Math with Computers

Last month I posted a link to Conrad Wolfram's Ted Talk when he argues that we waste time teaching students to calculate when we should be teaching them how to look at, think about, and solve problems mathematically. Wolfram and his allies are working toward this goal. For more, see the website computerbasedmath.org.

The Resources page links to more videos, news coverage, and some "explorations" (e.g., an essay explaining how a mathematician used computational techniques to figure out Hangman).

The Wolfram Demonstrations Project has thousands of examples of graphical depictions of problems.

In the list of topics, you find math, technology, economics, geography, and more. I chose "Kids & Fun" and then clicked on "Everyday Life."

The demonstration called "Blue Sky and Red Sunset" shows how the angle of the sun's rays changes the color of the sky.  You move the slider to change the angle and you see the colors change.




Blue Sky and Red Sunset screenshots

In the math section, I found this interactive demonstration showing the graphs of the derivatives of trigonometric functions:




Derivatives of Trig and Hyperbolic Functions screen shot

 It has been a very long time since I took calculus, but I suspect that being able to see the changes in the graphs would help a student see the relations among the functions.

There are over 200 puzzles.

To be able to interact with the demonstrations, you need to download Wolfram's free CDF (Computable Document Format) Player.

Vocabulary, Digital Content, Snowballs, and the State of the Union

Interesting comment about the importance of consciously working to develop childrens's vocabularies, all through school. Vocabulary, Digital Content, Snowballs, and the State of the Union, Teach, Learn, Grow: The Education Blog" Feb. 27, 2013. The author says, "students must be exposed to important words they can leverage across subjects (academic vocabulary) and they must be exposed to words repeatedly and in a context that allows them to add words to existing schema or frameworks of background knowledge."

The More You Know the More You Learn

Vocabulary.com's blog has a post about a study that show that students with larger vocabularies learn new words faster. I suspect the same is true of all areas. The more math you know, the more quickly you can learn math, the more history you know, the more quickly you can learn history. One implication of this is that kids who fall behind in the early grades will have a harder and harder time as they progress through school. Ninth-grade history, for instance, will be much easier for the students who learned a lot of history in elementary school and middle school—both in class and through leisure reading, talking with parents, watching documentaries, and so on. Just as knowing more makes it easier to learn, knowing more also makes a subject more interesting and fun to learn more. I don't think it's a coincidence. It's just challenging to persuade a student who finds everything "boring" that it will probably get interesting if she puts in enough work to learn something.

Bedtime Math!?!

Time has an article about a move to get children jazzed about math: Bonnie Rochman, Beyond Counting Sheep: Why Math Is the Hot New Bedtime Reading, Time, Feb. 25, 2013, at 52. You have to subscribe to see the whole article, but the title alone gives you the key message: having kids think a little about math regularly is as important as reading to them.  (A few months ago, the author had an online story: A Problem a Day Keeps Fear of Arithmetic Away, Time Health & Family, Nov. 21, 2012.)

The article features Bedtime Math. You can follow or subscribe to the blog to get three problems a day, aimed at pre-K, K-2, 2nd grade and up. According to the Time article, the site will add a higher level of difficulty for "tweens, teens and even adults" in late February. That's any day now! Hooray!

The Time  story says:

the strongest evidence that Bedtime Math can change children's skills comes from data collected from Snacktime Math, a program of Bedtime Math problems given to kids attending summer camp at a New Jersey Boys & girls Club: more than 70% of the largely low-income students improved their skills after a six-week session.

The article also mentions Math for Love, "a Seattle outfit that advises teachers on how to use games to spice up math education."  I haven't read through much, but Math for Love's blog looks very good—interesting, witty, and mathy.

Teaching Kids Real Math with Computers

Interesting Ted Talk by Conrad Wolfram (2010):



He argues that we act like calculating is all there is to math, so that we spend too much time teaching students how to calculate by hand and not nearly enough time teaching them to ask the right questions, frame the questions mathematically, and evaluate the results. (He does not say we should throw out all calculations. It's useful to be able to do some mental arithmetic to make estimates, for example.)

If you've never seen wolframalpha.com, by the way, take a look. It's very useful for statistics (e.g., area of the U.S., population of L.A.), formulas (volume of a cylinder, quadratic equation). You can also use it to check your answers for algebra (and other) math problems.

Ted Ed Has Cool Videos

Ted Ed has short educational videos on a wide range of topics. Most are animated, through the pairing of an educator (who does the content and the narration) and a professional animator. All of them are accompanied by quizzes or questions to think about and links to other sources. 

For students who think spelling is crazy, try:

• Making sense of spelling, and
• Why is there a "B" in doubt"?

Would you like to encourage your student to reach for a stronger, more lively vocabulary? Recommend The case against "good" and "bad."

For high school students learning about how to analyze literature, see

• In on a secret? That’s dramatic irony
• Situational irony: The opposite of what you think
• What makes a hero?

These are just some of the lessons listed under Language Arts. There are also interesting entertaining videos in many other areas (Science & Technology, Social Studies, and more).

Ted Ed's home page

Study Skills! Study Skills! Study Skills!

No matter what you're trying to learn, it helps if you know how to learn so you don't waste a lot of time.

HowToStudy.org is a great site that brings together lots of tips from many reliable sources (including lots of colleges). Some of the tips are aimed at a particular subject—for instance, Math or Speech. Other tips are good for studying in general—for example, how to develop and meet goals and how to deal with procrastination.

The site's most frequently accessed resource is the Assignment Calculator. You plug in the date a paper or project is due, and the calculator breaks it into steps (e.g., develop topic, write preliminary thesis, gather sources). The steps are spread out over the period you have to work on the assignment, so you don't fall into the trap of thinking you'll do everything at the last minute. It also helps you structure your work so you do a better job.

Check out the How to Study Model, a diagram that shows all the different functions you need to perform when you study.

One neat thing about the site is that students can write reviews of the different resources. For example, here's what 16 students said about using a day planner.

The person who runs HowToStudy.org is a retired community college instructor, with years of experience working with students, and the site has won awards from education groups.

---

This blog post has some interesting news about different study techniques: Annie Murphy Paul, Highlighting Is a Waste of Time: The Best and Worst Learning Techniques, Time Ideas (Time Magazine's site), Jan. 9, 2013. The author explains that research shows that highlighting doesn't really help people remember what they read! What is effective is testing yourself with flashcards, and she tells us about three flashcard apps: Quizlet, StudyBlue and FlashCardMachine.

I tried out Quizlet last week and like it. You can create your own flashcards, or you can use sets that other people made (I tried out trigonometry definitions, geometry formulas, and beginning French vocabulary). You can run through the flashcards and then, when you're ready take a quiz. It's kind of fun and seems like a good tool.