Csrqi Nmsa Presentation2

From Wall Charts to Web
Sites:
The National Forum
Mathematics Improvement

Sara Freedman
Steve Best
(in lieu of Deborah Kasak)

NMSA Conference, Denver, CO
Toolkit
Wednesday, March 18, 2009

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
2
Toolkit

What is the Mathematics
Improvement Toolkit?

Toolkit

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

Toolkit

Goals of the Project

Toolkit

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
Toolkit

Partners

Toolkit

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)
Toolkit

6
Toolkit

Common Ideas /

Toolkit

Common Ideas /
Mathematics instruction needs to

focus on building deeper
conceptual understanding
 Resources are designed for use in
professional development with
math teachers and others
supporting mathematics learning
for ALL students
 Materials need to focus on getting
teachers to reﬂect NMSA Conference, Denver, CO
on practice
Toolkit

Professional Development

Toolkit

Focus 1: English Language

Toolkit

Focus 1: English Language
Issues: 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.
Toolkit

Let’s try a task...
What student engagement on a high level looks
like for English language learners

I wonder if/how/
I notice that...
whether...

On this side, “talk back to
Write down
the text” – ask questions,
everything you
make comments
see on this side.

Toolkit

What did you think?
What student engagement on a high level looks
like for English language learners

I wonder if/how/
I notice that...
whether...

Toolkit


Toolkit

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?

Toolkit

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?
1) What are some language difficulties in this problem?
2) What are some math difficulties in this problem?
3) What are some cultural features that could cause
difficulty in understanding this problem?
Toolkit

Focus 2: Students with Special
Learning Needs

Toolkit

Learning Needs
Issues: Curriculum materials do

not support students with special
learning needs.

Toolkit

Learning Needs

learning needs.
Modiﬁed curriculum resources,
student materials, and instructional
practices based on Universal
Design for Learning principles

Toolkit

Learning Needs

learning needs.
Modiﬁed curriculum resources,
student materials, and instructional
practices based on Universal
Design for Learning principles
 Resources need to be

Toolkit

Learning Needs
Students come into

a class with varying
levels of
understanding

Toolkit

Learning Needs
Students come into

levels of
understanding
Some students

need explicit
instruction to get
to a functional level

Toolkit

Learning Needs
Demonstration - I do
Students come into

a class with varying 0 - 20% proficiency
levels of
understanding Guided Practice - We do
Some students

20 - 80% proficiency
need explicit
instruction to get
Independent - You do
80 - 100% proficiency

Toolkit

Learning Needs
Students come into

levels of
understanding
Some students

need explicit
instruction to get
Students need

support for visual,
Toolkit

Learning Needs
Issues: Teachers need support for

instruction of students with special
needs

Toolkit

Learning Needs

needs
Videos and facilitator guide for
workshops to support co-teaching
and literacy strategies to address
the needs of all learners

Toolkit

Learning Needs

needs
Videos and facilitator guide for
workshops to support co-teaching
and literacy strategies to address
the needs of all learners
 Teachers often need to SEE what

Toolkit

Learning Needs
Language Module
 !

topics:
!
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!
2&3.'0%#*!!quot;!#$$!%&'!(')%#*+$',!%&#%!)#*!-'!quot;.(/'0!quot;(./!12!,34#('!%5$',6!7&#%!#('!

 Challenges of
%&'!05/'*,5.*,!.quot;!%&'!(')%#*+$'!75%&!%&'!+('#%',%!8'(5/'%'(9!
!
!
!

vocabulary in 4'&$3#'!53.6%#.3!
!:;&'!,50',!.quot;!%&'!,&#8'!75%&!%&'!

mathematics
$.*+',%!7#<!#(.4*0!5,!12!#*0!1=!
;&'!,&#8'!75%&!%&'!$.*+',%!7#<!
#(.4*0!&#,!#!>'(<!$.*+!,&#8'=?!

