The New Math

Too many parents cannot help their kids with their math. They want help because their kids cannot understand the math.  The methods students are given in the modern constructivist way of solving simple math problems are complicated. While learning to do math is foundational to learning to do a budget, or knowing which product is more economical, the new math is aimed at a goal understood only by lofty administrators who want children to understand “numeracy”. In the Alberta curriculum, numeracy is defined as:

“the ability, confidence and willingness to engage with quantitative and spatial information to make informed decisions in all aspects of daily living. A numerate individual has the confidence and awareness to know when and how to apply quantitative and spatial understandings at home, at school, at work or in the community.

Quantitative information refers to information that can be measured and expressed as an amount. This includes:

• having a sense of the magnitude of numbers
• using numbers in real-life situations
• estimating amounts
• interpreting statistical information
• recognizing patterns
• determining probability

Spatial information refers to the physical location of objects or people, or the relationship between objects or people. This includes:

• understanding shape and space
• measuring time, weight, height or amounts
• determining location and direction
• interpreting and creating maps and schematic diagram
• visualizing shapes from different perspectives

Every day we are presented with quantitative or spatial information that needs to be interpreted and used in order to help us make sense of our world. As we go through life, our need for numeracy skills evolves.

• Young children develop numeracy as they judge the distance needed to grasp a toy, recognize patterns and routines or learn how to manipulate shapes to complete a puzzle.
• Older children use numeracy to play board games, estimate the cost of a purchase with tax, judge how far to kick a ball or determine when to leave to arrive on time.
• Young adults require numeracy to interpret sports statistics, navigate their way to a destination, track cellular data usage, or budget to save up for a special purchase.
• Adults need numeracy to compare costs, choose a cellphone plan, interpret statistics, park a vehicle, double the ingredients for a recipe or engage in home renovation projects.”   (education.alberta.ca/literacy-and-numeracy/numeracy/everyone/what-is-numeracy/)

If this definition is confusing and even overwhelming, join the club. Do teachers keep all this in mind when they are trying to get a child to understand 2 plus 3? Are they responsible to make sure a child can understand a recipe, or are they responsible for making sure the child knows what the symbols for two, three, and four mean? Children come to school ready to learn math, but they need to know what they need to learn and how to learn it. The teaching of math needs to be simple and straightforward. The new math, a constructivist method, tries to put the understanding before the learning, and it confuses the students. Having been in place for more than thirty years, this theoretical rather than practical approach has resulted in the falling scores in Canada.

This chart tells the story accurately. It indicates how far we began to fail when the new math was introduced. There were some declaring that Covid 19 stay-at-home mandates were to blame, but that does not account for the 17 years before that. There are many who don’t want to blame the curriculum or the schools’ administration, and certainly we cannot blame teachers who simply do as they are told. So what is the problem?

Without sounding too condemnatory, one researcher, Anna Stokke, a math professor at the University of Winnipeg, noted the gradual decline. “I do think part of the problem is the philosophy of how to teach math,” Stokke told CBC News. “First of all, we’re not spending enough time on math in schools. And second of all, kids just aren’t getting good instruction in a lot of cases. They’re not getting explicit instruction. They’re not getting enough practice. And that really needs to change.”

This researcher gently pointed to the correct reason for the lack of math success. She says it’s “the philosophy of how to teach math.” At its root is the same philosophy of learning that made non-readers out of half the population. Dubbed “Whole Language Learning” it is also ruining the learning of math. When students were required to understand “concepts” instead of memorizing math facts like the addition and multiplication tables, the focus turned to “discovering” how math works. 

According to The Straight Dope, “the main thrust of these changes was a switch from teacher “telling” and student recitation to ‘inquiry’ and ‘discovery,’ with the hope that students would be more likely to retain information they found out themselves than what was just told to them in lecture form and memorized. In the hard sciences, and to a lesser extent the social sciences, this was described as ‘hands-on learning’” (https://www.straightdope.com/ 21342664/what-exactly-was-the-new-math).

