Raising Achievement Through Reading and Writing Mathematics

Neil Hatfield

Northwest Missouri State University

Background

Developing communication skills in addition to guiding students through the mathematical landscape can be challenging.

I have observed various degrees of blending reading, writing and mathematics.

Results have been unclear.

Why?

Push for tougher standards.

Call from state Boards of Education for Reading/Writing across the curriculum.

A closer investigation into pedagogies that blend reading, writing, and mathematics together over a whole course is warranted.

Guiding Question

Can mathematical pedagogy blended with reading only emphasis, writing only emphasis, or emphasis in both reading and writing lead to improvement in student understanding of mathematical concepts?

Research Questions Is there significant evidence to suggest that there

is a difference in student mathematical achievement between the various pedagogies?

Is there significant evidence suggesting that students exposed to reading pedagogy scored higher than the students in the control group?

Is there significant evidence suggesting that students exposed to writing pedagogy scored higher than the students in the control group?

Is there significant evidence suggesting that students involved in the reading only class scored higher than the students in the control group?

Writing Research

Appears to be little research

Writing is an extremely organic process unique to each person

The writing process behaves in a similar fashion as the reading process…they are inextricably linked. Rosenblatt, 1994

Writing Research, cont. Writing allows for students to develop both

academically and personally.

Students need a wide range of writing activities in various academic contexts with both overtly self-reflective and overtly subject-focused tasks. Curtis and Herrington (2003)

73% of students reported that writing was important or very important in understanding/applying the ideas of the course. Sommers and Saltz (2004)

Writing Paradox Sommers and Saltz found a paradox.

Novice writers viewed as experts Students are required to write about material

they are still coming to grips with, while at the same time, place that knowledge into a larger context.

Build authority not by writing from a position of expertise, but by writing into expertise.

Rosenblatt’s Transactional Theory

Reading Research

Key Action to create successful readers: get the students to engage actively with the text.

Proposed strategies for reading: Reciprocal Teaching (Palincsar and Brown, 1984)

Transactional Theory (Rosenblatt, 1994)

Constructively Responsive Reading (Pressley and Afflerbach, 1995)

Others (Exner, 1996; Barton and Heidema, 2002; Pape, 2004; Friedman, Myers, and Wright, n.d.; Flood and Lapp, 1990)

Small episodes with limited number of participants.

Reading Research, cont.

Flood and Lapp (1990) provide a framework for working with “at-risk” students and reading comprehension.

1. Preparing for Reading Practices

2. Reciprocal Teaching Practices

3. Understanding/Using Text Structure

4. Questioning Practices

5. Information Processing Practices

6. Summarizing Practices

7. Voluntary/Recreational Reading

The Research Project

Using Math Skills 2 (Intermediate Algebra) Control Group

Reading Only

Writing Only

Reading and Writing

Each group sans Control receives additional mathematics instruction from the researcher. Control group has another leader.

The Reading and Writing group does the same activities as both of the single emphasis groups.

Writing

Based on my own past experiences with writing.

Journal Prompts are Word 2007 forms

One-on-one approach Provides differentiation

Preserves individual student voice

Example Journal Prompt

Example Journal Prompt

Early Writing Results

Very difficult to get students to complete the prompts. (Not surprising.)

May have been worthwhile to spend time in class building what a “good” response is.

Benefit: Allows for the detection of misconceptions that may not surface. “F.O.I.L” as the [only] way to factor any trinomial.

Difficulty understanding the Distributive Property

“Addressing” misconceptions Curse: students must actually read the teacher responses.

Benefit: Private, non-threatening atmosphere

Student Journal Responses

“F.O.I.L” Response

Distributive Property

“Good” Response

Reading

Two Mini-Strategies Unknown Words/Symbols

Matching Homework to Examples

Four Full Strategies1. Summarizing Text

2. Summarizing Text and working Examples

3. Guided (Structured) Reading

4. Student Personal Synthesis

Guided Reading

Blending of both Mini-strategies and the previous two Full strategies.

Instructor Prepared Reading Guides

Additionally Activation of Prior Knowledge

Question-Generation

Reflective Thinking

Implements a gradual release of responsibility

Example Reading Guide

Reading Guide Example 1

Reading Guide Example 2

Reading Guide Example 3

Student Reading Work

Example 1 (Reading Strategy 1)

Example 2 (Reading Strategy 3)

Example 3 (Reading Strategy 3)

Example 4 (Reading Strategy 3)

Student Personal Synthesis

Result of the gradual release of responsibility.

