What Are Your Best Pre-Algebra Websites?

My Math Department is building a website with resources to help incoming (and existing) freshmen with some of the math skills that will help them be successful in high school mathematics. At this time, they are focusing on three areas:

• Fractions (adding, subtracting, multiplying and dividing)
• Integers (adding, subtracting, multiplying and dividing)
• Order of Operations

We would really appreciate it if you would share websites (either explanatory or skills practice, or both) that you think are helpful for students in these areas. If you have a website you think would be really helpful that doesn't fall into one of these areas, feel free to add that as well, as they hope to expand on this site in the future.

If you'd like to contribute, please fill in the following form. The results will automagically update below the form. Thanks for your help.

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Free Rice Has Added Additional Subjects

I blogged about Free Rice previously, a website where students (or anyone) can practice building their vocabulary and at the same time donate rice to the United Nations World Food Program. Well, it appears as though they've added some subjects:

ART - Famous Paintings
CHEMISTRY - Chemical Symbols (Basic), Chemical Symbols (Full List)
ENGLISH - English Grammar, English Vocabulary
GEOGRAPHY - Identify Countries on the Map, World Capitals
LANGUAGE LEARNING - French, German, Italian, Spanish
MATH - Basic Math (Pre-Algebra), Multiplication Table

This is not higher order thinking, but as I said before:

I think this is another interesting use of the web, combining educational activities (not just the fairly simple vocab building activity, but educating folks about hunger itself - including links to the sister site poverty.com) with contributing to the greater good. I could see this being a springboard for writing activities, social studies units on developing countries or poverty, and even some math and science activities (calculating how many grains of rice it takes to feed a certain number of people, nutritional value of the rice, caloric intake, etc.)

Lots of possibilities here for creative teachers and students and maybe, just maybe, doing some good in the process. And it's also, you know, kinda fun.

So, point your students (and your friends) to Free Rice and perhaps they can have a little fun, learn a little, and help provide rice to those in need.

Macbeth, Music, Mathematics, and Teaching: Can a Good Teacher Teach Anything from Anything Else?

I recently posted about Anne Smith�s classes creating musical compositions to represent characters in Macbeth. I think you should take another look at the comments on Anne�s post, as the discussion has moved in several different directions since then.

After many comments discussing the process and merits of using music to think more deeply about a literary work, Gary Stager asked this question:

So, do you think one lesson from this experience might be that a good teacher can teach anything from anything else?

The students had some interesting thoughts about that. Some of those thoughts touched on the subject of mathematics, including this comment:

In math, there is one answer and one answer only.

That led me to ask a question about whether the students all agreed with that statement and asked them to think about a couple of "math" problems. Since then Gary chimed in briefly again about math, and Sylvia Martinez has stopped by a couple of times to add to the discussion, but the students have really done the bulk of the commenting.

I think it would be worth your time to read through the discussion (set aside some time, as there are currently 194 comments) and perhaps add a comment with your perspective on the various topics.

Why Math?

James has tasked his students with contacting folks in a profession they'd like to pursue and asking them a few questions about their use of mathematics in their profession. Here are the questions they are asking:

1. How do you use math in your profession? Outside of your profession?
2. Are there any experiences � academic or otherwise - that particularly helped you learn and apply math in your profession?
3. What specific advice would you give to someone thinking about entering your profession if they want to help prepare themselves in the best possible way?
4. Knowing what you know now, what would you have done differently as a learner?
5. Please add any additional comments or questions that you feel you would like to share.

I thought that in addition to the great responses they are hopefully going to get back from the folks they contact, some of you might be interested in responding. If you have some thoughts you'd like to share with the students - or know someone else you could pass this along to - please stop by James' blog and leave a comment.

Google Maps, Google Earth and the Summer Games

Just a quick post to point out this story from the LA Times:

From where do the most Beijing Summer Olympic medal winners hail? Despite Michael Phelps being well on his way to breaking Mark Spitz�s record of seven gold medals at a single Games, it�s not North America that has the most gold medals so far. According to the Google Maps� Summer Games 2008, as of Aug. 12, 2008, China has won the most Olympic gold. The United States has won the most overall medals.

The Stadium page is my favorite of all the maps. Click on a stadium and watch a video as Google Earth zooms in. They also offer a photo and info about the venue.

Nothing major here, and probably no real educational relevance (other than curiosity, which isn't such a bad thing), just thought it was interesting. I bet there are more creative uses of Google Maps/Earth and the Olympics. If you know of any, please leave a URL in the comments.

