I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

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Tag Archives: algebra

The Math Show Stars are All the Same

This is Day 31 of 31 Days of Math Learning Success – THE FINAL DAY! See all the days here and check out others that are wrote for 31 days here.

There’s only a handful of actors in “math world.” Depending on the show, they play different parts: inverses, identities, etc.I’ve never thought of acting as rocket science – you put on the costume, get your hair cut, and that’s it, really.
~Marc Warren

There’s only a handful of actors in “math world.” Depending on the show, they play different parts.

For instance, Ignatius P. Identity will play Zero in The Addition Show and One in The Multiplication Show.

In The Function Show, Ignatius plays f(x)=x.

And in The Matrix Show, he plays \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}.

Depending on the episode, Ivey McInverse may play -3 or \frac{1}{8}.

Or even g(x) = \frac{1}{4}x +3, the soul mate of f(x)=4x-12.

Ivey McInverse only plays inverses.

They’re not Method Actors.

The “actors” in math are popular. You can’t see a show without spotting them.

The key is to figure out the actors and then watch the shows closely.

Every actor behaves the same way. Kind of like how Bruce Willis always acts like Bruce Willis.

There are some slight differences, sure. But overall Bruce Willis plays Bruce Willis. Just like Ignatius P. Identity always plays an identity element.

In other words, it’s all the same stuff.

If you learned anything in math, ever, you mostly know everything.

The challenge is figuring out how the new stuff is like the old stuff. Who from last night’s math show is playing whom in today’s math show.

And what parts of the story line are the same.

Math isn’t hard, it’s just detailed.

Like a great Quentin Tarantino movie, it’s deceptively simple. Or deceptively complex.

It’s funny, frightening and at times confusing.

But it’s worth the ride.


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4 Responses to A Different Way to Teach College Algebra

  1. I’ve often thought the key to math is doing a lot of it until it becomes second nature. I tell my students to compare it to learning to walk. Watch a toddler and see how much effort it takes to learn, but you haven’t given it a thought in years.

    How do you get that number sense? With our games we try to have lots of different activities of different types, so that students see the same concept over and over but in different situations.

    However you do it, I agree, number sense is a foundation too many people do not have, and just like in construction, you can’t build very high without a foundation.

    • Thanks for your thoughts, AnnMaria.

      Repetition is important, but only if the foundation gives you the ability to make it compress. Otherwise you’re just trying to be a computer running a gazillion subroutines!

  2. Great illustration, Bon. The only thing I’d suggest is to replace is the “younger” vs “older” labels in your comparison with “novice” vs “expert”.

    Have you read any of David Tall’s stuff about mathematical thinking (http://homepages.warwick.ac.uk/staff/David.Tall/themes/three-worlds.html) ? He says that as expertise in math develops, processes become encapuslated (aka: compressed) into what he calls “procepts” — “thinkable concepts” or hybrids of process + object which can be manipulated in their own right.

    Working memory (WM) is known to have a very limited capacity (newer research has lowered this from 7 plus/minus 2 items to 3 plus/minus 1). Without encapsulization/compression, WM fills to capacity with the calculations and single steps which all must be juggled individually and sort of held in suspension there until they can be assembled into a problem solution.

    When students have to deliberately recall and then ‘drive’ each little step in a more complex process, WM capacity is exceeded and cognitive overload ensues. Some of the little pieces may be displaced by other little pieces which need attention. Unable to recall how the individual steps contribute to the solution, the student may become lost inside the bigger process. Unable to ‘see’ a solution taking shape, the student may shut down.

    Developing fluidity is essential, and facility in fractions especially is now seen a sort of bellwether of future success in math.

    • Very nicely articulated Sue!

      I had no idea that working memory was so small. I was still back on the 7.

      My brain just realized that it can’t take much more and is wanting to shut down. Time for coffee!

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2 Responses to How to Teach Square Roots

  1. Sorry, The idea of teaching square roots without any mention of geometry (or squares) at any level makes me a little sad.
    It was otherwise very nice with some very good ideas.

    • I can see that, Pat. But at this point (when the students are all grown up) I’ll do whatever I have to so they can get it.

      Thanks for stopping by.

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3 Responses to Fahrenheit to Celsius – Graphically!

  1. what i’m trying to noodle through is 1) why do they mirror each other at 45 degrees x=y and 2) why do they converge at about -40 degrees? why that point rather than zero? Can you help?

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5 Responses to Teaching Square Roots with a Non-PC Analogy

  1. No, I probably wouldn’t use this analogy. We are Christian, and homeschool. And usually when you are teaching this concept in square roots, kids are still fairly young…. And despite the fact that my kids know people go to honky tonks and get divorced, I don’t think I’d use this analogy to teach square roots. I did think of earthquakes — altho that may be offensive to someone who lives in an earthquake-prone area!! You know, two houses smash together in the earthquake, then they need to sort it all back out…..

  2. It’s only words, folks, and if it works then it works. In any event, it provides a impetus for communication. I’d use it to teach stereotypes (what is a “redneck”?). If kids are asking questions and thinking, that’s good.

    Keep thinking outside the box!

    • Manisha, this is awesome! I love your distributive property example. I do something similar with multiplying binomials. Two brothers, Abel and Ben, come to a dance and meet two sisters, Caroline and Danielle. Each brother dances with each sister. But the brothers don’t dance with each other. Nor do the sisters. And it looks like: (a+b)(c+d)=ac+ad+bc+bd

      I would love to see the full article!

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One Response to How to Introduce Function Transformations

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