In the fall of 2015, Triton Regional School District adopted and implemented the Math in Focus®: Singapore Math program in grades Kindergarten through eighth. Math in Focus is the United States version of the curriculum developed in Singapore. Singapore, a top performing country in international assessments such as the Trends in International Mathematics and Science Study (TIMSS) and the Program for International Assessment (PISA), developed their mathematics program over the last thirty years. Due to Singapore’s success, its standards were consulted during the development of the Massachusetts State Curriculum Frameworks.

Math in Focus was developed utilizing the Singapore Ministry of Education Mathematics Framework (shown below). At the heart of the program is mathematical problem solving that is connected by five equal components of a well-articulated framework for learning mathematics. A mathematics program, focused on problem solving, must involve the concepts, skills, and processes that support positive attitudes and metacognition (the ability to reflect on learning).

Staff Members
Concrete-Pictorial- Abstract
Concrete pictorial abstract

The pedagogy of this program lies in Dr. Jerome Bruner’s and Jean Piaget’s learning theories.  Most significant in these theories is the idea that to fully understand the mathematics, students must be able to visualize the mathematics.  Teachers engage students in these theories by involving them in the nonlinear progression of the concrete- pictorial- abstract (CPA) pedagogy.  In order to fully understand mathematical concepts, students must first use concrete, hands-on materials.  Next, students begin to visualize the mathematics through pictorial representations.  Lastly, students can build upon these pictorial representations to understand the abstract (the use of numbers and symbols to represent the mathematics).

Bar Modeling
Bar modeling

An important component of the Math in Focus program is the bar modeling approach.  Bar modeling is a “planning tool” that allows students to visually represent a mathematics problem with the use of rectangular bars, which help transform the words of the problem into a numerical operation. Consider the following problem:

Emma and Mary have 1,483 baseball cards in all.  Emma and Jennifer have 1,765 baseball cards in all.  Jennifer has twice as many baseball cards as Mary.  How many baseball cards does Emma have?

Copied from Math in Focus®: Enrichment 3A (2015).

At first glance, this may be a difficult problem for students to understand.  Below is a bar model that visually represents the problem, making the solving of the problem much easier.


Mary’s baseball cards:

1,765- 1,483 = 282

Emma’s baseball cards:

1,483 – 282 = 1,201

Emma has 1, 201 baseball cards.


Kheong, Fong Ho. Math in Focus: Singapore Math by Marshall Cavendish: The Underpinning Concept. Houghton Mifflin Hartcourt.

Massachusetts Curriculum Framework for Mathematics(2011).  Massachusetts Department of Elementary and Secondary   Education.  Malden, MA.

Math in Focus: Enrichment 3A (2015). Houghton Mifflin Hartcourt.

Math in Focus: Implementation Guide (2015). Houghton Mifflin Hartcourt.  Boston.

Problem Solving in Singapore Math. Houghton Mifflin Hartcourt.