 instructional
!
!
1= @*0'($5*'!%&'!>.)#-4$#(<!%'(/,!5*!%&'!34',%5.*!#*0!%&'!/#%&!>.)#-4$#(<!

strategies
4,'0!-<!%&'!,%40'*%=!
!
!
!
!

 planning for
A= B&#%!>.)#-4$#(<!%'(/,!0.!<.4!quot;''$!#('!/5,,5*+!quot;(./!%&'!,%40'*%C,!7.(D9!
!
!

vocabulary
!
!
!
!

instruction
E= F5,)4,,!<.4(!#*,7'(,!#*0!,./'!8.,,5-$'!,%(#%'+5',!%.!&'$8!%&5,!,%40'*%=!
!
!

 assessment of ©2008, Education Development Center, Inc.

vocabulary
Toolkit

Question: Of all of the
rectangles that can be formed
from 16 square tiles, what are
the dimensions of the rectangle
of the greatest perimeter?

Student response:
“The sides of the shape with
the longest way around is 16
and 1. The shape with the
longest way around has a very
long shape.”

Toolkit

Question: Of all of the
1. Identify the vocabulary
rectangles that can be formed
terms in the question and
from 16 square tiles, what are the math vocabulary used
the dimensions of the rectangle by the student.
of the greatest perimeter?
2. What vocabulary terms
do you feel are missing
Student response: from the student’s work?
“The sides of the shape with
3. Discuss your answers
the longest way around is 16
and some possible
and 1. The shape with the
strategies to help this
longest way around has a very
student.
long shape.”

Toolkit

Learning Needs
Language Module

Resources:
 Video Clips
 Facilitator Notes
 Presentation
materials
 Handouts and
other resources

Toolkit

Learning Needs
Co-teaching Module topics:
• Models of collaboration / co-
teaching
• Co-teaching strategies
• Co-teaching roles
• Communication and planning
between co-teachers

Toolkit

Focus 3: Rural Education

Toolkit

Biggest hurdle:

Access to quality mathematics PD

Toolkit

Biggest hurdle:

Online professional development
program,
PD materials focusing on depth of
understanding and appropriate
instruction

Toolkit

Biggest hurdle:

Online professional development
program,
PD materials focusing on depth of
understanding and appropriate
instruction
 High quality PD in mathematics

Toolkit

Online community


Toolkit

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

middlestart

Toolkit

Modifying a Task: Task 5
Online community

What type of sequence is shown in the ﬁgures
at the right? Explain.

tasks as a lens to
a) Linear
b) Quadratic 1 3 6
examine teaching c) Exponential

practice and student
d) None of the above

understanding 10 15

middlestart

Toolkit

Online community

 Focus on mathematics Mathematical Task
tasks as a lens to Framework
examine teaching (Stein and Smith, 1998)
practice and student
understanding

Tasks as
Tasks as
enacted
they Tasks as
by
appear in set up by
teachers
Student
curriculum teachers
and
materials learning
students

Toolkit


31
Toolkit

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.

31
Toolkit

Online community

tasks as a venue for
examining student
understanding and
teaching practice
 Review student work

Toolkit

Online community

examining student
understanding and
teaching practice

Tasks as
Tasks as
enacted
they Tasks as
by
appear in set up by
teachers
Student
curriculum teachers
and
materials learning
students

Toolkit

Online community
 middlestart

 Focus on mathematics Module 1 - Case 1: David Orcutt

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.

examining student 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

understanding and
includes two villages. The school is a 7-8 school in a small school building next to the district’s
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.

teaching practice In his three years of teaching, he has learned that students coming in from the two K-6 schools in
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
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.

