Research
Summary
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: Indepth 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 reteach.
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.
