1. The National Forum Mathematics
Improvement Toolkit
Presented by:
Sara Freedman
Kimberly Keniley-Ashbrook
Anna McTigue
Stephen Best

2. Goals for this Presentation
• Provide background on the purpose of the
toolkit, and the teaching and learning needs
it was designed to meet
• Introduce the toolkit and its components
• Walk you through some of the actual PD
activities embedded within these tools
• Provide additional information for future use
and identify interested sites for field testing

3. What is the Mathematics
Improvement Toolkit?
 Joint venture of four groups to utilize
expertise to address special populations
 Provides support for teachers,
professional developers, decision
makers, and students around middle
grades mathematics instruction
 Addresses specific instructional needs
that are often ignored.

4. Goals of the Project
 Resources to address instructional needs
of:
English Language Learners
Students with Special Needs
Students and Teachers in Rural Settings
Communities and Families
 Develop an online tool to guide decision
makers and educators in planning and
implementing professional development

5. Partners
 National Forum for Middle Grades Reform
 Talent Development
(Johns Hopkins University)
 Turning Points
(Center for Collaborative Education)
 Educational Development Center
 Middle Start
(Academy for Educational Development)
 Funded by the U.S. Department of Education
(Comprehensive School Reform program)

6. Common Ideas and
Considerations
 Mathematics instruction needs to focus on
building deeper conceptual understanding
 Resources are designed for use in PD with math
teachers and others supporting mathematics
learning for ALL students
 Materials need to focus on getting teachers to
reflect on practice
 Effective PD requires extensive time and ongoing
implementation

8. Tool #1
Tool #1
 Issue: Teachers need support to ensure that
English Language Learners have access to and are
successful in learning high-level mathematics.
 Primary Resources:
Videos and facilitator materials to guide mathematics
instructors in recognizing issues and modifying
instructional practices and tasks.
 Combines the focus of ELL with general issues
regarding deepening understanding of concepts in
mathematics

9. Tool #1
Tool #1
Who are the English language learners in
our schools today?
 English language learners are the fastest growing
segment of the school population. 1 out of 10 students
enrolled in public schools is an English language learner.*
 Nearly 1 out of 3 students enrolled in urban schools is an
English language learner.
 The percentage of English language learners enrolled in
schools is increasing throughout the United States, in
suburban and rural, as well as urban, communities.

10. Tool #1
Tool #1
What do we know about their experience
in our schools?
 English language learners have a strong desire to
receive an education. They have the highest daily
attendance rate of any segment of the school
population.
 English language learners have the lowest out of school
suspension rates of any segment of the school
population.

11. Tool #1
Tool #1
However...
 English language learners have the lowest standardized
test scores of any segment of the school population.
 English language learners have the highest dropout rate
of any segment of the school population.
Why do you think this is so?
THINK WRITE PAIR SHARE

12. Tool #1
Tool #1
Who are the English language learners in our schools today?
*Great City
Schools are the
60 largest urban
districts in the
country.
Take turns
analyzing the
graph with a
partner.
SPEAK RESPOND QUESTION RESPOND

13. Letʼs look at a typical word problem
A certain construction job usually takes four workers six
hours. Today, one worker called in sick, so there are only
three workers. How long should it take them to do the job?
What specific challenges do you think an English
language learner in the middle grades might have in
trying to answer the question posed by this problem?
(Notice that you are NOT solving the problem; instead, you
are analyzing the difficulties raised for a diverse group of
English language learners as they approach the problem.)

14. WRITE: Use the handout to record
your responses
A certain construction job usually takes four workers six
hours. Today, one worker called in sick, so there are only
three workers. How long should it take them to do the job?
BEST PRACTICE:
PROVIDING an
ORGANIZING
TEMPLATE
• saves time
• focuses English
language learners’
attention on the
mathematical
concepts rather than
copying in a new
language
• creates expectations
about # and quality
of responses

15. Tool #1
Tool #1
What are the LANGUAGE challenges in this problem for English
language learners?
A certain construction job usually takes four workers six
hours. Today, one worker called in sick, so there are only
Small Group
three workers. How long should it take them to do the job?
discussion
GROUP #1 #2 #1 #2
Get into groups of four. Assign
one person to chart the responses
to the first question, one at a time.
Take turns listening to each others’
➟ ➟
responses.
➟
➟
As each person speaks, ask any
questions or make comments that
help expand their comments
further. ➟ #4
➟ #3
#4 #3

16. Focus 2: Students with Special
Tool #2Learning Needs
 Issue: Curriculum materials do not support
students with special learning needs.
 Primary Resources:
Modified curriculum resources, student
materials, and instructional practices based
on Universal Design for Learning principles
 Resources need to be comprehensive in
nature to have full impact on learning.

