Session I: Thinking Through a Lesson:
Successfully Implementing High-Level Tasks
Time Allotment
80 minutes
Objective(s)
Participants will experience and be able to transfer to other teachers how to:


Discuss and examine the thought process of developing a lesson/unit that is standardsbased.
Select rich tasks that match student friendly outcomes and provide evidence of student
learning.
Lesson Flow
Welcome participants to 3rd
Quarterly Meeting
Research/Helpful Hints
Share the outcomes of the
presentation.
Before (Engage)
Welcome participants to the
training. Have them reflect on the
past quarterly meeting.
Participants should have their
reflections from the lessons they
shared at the previous meeting.
Have them address the following
questions:
 What went well in regard to
the lesson?
 What did not go well in regard
to the lesson?
 How can we revise the lesson
to improve it?
Do not spend too much time
here; participants will have
opportunities to reflect
throughout the entire session.
Participants can use the lesson
plan reflection to take notes
about their lessons.
Show lesson planning slides.
5-10 minutes
Have participants read the research
on the slide. Explain to
participants that lesson planning
will determine the effectiveness of
the implementation of the College
and Career Ready Standards
(CCRS).
Show slide.
Have participants read the quote
on the slide (5).
Say, “Now that we have gone
through the process of identifying
and evaluating an exemplary
CCRS lesson, today we are going
to model a process you can use to
help other teachers think through
and plan an exemplary CCRS
lesson.
During (Explore, Explain)
Now have participants take out
excerpt #1 from the article
“Thinking Through a Lesson:
Successfully implementing high level task”
Have participants read the passage
and share one idea from the
passage with members of their
groups. Allow a few participants
to share with the entire group.
Have participants discuss the
Ask, What causes high-level
cognitive demand tasks to decline? challenges they experience in
implementing cognitively
Have participants write their ideas challenging tasks that promote
thinking, reasoning, and
on a list.
problem solving. At the end of
Allow some participants to share
the discussion, suggest that
their thoughts.
this article presents a
framework for lesson planning
that may help with these
challenges.
10 minutes
Have participants find the ACOS
Alabama College and Careerstandards to address the tasks.
Ready Standards for
Mathematics:
See the Notes on the slide for
a complete list of standards
addressed.
Let’s explore two tasks to help us
better understand how to
implement cognitively challenging
tasks.
Have participants work each task
on their own first, and then share
with a partner at their table.
Note various solution paths used
by participants.
Prepare to have them share
solutions in the following order.
Say, “As we work through the
following tasks, consider the
mathematical task that you provide
for your students.” At the heart of
teaching well is the core challenge
of getting learners engaged in
productive work. Mathematical
tasks are the sites for engaging
students in core mathematical
activity.
Note various solution paths
used by participants. Prepare
to have them share solutions
in the following order:
Martha’s carpeting

Formula

Diagram
Fencing Task






Trial and error
Ordered set of
diagrams
Information organized
in a table
Algebraic equation in
vertex form
Graph of parabola
showing vertex
Calculus using
derivative
Choose participants to record
solutions and strategies on chart
paper, and to share out to the
whole group.
Brainstorm some other ways
students may solve the problem
(other than the ways shared).
Ask participants “Do the
differences between the Fencing
Task and Martha’s Carpeting Task
matter? Why or why not?”
Ask: Why do you think this
task is classified by the
authors as high-level?
In small groups, have participants
view the similarities and
differences in the table.
Show slide.
Ask participants to discuss the
question on the slide.
High-level mathematical tasks
are often challenging for
teachers to implement.
25-30 minutes
Show slide.
Have participants take out the
Task Analysis Guide.
Allow them a few minutes to
identify characteristics of each
task in their group.
The Math Tasks Framework is
designed to consider the evolution
of tasks during a lesson. The fact
that tasks take on lives of their
own after being introduced into
classroom settings has been noted
by a variety of classroom
researchers.
As mathematical tasks are enacted
in classroom settings, they become
intertwined with the goals,
intentions, actions, and
interactions of teachers and
students.
The first phase – Tasks as they
appear in curricular or
instructional materials.
The Set-up Phase includes the
teacher’s communication to
students regarding what they are
expected to do, how they are
expected to do it, and with what
resources.
During the implementation
phase, both students and the
teacher are viewed as important
contributors to how the task is
carried out. Although the
students’ levels of cognitive
engagement ultimately determines
what is learned, the ways and
extent to which the teacher
supports students’ thinking and
reasoning is a crucial ingredient in
the ultimate fate of high-level
tasks.
Have participants read and discuss
the slide.
The QUASAR Project:



Assisted schools in
economically
disadvantaged
communities to develop
instructional programs
that emphasize thinking,
reasoning and problem
solving in mathematics.
Worked with lowest
achieving middle schools
in six urban sites.
Studied the impact of high
quality curricula and
professional development
upon student achievement.
The ultimate reason for focusing on
instructional tasks is to influence
student learning. Research has
demonstrated that the cognitive
demands of mathematical
instructional tasks are related to the
level and kind of student learning.
Within the QUASAR project,
students who performed best on the
QUASAR Cognitive Assessment
Instrument were in classrooms in
which tasks were more likely to be
set up and implemented at high
levels of cognitive demand. For
these students, having the
opportunity to work on challenging
tasks in a supportive classroom
environment translated into
substantial learning gains on an
instrument specially designed to
measure student thinking, reasoning,
problem solving, and
communication. This suggests the
importance of being mindful, both at
the outset and during the various
task phases, of the kinds of
cognitive activity with which the
students should be and actually are
engaged in the classroom.
Patterns of Set up,
Implementation, and Student
Learning
Task Set Up Task Implementation
Student Learning
A.
High
High
High
B.
Low
Low
Low
C.
High
Low
Moderate
Stein & Lane, 1996
Ask, What do you notice? What
are the implications for
instruction?
Results from QUASAR also
show that students who had
the lowest performance on
project assessments were in
Evidence gathered across scores of classrooms where they had
middle school classrooms in four
limited exposure to tasks that
QUASAR middle schools has
required thinking and
shown that students who
reasoning (Stein & Lane,
performed the best on project1996).
based measures of reasoning and
problem solving were in
classrooms in which tasks were
more likely to be set up and
implemented at high levels of
cognitive demand.
This slide identifies the classroom
factors that researchers observed
when high-level tasks declined
during a lesson.
After (Explain, Extend)
By contrast, this slide identifies
the classroom factors that
researchers observed when the
cognitive demands of high-level
tasks were maintained during a
lesson.
Have participants compare /
contrast the factors in terms of
classroom instruction. Ask, What
would it require for teachers to
understand how to routinely
maintain the implementation of
high level tasks for increased
student achievement?
Remind participants to think
about their response to the
question posed at the
beginning of the PD.
What causes high-level
cognitive demand task to
decline?
Have participants think
about how these factors
relate directly to the 8
standards for mathematical
practices.
Most importantly, help
participants think about the
importance of selecting highlevel mathematical tasks to
increase student achievement.
20 minutes
Have participants reflect on the
quotes on the following slides.
It is “self-explanatory.”
Note that each quote represents
components of this professional
development.



Mathematical Tasks
Student Achievement
Teacher Effectiveness
Lesson Reflection
Have teachers reflect on
questions 3 & 4 on their note
taking tool.
3. How can we help teachers
improve their capacity to
plan (and enact) lessons that
support student learning?
4. How would you conduct
professional development
with teachers to see how
lesson planning addresses
content rigor, task selection,
student engagement, math
practices, and formative
assessment that generate
student work samples for
assessment and assisting of
struggling students?
10 minutes
During the reflection,
encourage teachers to discuss
ideas and strategies that they
currently use to plan lessons.
Time Allotment
Session II
90 minutes
Thinking Through a Lesson Protocol
Objective(s)
Participants will experience and be able to transfer to other teachers how to:



Develop student friendly outcomes that reflect the rigor and depth of content.
Select rich tasks that match student friendly outcomes and provide evidence of student
learning.
Model teacher collaboration on identifying resources for implementing College-and
Career-Ready Standards for mathematics.
Lesson Flow
Research/Helpful Hints
Share slide.
Allow participants to read
outcomes and discuss
expectations for the second
session.
Inform participants that
they will use the Thinking
Through a Lesson Protocol
(TTLP) to plan a lesson
using high level
mathematical tasks.
Have participants count
off into groups of three.
Tell participants that the
ones will read the 1st phase,
twos will read the 2nd
phase, and finally the
threes will read the 3rd
phase.
Allow participants to read
their individual sections
first.
Use a timer to make sure
the reading and discussing
of the phases do not take
time away from the actual
working through of the
TTLP.
Hint: Have groups to select
a timekeeper, recorder and
reporter to same time.
15 – 20 minutes
Then tell them to join at
least 2 other people who
have the same section.
Allow participants 2 to 3
minutes to discuss the
passage.
Finally, inform participants
that each person will return
to their original group of
three.
Tell participants that they
will work through the
Thinking Through a Lesson
Protocol (TTLP) in their
groups.
Each person will lead the
section of their phase that
they read.
Allow participants 10
minutes to discuss each
phase of the TTLP.
Share slide.
Remind participants of
each phase of the TTLP.
 What questions will you
ask to focus student
thinking?
The Purpose of the TTLP
 What will you see or
hear that lets you know
how students are
thinking about the
mathematical ideas of
the lesson?
 Which solution paths do
you want to have shared
during the class
discussion? In what
order will the solutions
be presented? Why?
Be sure to facilitate groups
making sure they are aware
of time.

To prompt teachers to
think deeply about a
specific lesson in order
to consider how to
advance students’
mathematical
understanding

To focus on students’
mathematical thinking

To help anticipate a
range of student
solutions or solution
strategies
 What will you see or
hear that lets you know
that students in the class
understand the
mathematical ideas that
you intended for them to
learn?

To prompt the
development of
questions that will
support students’
engagement and
learning

To address ways to
facilitate the learning of
all students

To move beyond
structural
components of
lesson planning
See additional facilitator
handouts that explain and
provide content
information for grade
level sample tasks.
Remind participants that
they can use the Alabama
Insight Tool to help
develop student friendly
outcomes on the TTLP.
Please do not spend time
going to Internet to identify
standards. Participants can
use the Math Course of
Study to write objectives.
35 – 40 minutes
Take time to have
participants take out their
grade level sample tasks.
Tell them that each sample
is an example of a highlevel cognitive demanding
task.
As participants are working,
use your notes to help
participants identify content
information needed to
complete the TTLP.
If you are training K-5
hide the slides for 6-12.
If you are training 6-12
hide the k-5 slides.
Tell participants that they
will use these tasks to help
them work through the
TTLP.
After participants have had
time to work through the
phases of the Thinking
Through a Lesson Protocol
(TTLP), show the reflection
slide.
Be sure to share that the
Alabama Insight Tool
would be very useful in
identifying student
knowledge, skills and level
of student attainment.
As participants/groups are
developing posters, have
them read the final excerpt
from the article: Thinking
Through a Lesson:
Implementing High Level
Mathematical Tasks in.
Tell participants to create a
poster that describes their
10- 15 minutes
thinking about each of the
questions in their groups.
Allow at least 10 minutes
for participants to create the
posters.
Select participants/groups
to share posters with the
entire group.
Have participants look at
the chart on this slide and
reflect on the process they
just completed.
Tell participants this slide
summarizes the key focus
of each phase.
Allow participants to read
the conclusions.
Allow time for comments
or questions.
Reflection
Have participants read the
quote and discuss their
thoughts.
5. Are there any aspects of
your own thinking and/or
practice that our work
today has caused you to
consider or reconsider?
Explain.
6. Are there any aspects of
your students’
mathematical learning that
our work today has caused
you to consider or
reconsider? Explain.
6a. What would you like
more information about?
10 minutes