I'm way behind in my aggregator (with no hope of catching up now that school is officially upon us), but it sure seems like somebody, perhaps dy/dan, should have a post coming soon with some great problems using current Olympic data. (I'm pretty sure he posted a while back doing some predictions with Olympic data, but I can't find it at the moment - somebody leave that URL in the comments as well and I'll update the post.)

Calculus: The Musical!

If your high school or college teaches Calculus, then you need to book these guys.

Calculus: The Musical! is a comic �review� of the concepts and history of calculus. It was born as a teaching tool in Marc�s classroom. He found that setting formulas and rules to music helped his students learn and retain tricky information. �Maxima� and �minima� is an abstract concept to a lot of us, but when sung as a rousing �Can-Can� chorus, it�s fun and easy to remember! A blend of sketch comedy, musical theatre and classroom lecture, MATHEATRE has created a performance piece to show that although calculus is used in rocket science, well�it isn�t exactly rocket science.

I just watched their performance in our theatre and it was very well done. What I also like is that they also provide everything on their website, including lyrics and audio (mp3's), but I think it would be great if you purchased a CD to help support them. You should also check out their tour calendar, as some of the performances are open to the public, or, once again, book them.

Come on, who wouldn't love these lyrics to L'Hopital (I have Calculus in the Heart) - sung to Bonnie Tyler's Total Eclipse of the Heart:

L�H�pital
Every now and then I get a little bit of trouble when I�m taking a limit.
L�H�pital
Every now and then I get a zero for the numerator and the denominator.
L�H�pital
Every now and then I get a limit that�s confusing in some kind of indeterminate form.
L�H�pital
Every now and then I get a little bit terrified but then I think of all your advice.
L�H�pital
Guillaume Fran�ois Antoine Marquis de
L�H�pital
Guillaume Fran�ois Antoine Marquis de L�H�p!

And that's just the first verse . . .

Fight Hunger While Learning Vocab

In the spirit of my last post, here's a chance to have your students work on their vocabulary (English) and fight world hunger at the same time. Free Rice is a website that has a fairly simple premise:

• Click on the answer that best defines the word.


• If you get it right, you get a harder word. If wrong, you get an easier word.


• For each word you get right, we donate 20 grains of rice to the United Nations World Food Program.

FreeRice has a custom database containing thousands of words at varying degrees of difficulty. There are words appropriate for people just learning English and words that will challenge the most scholarly professors. In between are thousands of words for students, business people, homemakers, doctors, truck drivers, retired people� everyone!

FreeRice automatically adjusts to your level of vocabulary. It starts by giving you words at different levels of difficulty and then, based on how you do, assigns you an approximate starting level. You then determine a more exact level for yourself as you play. When you get a word wrong, you go to an easier level. When you get three words in a row right, you go to a harder level. This one-to-three ratio is best for keeping you at the �outer fringe� of your vocabulary, where learning can take place.

There are 50 levels in all, but it is rare for people to get above level 48.

There are several pages on the World Food Program website that indicate that this is legitimate. I'm going to assume that the ads it displays are "appropriate," but your mileage may vary.

I think this is another interesting use of the web, combining educational activities (not just the fairly simple vocab building activity, but educating folks about hunger itself - including links to the sister site poverty.com) with contributing to the greater good. I could see this being a springboard for writing activities, social studies units on developing countries or poverty, and even some math and science activities (calculating how many grains of rice it takes to feed a certain number of people, nutritional value of the rice, caloric intake, etc.)

Lots of possibilities here for creative teachers and students and maybe, just maybe, doing some good in the process. And it's also, you know, kinda fun.

Geeky Thought For The Day

As seen on someone's t-shirt today.

There are 10 types of people in the world. Those who understand binary numbers and those that don't.

I warned you it was geeky.

Update 10-27-07: John pointed out in the comments that you can order this shirt online. Please note that I have no knowledge of this company nor am I recommending it.

A Formula For Success?

A question came up during one of our Cohort 2 sessions today when we were discussing the reading (the article discussed incorporating the student�s point of view into instruction.). It was something along the lines of, �How do we honor the student�s point of view on a math assessment where there is typically one �right� answer?� We didn�t get a chance to really discuss that question during the session, but I wanted to revisit it on the blog.

It won�t be a surprise to most of you that I want to focus on the concept of �one right answer.� The initial thought that came to my mind was that it depends a whole lot on what you�re assessing. If you�re assessing a particular math skill, taken out of context, then there may indeed be a �right� answer. Although even then I think in the long run the most important part might be their ability to describe the process, how and why they obtained the answer they did and why they think it�s �right.� Because unless they are presented with that exact same problem again � in some kind of context and where it actually matters � getting the right answer on that particular problem isn�t really all that important in the scheme of things.

