# Singapore Math in the Lehigh Valley

This week I would like to talk about math, because I like it. In fact, it is one of my favorite subjects. I am very proud of the efforts our school has made in math. I look forward to analyzing the data we will be collecting over the next few years. Great commendations should go to the teachers, recognizing their ability to deliver such a promising program. Specifically, I would like to share about our Elementary math program.

### Covers fewer topics in greater depth

Compared to a traditional and Common Core math curriculum, our program, Singapore math, Math in Focus, focuses on fewer topics but covers them in greater detail. Each math textbook builds upon prior knowledge and skills, moving the students towards mastery and automaticity. We work hard so that the students are ready for their next level. By the end of sixth grade, Singapore math students have mastered multiplication and division of fractions and can solve difficult multi-step word problems, including basic algebraic understandings.

Our Math was found to emphasize the essential math skills recommended by the National Council of Teachers of Mathematics (NCTM). They do this by focusing in on the essentials that build strong number sense and mathematical reasoning skills.

### Three-step learning process

The younger grades spend a significant time building number sense through their work in part-part-whole. This is the mathematical equivalent to phonics in reading. The students learn that numbers, quantities, and algorithms are representative of something. They learn how to take numbers apart and put them back together in a way that gives meaning.

They learn practical steps to solving word problems. I loved math but loathed story problems. No one taught me how to approach them or gave me the tools and confidence necessary to attack them. Our students are taught the bar model beginning in grade two. Our second grade teacher helps her young pupils see that 100 is comprised of other things. We can find whole parts and missing parts, just by using the bar model. Later in the intermediate grades, the teachers and students work through more challenging and complex uses of the bar model. Just a bit of secret, I used the bar model to quickly solve ratios on the GRE (Graduate Records Exam) that I took for entrance into graduate school.

A bar model used to solve an addition problem. This pictorial approach is typically used as a problem-solving tool in Singapore math.

**Three Step Process: Like We Learn**

SCS math program teaches students mathematical concepts in a three-step learning process: concrete, pictorial, and abstract. This learning process was based on the work of an American psychologist, Jerome Bruner (1960). In the 1960s, Bruner found that people learn in three stages by first handling real objects before transitioning to pictures and then to symbols. That is why we teach the students in this matter.

The first of the three steps is **concrete**, wherein students learn while handling objects such as chips, dice, or paper clips. They use something that teachers call manipulatives, anything that the student can move around, touch, or manipulate in order to learn the concept or skill. Students would learn to count these objects (e.g., blocks) by physically lining them up in a row counting them or grouping them. They would then learn basic math operations like addition or subtraction by physically adding or removing the objects from each row.

Students then transition to the **pictorial** step by drawing diagrams called “bar-models” to represent specific quantities of an object. This involves drawing a rectangular bar to represent a specific quantity. For instance, if a short bar represents six books, a bar that is twice as long would represent a collection of twelve. By conceptualizing the difference between the two bars, students could learn to solve problems of addition by adding one bar to the other, which would, in this instance, produce an answer of eighteen books. Multiplication, division and subtraction can be solved by this model. Additionally, they can use this model to begin to conceptualize algebra with missing parts to a math algorithm (problem).

Bar Modeling allows the student to model the thought process used to solve the math problem. And, the teacher can provide strong feedback in order to help prevent errant thinking. The student can move onto more complex mathematical problems with exclusively abstract tools such as symbols and numbers.

The third part, **abstract** is simply writing the algorithm with symbols. 3 +4 = ? or 3 + x = 7.

We don’t spend much time on math facts like the addition facts and multiplication facts. But, that doesn’t mean that they are not important. The teachers review them in the morning meeting. However, this is something parents can do at home with their children to ensure they are prepared by playing a game, flashcard etc…