Crafting Teaching Sequences for Extended Interventions – Abbr. Version
Sequence of Sessions
Overarching Objectives of this July 2014 Network Team Institute

Identify ways to support crafting teaching sequences for student interventions that efficiently develop and enhance student understanding of the
material.
High-Level Purpose of this Session
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Focus. Participants will be able to collect and analyze student data to help identify areas of needed intervention and to formulate plans to guide student
understanding of the material. They will explore approaches professional development that provides structured planning time designed to deepen
data analysis and develop Profound Understanding of Fundamental Mathematics.
Coherence: P-5. Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that
develop between the grades, thereby enabling participants to understand cross- grade coherence in their classrooms and support their colleagues to do
the same.
Standards alignment. Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how those
interconnect and develop across grade levels throughout the curriculum.
Implementation. Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their
students while maintaining the balance of rigor that is built into the curriculum.
Related Learning Experiences
●
This session is part of a sequence of professional development sessions examining the implementation of the A Story of Units curriculum across grade
levels.
Key Points
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Doing math and sharing strategies with both students and colleagues gives us multiple perspectives.
Analyzing and studying different “rounds” allows participants to have a better picture of how the curriculum connects across the
grades.
Session Outcomes
What do we want participants to be able to do as a result of this
session?

Focus. Participants will be able to collect and analyze student data to
help identify areas of needed intervention and to formulate plans to
guide student understanding of the material. They will explore
approaches professional development that provides structured planning
How will we know that they are able to do this?
Participants will be able to articulate and demonstrate the key
points discussed.



time designed to deepen data analysis and develop Profound
Understanding of Fundamental Mathematics.
Coherence: P-5. Participants will draw connections between the
progression documents and the careful sequence of mathematical
concepts that develop between the grades, thereby enabling participants
to understand cross- grade coherence in their classrooms and support
their colleagues to do the same.
Standards alignment. Participants will be able to articulate how the
topics and lessons promote mastery of the focus standards and how
those interconnect and develop across grade levels throughout the
curriculum.
Implementation. Participants will be prepared to implement the
modules and to make appropriate instructional choices to meet the needs
of their students while maintaining the balance of rigor that is built into
the curriculum.
Session Overview
Section
Time
Overview
Prepared Resources
•
Introduction
35 min
Introduces concepts and strategies
for creating solutions that require
one to go beyond one’s “round.”
•
•
Analyzing Student
Work
74 min
Explores using student work from
grade level and areas different
than one’s own to help develop
better intervention strategies.
•
Crafting Teaching
Sequences for Extended
Interventions – Abbr.
Version PPT
Crafting Teaching
Sequences for Extended
Interventions – Abbr.
Version Facilitator Guide
Crafting Teaching
Sequences for Extended
Interventions – Abbr.
Version PPT
Crafting Teaching
Sequences for Extended
Interventions – Abbr.
Version Facilitator Guide
Facilitator Preparation
•
•
•
Review Crafting Teaching
Sequences for Extended
Interventions PPT
Review Crafting Teaching
Sequences for Extended
Interventions Facilitator
Guide
Review selected Module
Materials
•
Conclusion
68 min
Research within topics and
lessons to investigate teaching
sequences more deeply with an
eye towards creating teaching
sequences.
•
Crafting Teaching
Sequences for Extended
Interventions – Abbr.
Version PPT
Crafting Teaching
Sequences for Extended
Interventions – Abbr.
Version Facilitator Guide
Session Roadmap
Section: Introduction
Time: 35 minutes
In this section, you will be introduced to concepts and strategies for Materials used include:
creating solutions that require one to go beyond one’s “round.”
• Crafting Teaching Sequences for Extended Interventions – Abbr.
Version PPT
• Crafting Teaching Sequences for Extended Interventions – Abbr.
Version Facilitator Guide
• Professional Reading: Teaching Round by Round
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
0 min
NOTE THAT THIS SESSION IS DESIGNED TO BE 180 MINUTES IN LENGTH.
3 hours, including 1 fifteen-minute break
Structure: Tables of 9: Three GK, three G1, three G2 or Three G3, three G4,
three G5
Materials:
2 Professional Readings “Intensive Textbook Study” and “Teaching Round
by Round”
Student work samples K-5 for independent teacher analysis
MP Protocol(fresh copy)
Curricular Map
Kindergarten video of Jourdyn’s interview assessment
Print outs of 6 Module Overviews relevant to the assessed questions.
1.
GROUP
3-5 Educators
Grade K: Module 4
Grade 1: Module 2
Grade 2: Module 4
K-2 Student Work (with errors, perfect and empty)
K-2 Educators
Grade 3: Module 1
Grade 4: Module 3
Grade 5: Module 4
3-5 Student Work (with errors, perfect and empty)
All Modules on Computer or Flash Drive
Poster Paper and Markers
Paper and Pencil
3 min
2.