I learned this gradually as I tutored students who did not know their times tables and used their fingers to add. Subtraction was a mystery to them, however, and the time taken up consulting their tables of math facts slowed their ability to grasp the concepts. Algebra became a focus for me to tutor because multiplication and division were not well understood in spite of, or because of, the way they were taught. And to do algebra, a thorough understanding of fractions and how to add, subtract, multiply, and divide them, is essential. Most students had only a rudimentary knowledge of what a fraction is.

New Math in Practice

To try to get students to get to the concepts first, they are given sheets of math facts to consult. They have fact sheets for addition and sheets for multiplication, or they are allowed to use a calculator. All they have to do is look the number up each time they need a fact. However, the shift from the fact page or the calculator back to the problem they are working on breaks their focus. They cannot concentrate on the concept because it takes too long. I once tutored a Grade 9 student who was struggling with math. Each time she used her calculator, it was a distraction and she could not remember why she looked up the number. I finally convinced her to memorize her multiplication tables, and by the middle of Grade 10, she was explaining functions to me. 

Calculators have also created issues. When I tutored at a university, I met too many who were lost without a calculator. They cannot multiply a 4-digit number by a 3-digit number or even 8 x 9 without it. I had to run many remedial math classes to allow some to take the trades curricula. They quickly learned that they cannot use a calculator unless they know why they are using it.

Manipulatives have also become popular. Students take brightly coloured blocks of ones, tens, and hundreds and pile them up or break them into groups according to the problem, and then they count what is created. However, when shown a problem like 15 divided by 3 = ?, they are stumped. No one shows them how to do long division, and while they can divide the groups into smaller groups, what will they do when they no longer have a set of manipulatives?  They are allowed to use a calculator, but it does not help them understand how numbers work together. Formulas are torture to them.

One other problem is that the students are not given enough time for their brains to grasp what they are learning. Math takes so much practice to master. I have taught kids who had to understand one chapter of math per day, practising on only 5 to 10 questions. They were expected to learn a whole curriculum in 10 to 12 weeks. If they did not pass a section, they were not asked to repeat it. They were sent through to the next section where they got more lost. Often a parent does not even discover their child is struggling in Math until halfway through the course. The chances of a student’s catching up are nil. Their attitude becomes on of “I can’t do this”, and this attitude is shared by many of their classmates, so the attitude get worse. They know they are not learning well and they feel stupid. It is unfair to give them a minimal mark and let them pass when they could have learned the material if given more time and practice.

What students need is direct, explicit instruction in math, beginning with the memorization of facts that are the foundation of understanding numbers. The Whole Language method puts the cart before the horse. No one can think clearly about how numbers work until they can quickly recall the facts. Knowledge comes long before understanding. We teach people how to do practical things before we explain why they need to do it that way. Vague experiments on shapes and counting leave students with a vague sense of what numbers are, but no concrete methods for knowing how to DO math problems.

The students aren’t unwilling to learn math, but when they are told that they need to understand numeracy, which is how numbers work, they couldn’t care less. All they want to know is how to get the right answer.

The fallout of this failure of teaching what kids need to learn is the poor results in the PISA scores. The PISA test measures a student’s ability to apply their knowledge to a real-world problem. The test is meant to measure “reasoning, interpretation, and critical thinking, not just memorization.” But if the memorization does not come first, there is no foundation for reasoning or critical thinking. 

When a student does not do well in Math, he is limited in his ability to use that knowledge to attain a career that requires good mathematical skills. When they are denied the basics, students have a difficult time catching up, and by high school, they opt for the foundational math programs, leaving the algebra to those who got good teaching.  

Let’s give students the tools they need to succeed. Let’s allow them the time they need to really learn deeply. Let’s provide the basics of math before we give them the loftier numeracy concepts. Kids today are just as smart as the previous generations. With the right teaching, they can develop the skills they need to become good math students.

Here is an excellent outline of the decline in teaching math: https://cdhowe.org/publication/time-to-address-canadas-falling-math-scores/