The Question

Does Right = Write?
How does student writing about math connect to the assessment of students’ mathematical understanding?

Rationale for Study

As the Math Lead Teacher in Grade 3 I was concerned about an apparent disconnect between math understanding and “getting the right answers” on work pages and quizzes. Students were unable to explain what they had done to solve a problem. Getting the answer was all that mattered – the process was not important. I was troubled by what appeared to be a lack of math comprehension.

Background/Context

P.S. 64, on Walton Avenue in the Highbridge section of the Bronx, has 1100 students. 80.6% are Hispanic, 17.9% are African American, 1.5% are Asian and others. Of the 80.6% Hispanic students, 37% have been identified as English Language Learners. Of this 37%, 8.3% are recent immigrants to the United States, that is, they immigrated within the last three years. Students identified as ELL’s receive exemptions in reading exams for three years, but all students take the Math test.

Research

Marilyn Burns advocates math writing because it requires students to organize, clarify, and reflect on their ideas. Writing also helps the teacher identify which individual students do not understand athematical concepts.

Joan Countryman writes that students generally memorize examples, follow instructions, do homework and take tests. Math knowledge for many of them is about pages to be covered and assignments to be completed. Using writing in Math can change this paradigm.

Krulik and Rudnick discuss the importance of developing thinking skills in young children. Their study points out that thinking/reasoning skills are an integral part of math development. The authors propose that writing is one of the ways to develop critical and creative thinking.

Tools

Math Journals: a collection of work in which students solved
problems on a weekly basis, and explained their strategies. These
Journals also include student reflections on different math
concepts.

Field Notes: Teacher observations about students strategies
and work.

Student Work: Responses to six math problems that call on a variety of math concepts.

Case Studies: In-depth studies of 3 students who represent the breadth of learning styles in the class.

Data

A sampling of six math problems was chosen. I observed that some students got correct answers but could not explain why. For other students, “language” was an impediment. Some students creatively solved the problem, but made computational errors. In each of the problems there were students who found it difficult to work outside of the structure and wording of the text book.

Case Studies:
Student 1 is bright, alert, competitive child, but loses confidence when challenged to think “outside the box”.

Student 2 is an average , hard working child who is intimidated if
a question “looks” hard. Writing in Math allowed him to explore different ways to figure out problems.

Student 3 loves to write and illustrate his stories, but does not like Math in any size or shape. Through the use of the Journal, in which he was able to use his favorite mediums of writing and drawing, he is beginning to dismantle his math block and experience success.

Analysis

The data that I have gathered suggests that writing about math should be an integral part of an elementary math course of study. I learned that students come to frame their math knowledge in the familiar presentation of a given text and experience great difficulty in transferring that knowledge to new situations.Writing about math requires students to analyze and identify patterns and relationships within problems and between problems: critical thinking development. I learned that sometimes the students really didn’t understand what I had taught and it was necessary to re-teach. I learned that there is no complete assessment of a student’s mathematical understanding without a writing component.

Policy Recommendations

• One day each week should be dedicated to the development of
  critical thinking skills through the use of journaling, problem solving and math explorations.
• Pacing calendars must have more flexibility to permit teachers
  to engage in differentiated instruction.
• Assessments must have a portfolio component.