Improving Mathematics Problem Solving Through Written Explanations

Report on action research project by Janet Schlattmann

My Background

o Alliance Middle Schoolo 7th grade math 8th grade algebra 23 years teaching-17 in Alliance

Grades 7-8 currently Grades 7-12 in the past

100 students in 7th grade 12 students in SWS and 14 in regular 7th

grade class in my study

Problem of Practice Low problem solving scores on Terra

Nova No confidence in problem solving Difficulty explaining answers or thinking NCLB requirement District’s math goal NCTM process standards of

communication, reasoning, and problem solving

Literature Review

Kjos and Long, 1994 Millard, Oaks and Sanders, 2002 Ishi, 2002 Jurdack,1998 Pugalee, 2001 Research not found

Purpose

The purpose of this study is to determine the effects on low achieving students as well as other students of using written explanations and /or representations of thinking and reasoning in mathematical problem solving.

Question and Methods1. What is the effect of students expressing their thinking

and reasoning through writing/representation in math problem solving on their ability to solve problems?

Pretest and Post test of problem solving scored with a rubric on concepts and computation.

Schools scores from District problem solving assessments (previous year and this year).

Scores on problem solving assignments given during research time frame

Question and Methods

2. How will student attitudes about themselves as problem solvers change when written communication is used?

Attitude survey at beginning and end

Observations kept as a journal

Interviews

Question and Methods

3. What is the effect on students’ ability to communicate their thinking when written communication is used?

Pretest and post test scored with rubric on explanation and representation.

Teacher observation and journal

Scores of problem solving assignments scored with explanation and representation.

Question and Methods

4. How will low achieving students’ problem solving growth compare to the scores of students in a regular class?

Compare pretest and post test scores

Compare scores of problem solving assessments

Compare scores of problem solving assignments

Analysis Mathematical Concepts

SWS Concept Scores

0

0.2

0.4

0.6

0.8

1

1.2

1.4

SWS Class

Sco

res

1-4

Pretest Mean

Posttest Mean

Analysis Mathematical Concepts

5th Period Concepts Scores

0

0.5

1

1.5

2

2.5

3

3.5

5th period Class

Sc

ore

s 1

-4

Pretest Mean

Posttest Mean

Analysis Mathematical Concepts

Concepts Tests Scores

0

0.5

1

1.5

2

2.5

3

3.5

4

1 2 3 4 5 6 7 8 9 10

Students 1,2,3 SWS, 5thperiod 4-10

Sco

res

on

4 p

oin

t sc

ale

Pretest score

Post test score

Analysis Mathematical Concepts

SWS Concepts

0

1

2

3

4

5

1 2 3 4 5 6 7

7 Daily Assignments

Sco

res

on

1-4

sca

le

Mean

Student 1

Student 2

Student 3

Analysis Mathematical Concepts

5th Period Concepts

0

1

2

3

4

5

1 2 3 4 5 6 7

7 Daily Assignments

Sco

res

on

1-4

sca

le Class Mean

Student 4

Student 5

Student 6

Student 7

Student 8

Student 9

Student 10

Attitude1. I am pretty good at

math problem solving.

2. Writing about my thinking or my reasoning helps me to better understand the problems I am solving.

3. Writing my ideas and reasoning is easy for me.

4. I am improving at problem solving.

5. I understand more about problem solving than I am able to put down in writing.

00.5

11.5

22.5

33.5

4

Mean 1 2 3 4 5

Question

SWS Attitude Survey

Pre

Post

Attitude6. The activities we are

doing in class are helping me be more confident in problem solving.

7. Others would clearly be able to understand how I solve problems by reading my explanations and looking at my charts or models.

8. I am good at writing.

9. I like mathematics.

00.5

11.5

22.5

33.5

4

Mean6 7 8 9

Question

SWS Attitude Survey

Pre

Post

Attitude1. I am pretty good at

math problem solving.

2. Writing about my thinking or my reasoning helps me to better understand the problems I am solving.

3. Writing my ideas and reasoning is easy for me.

4. I am improving at problem solving.

5. I understand more about problem solving than I am able to put down in writing.

00.5

11.5

22.5

33.5

44.5

Mean 1 2 3 4 5

Question

5th Attitude Survey

Pre

Post

Attitude6. The activities we

are doing in class are helping me be more confident in problem solving.

