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Last month, I was fortunate to lead a math skills workshop for Frontier College‘s volunteer tutors to discuss strategies on effectively improving student numeracy skills. Frontier College is Canada’s first and oldest literacy organization that delivers free educational programs for marginalized communities. The organization conducts annual educational research across Canada in low-income neighbourhoods to understand the impact of their literacy programs in the areas, and this year, I am directly involved in the testing procedure as well as tutor strategy development.

We conducted local studies in Toronto for students between ages 6 – 14 (Grades 1 – 8) to understand their level of academic performance. In this article out of two parts, I will be discussing the common problem areas we noticed from the research results. In the next article, I will be sharing effective strategies to target these pain points.

Here are the five most problematic areas in math for students:

1. Multiplication

Multiplication is arguably the most widely used concept in mathematics and everyday life. I think of multiplication at the bottom of the math food chain, and with a limited understanding of it, everything else that follows struggles to survive. Elementary and high school students alike struggle with both the concept and the execution of multiplication. Teachers try to find new ways to help students understand this behemoth, but it only confuses them further. One reason is that some teachers teach multiplication with addition.

Consider 4×4=?

Some teacher uses the logic that 4×4 is the double of 4×2, which is 8.

So, if we take 8 and double it, 8+8=16. (The student can think [4×2]+[4×2]=16).

Therefore, 4×4=16.

Were you confused? Don’t worry, so are our students. Undoubtedly, it is a great way to help students understand the concept of multiplication and notice patterns in the times table. The problem is that students follow this method in executing multiplication problems.

Elementary and high school students alike struggle with both the concept and the execution of multiplication.

First of all, it is a complicated process that requires students to go back and forth between multiplication and addition (and we are still confused why our students are confused?). Secondly, it is a time-consuming 3-step process that should be accomplished in one. Thirdly, this method does not work with every question, which requires the student to understand why it works sometimes and does not in other times. Most importantly, although both methods yield the same answer, thinking through 4×4 is not the same as 8+8. The former shows 4 groups of 4, the latter shows 8 more of 8. They are completely different concepts. Furthermore, the purpose of multiplication is defeated when we execute with addition, because multiplying is meant to be a shortcut for doing really long addition.

2. Division

The problem mounts when a student, with a questionable handle of multiplication, advances to the next grade and is expected to perform the reverse of it – division. How are they supposed to go backwards when they cannot even go forwards confidently? If the student is using addition to multiply, how are they supposed to divide now?

3. Fraction

With an even more shaky grasp on division, the student is now expected to use fractions, which is a form of division. The confusion grows still.

   3   x
   4     is 3 of 4 parts, or 3 divided by 4.

4. Decimals

If a student fails to understand fractions, then they will fail to understand decimals, because decimals is another form to represent fractions. That leads to…

Progressively, we see that a lack in basic math skills snowballs into a lack of important life skills.

5. Money Problems

From the research results, the top four word problems that were answered incorrectly were all money-related. It comes as less surprising to know that these students struggle with fractions and decimals.

Consider a penny in decimal form: 1/100 of a dollar, or $0.01.

Progressively, we see that a lack in basic math skills snowballs into a lack of important life skills. For many students, the problem starts in elementary school and continues into high school. Ultimately, they carry the same math confusion into their adult life, possibly with large financial implications.

It is essential to understand where weaknesses lie that hinder math understanding. In the next article, I will share some effective strategies to tackle these problematic areas. If you have questions or suggestions to bridge students’ learning gap, please share below. I would be glad to incorporate your strategies in my next article.

For additional readings on re-engaging students in math, see Education Ink’s Re-engaging Students in Math or the Atlantic’s The Math-Class Paradox.