Students generated their own reading strategy based off what they have learned.

Idea: to see what students apply after instruction in the various strategies.

Early Reading Results

In addition to “math” words/symbols identified as unknown, “non-math” words were also identified.

Students struggle with buying into the first two Full Strategies. Repetition, monitoring and constructive support

Students seem to clasp onto the third strategy more readily.

Students also felt that it was helping them.

Results

The following slides contain some “rough” results.

The power of the tests is really low.

Further analysis is underway.

Table 1 ANOVA for “Is there significant evidence to suggest that there is a difference in student mathematical achievement between the various pedagogies?”

Exam Reading Strategy p-value (α = 0.10)Test 1 Mini-Strategies 0.7436

Test 2 Full Strategy 1 0.2321

Test 3 Full Strategy 2 0.4247

Test 4 Full Strategy 3 0.6672

Final Final Synthesis 0.6892

Table 2 t-Test for Is there significant evidence suggesting that students exposed to reading pedagogy scored higher than the students in the control group?

ExamReading Strategy

Control Mean

Control Variance

(SD)Reading

Mean

Reading Variance

(SD)

t-Test Statistic

(d.f. = 25) p-value

Test 1Mini-

Strategies59.455

338.623 (18.402)

62.5253.2

(15.912)0.9759 0.1692

Test 2Full

Strategy 169.273

239.218 (15.467)

74.327171.179 (13.084)

1.9698 0.0300*

Test 3Full

Strategy 261.218

225.794 (15.026)

67.48198.970 (9.948)

3.2099 0.0018*

Test 4Full

Strategy 356.5

395.66 (19.891)

55.596309.884 (17.604)

-0.2618 0.6022

FinalFinal

Synthesis104.273

366.818 (19.152)

109.308297.422 (17.246)

1.4887 0.0745*

Note: Sample size for Control: n = 11; sample size for Reading: m = 26*Significant at that 90% confidence level.

Table 3 t-Test forIs there significant evidence suggesting that students exposed to writing pedagogy scored higher than the students in the control group?

ExamControl Mean

Control Variance

(SD)Writing Mean

Writing Variance (SD)

t-Test Statistic

(d.f. = 32) p-value

Test 1 59.455338.623 (18.402)

59.5196.1875 (14.007)

0.0186 0.4926

Test 2 69.273239.218 (15.467)

70.561170.981 (13.076)

0.5658 0.2877

Test 3 61.218225.794 (15.026)

65.497141.960 (11.915)

2.0630 0.0237*

Test 4 56.5395.66

(19.891)51.445

381.585 (19.534)

-1.4864 0.9265

Final 104.273366.818 (19.152)

106.818292.591 (17.105)

0.8549 0.1995

Note: Sample size for Control: n = 11; sample size for Writing: m = 33*Significant at that 90% confidence level.

Table 4 t -Test for Is there significant evidence suggesting that students involved in the reading only class scored higher than the students in the control group?

ExamReading Strategy

Control Mean

Control Variance

(SD)Reading

MeanReading

Variance (SD)

t-Test Statistic

(d.f. = 10) p-value

Test 1Mini-

Strategies59.455

338.623 (18.402)

63.273254.768 (15.961)

0.7934 0.2230

Test 2Full

Strategy 169.273

239.218 (15.467)

73.818114.364 (10.694)

1.4097 0.0945*

Test 3Full

Strategy 261.218

225.794 (15.026)

65.59180.141 (8.952)

1.6200 0.0681*

Test 4Full

Strategy 356.5

395.66 (19.891)

57.864248.513 (15.764)

0.2869 0.3900

FinalFinal

Synthesis104.273

366.818 (19.152)

112.09192.291 (9.607)

2.6991 0.0112*

Note: Sample size for Control: n = 11; sample size for Reading: m = 11*Significant at that 90% confidence level.

Implications

Continued research to refine methodology and remove confounding variables (primarily, researcher).

Provides insight into whole-classroom reading/writing instruction in a content area.

Provides a starting platform for the development of pedagogy.

Offers ideas for professional development.

Future Research

This study did not provide a clearer picture on the impacts of blending reading and writing with mathematics.

It does help to move the research forward from one-on-one interactions to whole classroom instruction.

We need to refine the blended pedagogies and conduct additional research.