Ask participants to solve one or more of the problems in any way they choose
and in more than one way if they so choose. Have them quietly share
strategies.
Tell the participants that another way Liping Ma talks about attaining PUFM
is by doing math and sharing strategies with both students and colleagues.
These practices give us “multiple perspectives”.
8 min
3.
3 minutes to develop short sequence
3 minutes to share logic of sequences
2 minutes to share stretch out/ break down
Note: Use animation on this slide so that one bullet appears at a time.
Note: Have participants talk to a partner or as whole group, whatever best
engages your participants.
10 min
4.
Ind  SG  WG
Materials: Professional Reading “Teaching Round by Round”
3 minutes for reading.
7 minutes for the protocol
Teaching “Round” by “Round”
“When asked how they (the Chinese teachers) had attained their
mathematical knowledge in “a systematic way,” these teachers referred to
“studying teaching materials intensively (zuanyan jiaocai) when teaching it.
First of all, you have to teach it personally, and you have to study teaching
materials intensively when you teach it. In normal school you take courses
such as “The Content and Teaching Methods for Elementary Mathematics.”
But that is not nearly enough. You only get a brief and rudimentary idea of
what elementary mathematics is but it is not relevant to real teaching. Only
through teaching a grade personally can you get to really know what is
taught in that grade. Moreover, you should not stick to teaching one single
grade but you should teach “round” by “round.” People divide elementary
school education into several small rounds. In our school we have the first
round, which includes first through third grades, and the second round,
which includes fourth and fifth grades. In each round, several grades are
connected together and cover a subfield of elementary math. If you have
taught the first round, you become familiar with the picture of what is
taught in the first three grades and how they are connected. If you have
taught the second round, you become familiar with the picture of what is
taught in the whole picture of the curriculum of elementary school
mathematics. The more times you have taught a round, the more familiar
you become with the content in that round. But merely teaching is not
enough It only makes you know the content, yet not necessarily know it
well. To know it well you have to study teaching materials intensively
through teaching.”
Tr. Sun ([pg. 130, Ma. Knowing and Teaching Elementary Mathematics, 1999)
Reflection (both days): Use the “Save the last word for me protocol.
Whole Group Reflection: Share out thoughts.
2 min
5.
Since many of us will be working out of our “round” this afternoon, rather
than creating a sequence, we will analyze and study the curriculum and then
study the sequences created by participants on Day 1.
2 min
6.
Assess: We start our day with student work from an assessment in hand.
Analyze: We analyze both the student work and teaching materials.
Plan: We plan based on our analysis of content and of our understanding of
our student.
Today, our goal is to move through the cycle and culminate our session by
making a poster of a teaching sequence for an extended intervention. The
posters will be shared across grade level groups so that all triads learn
about the mathematical content of other grade levels.
Section: Analyzing Student Work
Time: 74 minutes
In this section, you will explore using student work from grade level Materials used include:
and areas different than one’s own to help develop better
• Crafting Teaching Sequences for Extended Interventions – Abbr.
Version PPT
intervention strategies.
• Crafting Teaching Sequences for Extended Interventions – Abbr.
Version Facilitator Guide
• Sample Student Work Grades K-5
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
GROUP
45 min
7.
Triads Analyze Student Work
50 minutes
4 minutes:
Show the Kindergarten Video of Jourdyn and point out that the
interviewer’s comments are included in as “student work”
9 minutes: Each grade level studies their student work using the MP
Protocol.
8 minutes: Write questions that might help define the nature of the
student’s error and the last point the student was successful.
15 minutes: Read and Analyze the corresponding Module Overview and
Objective Sequence. What is the logic of the sequence?
How does it create a ladder to the objective targeted by the assessment
question?
12 minutes: Share work analysis to Grade Level Triads, 4 minutes per group.
2 minutes
4 min
8.
Share thoughts and learnings whole group regarding each of this day’s
student work, since this body of work may be out of the comfort zone of the
educators present.
In particular, ask participants what they noticed about connections to their
own grade level. Allow them to ask questions, too.
4 min
9.
Share thoughts and learnings whole group regarding each of this day’s
student work, since this body of work may be out of the comfort zone of the
educators present.
In particular, ask participants what they noticed about connections to their
own grade level. Allow them to ask questions, too.
4 min
10.
Share thoughts and learnings whole group regarding each of this day’s
student work, since this body of work may be out of the comfort zone of the
educators present.
In particular, ask participants what they noticed about connections to their
own grade level. Allow them to ask questions, too.
4 min
11.
Share thoughts and learnings whole group regarding each of this day’s
student work, since this body of work may be out of the comfort zone of the
educators present.
In particular, ask participants what they noticed about connections to their
own grade level. Allow them to ask questions, too.
4 min
12.
Share thoughts and learnings whole group regarding each of this day’s
student work, since this body of work may be out of the comfort zone of the
educators present.