17. Focus:
Students with
Special Learning Needs
 Students come into a
class with varying
levels of
understanding
 Some students need
explicit instruction to
get to a functional
level

18. Focus:
Students with
Special Learning Needs
 Students
need
support for
visual,
auditory,
attention,
and
memory
functions.

19. Focus 2: Students with Special
Tool #3Learning Needs
 Issue: Mathematics and Special Educators are
sometimes paired to co-teach without specific
professional development and preparation
 Primary Resources:
Video, a PowerPoint presentation, and a
facilitator guide for a workshops to implement or
strengthen co-teaching.
 Teachers benefit from seeing and discussing a
video example of co-teaching

20. Letʼs try a task...
• Watch a video clip from a lesson taught
by co-teaching
• As you watch, jot down your ideas
about the questions
• What roles did the co-teachers take?
• What actions did they take to support
student learning?

21. Letʼs try a task...
We will insert the video here.

22. Co-teaching Roles
• Work with a
partner and
brainstorm roles We will insert the
that co-teachers handout here.
could take to
benefit students.
• Record your
ideas on
Handout 2

23. Focus 2: Students with Special
Learning Needs
Tool #4
 Issue: Sometimes the greatest obstacle to learning
mathematics is difficulty with language
 Primary Resources:
Video, a PowerPoint presentation, and a facilitator
guide for a workshop exploring the language
demands and challenges in mathematics and
offering vocabulary and writing strategies to address
these challenges.
 With instruction and support in communication skills,
students can more deeply develop and express their
mathematical ideas.

24. Focus 2: Students with Special
Learning Needs
Tool #4
Language Module topics:
✦ Demands and challenges of language
✦ Instructional strategies
✦ Planning for vocabulary instruction
✦ Writing strategies for mathematics

25. Tool #5
Focus 3: Rural Education
 Issue:
Access to quality mathematics PD
 Primary Resources:
Online professional development program,
PD materials focusing on depth of
understanding and appropriate instruction
 High quality PD in mathematics education
requires reflection on practice and sample
tasks and cases.

26. Tool #5
Focus 3: Rural Education
 Online
community

27. Tool #5
Focus 3: Rural Education
 Online
community Modifying a Task: Task 1
 Focus on mathematics The Old Farmer’s Almanac
tasks as a lens to suggests that you can tell
the temperature outside by
counting the chirps a cricket
examine teaching makes in 14 seconds and
adding 40 (to get the
practice and student temperature in degrees
Fahrenheit). Use this to find
understanding how many chirps the cricket
makes when it is 72 degrees.
middlestart

28. Letʼs try a task...
Shade 6 of the small squares in the rectangle shown
below. Using the diagram, explain how to determine
each of the following:
1. the percent area that is shaded
2. the decimal part of
the area that
is shaded
3. the fractional part of
the area that
is shaded.

29. Tool #5
Focus 3: Rural Education
 Online
community
 Focus on mathematics
tasks as a lens to
examine teaching
practice and student
understanding
 Review student work
Tasks as
Tasks as
enacted
they Tasks as
by
appear in set up by
teachers
curriculum teachers Student
and
materials learning
students

