Confession: I Am Not Good at Math

I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers. People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.

Apply logic to that statement. The conclusion simply isn’t valid. …

Update: This post has moved.

Click here to read the new, expanded version

Project Follow Through Story Looks Interesting

Project Follow Through was an almost-30-year study that compared the effect of different teaching methods on over 20,000 students nationwide. I have started reading The Outrage of Project Follow Through: 5 Million Failed Kids Later [site no longer exists, but try this book: Project Follow Through: A Case Study of Contingencies Influencing Instructional Practices of the Educational Establishment], which explains the research and its results in layman’s terms. So far, I have enjoyed the book, which is being released chapter-by-chapter every Monday. The introductory chapter will be available only for the remainder of this week, however, so if you are curious, you had better act now. I recommend downloading the pdf file to read at leisure: Right-click on the link for each chapter, then choose the “Save” option.

[Hat tip: D-Ed Reckoning, who is running a series of articles (part 1 here) highlighting his favorite parts of the book.]

Elementary Teacher Education

Unfortunately, this is all too believable:

Received an email from a parent.

Not one of our students, but rather the parent of a high school student who plans to attend this university. The parent is looking for advice on how to get the kid out of math. Seems that the kid has already taken the bare minimum number of units of high school math needed for graduation and has stopped taking math. The parent is wondering if the kid can take some sort of test (before forgetting any more math) to fulfill the university’s math requirement.

Guess what career the kid is planning on? School teacher.

From Rudbeckia Hirta at Learning Curves.

Percents: The Search for 100%

[Rescued from my old blog.]

Percents are one of the math monsters, the toughest topics of elementary and junior high school arithmetic. The most important step in solving any percent problem is to figure out what quantity is being treated as the basis, the whole thing that is 100%. The whole is whatever quantity to which the other things in the problem are being compared.

Continue reading Percents: The Search for 100%

Common Sense and Calculus

One more quote from W. W. Sawyer’s Mathematician’s Delight before I have to return the book to the library:

If you cannot see what the exact speed is, begin to ask questions. Silly ones are the best to begin with. Is the speed a million miles an hour? Or one inch a century? Somewhere between these limits. Good. We now know something about the speed. Begin to bring the limits in, and see how close together they can be brought. Study your own methods of thought. How do you know that the speed is less than a million miles an hour? What method, in fact, are you unconsciously using to estimate speed? Can this method be applied to get closer estimates?

You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply the same common sense to stones rolling down hillsides, and the calculus is at your command.

Mathematics and Imagination

Comments by W. W. Sawyer, in his wonderful, little book, Mathematician’s Delight:

Earlier we considered the argument, ‘Twice two must be four, because we cannot imagine it otherwise.’ This argument brings out clearly the connexion between reason and imagination: reason is in fact neither more nor less than an experiment carried out in the imagination.

Continue reading Mathematics and Imagination

Percents: Key Concepts and Connections

[Rescued from my old blog.]

Paraphrased from a homeschool math discussion forum:

“I am really struggling with percents right now, and feel I am in way over my head!”

Percents are one of the math monsters, the toughest topics of elementary and junior high school arithmetic. Here are a few tips to help you understand and teach percents.

Continue reading Percents: Key Concepts and Connections