 Use of brief case studies CLASSROOM ACTIVITIES
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

to encourage reflection
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.
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
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

Toolkit

Online community

same answer as the original student, or if they had something different. At every problem in which

all students agreed on the answer, he would quickly ask if any other answers were out there, and
unless a quick response came, he would say “correct” and repeat the problem number and
answer and move on. When students disagreed, he would quickly survey students in the room to
see which of the stated answers other students got, or, what other answers people came up with,

and unless it seemed that one was an outlier, would note that problem number of the whiteboard,
so that the class could go through it after checking homework. Six of the problems were noted on
the board, and he they asked, problem by problem, if there were any volunteers to go to the board
and do the problem. Two of the problems had no volunteers, so he asked one student what

examining student
answer they got for the problem, then asked if anyone had a different answer, and had both (or
more if several different answers arose) go up to the board to write their explanation or procedures
for the problem.

understanding and One of the two problems that had contested answers was the following:
! Emma was asked to order the following numbers from smallest to largest: .43, 8%, and .7
! Emma’s order was: .7, 8%, .43
! Is she correct? Why or why not?

teaching practice Two students wrote their answers on the board initially as shown below.

Student D: No because .43 is just about half and .7 is almost full and 8% is like 8 1s. .43 .7 8%

Student F: She is correct because 7 is the smallest and 43 is the biggest

 Review student work The following dialog is taken from this activity:

DO: “So, what do we think everyone. We have two answers here. What do we think?”

 Use of brief case studies Student H: “[D] is right. Emma didn’t get the right answer.”

DO: “And why is that?”

to encourage reﬂection H: “Well, sort of right. Emma didn’t get the right answer, but [D] didn’t get it right either.”

DO: “[F], what you you think? You said Emma got the right answer. Explain what you said.”

F: “Well, the numbers get larger, um, in Emma’s order, and, um, the dots and percents are the
same cause you can change from dots to percents and so I, um put them in order, and so, um, 7
is smallest, then 8, then 43.”

H: “But they aren’t the same. Dots are two places different.”

DO: “[D], what do you think? You said Emma wasn’t right, just like [H], but she said you weren’t
either. What do you think?”

D: “I was just trying to see what they are close to, and .43 is close to .5, which is a half. .7 is
bigger. It is nearly a whole thing, and deﬁnitely more than half. The percents don’t have the
decimals, so I thought 8% is like 8 whole things. But I think [H] is kinda right, um, ‘cause you have
to do move the dot two places.”

Toolkit

Online community

DO: “Let’s see what someone else says. [G], how about you? What did you say?”

 Focus on mathematics G: “I said Emma was wrong. It should be 8%, .43, .7 in that order because I put them all in
percents.”

DO: “Aha. There we go. You put them all in percents. All in the same units. That is exactly what
we want to do when we have decimals and percents together is put them in the same units. [H], is
that what you meant? Is that what you did?”

examining student
H: “Yeah, I made them all the same, but I didn’t do percents. I changed percents to fractions, so
they were all some part of 100.”

DO: “Excellent. There we go. We want to change them all to the same, and the best way is to

understanding and change them to fractions. Since we have percents, we should change them to parts of 100. That
is what percents really are. They are parts of 100. So, when you have all of your test right, for
instance, you have 100%. You get everything out of 100. So, how do we want to change these to
fractions of 100?”

teaching practice C: (called on after raising hand) “If it is one place. like .7 was, that is 7 out of 10, because the first
place is tenths. Then hundredths. so we could add a zero to the end of that, because .7 is the
same as .70, and that is seventy out of a hundred.”

 Review student work DO: “Great. That’s exactly it. Are we okay? Can we move on?”

No responses, so they go on to the next question. Shortly thereafter, David moves through the
other answers, and to the boardwork task. This task is written on the board already. It was
modified by David from a task he had seen in a workshop focusing on differentiation, which was

 Use of brief case studies addressing visual learners. The original task from the workshop is below.

Shade 10 of the small squares in the rectangle shown below. Using the diagram, explain how to determine
each of the following: a) the percent area that is shaded, b) the decimal part of the area that is shaded, and

to encourage reflection c) the fractional part of the area that is shaded.

