Archive for ‘math’

April 7, 2015

Where Direct Instruction Fails: Willingham, Memorization, and Conceptual Understanding (2)

In my previous post I wrote about the overemphasis on memorization and drills and brought some arguments for balancing all three aspects of knowledge in mathematics: factual, procedural, and conceptual. Let’s review:

  1. Memorization of math facts is important. It allows for complex tasks to be carried out.
  2. Procedures should be taught after or in tandem with concepts. One supports the comprehension of the other.
  3. Block practice (in textbooks and in teaching) is detrimental to learning. The overlearning as well as familiarity effects occur.
  4. Excessive modeling and examples in math can actually interfere with learning. They increase performance in the short term but hinder learning in the long run.
  5. Space out practice and interleave mathematical concepts. If you focus on a topic (i.e. fractions) make sure your students not only apply it in different contexts, but are also engaged in solving problems you previously taught (i.e. geometry or measurement topics). Even better, use fractions, measurement, and geometry together (Example: 1/3 of the area of a rectangle is red. Knowing that the perimeter is 64m and one of the sides is 1,000cm, find out what part of the rectangle is red. – Knowledge of area and perimeter, knowledge of fractions, and knowledge of measurement conversion).

April 7, 2015

Where Direct Instruction Fails: Willingham, Memorization, and Conceptual Understanding (1)

I have been on Twitter long enough to notice an idea that is increasingly taking hold, especially in the U.K. education: memorization as the main tool for learning. Danniel T. Willingham, a cognitive scientist whose work I consistently shared for a few years now, has irrevocably (and most likely unintentionally) created a meme when he wrote in one of his widely known books (Why Don’t Students Like School?): “Memory is the residue of thought.” The truth of the sentence is obvious, almost trivial: to remember something you need to have thought about it quite hard. What happened though is that its meaning got completely twisted in some educational settings and turned into “Memorization is the only way to learn”.

August 15, 2014

Gender, Math, and Achievement Gap

Jo Boaler’s article was interesting (Britain’s Maths Policy Simply Doesn’t Add Up) and prompted me to blog.  She shows concern about girls’ math achievement in Britain:

 “But when I sat with the PISA team recently, I was horrified to see that of 64 countries assessed, Britain has the biggest gender gap in ‘maths mindset’. Simply put, the data showed that British boys believe they can do well in maths; girls don’t.”

I was curious whether the claim was true and I checked PISA reports, summaries and Excel tables. She was right. Boys not only outperform girls in math but also have higher confidence and are more likely to pursue math-related careers.