In particular, ask participants what they noticed about connections to their
own grade level. Allow them to ask questions, too.
4 min
13.
Share thoughts and learnings whole group regarding each of this day’s
student work, since this body of work may be out of the comfort zone of the
educators present.
In particular, ask participants what they noticed about connections to their
own grade level. Allow them to ask questions, too.
5 min
14.
(Optional. Do this if the group seems very uncomfortable with being at the
different grade span.)
5 minutes
1 grade level at a time, as a whole group use the curricular map to quickly
analyze what are potentially fruitful modules for a particular piece of
student work.
Section: Conclusion
Time: 68 minutes
In this section, you will research topics and lessons from the Module Materials used include:
Overview to investigate teaching sequences more deeply with an
• Crafting Teaching Sequences for Extended Interventions – Abbr.
eye towards creating teaching sequences.
Version PPT
• Crafting Teaching Sequences for Extended Interventions – Abbr.
Version Facilitator Guide
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
45 min
15 minutes:
Analyze the Foundational Standards from the Module Overview to find
modules relevant to meeting the targeted objective and read and analyze
the Module Overview text and objective sequence.
15.
15 minutes:
Research within the topics and lessons to investigate teaching sequences
more deeply with an eye towards creating your teaching sequence.
12 minutes:
Share your learning about teaching sequences with your table triads.
3 minutes:
Share whole group about the process. What connections are participants
seeing between the grade levels?
17 min
16.
5 Minutes: Study a poster done by the GL triads on Day 1.
12 minutes: Share the logic of the sequence with the triads in your table
round robin.
GROUP
6 min
17.
6 minutes
We’ll close today by reading “Studying Teaching Materials,” which is an
excerpt from Liping Ma’s Knowing and Teaching Elementary Mathematics.
Ask them to take a moment to synthesize their thoughts about the day using
the sentence starters. Next have them share a thought with a partner, and
then ask participants to share out with the whole group.
“Intensive Textbook Study”
Part 1
“The textbook is the material on which Chinese teachers spend most of
their time and devote most of their efforts to “study intensively.” They study
it constantly throughout the school year when they teach it. First of all, they
work for an understanding of “what it is.” They study how it interprets and
illustrates the ideas in the (Standards), why the authors structured the book
in a certain way, what the connections among the contents are, what the
connections are between the content of a certain textbook and its
predecessors or successors, what is new in a textbook compared with an old
version and why changes have been made, and so on. At a more detailed
level, they study how each unit of the textbook is organized, how the content
was presented by the authors, and why. They study what examples are in a
(topic), why these examples were selected and why the examples were
presented in a certain order. They review the exercises in each section of a
unit, the purpose for each exercise, section, and so on. Indeed, they conduct
a very careful and critical investigation of the textbook. Although teachers
usually find the author’s ideas ingenious and inspiring, they also sometimes
find parts of the textbook that from their perspective are unsatisfactory, or
inadequate illustrations of ideas in the framework.”
(Liping Ma, Knowing and Teaching Elementary Mathematics, pg. 131)
“To study teaching materials is extremely important. To study teaching
materials is to study what we are to teach and how to teach it to our
students: in other words, to find links between the knowledge and the
students. The student teachers from normal schools doing their student
teaching with me usually can’t understand why we spend so much time
studying teaching materials and what we can learn from studying. For them,
it seems to be too simple and too plain to study: there are just several
example problems, one of which you can solve in a minute and explain to
students in two minutes. But I told them that even after teaching for more
than thirty years, every time I study a textbook I see something new. How to
inspire students’ minds, how to explain in a clear way, how to spend less
time and let students benefit more, how to motivate students to learn these
topics… Your answers for all these questions are supported by a deep and
broad understanding of what the teaching material is about. And every time
you study it, you get a better idea of what it is and how to teach it. You never
will feel you have nothing more to learn from studying teaching materials.”
(Teacher Mao, as quoted in Knowing and Teaching Elementary Mathematics,
Ma (1999, pg. 135)
Turnkey Materials Provided
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Crafting Teaching Sequences for Extended Interventions – Abbr. Version PPT
Crafting Teaching Sequences for Extended Interventions – Abbr. Version Facilitator Guide Grade K Module 6 Facilitator Guide
Professional Reading: Intensive Textbook Study
Professional Reading: Teaching Round by Round
Mathematical Practices Protocol
Curriculum Map
Kindegarten video of Jourdyn’s Interview Assessment
Grade K Module 4 Module Materials
Grade 1 Module 2 Module Materials
Grade 2 Module 4 Module Materials
Grade 3 Module 1 Module Materials
Grade 4 Module 3 Module Materials
Grade 5 Module 4 Module Materials
Sample Student Work Grades K-5
Additional Suggested Resources
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How to Implement A Story of Units
A Story of Units Year Long Curriculum Overview
A Story of Units CCLS Checklist
Operations and Algebraic Thinking Progression Document