7. Others would clearly be able to understand how I solve problems by reading my explanations and looking at my charts or models.

8. I am good at writing.

9. I like mathematics.

00.5

11.5

22.5

33.5

44.5

Mean 6 7 8 9

Question

5th Attitude Survey

Pre

Post

Attitudes

Interviews Did writing in problem solving help

them? Did they like it? What helped them to be better

problem solvers? Have feelings about problem solving

changed?

Attitudes

Observations Negative behaviors Attempting problems Confidence and reliance on self

instead of the teacher

Explanation/Representation

SWS Explanation/Representation Scores

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

SWS Class

Sc

ore

s 1

-4

Pretest Mean

Posttest Mean

Explanation/Representation

5th Period Explanation/Representation Scores

0

0.5

1

1.5

2

2.5

3

3.5

5th Period class

Sc

ore

s 1

-4

Pretest Mean

Posttest Mean

Explanation/Representation

Explanation/Representation Scores

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 5 6 7 8 9 10

Students SWS 1-3, 5th period 4-10

Sc

ore

s o

n 4

po

int

sc

ale

Pretest Scores

Posttest Scores

Explanation/Representation

SWS Explanation Scores

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 5 6 7

7 Daily Assignments

Sco

res

on

1-4

sca

le

Class mean

Student 1

Student 2

Student 3

Explanation/Representation

5th Period Explanations

00.5

11.5

2

2.53

3.54

4.5

1 2 3 4 5 6 7

7 Daily Assignments

Sco

res

on

a 1

-4 S

cale Class Mean

Student 4

Student 5

Student 6

Student 7

Student 8

Student 9

Student 10

Explanation/Representation

Observations Difficulty in expressing thoughts in

writing Writing as they solved Writing for others to understand Variety of solutions More detail and depth of thinking

0

0.5

1

1.5

2

2.5

3

Mean

Pretest Posttest

Concept Comparisons

SWS

5th period

Comparison

Comparisons

Daily Assignment Concept Mean

00.5

11.5

22.5

33.5

4

1 2 3 4 5 6 7

Week Assignment given

Sco

res

on

a 1

-4 s

cale

(4

hig

h) SWS

5th

Interpretation

Written expression slight improvement SWS improvement in problem solving over

time Improvement in willingness to try Student differences on what helped them

improve Writing explanations helped students think

through steps Writing and problem solving takes time Writing helped me see the misconceptions

students had about their mathematics and perceptions about problems

Connections to Previous Research

Jurdak, 1998 –positive effects of expository writing

Pugalee,2001-metacognitive development through explaining actions

Low achievers and problem solving not addressed in any research I found

Implications

For me Have students continue writing

explanations in problem solving Start at the beginning of the year Incorporate more strategies to know

how to express thinking Have students share solutions and

explanations Continue collection of data to study

effects of written expression

Implications

For others NCTM-process standards of

communication, reasoning, problem solving

Struggling students can show growth Attitudes not always positive when

work is more difficult Writing can improve student growth in

expression, problem solving and willingness to try

Implications

Further research More research is needed as there is

little research on this topic More students need to be studied Study needs to be over a longer period

of time Research is needed to study low

achievers to find improvement in problem solving and reasoning

All math staff will experience a problem solving session All math staff will experience a problem solving session that entails using “Habits of Mind” problem, solving the that entails using “Habits of Mind” problem, solving the problem, presenting solutions to the group and problem, presenting solutions to the group and brainstorming modifications and uses for particular grade brainstorming modifications and uses for particular grade levels and classrooms.levels and classrooms.

We will meet a minimum of once a quarter.We will meet a minimum of once a quarter. We will display our solutions in our rooms or hallways to We will display our solutions in our rooms or hallways to

see what the different grades have come up with for see what the different grades have come up with for solutions.solutions.

We may collect data to measure growth if we can decide We may collect data to measure growth if we can decide what the group wants to collect and how to assess it.what the group wants to collect and how to assess it.

School PlanSchool Plan

Problem solve with written explanations Problem solve with written explanations once a week if possible.once a week if possible.

Teach writing strategies to help students Teach writing strategies to help students get thoughts on paper. Teach more get thoughts on paper. Teach more reading of problemsreading of problems

Use “Habits of Mind” problems with my Use “Habits of Mind” problems with my students and have them display and students and have them display and discuss solutions and explanations.discuss solutions and explanations.

Individual PlanIndividual Plan