Summary process for a new area

Opinion – Processes matter

This opinion applies directly to the two lessons to follow. In this post, I will discuss the process for addressing a new math domain, such as counting, arithmetic, algebra, or geometry. In the next post, I will put forward a process for solving problems. Each process draws from the practice standards reviewed in the previous 8 posts.

Imagine that you and your family will be visiting, or even moving to, a new place, where people speak a different language and engage in different activities. My guess is that before you go, you will discuss with your family what it will be like, why you are going, what each person should bring, and how they might prepare. If there is anything really scary about the place, such as “they do long division there” (it’s okay to scream), that you would reassure your family that you will be close by to help if needed.

One reason to prepare everyone for the journey is that, as you already know, children have no end of “why” questions. The better informed they are in advance, the more open they are likely to be to the experience. In the case of a new math domain, once they know about the benefits – for example, becoming even more competent at math – they will be eager to begin the journey. Of course, to answer those questions in advance, you will need to do some preparation yourself. Never fear, I am here to help.

CCM Lesson of the day: Process for entering a new math domain

Learn a little about the history and depth of the domain

A simple example of this, which will be repeated, occurs in the domain of counting. As anglophones, we tend to count in English. In spite of a number of anomalies, over the years most of us have come to accept our English-language numbers as “normal.” This is not surprising, but a close examination does reveal irregularities.

·         Where do the names of numbers such as ten, eleven, and twelve come from?

·         Why does the spelling change from three and five to thirteen and fifteen?

·         And from two, three, four, five to twenty, thirty, forty, fifty?

·         And then there is zero – is that even a number?

More. When learning to read, children are confronted with two, which sounds a lot like too and to. In addition, as you well know, children may also hear people counting in other languages, even in your own family. There are other examples, some of which will be highlighted when we get to the counting domain.

Learn the definitions

This principle repeats and repeats and repeats. I found it a little shocking how much of math, especially advanced math, comes down to definitions. I consider definitions to be shortcuts for describing complex math structures. For example, once we agree that plus means to add two quantities, I can say five plus seven and you know what I mean.

Teach to learn

Teaching helps two people: to teach a subject, a teacher must learn it well; then, the person being taught learns from the teacher. In the case where a child is teaching a sibling – usually but not always younger – the coach (you) can make sure that each child benefits, an excellent win-win.

Use math in routine activities to reinforce concepts and operations.

This principle offers repeated evidence of the utility of the math that applies to the activities as well as practice in using the math. Using math regularly fosters respect and appreciation for math based on objective results rather than opinion.

Learn to use math tools, particularly calculators and spreadsheets.

Tools help us in several ways:

·         they remind us that our primary job as mathematicians is to formulate problems correctly.

·         they can save time by performing repetitious operations rapidly.

·         given a correct formulation of the problem, they yield correct solutions.

·         they help us to achieve precision; and

·         they allow us to verify results generated in other ways.

Memorization is a part of mathematics

Accurate memorization is a time saver in math. Memorize the numbers, their spelling, and their numerical representation. Memorize single-digit addition and multiplication. Derive and approximate value of Pi (π) and then learn it to 5 decimal places. Derive and memorize the quadratic formula and Pythagoras’ Theorem. Those and many others can be helpful when you are away from a computer or other tools.