Additional Math Pages & Resources

Monday, September 12, 2011

Where were you at 4 pm on the 9th?

I like detective stories. You might have deduced that from my blog post about a briefcase full of money. I like reading them - and have acquired over 500 detective and mystery stories. Here are a few bookshelves full of Sherlock Holmes, Ellery Queen, Perry Mason, Lovejoy, Nero Wolf, etc. [click on images to enlarge]

Since you can't always be reading, it's entertaining to watch detective stories and movies. In the past year, thanks to Netflix and Apple TV, my wife and I have watched virtually all the episodes from
  • Rockford Files
  • Perry Mason
  • Columbo
  • Hercule Poirot
  • Sherlock Holmes (various versions)
  • Hawaii Five-O (old version; we are half-way through its 248 episodes)
Now I would like to take an article I read in the New York Times today, and share with you its 3 main points about learning styles which (thank goodness) we have already incorporated into Excel Math. Let's assume these learning styles work for detectives, as well as kids in math class.

“Spaced repetition” means learners encounter the same concepts in brief sessions spread over a longer period of time. Students are introduced to fractions and exposed again to fractions two dozen times over a year rather than spending 3 weeks on it in February.

Our memories are fickle. They can change - the information can disappear. Detectives always want to talk to witnesses BEFORE they forget, and AFTER A WHILE, when some things come back about what was seen.  If our minds are exposed to the same information, in different ways at different times, it gets fixed in our minds. Seven might be the magic number for some of us to remember math concepts.

This is a tricky one - “Retrieval Practice” means that we can use quizzes and tests not just to assess what students know, but to reinforce what they know. You may consider memory like a big tank. Normally tests are thought of like a dipstick - a tool that measures how much information is in the tank.

But every time we dredge up a thought (like when the witness is questioned a second time by the detective), we make our memory stronger. A robust quiz doesn’t just measure what we know, it changes our relationship to what we have learned. We remember more.

Reading and cramming on our own does not have the same effect. Self-quizzing involved in retrieval practice or quizzes applied by a study partner (even a "study partner" down at the precinct) may in some cases provoke anxiety. But because we have focused our minds not on the input of knowledge (passively reading textbooks or notes - yawn) but on its output (actively recalling information from our own brain), we remember it better and longer.

A third technique, called interleaving, can also be applied to homework (or interrogation). An interleaved assignment, like kids encounter on our Lesson Sheets, mixes up different kinds of situations, instead of grouping them by single subject.

When students (or witnesses) don't know in advance what kind of knowledge will be needed for an answer, their brains have to work harder to come up with the solution. We can't fake it as easily, and we remember the material more thoroughly.
  1. Where were you at 4 pm on the ninth of September?
  2. That's a beautiful ring, who gave it to you?
  3. Are you sure you were in the library studying for the test?
  4. Was that at 4 pm on the ninth of September?
Researchers at Cal Poly conducted a study of interleaving with batting practice. When baseball players practiced hitting, interleaving different kinds of pitches improved their performance on a later trials where they didn't know what pitch would be coming (as in a real game). Interleaving improves academic learning too. A study asked 4th graders to work on solving four types of math problems and then take a test. The scores of students whose practiced on a variety of concepts were higher than the scores of those practiced one math concept at a time.

Remember how Columbo used to pause at the door and say, "just one more thing...?" Which technique was he using?