Research Summary
“If you really care about a child’s learning,
you will naturally adopt a constructivist approach”
– Frances Rust
Introduction
In the fall of 2004, my school switched to the
Chicago Everyday Math program. This new math curriculum
is constructivist. Teachers at my school were divided
in their feelings about the new program. It was
my second year of teaching, and in graduate school
constructivism was touted as the ideal. I participated
in a twoweek summer institute in 2004 (Mathematics
in the City) at City College where I was further
indoctrinated in the gospel of constructivism. I
wondered about the results of a constructivist approach
on students and on my practice.
Charter schools such as KIPP Academy in the Bronx
teach math using traditional methods while Region
1 mandates progressive methods. I researched how
different schools approach the teaching of mathematics.
I found top elementary schools in Manhattan such
as P.S. 6 and P.S. 290 (The Manhattan New School)
use a progressive math program call TERC (which
is investigationsfocused) while charter schools
preferred traditional approaches to the teaching
of mathematics. Are progressive methods the best
way to help students in low achieving schools? I
work in a district that has struggled to raise student
achievement for years. Will a progressive approach
to math help me to raise student understanding in
my classroom?
P.S. 90
P.S. 90 is a K4 school serving 1,500 students
in the South Bronx. The fourth grade alone contains
300 students. This year, in the fourth grade, we
decided to implement a Middle School Model. Teachers
were paired up and asked to teach either ELA or
Mathematics. I became a math teacher, and worked
with two groups of students. I was given the opportunity
to delve into the content area of mathematics and
to focus on developing my practice in this content
area.
Review of the literature
I focused my readings on the writings of Catherine
Twomey Fosnot (Young Mathematicians
At Work, 2001), H. Wu (Basic
Skills Versus Conceptual Understanding: A Bogus
Dichotomy in Mathematics Education,
1999), and Richard Askey (Knowing and
Teaching Elementary Mathematics, 1999).
Catherine Fosnot helped me to understand an alternative
way of teaching math through having children construct
their own understanding. H. Wu offered a critique
of Dr. Fosnot’s approach arguing that the dichotomy
between constructivist math and learning “basic
skills” is a false one, and that skills and understanding
are completely intertwined. Richard Askey helped
me to understand that elementary math is not so
elementary. Teaching elementary mathematics to kids
requires much deeper mathematical knowledge than
most people think.
Data Collection
Test Scores  I used the Princeton Review
diagnostic test as my baseline, and then assessed
understanding based on weekly quizzes, and compared
baseline data with results on the NYS mathematics
test
Anecdotal – I kept notes on student’s
progress in a journal especially after lessons where
I used manipulatives. I also worked oneonone with
struggling students, and kept records of their progress.
Student Writing – Student’s writing in
their math notebooks was used to determine whether
mathematical ideas were mastered.
Conclusions
1. Constructivist math requires a robust
understanding of topic
The teaching of mathematics, especially elementary
school math is so easy to do badly, yet so difficult
to do well. Innumeracy or math phobia, I am convinced,
has its origins in how basic topics in mathematics
were presented to children in primary school. In
order to help children construct their own understanding
of mathematics, it is necessary that teachers have
a deep understanding of the topic, otherwise, teachers
fail to be the guides children need. Teaching mathematics
constructively can be messy and disorderly. Manipulatives
fly around the room, and students talk. Yet, if
the teacher has a clear idea of where he/she wants
students to end up, then there is a method to what
is oftentimes madness in the classroom (at least
in mine). Teachers have to move away from their
own procedural understanding of math concepts such
as the basic operations, fractions and decimals.
I learned a great deal working with my students
on mental math strings. I learned students solve
problems differently, and are often imaginative
in their derivation of solutions.
2. A strong classroom community is a prerequisite
One of the foundations of a constructivist classroom
is that students are able to dialogue with each
other and with the teacher. As a teacher, I need
to be able to hear students articulate to me and
each other their method of arriving at solutions.
Students learn from each other, but this is impossible
if students do not trust each other, or themselves.
This was one of my struggles this year. It is a
challenge to foster an environment where students
work to construct their own understanding of math
when they are used to having teachers tell them
the algorithm and procedures. An investment has
to be made at the beginning of the year to set classroom
tone and standards of behavior.
3. Students are engaged by lessons that
relate to their lives and that provide opportunities
for genuine mathematizing
My observation this past year has been that a lesson
that is well thought out and prepared and allows
students to work with manipulatives in a meaningful
way engages students. My most successful lessons
in math this year have been the ones where I did
not do all the talking. Students have a deep desire
to engage in tasks that are meaningful and genuine.
Policy Recommendation
Professional Development – Teachers need
training in order to teach math well. I have noticed
that greater emphasis is given to literacy while
math is often relegated to second place. Even at
my school, literacy was referred to for years as
“Golden Hour” while the math block was called “Silver
Hour.”
I participated in Math in the City, which is a
twoweek summer institute where teachers come together
from all over the city to solve math problems, talk
about math, and discuss ways in which to help students
learn math more efficiently. Teaching math constructively
is not an automatic process. Imposing a progressive
math curriculum does not lead to the proliferation
of constructivist classrooms. Schools that have
successful progressive math programs make an investment
in teacher training. Quality and meaningful professional
development that help teachers develop mathematically
will help their instruction.
