The National Forum Mathematics Improvement Toolkit

Presented by:

Sara FreedmanKimberly Keniley-AshbrookAnna McTigueStephen Best

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

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.

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

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)

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

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

Tool #1

Tool #1Who 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.

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.

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

Tool #1

Tool #1Who are the English language learners in our schools today?

Tool #1

*Great City Schools are the 60 largest urban districts in the country.

Take turns analyzing the graph with a partner.

SPEAK RESPONDRESPOND QUESTION

Letʼs look at a typical word problem

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.)

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?

WRITE: Use the handout to record your responses

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

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?

#1 #2

#4 #3

➟

➟

➟

Small Group discussion

Tool #1What are the LANGUAGE challenges in this problem for English language learners?

Tool #1

GROUPGet 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.

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?

#1

#3#4

#2

➟

➟

➟

Focus 2: Students with Special Learning 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.

Tool #2

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

Students need support for visual, auditory, attention, and memory functions.

Focus: Students with Special Learning Needs

Focus 2: Students with Special Learning 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

Tool #3

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?

Letʼs try a task...

We will insert the video here.

Co-teaching Roles• Work with a

partner and brainstorm roles that co-teachers could take to benefit students.

• Record your ideas on Handout 2

We will insert the handout here.

Focus 2: Students with Special Learning Needs

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.

Tool #4

Focus 2: Students with Special Learning Needs

Language Module topics:

✦ Demands and challenges of language

✦ Instructional strategies

✦ Planning for vocabulary instruction

✦ Writing strategies for mathematics

Tool #4

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.

Tool #5

Focus 3: Rural Education Online

community

Tool #5

Focus 3: Rural Education Online

community Focus on mathematics

tasks as a lens to examine teaching practice and student understanding

Tool #5

middlestart

Modifying a Task: Task 1

The Old Farmer’s Almanac

suggests that you can tell

the temperature outside by

counting the chirps a cricket

makes in 14 seconds and

adding 40 (to get the

temperature in degrees

Fahrenheit). Use this to find

how many chirps the cricket

makes when it is 72 degrees.

middlestart

Modifying a Task: Task 1

The Old Farmer’s Almanac

suggests that you can tell

the temperature outside by

counting the chirps a cricket

makes in 14 seconds and

adding 40 (to get the

temperature in degrees

Fahrenheit). Use this to find

how many chirps the cricket

makes when it is 72 degrees.

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.

Focus 3: Rural Education

Tasks as they appear in curriculum materials

Tasks as set up by teachers

Tasks as enacted by teachers and students

Student learning

Tool #5 Online

community Focus on mathematics

tasks as a lens to examine teaching practice and student understanding

Review student work

Focus 3: Rural Education

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.

INTRODUCTION AND CONTEXTDavid 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

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

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.

CLASSROOM ACTIVITIESDavid 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.

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

middlestart

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.

INTRODUCTION AND CONTEXTDavid 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

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

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.

CLASSROOM ACTIVITIESDavid 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.

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

middlestart

Tool #5 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

Focus 3: Rural EducationTool #5 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.

Focus 3: Rural EducationTool #5 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

Focus 4: Family Engagement 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 engagementResources to guide communication with parents

Audience for these resources needs to be broader than mathematics teachers alone.

Tool #6

Focus 4: Family Engagement Needs assessment

and introductory activities

Tool #6

Focus 4: Family EngagementTool #6

Needs assessment and introductory activities

Sample discussion materials (big picture) and communications

Focus 4: Family EngagementTool #6

Needs assessment and introductory activities

Sample discussion materials (big picture) and communications

Strategies to provide an awareness of approaches to learn mathematics

Focus 4: Family EngagementTool #6

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

For more information… Complete the email signup sheet Denote any specific tools that you are

interested in using Visit:

http://www.middlegrademath.org