K-5 Principal Session – Creating Teaching Sequences for
Extended Interventions
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




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
We want to create a culture in our schools where assessment and date result in analysis that drives planning practices, and from
there teaching.
● Three major goals for professional development should be to:
○ create extended interventions for students
○ deepen data analysis to make interventions much more targeted and efficient
○ structure PD/coaching so that PUFM is developed while the first two goals are being met
●
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
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.
How will we know that they are able to do this?
Participants will be able to articulate and demonstrate the key
points discussed.
Session Overview
Section
Time
Overview
Prepared Resources
•
Introduction
Introduces the objective of the
session and discusses how
application of processes will guide
participants through a structure
for crafting professional
development to support teachers.
Crafting a
Explores the steps used to craft a
•
•
Facilitator Preparation
Creating Teaching
Sequences for Extended
Interventions – Principal’s
Review Grade 4 Module 1
Session PPT
Overview
Creating Teaching
Review Grade 3 Module 2
Sequences for Extended
Interventions – Principal’s
Session Facilitator Guide
Creating Teaching
Review Grade 4 Module 1
Professional
Development
Structure
professional development
structure focusing on data and
analysis as a basis for creating
extended interventions for
students that are more targeted
and efficient.
•
•
Closing
Encourages reflection on the three
major goals of this session:
creating extended intervention,
deepening data analysis, and
developing PUFM.
•
Sequences for Extended
Overview
Interventions – Principal’s Review Grade 3 Module 2
Session PPT
Review Curricular Map
Creating Teaching
Sequences for Extended
Interventions – Principal’s
Session Facilitator Guide
Creating Teaching
Sequences for Extended
Interventions – Principal’s
Session PPT
Creating Teaching
Sequences for Extended
Interventions – Principal’s
Session Facilitator Guide
Session Roadmap
Section: Introduction
Time:
In this section, you will be introduced to the objective of the session Materials used include:
• Creating Teaching Sequences for Extended Interventions –
and see how the application of processes will guide you through a
Principal’s Session PPT
structure for crafting professional development to support teachers.
• Creating Teaching Sequences for Extended Interventions –
Principal’s Session Facilitator Guide
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
GROUP
1.
NOTE THAT THIS SESSION IS DESIGNED TO BE 180 MINUTES IN LENGTH.
Welcome! In this module focus session, we will examine Grade K – Module
6.
Materials: (All handouts can be passed out at once)
• Handout 1: Side 1, PUFM reading/Side 2:, Student work
• Handout 2: Mathematical Practices Protocol for Data Analysis
• Handout 3: A Story of Units Curriculum Map
• Handout 4: G4-M1 Module Overview (Truncated)
• Handout 5: Flow chart
• PDF of Grade 3-Module 2 downloaded on the presenter and
participants’ computers
Chart paper (1 piece per pair) and markers
2.
Ask participants to solve for angles g, h, and i. Do not provide further
direction; the idea is for participants to solve using slightly different
approaches. Allow about 3 minutes to solve.
Think about the steps you took to solve. Take a few minutes to list the key
ideas of a sequence you might use to teach another person your method.
Allow participants about 3 minutes to develop the key ideas of their sequence.
Share your sequence with a partner. As you do, explain as specifically as
you can what you took into consideration to put it together.
Allow partnerships about 4 minutes to share. Then facilitate a brief whole
group share in which you ask participants to name what they/their partner
took into consideration as they created sequences.
Please set your sequences aside for a moment. We will come back to them
shortly.
3.
Before we do, I’d like to ask you to spend a few minutes reading an excerpt
from Liping Ma’s Knowing and Teaching Elementary Mathematics. It’s the
handout you have that looks like the image on the screen.
As those of you who are familiar with Liping Ma’s work know, PUFM stands
for ‘profound understanding of fundamental mathematics’, which includes 4
properties that she uses to describe the dimensions of a teacher’s subject
matter knowledge. PUFM and those 4 properties are what this reading is
about.
As you read, think about the information in terms of yourself and the
sequence you just created. After we read I’ll as a few questions to help you
put your thoughts together, and then ask you to share with a partner.
Allow enough time so that the majority of participants finish reading.
