By WALT WEGENER

Numbers can represent real things, but we really need our kids to understand their math questions easily. To help our kids “get” their math we need to help them think deeply by letting them talk about math.

The real question to the math learner from us, the parents: Can they explain “Why?”

In school, we often tell stories about events that involve math and then ask questions about “what if.” Other times, math is drill and drill, hoping to form quick reflex to numbers. No matter what it is, students will need to make sense of the questions, find meaning in the reason for the question and, to make an explanation (“Why?”), be able to translate, internalize and tell. The learner must talk about the learning.

Things are loaded in memory by how they are alike (we link things, like a chain), but math problems are solved by recognizing what is different (we pick an ornament off a tree). No easy task. When your child explains “Why?” they may become frustrated. It is a tough question, especially if asked more than once.

Students read the math words and numbers without comprehending the math story. Kids can often decode, meaning they can read the questions but they see no “realness” between the question and anything they can touch or that they care about. Often, unfortunately, math facts alone do not make mathematicians. “Why” is someplace else, hidden in a language place.

Math is a language and numbers are only like the sounds of the language, not the concepts. So kids are bombarded with a ton of math-stuff, but it does not make them “own it easily” — it only makes them able to read math-stuff, not know the question. And, when they don’t get immediate real feedback from a right answer, even well-motivated kids become frustrated. Welcome to math! Puzzles without end and no picture as a guide.

Math is a foreign language, not just a language. A very special one, frankly; a too-big-to-count set of specific facts about numbers, organized around a few rules. Sadly, there are people who actually believe every question is a rule or formula hiding in the weeds. But, ask “Why?” and they are completely befuddled.

Never be afraid to explore “Why” with your child. Maybe they guessed. Why did they guess and why is it right, or more important, wrong? Explanations for wrong are better.

We know a strong set of math skills and number knowledge is important. It is difficult to find small differences that allow decision. Whether to add then divide or subtract then multiply? In a day-gone-by, we spent uncounted hours memorizing math facts. That didn’t actually help with “Why?” Did it hurt? I don’t know.

Unfortunately, in real applied math, some formulas have to be made by the user. How does a parent help at home to find the magic method? What is the answer to “Why?” Once again, we are discussing memory, except this time we are focusing on using it. When you use your memory to solve a question it is not just make a memory backwards.

You are looking for differences. Oddly, when we make a memory we are associating things that are alike to us, when we are using the memory we are separating all the things we linked as alike, by their differences. What is the key needed?

The key is when you listen to your child defending their answer; how do they support their process? If they identify the specific trigger to choosing a process, they have identified the “critical attribute” of the question; they answer “Why?” It guides their choice of steps.

Unfortunately, most times this trigger is exactly what they don’t get.

Most kids are very good at looking in the current section and chapter in their textbook and figuring the trigger must be the bold type or underlined or italics stuff. Usually, they are right, but did they think deeply, connect to the “before stuff,” link it together and make a memory?

“Patience, grasshopper, patience.” As more and more problems are solved, together with each question explained and reasoned (as often as possible with real things), more and more keys will become second nature. Math is much deeper than other subjects; the links are much more complex and stuck in the language center of the brain.

Yes, it helps if the learner has done the drill-n-kill to know their math facts, but more than that, the learner needs someone to ask, and listen to, “Why?” Math is no less of a foreign language than Greek; it is learned by speaking it together with doing it.

— Walt Wegener is superintendent of the San Juan Island School District. E-mail him at wwegener@sjisd.wednet.edu