Teaching Numbers 11-20 With Number Studies
This blog post is part of my series on Gattegno's Mathematics Textbook 1. We are on chapter 5 where we are teaching the numbers 11-20 through number study.
Number study is likely new to most folks. But, once you understand the principles behind number study, it sets you and your students free. With number study, we are doing exactly as the term implies, we are taking up a systematic study of a number.
Number Studies Create Disciplined Thinkers
If you do number studies properly, they have the ability to create a disciplined thinker out of your child. The various areas of mathematics, that in other curriculum seem disjointed and unrelated, are all brought together when students begin their studies of numbers 11-20.
The biggest benefit that I've noticed from number study work (there are a lot) is the fluency with the symbols which allows him to notice patterns. Here I don't mean number patterns, but patterns in the rules and how math works. P. knows, when calculating, that certain things will happen because a number is odd, or that it has 4 factors, or that it is a certain distance from 5 or 10.
In those classes where the adult teacher alone has the privilege of using the mathematical vocabulary and where the notation is handed out finished and complete, dictated by a teacher, children are in the situation of a foreigner who, by hearing a language, can understand some of it but never dares to use it because of the absence of a true awareness of what is required. To use it for personal ends, creatively and adequately, requires involvement in the situation to an extent that only the individual can judge.
- Madeleine Goutard
These ideas have not been forced upon him to memorize or use as strategies for calculating, they are things he has become aware of because he has made an in depth study of numbers and he just knows.
Number Studies Save Time
It is the in depth study of numbers that will shave years (I do mean years) off your child's math education. Provided, of course, you spent enough time in chapter 3. There are things that I just don't need to teach because P. has internalized the algebraic rules.
How To Study Numbers 11-20
One of the greatest joys of using Gattegno is that I am liberated from the textbook. Honestly, I don't use it other than to write blog posts. I look in it to see what Gattegno is teaching; what new exercise, if any, he has added; and I throw that into our rotation of activities.
Instead of using the blog to go over each exercise Gattegno is using with numbers 11-20, I am going to take the number 11 and do a full study of it with every possible exercise we would use. I'll try and record as many of our lessons as P. will allow, so you can see how the conversation goes in our house.
Make A Pattern - The Foundation Exercise
When we begin our study of a number, we always start the same way: Make A Pattern for the number. How many patterns do we make? As many as your child wants to make - we do at least 10.
In the above video, P. made his patterns while I put in a load of laundry and started dinner. He let the dog out and then we started recitation. It took him about 5 minutes to create the patterns. Both videos are the entirety of the session recorded in one single video that I broke into two.
After P. creates a pattern, he reads the individual trains, usually with addition first and I write those in his math notebook. Then I will ask him to reread the patterns using multiplication or fractions and I will write those in his math notebook.
This first step is to get a sense of the number - it's a casual introduction. We will move on to more formal exercises, but here were are just getting a feel for how this number behaves.
Now that we have these statements written in our math notebook, it provides fodder for deeper study of a number using various activities like the Substitution Game, number webs, The True or False Game and more.
As I finish out this series on Gattegno Mathematics Textbook 1, I will be covering all these activities in depth. I trust that by the time we are through with number studies, you will have the tools you need to sharpen your child's investigation and problem solving skills.