David’s modified version that is on the board is the following:

Shade 10 of the boxes in the rectangle shown below (same rectangle). Find the percent area that is shaded.

David says that, in the interest of time, he is going to go through it, and asks students to watch.
He shades in 10 of the rectangles, picking them at random, and shading individual rectangles.

Toolkit

Online community

DO: “So, it really doesn’t matter which ones I pick, it will be the same. What I really care about is
how many total ones we have. [A], how many total boxes are there?”

A: “40”

tasks as a venue for DO: “And how did you get that?”

A: “I counted ten across, and there are four rows, so it was four times ten.”

examining student DO: “Exactly... or you could count everyone of them if you didn’t ﬁgure that out. So, what next
(looking at A)?”

understanding and A: “Well, it is a quarter. There are 10 out of 40, and if we write that as a fraction (DO pauses A with
a hand gesture and writes this on the board as the fraction 10/40, and then motions for him to
proceed)... so yeah, that’s it. And then you can cross out the zeros, cause 10 out of 40 is like 1
out of 4, and that’s a quarter. And a quarter is always 25%.”

teaching practice DO: “Exactly. Does everyone see that? Once [A] got it to a fraction, he could easily change it to a
percent. If it was a fraction you didn’t know already, like... suppose we had 12 shaded boxes
instead? You could make it 12 out of 40, and then cross multiply to ﬁgure out the number out of
100 (as he draws on the board ‘12/40 = n/100’ and then proceeds to write, ’12 x 100 = n x 40’),

 Review student work and so in this case you could multiple 12 and 100...[A], what is that?”

A: “Twelve and a hundred? That’s one thousand two hundred.”

DO: “and divide that by 40 and we would get 30. Thirty percent... if it was twelve out of 100.” Do

 Use of brief case studies you all see that?

The class seems to agree quietly, and David moves on to the next part of class...


Toolkit

Online community

Focus on mathematics

examining student
understanding and
teaching practice
Review student work

Use of brief case studies

Teachers share examples,

observations, and
reﬂections on own and
others practice

Toolkit

Online community Online discussion


examining student
Lesson library
understanding and
teaching practice
Review student work Chat/room and live


whiteboard

observations, and

Video and
artifact
upload
others practice

Toolkit

Online community


examining student
understanding and
teaching practice
Review student work



observations, and
others practice
Develop deeper

understanding of content
Toolkit

Online community Introductory
 
Content and

tasks as a venue for processes
examining student
understanding and
Ratio/Proportion
teaching practice 
Review student work

Use of brief case studies Algebraic
 
Reasoning/

Patterns/Functions
observations, and
Geometry and

others practice
Measurement
Develop deeper

understanding of content
Toolkit

Focus 4: Family

Toolkit

Focus 4: Family
Issues: Schools struggle with this in

general
and many mathematics issues for
students arise from parent/
community misunderstandings,
stereotypes, and attitudes toward
math.

Toolkit

Focus 4: Family
Issues: 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
Toolkit

Focus 4: Family
Needs assessment

and introductory
activities

Toolkit

Focus 4: Family
Needs assessment

and introductory
activities
Sample discussion

materials (big
picture) and
communications

Toolkit

Focus 4: Family
Needs assessment

and introductory
activities
Sample discussion

materials (big
picture) and
communications
Strategies to

provide awareness
of approaches to
learn
Toolkit

Focus 4: Family
Needs assessment Family Math Night

and introductory
activities Career
Sample discussion
 awareness
materials (big programs
picture) and
communications Afterschool tutoring
Strategies to

provide awareness Regular
of approaches to communication
learn with parents
Toolkit

Focus 4: Family
Needs assessment

and introductory
activities
Sample discussion

materials (big
picture) and
communications
Strategies to

provide awareness
of approaches to
Toolkit

For more information…

Toolkit

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

Toolkit

Csrqi Nmsa Presentation2

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