30. Tool #5
Focus 3: Rural Education
 Online middlestart
community Module 1 - Case 1: David Orcutt
Focus on mathematics
This mini-case provides an introduction to the use of cases as a reflective professional development tool, and is not intended
 for sustained use. This also uses student work examples to explore understandings and misconceptions around fractions,
percents, and decimals.
tasks as a lens to
INTRODUCTION AND CONTEXT
David Orcutt is one of two 7th grade mathematics teachers in the lone junior high school for this
district. The district serves students from a largely rural agricultural and recreational area which
includes two villages. The school is a 7-8 school in a small school building next to the district’s
examine teaching
high school. In fact, a number of teachers are on the faculty of both schools to provide appropriate
coverage for topic areas. David has four classes among his other duties as the 7th grade advisor
and a track coach.
In his three years of teaching, he has learned that students coming in from the two K-6 schools in
practice and student
the district (as well as a small but growing migrant labor population that is becoming a more
permanent fixture in the area) often have varying skills and understanding in mathematics. To
understand each of the student’s abilities and conceptions about basic topics, he has devised a
two week introduction to his course which addresses a different topic from the grade 4-6
understanding
standards each day or two, and uses this to establish norms for classroom participation, work
expectations, etc. The following sample of classroom interaction starts by asking students to take
out the homework task from the previous day, which was really a pre-assessment of sorts to
understand student knowledge of decimals, percents, and fractions.
CLASSROOM ACTIVITIES
 Review student work
David starts class by greeting all students at the door as they come in, and has a problem on the
board, which he reminds students to get a paper out and copy the problem down after they have
taken their homework out from the previous day. Meanwhile, he checks attendance and missing
assignments from the previous day, and then begins wandering through the aisles to see what
students are doing with the problems on the board, and whether they have their homework out.
Review brief case studies
He quickly scans the homework for each student, noting whether they have all twenty problems
 done, and whether they have them numbered, the problem written down, and the answer
underlined for each. Most do, which results in him writing a “10” on the top of the page, but a
couple did not finish, receiving 5 and 7 points respectively, and three others had 3 points deducted
from these for not organizing their work properly. For these, David underlined a few of the answers
to encourage reflection
they had in their work that were not already underlined, and had jotted down the words “show your
steps” on some of these papers. While doing this, he marked on a copy of a grade sheet the
points for the homework assignment for each student.
Following this fairly quick review (which took four minutes from the time he started moving around
the room), he told the students they would review the answers of the homework. He circled the
room as he called out problem numbers, and would look around the room to see who was looking
at him (or not) and would call out the names of students to state what their answer was. Once one
student gave the answer, he would call on two other students and ask if they came up with the

31. Tool #5
Focus 3: Rural Education
 Online
community
 Focus on mathematics
tasks as a lens to
examine teaching
practice and student
understanding
 Review student work
 Review brief case studies
to encourage reflection
 Teachers share
examples, observations,
and reflections on their
own and others practice.

32. Tool #5
Focus 3: Rural Education
 Initial module: Developing Student Understanding of
Mathematics
 Content modules: Issues in the instruction of...
 Ratio and Proportion
 Patterns, Functions, and Algebraic Reasoning
 Measurement and Geometry
 Skill and strategy module: Issues in the instruction of
Problem Solving and Use of Inquiry

33. Focus #6Family Engagement
Tool 4:
 Issue: Schools struggle with this in general
and many mathematics issues for students arise
from parent/community misunderstandings,
stereotypes, and attitudes toward math.
 Primary Resources:
Online PD tools for schools and teachers that
guide them through family engagement
Resources to guide communication with parents
 Audience for these resources needs to be broader
than mathematics teachers alone.

34. Focus #6Family Engagement
Tool 4:
 Needs assessment
and introductory
activities

35. Focus #6Family Engagement
Tool 4:
 Needs assessment
and introductory
activities
 Sample discussion
materials (big picture)
and communications

36. Focus #6Family Engagement
Tool 4:
 Needs assessment
and introductory
activities
 Sample discussion
materials (big picture)
and communications
 Strategies to provide an awareness of
approaches to learn mathematics

37. Focus #6Family Engagement
Tool 4:
 Needs assessment
and introductory
activities
 Sample discussion
materials (big picture)
and communications
 Strategies to provide an awareness of
approaches to learn mathematics
 Discussion of deeper issues and research

38. For more information…
 Complete the email signup sheet
 Denote any specific tools that you are
interested in using
 Visit:
http://www.middlegrademath.org