But I think it�s more interesting to ask if that�s the type of assessment we really want to be doing. I�m not saying that we don�t need a way to evaluate whether they have mastered a particular skill, but I think the question that was posed was more along the lines of a unit test or semester final kind of assessment. And for that, I would suggest that the type of questions I think we should be asking might not have one �right� answer. For example, what if your assessment question was, �You�re designing a new school. What size and shape should the math classrooms be? Why?� To me, that is a much more interesting question and I think most of us would agree does not have one right answer. It also would require a whole lot of applied math skills, as well as research and critical thinking.

Which leads me to a larger question � why do we still insist on teaching mathematics as an isolated subject? As a set of skills, taken out of context, with the primary goal being to master the skills? Before you start throwing compasses at me, please realize I�m not saying this as someone who doesn�t like math. I happen to love math, and used to teach it, so this is not coming from someone who is math phobic or harboring deep-seated resentments to all things mathematical. It is said by someone who truly wonders if this is the best way to teach students about mathematics and how it applies to their world. Shouldn�t we be focusing more on the application of mathematics, not on the theory of mathematics in the abstract?

Let�s try an example. Actually, a quiz, since this is about math after all and math quizzes are something we�ve all experienced. It�s only four questions, and they�re all related, so don�t panic. (The very fact that so many of you smiled at the words �don�t panic� says something in and of itself.)

1. Write down the quadratic formula from memory.
   
   
2. Assuming you were able to complete number one, explain what a, b and c stand for in the quadratic formula.
   
   
3. Assuming you were able to complete both number one and number two, explain �in detail - when, why, how and for what you would use the quadratic formula in a math class.
   
   
4. Assuming you were able to complete numbers one through three, now explain � in detail � when, why, how and for what real-world situation you would use the quadratic formula.

Now, give this quiz to everyone who has graduated from high school in the United States between 1955 and 2005. (And, of course, please take it yourself.) The quadratic formula is covered in Algebra � and even Pre-Algebra where that is offered - and a very large percentage of high school graduates completed at least Pre-Algebra.

So, what percent of those high school graduates were able to answer all four questions correctly? (As an aside, I think percent is a math concept that we should have our students spend more time thinking about, as opposed to just computing.) I�m assuming your answer is close to 100%, correct? Especially considering that just about every day I read how much better schools were in the 1950�s (and 1960�s and 1970�s and 1980�s and well, just about anytime other than now). And certainly the answer was 100% among the highly-educated, clearly above-average-intelligence readers of The Fischbowl.

Now, let me be clear here that I think the quadratic formula is something that students might spend some time thinking about, investigating and applying. But not in isolation � not just so they can complete one through thirty-one odd. But in context, in a way where they are thinking deeply about solving a problem (as real-world as we can make it) that is important and relevant. They should be thinking about the quadratic formula because it would be helpful in solving a meaningful problem, not just because they need it for the next unit (or math class). Because what exactly is the point of teaching mathematical skills in isolation that the vast majority of adults will not be able to remember as soon as they are done with their last math class, much less even remember or be able to apply a few years later?

Some folks would answer that question by saying that even if people don�t remember the specifics of the math, that learning it helped them to �think logically.� Now, I�ve heard that an awful lot, but I�ve never read any research that proves that. (I�m not saying the research doesn�t exists, just that I haven�t seen it.) But even if the research does exist, what I�m suggesting we think about would accomplish that purpose as well, without the completely out of context, learn the skill to pass the test and then forget it approach. If we approach mathematics � and mathematics assessment � in this way, then I think it�s much easier to see how the student�s point of view becomes more relevant. (Because wouldn�t point of view be more relevant when discussing what the size and shape of a new math classroom would be?)

Now I know this is tricky territory, and I don�t want to get bogged down in the �math wars,� so please take this in the context of thinking about what we believe the essential learnings are for our students. But also please realize that I am not stating that we need to make math easier, or watered down. In fact, this is a whole lot more difficult than the way we�ve been teaching math. Because we�re not just asking them to memorize the formula and plug in the right numbers, we�re asking them to understand. And that�s a whole different ballgame.

This was written rather spur of the moment, so I probably haven�t given this the full attention it deserves, and probably have left some holes in the above argument. So add your comments below, but please try to focus on the bigger picture here, and not some isolated horror story of some clerk who can�t make change at a convenience store. Because, really, is making change a skill that�s all that important in the 21st century? Yes, I think they should be capable of figuring it out, and the approach I suggest above would actually help with that problem, but at this point I�m more interested in making change (in education) than in making change (at the store).

Oh, and for those of you who were wondering . . .

Image Citation: Maths humour, originally uploaded by Rich Watts.