Everyday Mathematics

Nicole Musil

EDSP 765©2006

Why Math?

• Are we math haters?– “I’m not a ‘math person’.”

• “Instead of having 'answers' on a math test, they should just call them 'impressions' and if you got a different 'impression' so what, can't we all be brothers?” –Jack Handey

Resistance to Change

• “If there was a big gardening convention, and you got up and gave a speech in favor of fast-motion gardening, I bet you would get booed off the stage. They're just not ready.”

• However, with the current disillusionment with math programs, it seems “they” are ready (at least some of “them”)

Mathematically Correct

• American education is under intense pressure to produce better results. The increasing importance of education to the economic well-being of individuals and nations will continue feeding this pressure. In the past—and still today—the profession has tended to respond to such pressures by offering untested but appealing nostrums and innovations that do not improve academic achievement.”– Douglas Carnine

Overview

• Background

• Underlying theory / philosophy

• Classroom-based research

• Program evaluation

• Evaluation of the research

• Should schools implement this?

Motivation for Evaluating EM• Widely used in local area • Guru effects?

Keep this in mind

• Suppose your district tells you they are pilot-testing EM in some classrooms but not others

• How do you react?

National Commission on Excellence in Education, 1983

“A Nation at Risk”

• A “crisis”- businesses, educators, and governmental agencies

• American adults lack – mathematical knowledge, – problem-solving, – reasoning skills needed to function in academic and

occupational settings

TIMSS

• Other countries (Japan, Germany, Russia) doing better

• They also teach math differently

How we teach math

US• Spend more time on review• Less challenging problems• Fewer word problems• More rote than problem-solving• Textbook publishers

Others• Cover more concepts• Present topics earlier• “Realistic” problems• Students generate own methods• Discuss multiple methods• Use manipulatives

Implications for Practice?

The DebateNCTM Principles

• “Fuzzy math“

• The whole language version of math?

• Will these kids fall behind in basic skills?

• “Parrot math”

• Mathematically Correct

• Does “drill & kill” lead to long-term retention?

Basic Information

Everyday Math Program

Scope & Sequence

• Grades K-6

• Spiraling, introduces concepts at each grade level

• Reviews concepts at each grade level

Concepts

• Algebra and the uses of variables

• Data and chance

• Geometry and spatial sense

• Measures and measurement

• Numeration and order

• Patterns, functions, and sequences

• Operations

• Frames of reference

Addition & Subtraction

For more information

• Main website• http://everydaymath.uchicago.edu/index.shtml

• FAQs• http://everydaymath.uchicago.edu/educators/faq

s.shtml

• See handout

Level I Research: Theory

Underlying Idea

• Instead of teaching algorithms, teach students to think mathematically

• “Life 10, school 0” – Brazilian study

• Limited benefits of memorizing “spoon fed” instruction

How did you learn math?

• Preferences?– Calculation – Word/story problems– Direct instruction

• Applications– Chemistry, physics, biology– Economics

Simon, 1995

Constructivism

• Human beings lack access to objective reality

• Create or “construct” their knowledge based on their experiences

• Learning= process of adaptation to the experiential world – (who does this sound like?)

Social Constructivism

• Discussion, small group

• Team problem-solving

Spacing Effect & Recall

• Revisiting concepts year after year

• “Spiraling” scope and sequence (Fisher?)

• Leads to better retention than teaching all of the concept in one school year

• Problem solving => depth of processing?

Other underlying ideas

• Underestimation of children

• Capable of solving problems using own methods

• Addition, subtraction, and other operations

Use of Tools & Games

• Kindergarten:– Skip Count with Calculators to teach

numeration

• Use games to teach in school and at home

Family involvement

Take-home handouts for parents to reinforce lessons

Activities include• Grocery store• Car activities• Games

Red Flag Moment

• “Where fun goes to die” (Smith, 2003)

• Not a school of education

• What about pedagogy?

• Low achievers?

Another concern

• “How can mathematics teachers foster students’ construction of powerful mathematical ideas that took the community of mathematicians thousands of years to develop?”

– Simon, 1995

Level II Research

Does it work in the classroom?

"BOO!" says the Coalition for Evidence Based Policy (2003)

Research?

• Most research descriptive, one group

• Not even matched comparison groups

Some “possible” evidence

• Constructivism lacks a pedagogical model

• “Reform math” or “problem-centered instruction”

• Matched comparison groups

Woodward & Baxter (1997)

• Quasi-experimental, pre-post, b/t classes

• 3rd graders, 2 types of instruction

• Reform math students did better on ITBS and IMA (informal math assessment)

Woodward & Baxter (1997)

• Even low achievers did better

• BUT gained less than average peers

• Baxter, Woodward, & Olsen (2001) followed up

• Qualitative research– Interviews– observations

• Conclusions– Participation– Cognitive load– “Don’t abandon!”

Helping low-achieving students

• Teachers must actively involve– Baxter, Woodward, Voorhies, & Wong (2002)

• How? Journal writing helped– Baxter, Woodward, & Olson, (2005)

• Caveat: qualitative

Level III Research

Does it work at the district, region, or state level?

Coalition says POSSIBLE

Riordan, & Noyce (2001)

• State of Massachusetts

• 67 schools, matched for SES, previous achievement

• Using EM positively impacted student achievement (std. tests)– regardless of gender, race, and economic

status

Coalition says- NOT evidence

Schoenfeld (2002)

• Examined multiple studies of widespread implementation

• Fears about decrement in basic skills unwarranted

• Concluded that even “less wealthy” schools benefited

Wenonah Elementary School

Wenonah Elementary School

• Wenonah, NJ

• Using EM in grades K-6 since 2001

• Community 94% white, “middle class”

NJ state test scores

Percentage of Students Scoring at the Proficient or Advanced Level in Mathematics, 2003-2005

Year Grade 3 Grade 4 2003 n/ a 92 2004 95 71 2005 97 95

Problems

• Revisiting D153’s piloting policy

• Mobility- school and classroom

• Teacher readiness / preparedness

Summary / Conclusions

• Level I- has a theory / theories

• Level II- most research poorly done

Summary / Conclusions

• Level III- a few quasi experimental studies– Coalition: “possible evidence” at best– Lack of control groups– Changing the assessment instrument

changes what we’re measuring

• So do we recommend this to our school / district??

Final Points

• Will it last? Mktg cycle

The End

• Questions?