Think for a moment, what kind of a resident are you in math land? Are you
a taxi driver, a newcomer, or one of the in-between residents Liping Ma
describes?
Pause.
Now take a moment to look back at the 4 properties of PUFM. Think about
which are most evidenced in the sequence you created, and least evidenced
in the sequence you created.
Pause.
What experiences have you had or what steps have you taken – or not had
or not taken – as an educator that create your particular result?
Pause.
Go ahead and take a moment to share your reflections with your partner.
Allow partners time to share.
4.
Some of you might feel like you were set up to get “caught.” You might be
thinking:
• I only had 3 minutes to prepare.
• You didn’t tell me if I’d be teaching the sequence to a 1st grader, a 6th
grader, or to the professor of mathematics sitting next to me. I had
no idea which connections to make or how far back into the sequence
to go.
• I also didn’t know that I should have had the 4 properties of PUFM in
mind!
All of those things are true and certainly didn’t help set you up to create an
exemplary – or maybe even successful – sequence.
Now think about your staff. How many of them are teaching interventions
from some version of this very place?
• They’re short on time for planning daily lessons, much less extended
interventions.
They’re a teacher’s aide or a specialist with a small group, and may
not know the students inside and out.
• Or maybe they’re a teacher who doesn’t have regular opportunities
to analyze student work and then question students to better
understand their mistakes before setting up an intervention.
• They’re someone who’s only ever taught 5th grade, or who’s been
happily teaching and refining their craft in 1st for the past 10 years.
Maybe their teaching shows Connectedness, but not as much
Longitudinal Coherence.
When we think about these circumstances specifically in terms of
intervention, they get more complicated by the fact that now we’re talking
about a child who is behind, and who needs the fastest route through town.
There’s a lot here to consider in terms of how we create space in the day or
week for teachers to analyze data, plan, and collaborate; and even more to
think about when we start to consider the practices we might put in place to
help our teachers develop their PUFM.
•
5.
That brings us to our objective for this session.
Our objective is to lead you through a structure for crafting professional
development to support teachers with these challenges. The method does
this essentially by providing structured planning time for creating extended
interventions with A Story of Units that is strategically designed to develop
PUFM and deepen data analysis.
Section: Crafting a Professional Development Structure
Time:
In this section, you will go through the steps to craft a professional Materials used include:
development structure focusing on data and analysis as a basis for
• Creating Teaching Sequences for Extended Interventions –
creating extended interventions for students that are more targeted
Principal’s Session PPT
and efficient.
• Creating Teaching Sequences for Extended Interventions –
•
•
Time Slide # Slide #/ Pic of Slide
Principal’s Session Facilitator Guide
Grade 4 Module 1 Overview
A Story of Units Curriculum Overview Map
Script/ Activity directions
6.
The structure we’re proposing follows the cycle on the screen. First and
foremost, we want to create a culture in our schools where assessment and
data result in analysis that drives planning practices, and from there
teaching. That’s not new. However, what might be new in the application of
this cycle to crafting interventions is the context we’re proposing for
analysis
7.
Consider that 3 major goals for the type of professional development we’re
talking about are to:
• Create extended interventions for students.
• Deepen data analysis to make interventions much more targeted and
efficient.
• Structure PD/coaching so that PUFM is developed while the first 2
goals are being met.
A great bi-product of the process is that it’s also structured planning time.
In order to achieve those second two bullet points and create an
intervention that’s as targeted and efficient as possible, we’re suggesting
that an ideal context for analysis has 3 qualities:
CLICK.
1. A student’s response stays connected to the question so that analysis
happens side by side.
Elaborate: Remind participants that often we analyze electronically organized
data in a format that’s completely separate from the questions themselves.
While this type of data analysis is important, and certainly has a time and
place, it doesn’t lend itself to recognizing the subtleties of an error that
produce a targeted intervention. Generally this type of data analysis leads to
standards-based intervention, which is a great place to start, but not
GROUP
necessarily specific enough to be targeted and most efficient.
This is a step toward deepening data analysis for a targeted intervention.
CLICK.
2. Part of analysis includes an opportunity to clarify teacher
assumptions by asking students follow-up questions.
