On Teaching Math: Part One

Welcome to A Mother’s Thinking Love: Living Ideas, Lovingly Shared! In my last post, I introduced my background with math: from struggling student to a new teacher with no curriculum to a homeschool mother-teacher. I outlined how I learned to teach math without a curriculum and how, in my early twenties, I finally came to appreciate and delight in math. Join me today for: “On Teaching Math: Part One”!

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LINKS TO THE REST OF THE POSTS IN THIS SERIES

Some Early Lessons for the Teacher

As I said in the my last post in this series, I began to teach math from philosophy and principles. In those early days, I also learned a great deal from observing students in my classroom. I wasn’t giving a lot of quizzes and tests, as they were third graders, so these observations were critical. I was teaching math to 60 or so students each day, so I would often write down how things were going.

The skill of observation became important to me throughout my time in the classroom and even after I left it. For the two years after I left classroom teaching, our first two years of homeschooling, I took on a part-time position as a curriculum director. During that time, one of my tasks was to gather information about various math curriculums. Remember, I was very inexperienced in the math curriculum world. I spent three years teaching math without a curriculum. What I found in the pages of these popular and well-known curriculums showed me why I likely struggled with math during my school days.

Exactly & Precisely Backwards

As I perused each math curriculum, I found one truth common among them all. Each curriculum was set up: exactly and precisely backwards. Or, at least they were backwards compared to the way I had been teaching math. Let me explain what I mean.

If I, as the teacher, were introducing the concept of multiplication, the textbook might set up the lesson like this:

• Introduction – There may be some type of hands-on element or general explanation to begin. The teacher may present a diagram of two groups of five objects. The teacher then might introduce the term “multiplication”.
• Definition – The teacher might then be directed to explain to the students that multiplication is repeated addition or just adding the same number over and over again.
• Examples – There might be more examples given like the one in the introduction.
• Standard Algorithm – At some point, students are taught to write “2×5=10”.
• Practice – Students would likely be give a worksheet with several multiplication facts like 2×5 to solve. Students may learn skip counting or begin memorizing multiplication facts.
• Word Problems – After working with multiplication in this way for awhile, students would then be expected to apply their new found skills to word, or story, problems.

“I Don’t Get It”

Eventually, I learned, after interacting with other math teachers, that word problems brought sorrow to the heart of every math teacher and student. “I don’t get it” was the common refrain among all the math students. In my math classes this had not been an issue, so I wanted to understand why. Of course my students were given challenging word problems, but they did solve them, eventually. They usually solved them without my help too.

By starting with the standard algorithm, or a basic description of it, and ending with word problems, it was no surprise, to me, that students didn’t “get it”. What did those numbers and symbols have to do with those words? How were the two connected in anyway? Then, I found out how students were instructed to solve word problems. I’m not sure why or when word problems began to be solved in this way, but it was absolutely clear why students felt they had no connection to the numbers and symbols in a standard algorithm.

An Example

“Find the key word in the story problem. Match it to an operation on the keyword chart. Write down the symbol. Plug in the numbers. Calculate the answer. There, you solved a word problem.”

This is how students were taught to solve word problems. First, they must search the word problem to find a key word or phrase like: altogether, difference, or in all. Then, they looked at a chart to find this key word or phrase and match it with an operation. “Difference”, for example, meant subtraction. Next, they found the two numbers in the word problem. After that, they plugged the numbers in, often in the wrong places, on either side of the symbol. Then they wrote an equal sign, calculated the answer, and wrote the answer after the equal sign – which is a topic for another day.

Rules, Memorization, & Magic Tricks

This, according to the major curriculum providers, was math. Students are given rules. They are expected to memorize the rules along with the math facts. Then they proceed to follow the steps to the standard algorithm. This ends up seeming like a magic trick, only with no delight and wonder. Math was drained of any life and enjoyment. It was a list of stuff to memorize to pass a test. It’s no wonder so many students, including my self, lament “I just don’t get it”. Or, “I’m not a math person.”

“Gone is the thrill, the joy, even the pain and frustration of the creative act. There is not even a problem anymore. The question has been asked and answered at the same time – there is nothing left for the student to do.” – Paul Lockhart

There is Hope

But, there is hope! You don’t have to throw out your entire math curriculum today. Although, by the end of this series, you may find you don’t need to rely on it like you once did. In my next post, I’m going to talk about what a math lesson in my former math classroom looked like in those early days. I think you will find some ideas there that you can take off with. Yes, even though the next post will highlight my time in the classroom, the ideas will be applicable to the homeschool.

How do you approach math in your homeschool? Do you have any questions or concerns? Leave them in the comments below!