Building a Strong Mathematical Mind – Strand 2: Core Concepts

Give Bright Students Concepts they can “Sink their Teeth Into”

How often has your child come home from school with math homework involving memorizing steps and repeating them ad nauseam without really understanding what is going on? Even worse: do you have a bright child who has been turned off math because they are bored with the procedures, and find it meaningless? Or, have you ever heard your child say, “this is the way you do this kind of question” – doing what they were told, not because it was what they understood, but what they were told to do?

Math programs with a primary focus on procedures not only turns people off mathematics, but also develops people who learn how to follow without questioning.  On the other hand, a strong math program, such as Spirit of Math, that focuses on a solid understanding will produce creative, critical thinkers who are excited to learn more.

As explained in the last article in this series, the first of the Four Strands in a strong mathematics program, is the drill component. The purpose of the drill component is to develop an automaticity and fluency of number facts.

This week we take a look at the second strand: core concepts, or core material. This encompasses the different topics in math in order to develop an understanding of mathematics concepts.

Finding a program with good core material is tough, but essential – especially if you have a child who is very bright. The program must thoroughly teach the basic concepts and teach the student how to think better.

These pointers will help you evaluate the core of a math program and determine if it will meet the needs of your high-performing child.

  1. 1.     The program offers questions significantly different than the regular textbook type of questions.

Giving a high performing student a textbook a grade or two above their regular grade does not address their needs. The questions in a regular textbook, no matter what level, have been designed to meet the needs of the majority of students. The thinking required to do most of the questions is not to the depth needed for a high-performing student, especially in the younger grades.

  1. 2.     The core material goes deeper and broader in each topic.

High performing students crave something that they can “dig their teeth into.” Teaching a topic just to say that it has been covered is not sufficient. They must go deeper into topics and be given the opportunity to explore and discover the more complex ideas within them. This means taking more time on each topic. A strong math program develops concepts slowly and intently so that one idea can be linked directly to another.

  1. 3.     The program should expose students to concepts not normally seen in school.

There are so many very interesting ideas in math that just simply cannot be introduced in the regular school because of time constraints. A good program for a high performing student should be exposing them to other ideas, and getting the students to stretch their minds.

  1. 4.     The program has been developed with the intent to first establish very strong numeracy skills.

Math is based on numbers, so a proper understanding of how numbers work is crucial. This may seem obvious, but very few math programs actually focus on numbers. They will often just teach “how to do the next thing”. Most of the students I have helped over the years have problems in math simply because they don’t have a proper understanding of numeracy. In fact, some teachers don’t have this understanding either because they haven’t been taught it themselves.

Look carefully at the math your child is being taught – is it just rule based, or are they being taught first how to work properly with numbers and to understand all their properties? In Spirit of Math students are taught to work with integers in grade 1 so that they can form a concept of numbers that is not just based on manipulatives.  The grade 5 course focuses entirely on numeracy and by the end of the grade, students understand how different numbers work on their own, and in conjunction with other numbers. Their thinking and understanding is consequently well above the typical grade 5, 6, 7 or even 8 student.

  1. 5.     The program was developed over many years, in the classroom with students.

Most programs have been created from someone’s imagination… someone sitting behind a desk. New and innovative ideas do come from a good imagination; however, those ideas must be tested with students to see what works. This can only happen if the program is developed with students, in the classroom. This not only takes years and years, but very dedicated and bright people working with students.

There are so many math programs out there, and many more people who think they can teach math because they know “the steps” to answering certain types of questions. It takes a very discerning parent to look deeper into the program and to make sure that it is, in fact, going to teach their child how to think mathematically,  and not just how to do the next question. A person who can think mathematically is able to logically put ideas together and that is a skill that can be applied to every area of life.


  1. says

    Pretty nice post. I just stumbled upon your weblog and wanted to mention that I have really loved surfing around your blog posts. In any case I will be subscribing on your rss feed and I am hoping you write once more very soon!

  2. says

    Hi! This is my first comment here so I just wanted to give a quick shout out
    and tell you I really enjoy reading through your posts.
    Can you suggest any other blogs/websites/forums that deal with the same subjects?
    Thanks for your time!

    • kimlangen says

      Unfortunately, I don’t know any other blogs/websites/forums. Are you looking specifically for a math focus?


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