Rethinking Numbers: Teaching Higher Order Thinking for Math with More Than Just Numbers

The importance of higher order thinking for math is a skill that cannot be over emphasized. It is the foundation for a long and successful career, regardless of what field a child turns to as an adult. Being equipped with the right mathematical skills and the ability to analyze data is something that prepares a child for nearly every occupation. Whether a child becomes a scientist, engineer, coder, doctor, or financial analyst, most of the occupations that we consider prestigious or desirable use numbers.

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The younger our children are when they start to use higher order thinking for math, the easier it will be for them to understand it as they reach the higher levels of math, like trigonometry and calculus. Even if a child does not use math in their career, it is necessary for handling personal finances, particularly for loans, mortgages, and saving for retirement.

Higher Order Thinking for Math

This is not a new concept for most teachers, and over the years different approaches and strategies have evolved to further teach elementary children these skills. These activities go beyond the simple flashcards for memorization, providing a way to learn to work through math problems using critical thinking.


Posing the Right Kinds of Questions

If you ask a child what they like least about math, they will almost always say word problems. The problem is that we tend to think about math only in terms of numbers, so asking kids to look at words and determine what numbers go where immediately turns math into the impossible. Word problems also expect the child to determine what numbers are relevant to the question at the end.

One way to help children overcome this aversion to mixing words and math is to ask questions that start them thinking about math in terms of word problems. Open ended questions are an ideal way to help a child begin to think of numbers in terms of what they mean and not just a problem to solve. Take a word problem and analyze the different aspects of it, including the parts that do not pertain to the answer so that the child knows why that number is being excluded. Questions like “What happens if you use this number to …” and “How would you sort …” teach the child to think of the numbers in terms of meaning, not just a number on the page.

Assessment questions also help a student understand the numbers and why they were used. Questions like “How did you figure that out?” and “Why did you choose that way?” get the child to think about other ways to solve the problem.


Beyond Numbers: How to Use Words, Graphs, Diagrams

Higher order thinking for math should certainly include a visual aspect because that is one of the primary ways it will be applied in adulthood. Of course, the higher levels of math require students to use graphs and charts.

Word problems are a staple of learning, even adding and subtracting. However, these methods should be used as often as common math problems because they get children to think of math from many different angles. This also makes the more complicated types of math less scary because children will be accustomed to seeing mathematical problems as pictures and words instead of simply numbers.


Importance of Math Curriculum - Singapore Math

Using the appropriate math curriculum to develop our children higher order thinking skills is crucial.

Singapore Math provides a number of different activities, particularly emphasizing Heuristics and Thinking Skills so that kids learn to understand and solve the most difficult word problems. This is applied across all of the mathematical concepts, from basic geometry to algebra.

Why Singapore Math Ranks Among the Best

The Singapore Math approaches higher order thinking in math using a model or block method. From the basic functions, like adding and subtraction, children work on math sentences. This teaches students to think in terms of words, even when they are given numbers, giving them a way to understand numbers from another perspective.

Singapore also focuses on a few topics at a time, looking into the different functions and understanding them in detail before moving on to the next subject. Starting in grade school, students are taught math in terms of words and visuals, progressing from the concrete numbers used in most countries, to the visuals that show kids a different way to think of the data, and finally ends with math from an abstract approach. All of this is done through focusing on problem solving.

Creating a Foundation for Critical Thinking in Math

In grade school, children are introduced to these ideas so that math is more than just numbers. Kids are taught to look at the problem and break it down into what each piece of information means.

They create a visual to show where the problem started, such as with a bar to represent 10 apples. The problem is then analyzed further to understand what is happening to those apples: adding, subtracting, or working from a percentage. The child then changes the visual to show the change. The child then needs to think about the visual to understand what it is showing: this requires a mental visualization of the function going on to show how the problem went from the first step to the next. The child then progresses through the problem until the final question is answered.


Such framework of Singapore Math has resulted Singapore being consistent ranked number one in the Trends in International Mathematics and Science Study.


Start laying a strong foundation on higher order thinking in math for your child with these Singapore Math Worksheets.

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