By: Amos Tarfa
Struggling with math does not mean a child is inherently “bad at math.” It goes back to a broken link somewhere along the way. Mathematics as a subject depends on mastery of prerequisites. Did you know that there is a series of topics in mathematics that, if you were to master them, you would become very good and be able to flourish in your math journey?
The problem is that sometimes we are not always able to take the time required in a traditional classroom to spend more time on those topics that are essential for a student’s future success in mathematics. One of the best analogies for understanding how mathematics works is thinking of a building. You need to have a solid foundation before you can actually build more.
What are some of the fundamental topics that students need to master before they do more advanced topics in mathematics?
- Place value
- Prime factorization
- Solid understanding of number sense (estimation, rounding, expanded notation)
- Arithmetic: addition, subtraction, multiplication, and division
- The properties of real numbers
- Fraction arithmetic
- Ratios and proportions
These are some of the most important topics that anyone would need if they are to become exceptional in mathematics. One of the reasons why this is so important is because they determine how well a person gets prepared for algebra.
What is a Broken Link?
If a child is struggling in mathematics, generally after pre-algebra, it would generally be because they do not have a solid understanding of some of the topics listed above. What should a parent do when they observe this? My recommendation is that you go back and acquire materials that will focus on these topics.
Mathematics is also like a chain, and every single link on the chain needs to stay solid. Even if a student were to score 93% on a math exam, they should always ask, “Why did I not get 100%?” This helps them address any misunderstanding that may have led to the 93%.
When it comes to mathematics, grades are not enough. Understanding why is always very important. If a parent focuses on the areas listed above, they will give the child the opportunity to fix the broken link if they are struggling. This will allow the student to be able to press on and possibly start saying, “Maybe I’m not bad at math,” because mathematics is actually beautiful, but it has to be learned using a mastery-based framework. There is no other way to learn mathematics.
Mathematics Builds on Itself
When a student is doing an algebra problem, they sometimes have to apply multiple aspects of the chain:
- They might need to factor out a number, which would require them to understand how the greatest common factor works, which is actually connected to an understanding of prime factorization sometimes.
- They would need to know how to divide and other arithmetic operations.
- They might need to use properties of real numbers.
All of these happen within one problem, but students do not always understand why they might be lost. Therefore, this is important. This is why it’s important to teach them how to isolate skills and master each of those skills.
When it comes to fixing the broken link, having an expert who specializes in mathematical understanding can be very helpful. This could be a professor, an instructor, or a community member who loves mathematics and understands the nature of the topics and how they are connected to one another.
At the heart of understanding mathematics and excelling in it, a student needs to be able to make sense of numbers. A student needs to be able to make sense of patterns. Place value is one of the most fundamental topics that will help students flourish.
Once a student has mastered place value, then they can proceed to work on mastery in addition and subtraction, multiplication and division, prime numbers, and prime factorization. If a student follows this order, it will provide them with a solid foundation to then explore more concepts such as exponents, fractions, decimals, ratios and proportions, and then algebra.
Understanding mathematics depends on a sequential understanding of topics with a system for feedback.
What Does the Research Say?
According to one study, knowledge of fractions and division can predict high school algebra achievement five to six years later (Siegler et al., Psychological Science, 2012).
Not having an understanding of fractions and division will lead a student in Algebra 1 to get very frustrated and potentially begin to think that they’re bad at math. It’s like putting another brick on top of a shaky foundation.
There are certain topics in mathematics that need to be memorized well, including multiplication facts, for example. A student who does not have their multiplication facts will become frustrated in an algebra class when they have to do problems where multiple lines of multiplication have to occur. They would end up spending a lot of their time trying to get the multiplication facts instead of focusing on the problem at hand. This is especially important for algebra students.
They need to do all they can, including working all through the summer, to ensure that their pre-algebra foundation is solid.
Where Do We Go From Here?
We need to work on the attitude the students bring to mathematics. Before we even deal with the problems themselves, we have to ensure that we help students to fix their attitude toward mathematics.
They need to learn not to say, “I am not a math person,” and recognize that they just have a broken link that can be fixed. Therefore, giving them the opportunity to become good at math.
We also need to remind them that they should want to be good at math. Being good at mathematics opens doors to many fields.
Before a student starts taking algebra, for example, or starts taking any class, they need to ask, “What are the prerequisites that I need to master before I start this class?” They need to ensure that they’ve mastered those prerequisites.
They should keep the notebooks and the examples they have from that class because most likely they will need to refer to them again.
Becoming good at mathematics requires a solid foundation. Meeting the necessary prerequisites, taking excellent notes—which can be used to review later on—and bringing all these things together can help a child to realize that mathematics is for everyone.
A broken link should not stop your child from reaching their full potential. Find it and fix it.
There are many very good diagnostic tests that you can use, and The Freedom in Education will be happy to answer questions about assessments and resources as well.
Whenever a student is stuck, they should not say, “I’m bad at math.” Instead, they should say, “What is the broken link that needs to be fixed?”
Reference
Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691–697. https://doi.org/10.1177/0956797612440101
About the Author:
Amos Tarfa, also known as AmosTheMathGuy, is a mathematics educator and advocate for mastery-based mathematics education. He holds master’s degrees in Medical Physics and Medical Health Physics and has completed a year of PhD study in Chemistry and STEM Education. Originally from Nigeria, Amos came to the United States in 2007 to pursue his education.
Amos began teaching mathematics and other subjects in 2011 after working in the Math Lab at the University of Wisconsin–Superior. He is passionate about helping students develop a deep understanding of mathematics and believes that mastery of foundational concepts is essential for success in more advanced mathematics. He is the author of Tools for Mastering Mathematics, which explores challenges in mathematics education and approaches to addressing them.
