# Math Education Concepts

## Concept-Based Learning and Math

Concept-based learning is not a new idea, but one that should get far more attention than what I’ve seen.  I recently found the following definition on “What Is IB?”

“Concept based learning is about big transferable ideas that transcend time, place, situation. Content just focuses on facts while concept focuses on making sense of those facts and the world around us. Content based teaching may not get beyond information transmission/superficial learning. Concepts are a way to organize and make sense of learning.”

When thinking about teaching and learning mathematics, concept-based learning makes the most sense.  Why? Situations change, contexts change, numerical values change, students change, etc.  If a concept is taught and learned, then changing the context or situation will not affect how to apply a concept.

I recently helped a student prepare for the math section of the upcoming SAT.  One question in the practice book showed the graph of a line with no numbers.  The question asked the student to select the equation of the line.  If the student knew the concept of graphs of lines (slopes, y-intercepts, etc.) then they would have been able to solve the problem easily.  They could determine whether the slope was positive or negative and whether the y-intercept was positive or negative.  Without the understanding of these concepts, the student was not able to answer the question.  Once I explained the concepts and details, then the student understood.

Concept-based learning should be a central focus when teaching mathematics.  Otherwise, students will continue to stumble over content when situations and contexts change.

What are your thoughts on concept based learning?

## My Teacher Training Manual

Available on Amazon (Kindle Edition)

I finally did it!  I wrote a teacher training manual several years ago and I finally published it on Amazon in Kindle edition this morning.

The manual was written for secondary math teachers of African American urban students (hence, the title).  This topic has always been dear to me as a student, parent, mentor, teacher, and educator.  The goal of the manual is to help teachers teach their students more effectively.  Oftentimes teachers enter classrooms with their own ideas about learning and neglect to think about their students’ ideas about learning.  This manual helps teachers view learning from a different perspective.  It also offers ideas and suggestions for applying some of the concepts written.

Although this manual was written with secondary math teachers in mind, it can be used across several curricula and grade levels.

Order your Kindle edition of this manual and share what you learn with your colleagues, staff, family, friends, and anyone else who will benefit from its contents.

Enjoy!

## Do They Get It? The Instantaneous Rate of Change Exactly

Today in calculus I wanted to check if students really understood what they were doing when they were finding the instantaneous rate of change. (We haven’t learned the word derivative yet, but this is the formal definition of the derivative.)

So I handed out this worked out problem.

And I had them next to each of the letters write a note answering the following individually (not as a group):

A: write what the expression represents graphically and conceptually

B: write what the notation $latex \lim_{h\rightarrow0}$ actually means. Why does it need to be there to calculate the instantaneous rate of change. (Be sure to address with h means.)

C: write what mathematical simplification is happening, and why were are allowed to do that

D: write what the reasoning is behind why were are allowed to make this mathematical move

E: explain what this number (-1) means, both conceptually and graphically

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