Mike Kaechele

Category: math

  • Teaching math backwards

    As I have mentioned I will be teaching my first math class this year-6th grade (not counting student and substitute teaching). I want to drop the textbook as much as possible, but have to admit that I am a bit intimidated to commit to not using it at all. I see textbooks as a crutch for teachers because I think that they are terrible. But textbooks do make it easier to plan and teach and I am not sure I can prep without it every day.

    Today I was challenged by two blog posts to give it a realistic try. The first is by Nancy Stewart about 8 principals that she will use in teaching her special education math class. She mentions ditching the textbook which is encouraging just to hear that others are taking the same step. She also gives some good ideas on how to at the same time make math more real world and personally relevant to students.

    She also mentions one of my favorite bloggers Ira Socol and links to this post. Math teachers you must read this post as Ira paints alternative ways to teach math and turns much of my thinking upside-down. He shows examples of using sports, construction, cooking, and money to make math authentic and meaningful. I am sure he would argue that my times table idea is a waste of time.

    The most challenging thought to me was a comment (you must read the comments) by Homer the Brave:

    “Start with philosophy. Teach kids about logical systems. Teach them how to understand a provable statement and how to spot a fallacy. Then say, ‘We’re going to now apply this same set of rules about philosophy to math.’ Then teach algebra. The details of arithmetic will then follow, imbued with purpose and meaning.

    So basically we teach math backwards arithmetic, algebra, and then philosophy. I personally was an excellent math student in school because I was very good at memorizing and working algorithms. It was not until taking classes about teaching math in college that I understood the philosophy and reasoning behind the math. Homer argues that we should start with the philosophy (logic) and then move to algebra with arithmetic last. This is very new to me but does make sense.

    Of course this change would have to happen at the district curriculum level. The easy cop out for me is that I must teach to the standards assigned to me. But I can at the same time as teaching the standards, teach the logic and philosophy behind the math. I can teach authentically without the textbook as much as possible. I am up for the challenge. How about you?

  • Is rote memorization a 21st Century skill?

    A common theme in blogs and twitter feeds is the need to teach 21st century skills. The point has been made over and over that we should not be requiring students to memorize facts that can easily be googled. Without getting deep into the argument of what these skills are or whether they are new, let me say that I agree this should be a primary focus of education. I believe in focusing on problem-solving using authentic, real world learning with collaboration both inside my classroom and globally.

    But….this year I am teaching a 6th grade math class for the first time. One of the things that has amazed me in my 5 years of teaching a math-focused technology class is how many kids do not know the answer to simple math problems like 3 x 7. They want to use a calculator for basic math facts that I think they should know. So for my class I am thinking about starting the year off by requiring them to review and recite to me the times tables through 12 x 12. I believe that this foundation is necessary for most middle to advanced math concepts including fractions, multiples, factors, algebra, and calculus.

    I think memorizing spelling words is another similar set of facts that should be memorized. Even when you have spellchecker you need to be able to spell close enough that it can recognize what you are trying to spell. You also need to be able to pick out the correct word from spellchecker’s choices. I have read many papers where students lacked those two skills.

    So my question to readers is what do they think about rote memorization? Is it last century or still important. When is it useful or even necessary? Am I off-base or is it important to teach rote memorization of basic skills before students can perform many higher level tasks.