Elaborate: This is a piece that’s typically missing from the kind of data
analysis that usually leads to extended intervention. If an error happens in the
moment, follow up questioning feels natural, but very often we decide to make
extended interventions based on more formal, summative type data that we
analyze on our own or with others during collaborative planning time, in staff
meetings, in PLCs, or in another context that’s away from the action of the
classroom.
This may not sound realistic, but there are creative ways of thinking about it
that might make it doable. Consider, for example, a scenario where teachers
analyze data away from the action of the classroom, create small groups for
intervention based on the information they do have in front of them. But
rather than start the intervention in the first group meeting, that time is used
to further probe student errors. This validates (or not) the particular
grouping, and helps teachers develop shades of understanding about students’
needs that focus the intervention.
This is a step toward deepening data analysis for a targeted intervention.
CLICK.
3. Analysis includes not just student data, but teaching materials as well.
Elaborate: Studying materials helps teachers recognize the steps the student
should have mastered on the way to the point where they are now. Analysis of
the teaching materials helps clarify possible missing links in student
understanding, and also helps teachers more fully perceive the trajectory that
a teaching sequence for intervention will take.
This is a step toward developing PUFM, as well as a targeted and efficient
intervention. We’ll look more in depth at how these 6 points weave together in
just a moment.
Allow time for processing and group discussion:
• What reactions do you have?
• How do these suggestions compliment or describe what you’re
already doing?
8.
Let’s step into a teacher’s shoes for a moment to see what this looks like. Turn
your Liping Ma reading handout over to find this piece of student work on the
back. Take 2 minutes on your own or with a partner to analyze the work and
think about what’s happening with this child. Think about what follow-up
questions you might ask.
Allow a few minutes for participants to analyze. Note: They are likely to notice
that the child uses the population of San Jose rather than the stadium capacity
at LSU to answer questions 2 and 3. Although the question asked for the
student to use different information in question 2, the mathematics is correct.
Participants are likely to ask whether or not the student would get credit for
this question.
After participants analyze, facilitate a whole group discussion about what
they noticed. If they share what the student does understand, encourage it.
It’s important to know what the student does understand, and to begin from
that point.
Possibly use the following questions to facilitate a discussion about the process
participants used to analyze:
• What lens did you use to analyze the data? (e.g., mistakes only,
mistakes and successes, components of rigor, standards, etc.)
• How did your lens affect what you did or didn’t see?
9.
Let’s give a more nuanced lens to your approach. Take out your handout
titled “Mathematical Practices Protocol for Data Analysis,” that looks like the
image on the screen.
As our team practiced analyzing student work ourselves in preparation for
this week, we experimented with a variety of different ways to do it. We
first started as I just asked you to: using our own “usual” ways to see what
we noticed. We found that levels of insight varied quite a bit, as I expect
they would across the members of your staff. Next we thought about using
the components of rigor (procedure, conceptual understanding, and
application) to try and focus our analysis and take it deeper. But we found
that those lenses weren’t specific enough to generate more focused
understanding.
Then we considered the Mathematical Practices, which are each quite
layered and describe subtleties that, at times, move beyond what we
normally think of as we analyze student work. We found the MPs can be
helpful tools.
What you see on the handout are the titles of the Mathematical Practices in
bold, and a short list of questions that you might ask yourself as you look at
student work through the lens of each MP. Take a moment to look at the
front and back of the handout.
Allow a minute for participants to look over the handout – we’ll come back to
it again shortly.
It’s important to note that these lists of questions aren’t comprehensive.
You and your teachers will definitely be able to add to them with practice.
It’s also important to know that not every question – or for that matter
every MP – is applicable to every piece of student work you analyze. Use the
protocol flexibly. In a moment I’ll give you a chance to look back at our
student work sample using the protocol, and you’ll see what I mean.
I’m sure you noticed that the protocol has built into it a column for jotting
down possible strengths and weaknesses of student work, as well as a
column for writing down possible follow-up questions to ask the student.
Something important about the questions column: you see the example
question is very specific. The reason is that specific questions generally
return specific answers, and specific information is what helps define an
error.
Provide the following examples of other specific questions:
• Can you explain to me why you wrote a zero in this number bond?
• (Write 8 ÷ 4 = ___.) Can you tell me a story to match this equation
where the unknown is the number of groups?
