Why Doesn't Everyone Teach Real Mathematics?

 

Have you taken THE QUIZ?

We can only change what we know. 

In the quiz post, I make the case that our perceptions of what mathematics is and what it means to teach mathematics influence the way that we teach. 

It is only when we understand our past perspective that we can make the choice to teach in a way that aligns with our current perspective.

If you haven't already, check out the post and take the quiz to help you determine your childhood perspective of maths and teaching maths.

Because we have different perspectives and histories with maths, we talk past each other, not communicating well. Discussions get heated. Misunderstanding abound. Conversations are not productive nor help us make headway.

It is only when we understand our past perspective and acknowledge that others may have different perspectives that we can communicate more clearly.

NONE of these perspectives is the answer.

THE ANSWER is to teach REAL Mathematics!

After taking the quiz, you might be wondering about the other perspectives. Here you go:

X: Mathematics is okay if taught the way I was taught, because it worked for me.

You saw mathematics as patterns and relationships. You could figure out ways to do things and find answers and those ways were often not the way the teacher showed everyone. You could also do the teachers' way but sometimes it just made more sense to do something else that was easier, quicker, a shortcut. You were pretty sure that most of your classmates were doing the same things with shortcuts too, it just wasn't something one talked about.

The older you got, the more it seemed like fewer people were actually thinking about the maths. You are not quite sure why more people can't seem to naturally pick up on the patterns and use them the way you do. Maybe some people have the math gene and others just don't? When asked to show your work, you showed the teachers' steps because that's what the teacher meant. Numbers make sense to you. Somewhere along the line, the more abstract or complicated stuff might have gotten boring or too much and then you just did what the teacher said to, but you are still clear on the stuff that makes sense.

If you saw mathematics this way, you might teach the way you were taught, because hey, it worked for you! When your teachers showed you steps, you could use relationships to skip steps or be "lazy" when the numbers were just so nice, but only because you had seen the steps. Therefore, you need to show your students the steps too and if they don't just naturally pick up on the clever shortcuts then they must not have the math gene. You might viewing teaching all students as necessary, but recognize that really only those who are good at maths will go very far.

If you saw mathematics this way, you might not think there is any reason to change the way you teach because it will work for those who are naturally mathy. You might be surprised to learn that all can learn the kinds of things you do in your head, but they need to know it's a thing and see things visually/spatially, the way you do in your brain.

Y: If teachers would only explain why, I think I could do more maths.

You saw mathematics as a secret club where the members only allow certain people in. You weren't able to pass their initiation test for some unknown reason so they refused to explain what was really happening in the problems to you. You wondered about your ability, but you had this sense that you could have done much better if they would have just explained it all to you. You came up with some work arounds, things you do in your head, but you are pretty sure that they are not the "right" things to do. They seem to work for you so you keep doing them.

If you saw maths this way, you might want to change the way you teach maths. You might not be sure how. You probably work hard to help students understand what's happening by using concrete objects or examples that made sense to you. You might be intensely protective of your students who do maths their way or who also want to know why and how things work. You might not show students what you actually do to solve problems, because you are never quite sure if what you are doing is correct--It works for you, but will it work for them?

Z: Maths should be taught as rules and steps clearly and we must practice often.

You saw mathematics as an arbitrary set of rules and procedures made up by textbook writers. You knew that to do well, your job was to figure out what to do, in the right order, and copy the teacher's examples. The why, the background or the connection to other maths didn't seem to make a difference in you getting right answers so that discussion was irrelevant. "Please just tell me what to do and let me get my homework done." Maths had very little to do with your life's experiences.

If you saw maths this way, you might teach math now the same way you were taught. You might find ways to help students remember which rule to use when and the order of the steps. Since maths was all about remembering the steps, you might make it fun and easier with rhymes, raps, stories, cute drawings, songs. To help students get correct answers, you might provide many opportunities for them to practice and you give clear feedback about what they did wrong.

If you saw maths this way, you might want to do something different to teach maths now. You might be curious if there are better ways or if mathematics is really something wholly different than what you thought it was.

No matter what perspective you grew up with (X, Y, Z), we can all strive to shift our perspective to "R" and teach REAL mathematics! 

R: Real Mathematics. Students can be mentored to mathematize like mathematicians.

Mathematics is about creating and using relationships and connections, about thinking and reasoning, about finding patterns and forming viable arguments. Mathematicians do not mimic. They rote memorize very little. Rather, mathematicians structure and schematize; they use intuition and logic.

If you see maths this way, you conceptualize mathematics the way mathematicians do. 

If you see mathematics this way, you teach mathematics so that students can experience mathematical tasks in ways that help them find and use patterns, generalize relationships, and argue for the validity of their findings. You seek to set up experiences that have the potential for students to realize mathematical suggestions, that engender perplexity, that take advantage of students' innate curiosity. You help students to mathematize, to do what mathematicians do. You mentor mathematicians.

Great news! The FREE Developing Mathematical Reasoning workshop is perfect for you! This free workshop will help you understand the why behind all sorts of real mathematics. You’ll learn how to systematically help students learn the why and the how. You’ll learn all about the different domains of reasoning and how to help students develop into increasingly sophisticated thinkers. And it’s FREE! Click below to find out more and take the next step to being the maths teacher you want to be! 

Take me to the Developing Mathematical Reasoning Workshop registration!

Stay tuned for Part 2 of "Why Doesn't Everyone Teach Real Mathematics?" coming soon!

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