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IntMath Newsletter - resources, modeling and mistakes

By Murray Bourne, 24 Jun 2009

In this Newsletter:

1. Math tip (a) – Great list of math resources
2. Math tip (b) – Modeling
3. Math tip (c) – Summer math
4. Latest IntMath Poll
5. From the Math Blog
6. Final thought – making mistakes

1. Math tip (a) – Great list of math resources

I came across this extensive list of online math resources recently.

Math resources, by Alan Cooper, from Langara College, Canada.

The list contains resources on pre-calculus (algebra, trigonometry), calculus, vectors, statistics, recreational math and many other topics. Altogether, there are 850 links there!

It is an old list, so some of the links may not work any more, but everyone should find something useful.

2. Math tip (b) – Modeling

Reader Arun Prakash recently asked me:

I want to know how to make an equation from given data. For example, if we plot a graph for two variables, the output of the graph may be a parabola, linear, a circle, or exponential... Whatever it may be, we have to make an equation using the graph. How to form equations from the graph? How do we know that the equation we derived is correct or not?

This is a good question and I will address it over the next few IntMath Newsletters, starting today.

It's a good question because this is something that should be taught in all math courses (but this is rare). Why? Because it's more common in the "real world" to have a set of data but no equation representing that data, compared to your math text book, where you are almost always given the function first. Knowing how to get an equation that represents some curve is an important skill in math.

To start the ball rolling, here are some earlier articles I wrote that involve math modeling:

a. Earth killer – composite trigonometry CO2 graph - where we see an exponential curve model for CO2 growth.

b. Where is the Dow Jones heading? - where 2 models are presented for this important economic index (one is optimistic, the other is more realistic)

c. The melting Arctic - a disturbing application of math - where we learn about a simple climate change model.

In future Newsletters I'll give some more examples.

3. Math tip (c) – Summer math

Karon, another reader of the IntMath Newsletter recently wrote:

I'm a student but I'm also a parent of 3 children doing math: a 9th grader, a 5th grader and a 2nd grader so I need information for the whole family on math for the summer.

I mentioned the "summer math" topic in the last Newsletter and pointed readers to the article, The Summer Math Brain Drain, where I talk about how much math everyone forgets over the summer months.

Of course, the main thing is to ensure that whatever you get your children to do over the summer, if it even looks a little bit like math they won't want to do it. As you go through the following resources, choose the ones that can be enjoyed by each member of your family. The aim is not to "do math homework", but rather to "keep math bubbling" in their heads and on their radar. It's got to be fun, so games are a good place to start.

But before I suggest some resources, my first suggestion may surprise you. Over summer, encourage your children to read! Read what? Math textbooks? No!

One of the main factors for success in any school subject, including math, is the ability to read. If you can't read the math question, you won't be able to do it (or you'll do something else that the question doesn't want). Reading helps to increase your vocabulary and understanding of how the world works.

Certain books will help with math concepts more than others (science fiction comes to mind), but any kind of reading is way better than none. Remember, reading ability is essential for success!

I love the Internet and I spend a lot of time online, probably similar to your children. But I still love to read and I'd say encouraging a love of reading is one of the best things you can do to help your kids.

Back to the more math-focused suggestions... Here are some resources you may find useful:

I hope that gives your family some fun and useful things to do!

4. Latest Intmath Poll

A poll during Jun 2009 titled "Helpful Math Teachers" asked readers what they thought was the best way their math teachers could help them learn.

Poll results:

It’s best for me if my math teacher uses:

53% Plenty of examples
30% Good explanations of theory
 9% Plenty of diagrams
 8% Good rapport with the class

Total votes: 1500

Math teachers, take note! Students need a lot of examples to help them understand math. I was a bit surprised that "use of diagrams" and "good rapport" were rated so low.

The latest poll asks about summer reading. You can vote on any page in Interactive Mathematics.

5. From the Math Blog

1) Largest known prime: 2^43,112,609 - 1
Readers often ask me about the latest developments in math. Well, a huge 13 million-digit prime was found last year.

2) Friday math movie - Amazing competition
Feeling sleepy? Here's some good brain exercise for you.

3) Real World Math: Engaging Students through Global Issues
Here's a "real-world" math program that gives students a reason for learning algebra β€” the future of our planet.

4) Hubble math
The Hubble Space Telescope continues to amaze us with what it reveals about our neighborhood. Here's some math about the Hubble.

6. Final thought – making mistakes

Yesterday I was helping a reader with a differential equations problem. I was almost done and while checking my answer I realized there was a mistake somewhere. My stress levels rose because everything seemed fine — I was using the correct method and formulas, but the check step showed the answer was wrong.

Then I spotted the problem — I had missed a negative right back in the first row of the solution and it messed everything up.

We all hate making mistakes — it's a normal human reaction. We tend to avoid activities where we make lots of mistakes and do more of the things that we are good at. This is also quite normal.

But many math students tend to beat themselves up really badly when they make the odd mistake, and this can lead to higher math anxiety, and to giving up too early.

Here's a quote from Marva Collins that's worth keeping in mind when doing math:

If you can't make a mistake, you can't make anything.

Until next time.

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