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TNLI: Action Research: Curriculum Implementation: Manipulatives or Algorithms? A New Teacher’s Adventure with Constructivist math


Research Summary

“If you really care about a child’s learning, you will naturally adopt a constructivist approach” – Frances Rust


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 two-week 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 investigations-focused) 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 K-4 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 one-on-one 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.


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 two-week 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.


John Chew

Research Focus:
Constructivist Math

TNLI Affiliate:
New York City

PS 90-George Meany
1116 Sheridan Avenue
Bronx, NY 10456

If you would like to learn more about Teachers Network Leadership Institute, please e-mail Kimberly Johnson for more information.



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