Go ahead and take a few minutes to look at the student work sample again
using this protocol. Try and jot down possible strengths and weaknesses, as
well as specific questions you might ask the student. Do this next to the MPs
that help you analyze the work.
Allow participants time to work. After they’ve had some experience using the
protocol, facilitate a discussion:
• How did the protocol change your approach to analysis?
• What insights were you able to add to your original analysis?
• Which MPs were most/least useful to your analysis of this particular
work?
• What part of the process (using the questions, identifying
strengths/weaknesses, or writing potential follow up questions) was
the most challenging? What made it so?
• How might you use this tool with your staff? How do you think they’ll
respond? Why?
Background information for the presenter:
We found that using the MPs as part of our data analysis process sometimes
helped us ask questions about the work that we might not have otherwise.
Using them as a tool, we also observed and had a way to describe aspects of
the work that we hadn’t necessarily considered before.
Before moving on, ask participants to share what the student in question
might need. Establish why his/her work presents need for an extended rather
than short-term or instant intervention. (The student’s weakness appears to
be three-fold; the number line, rounding, and how to use the number line to
round.)
10.
With data analysis begun we have a sense of what this child might need, and
it’s time to incorporate analysis of teaching materials into our work. Having
just taught this material, we would bring background knowledge of the
recent teaching sequence to this part of the analysis.
Even still, the Module Overview for material we’ve just taught is a useful
place to begin thinking about how to map the sequence of complexity for a
particular concept backward to where the student’s most recent success
might have been.
In looking at the Module Overview, you’ll want your teachers to focus on the
narrative, which will reiterate the big picture sequence that they’re working
within. The Lesson Objectives quickly break that sequence down into the
smaller steps that comprise it. Since we’re assuming that this child needs an
extended intervention, we’ll likely have to take several steps back in order
to truly support understanding. To do that, teachers should pay special
attention to the Foundational Standards, which will give them a sense of
where to look in the grade level before.
Take a moment now to browse these 3 components of the Module Overview
for the student work that we’re examining. You have the Overview as a
handout that looks like the image on the screen.
Allow participants time to read.
Now that you’ve refreshed your background information about the
sequence, you might decide to go back into the lessons in this module and
build a sequence using the material there. In this case, are these lessons
going to go back far enough to support understanding? No.
What information did you get from reading the Foundational Standards?
Rounding is taught in Grade 3, but the Foundational Standards don’t tell you
where.
2 min
11.
Many times it’s possible to use the Curriculum Map as a resource to quickly
know which module in the prior grade level you should turn to. In cases
where that works, you’re usually looking for a key word or for the mention
of the concept in the title of the module. In this case we’re looking for
rounding, or maybe for the vertical number line. We’re presenting you with
the harder scenario: neither of those words appear in any of the Grade 3
module titles, nor do the titles really hint at where we might find either of
those things. This is where we turn to our PDF files and use the “search”
function.
Presenter models the following process for how the relevant lessons might be
found, given this scenario.
• Look at the title for G3-M1: Properties of Multiplication and Division.
This is probably not going to be where I’ll find lessons on rounding. I
think I’ll look at the title of the next module.
• G3-M2: Place Value and Problem Solving with Units of Measure. This
also doesn’t sound promising, but it might be worth checking since the
concepts in this module are analogous to the ones in G4-M1.
• Open the G3-M2 PDF. Model searching in various ways: by standard
(3.NBT.1), by the words “round” or “rounding,” and by “vertical number
line.” (G3-M2 is in fact where the relevant lessons are located.)
12.
Once we’ve located the lessons we’ll need, it’s time to start thinking about
constructing a sequence for intervention. As the writers of A Story of Units
crafted the curriculum, we kept the analogy of a ladder in mind as we wrote
sequences, long and short. The idea behind this analogy is that just about
every student should be able to step up onto the bottom rung of the ladder,
as the image on the screen shows. That means the material is simple
enough to reach back to where children can comfortably participate. In
order to truly support understanding and avoid creating band aids, we’re
consciously starting with success and building from that point “up”. Each
rung on the ladder represents another bit of complexity that grows step by
step toward the objective; the steps should move fairly quickly.
