“Look, I can do long division so fast!” said one of my students.
“Why do we do long division?” I asked.
“I don’t know,” he replied.
This student has memorized how to do math but has not understood why he needs to learn it. He would ace his tests but he might not recognize when he can use long division as a tool.
On the other hand, I have worked with students who know the why really well but stumbles upon calculation errors every other steps, with all ten fingers out, counting.
So what’s important? Knowing the why? Or knowing the how?
Math is a computational thinking tool to help us break down problems, as well as a language to make sense of numbers. Every math topic has five key coaching milestones we can aim for to ensure the readiness of the children for the next topic. Mastering math builds the foundation for all other STEM fields.
I will use division to explain the coaching milestones.
1. Coach the WHY and WHEN
When it’s time to learn division, we don’t want to start by saying “here’s how you do it.” The know-how is not at all useful without the know-why and the know-when.
Introduce situations wh
en division (tool) can be used. Show the children how to solve the problems with and without using division. When they realize that they can struggle without the most efficient tool, division, they will understand why the technique was invented.
“How can we fairly split a $500 prize with a baseball team of nine players?”
2. Coach the HOW – Calculation Technique
Once we’ve explained why division is handy to know, most children would be motivated to learn the tool. Break down the calculation algorithm into steps so we’re teaching the meaning behind the calculation rather than asking them to memorize it.
“We set up 500 divided by 9 in long division like so BECAUSE…”
3. Coach the Accuracy and Speed – Practice Makes Skill a Habit.
Knowing the WHY is important and knowing the HOW is great, but just knowing is not enough. We want to coach our children to use their calculation techniques so well that they gradually adopt it as a way of thinking. As soon as they hear a situation where they need to divide, they should be able to set up the long division algorithm and complete it without feeling frustrated from an unfamiliar multiplication fact.
This is a process. How it’s done depends on the individual’s learning style. Some kids learn efficiently through worksheets, but some might need more interactive activities.
How much practice is enough?
Practice makes perfect. This is true regardless the children’s intelligence. When we practice effectively, our brains wire to adopt to a new way of thinking, making the new skill a “muscle memory”. A focused practice routine has been far more effective than sporadic practice sessions in my students. Here are two distinct example:
Student A practices 15 division problems everyday for a week. The first day she starts with a pre-occupied mind of “I just saw division yesterday. It shouldn’t be bad.” The next day she starts the practice by thinking “I know this now. Let me get better at this.” Towards the end of the practice period, she’s confident to complete her 15 questions and is excited to do more!
Student B learns it today and doesn’t touch it for two days. Then he’s given a whole chapter in a workbook to complete. The concept of division is there but he’s forgotten what he learned two days ago. He’s starting with a hesitant spirit. And overall he would just take longer to gain the skill and perhaps never masters it before the next topic kicks in. Most importantly, he’s not excited about division.
Math is all about finding the patterns, which is innate to the human brains. I’ve coached all styles of learners. Those who can’t do math are not the ones who are not intelligent. They are the ones who don’t have a practice routine to train their brains.
Those who didn’t have a routine can start slow because of the lack of foundation, but can always pick up once the practice routine gets established.
4. Coach the Interpretation of the Results
Once the technique is mastered, we need to make sure math is not a mechanical skill. Connecting all the prior milestones together, now the children are ready to make sense of division.
When my student came to me with 20 division problems to check, I gave her my feedback in three minutes. She was shocked how I did it so quickly without looking at the answer key. I’m not a human calculator. I didn’t know the exact answers and I didn’t have to.
Our role as a math coach is to make sure that the children are understanding the math, more than just getting the correct answer. So my first pass is always making sure that the numbers make sense. For example:
“How can each player have more than $500 if there are nine players splitting the money? How does that make sense?”
By prompting the children to make sense of their answers, their focus shifts from getting the correct answer to thinking their process through. And the correct answer would just be an automatic end result.
A useful skill to master this milestone is through the understanding of estimation, which will be fully discussed in a future post.
5. Coach to Use it
Once we’re done with a topic, we move on to the next. It doesn’t mean we’re done with the topic. Rather, it means we’re ready to really use the concept.
This milestone has no end. It’s a continuous process that really solidifies computational thinking. The opportunities can show up anytime anywhere around us. Where there’s number, there’s math – calories, grocery shopping, tips, etc.
Be mindful about coaching opportunities. You will find your children, and even yourself, thinking in the logic of math all the time soon.