at a constant rate. Write an
equation for that machine. Explain your
reasoning.
PARCC Grade 8
Janae planted a seedling in her garden and
recorded its height each week. The equation
shown can be used to estimate the height in
inches, h, of the seedling by the end of each
week, w, after it was planted.
h = 3/4 w + 9/4
1. What does the slope of the graph of the
equation represent? Explain your thinking.
2. When will the height of the seedling be 8.25
inches?
PARCC Algebra I
A random sample of 200 teens participated in a
taste test. They tried 4 choices of fruit drink, A,
B, C, and D, and chose their favorite. The results:
Are these true or false? Explain your reasoning.
• 40% of the teens were girls.
• 20/120 of the boys chose D.
PARCC Geometry
How would you estimate the
• length of CD?
• the measure of CPD?
Explain your thinking.
"Think left and think
right and think low
and think high.
Oh, the thinks you
can think up if only
you try!"
Theodore Seuss
Geisel
Create a new
coin. Tell is value
and describe its
size and design.
How would you
convince
Congress that the
coin is a
necessary
addition to our
existing monetary
system?
Some mobile phone
plans sell a fixed
number of minutes for a
set price, and additional
minutes at a rate per
minute. What are some
other real-life situations
in which a fixed rate is
combined with an
undetermined variable
rate?
You have $5 to spend on lunch at a
fast food restaurant. How is selecting
your meal and drink solving an
inequality problem? What are some
other inequality problems you solve
in everyday life?
Television shows are paid for by their
commercial sponsors. What kinds of
data do you think sponsors collect
about the show before making a
decision to advertise on it?
How we define
educational success will
not be the quantity of
information mastered,
but the ability to deeply
understand the
information well enough
to generate new ideas
based on it.
[email protected]
www.robynsilbey.com
Using Higher Order Thinking Questions
For Differentiation, Rigor, and Assessment
03/02/15
Robyn Silbey
www.robynsilbey.com ◊ [email protected]