I’m going to give you 10-15 minutes to work with a partner and look at the
Grade 3 material that supports students with understanding the vertical
number line and rounding. In the interest of time, I’ll show you which are
the most relevant lessons for this sequence. CLICK. Today we’ll just use
these lessons, but as you look at them, consider that the Grade 3 material
may not go back far enough.
Participants should have downloaded G3-M2 onto their computers in
preparation for this session. Ask them to work with a partner for about 10-15
minutes to look at Lessons 2, 10 and 12-14. Once you’re happy with your
sequence, chart the steps and be ready to share with another group.
Allow time for participants to work.
13.
Ask 2 pairs of participants to group themselves to share their sequences and
critique one another’s work. Ask them to take out the student work, and
connect the steps of their sequence to the specific needs demonstrated by the
sample. Allow a few minutes for them to share.
Then facilitate a whole group discussion:
• What did you learn about your sequence from share and critique?
• Why is the share and critique an important step?
• With whom would teachers most benefit sharing? (Grade level
colleague, lower grade colleague, etc.)
• So far, what reflections do you have about this process?
• What will make it faster for teachers?
• What will make it slower for teachers? How can you mitigate those
challenges?
• Over time, how does this process support teachers to develop PUFM?
Sharing with a colleague is a critical step in this process. It’s at this point
that teachers will return to the student data and compare the steps of their
sequence with the demonstrated needs. Verbalizing the connection
between the sequence and the student’s need is likely to push the author’s
thinking, and also likely to result in collegial feedback that challenges the
author.
For example, some of you may have noticed that the student appears to have
very little understanding of units on a number line, much less how to use it
for rounding numbers. CLICK. In my haste to get the student to where they
can round, I might not have thought through the fact that the student
appears to have very little understanding of units on a number line. But in
looking at the student work alongside my sequence, my partner likely
noticed or reminded me that in fact the students’ weakness appears to be
three-fold. (The number line, rounding, and how to use the number line to
round.) An extended intervention that is designed to support conceptual
understanding takes each of those weaknesses into account.
At this point I would return to my work and make a revision, digging back
into the Grade 2 material using the same process of using the foundational
standards, the curriculum map, the lesson objectives, and possibly the
search function to find the relevant lessons.
14.
We just moved through a few key steps of what’s actually a slightly longer
process. You have a flow chart that outlines this structure in greater detail
as a handout that looks like the image on the screen. Take a moment now to
look it over. As you do, consider what’s missing from this that would be
important for you to have included.
Allow participants time to look at the handout. Invite them to share in table
groups or as a whole group depending on the energy in the room.
If participants do not share re-assessment and engaging the student in
reflecting on their growth toward mastery, mention them before proceeding.
Discuss a process for creating “second chance” assessment questions that
target the objective of the sample teaching sequence once the sequence is
complete.
If it hasn’t already come up, facilitate a whole group (or table group)
discussion about how students might be brought into the excitement of
mastering what was previously out of their reach.
Section: Closing
Time:
In this section, you will reflect on the three major goals of this
session: creating extended intervention, deepening data analysis,
and developing PUFM.
Materials used include:
• Creating Teaching Sequences for Extended Interventions –
Principal’s Session PPT
• Creating Teaching Sequences for Extended Interventions –
Principal’s Session Facilitator Guide
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
GROUP
15.
In closure let’s return to the 3 major goals for this type of PD that we named
earlier.
Ask participants to debrief using any combination of the following questions.
Depending on the energy level at this point, it might be an individual written
reflection, or in any grouping that meets the needs of participants.
• How does a process with these goals support teachers and students?
• How might it be used – or modified for use – in your school setting?
• What will teachers appreciate about this?
• What will teachers find challenging about this?
• What is the value of PUFM to facilitating use of a process like this, and
to creating extended intervention?
• In what ways is the study of materials instrumental to developing
teachers’ PUFM?
• What are the cultural implications for implementing a structure for PD
like this one at your school site?
Turnkey Materials Provided
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Creating Teaching Sequences for Extended Interventions – Principal’s Session PPT
Creating Teaching Sequences for Extended Interventions – Principal’s Session Facilitator Guide
Mathematical Practices Protocol for Data Analysis
Professional Reading: Knowing and Teaching Elementary Mathematics
G4-M1 End of Module Assessment Student Work Sample
Flow Chart Handout
A Story of Units Curriculum Overview Map
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