Tips For Teachers

Documenting Classroom Management

How to Write Effective Progress Reports

Building Relational Trust

"Making Lessons Sizzle"

Marsha Ratzel: Taking My Students on a Classroom Tour

Marsha Ratzel on Teaching Math

David Ginsburg: Coach G's Teaching Tips

The Great Fire Wall of China

As my regular readers know, I am writing from China these days, and have been doing so four years so far. Sometimes the blog becomes inaccessible to me, making it impossible to post regularly. In fact, starting in late September 2014, China began interfering with many Google-owned entities of which Blogspot is one. If the blog seems to go dark for a while, please know I will be back as soon as I can get in again. I am sometimes blocked for many weeks at a time. I hope to have a new post up soon if I can gain access. Thank you for your understanding and loyalty.

Search This Blog

Tuesday, November 6, 2012

Tricks and Shortcuts vs. Mathematics

The issue is not whether algebra should be taught in the eighth grade or later. The issue is not whether local schools should be able to make their own textbook adoption decisions. The issue is about how easily states make big changes based on flimsy research which asks the wrong questions, only to backtrack later because solutions that solve the wrong problem do not work. California reverted to phonics in 1995 after abandoning it for a faulty implementation of whole language based on research that answered some questions, but not the questions that matter.

The emphasis on algebra in the eighth grade is misplaced when even students with good math grades enter algebra weak in math concepts. I am working with an A student now who is solving for x in problems involving mixed numbers. She wrote these "computations:" 2 + ¼ = 2¼, 3 + (- ¾) = 3-¾, and -2 + ½ = -2½. Do you see the pattern? In her mind, numbers are disembodied entities with no real meaning. She thinks all she has to do is take out the plus sign and push the fraction up against the whole number.

These silly errors happen in an education system where children have been taught tricks and shortcuts since first grade. The problem is teachers call tricks and shortcuts "math," and when children do well on a test of tricks and shortcuts, they learn their good grade is proof they understand math. Actually the grade proves only that they can reliably implement tricks and shortcuts.

I have worked with children who have terrible math anxiety because they do not do well with the tricks and shortcuts. Some part of their mind has rejected the tricks and shortcuts as not making sense, so "math" does not make sense. If they ever get a chance to acquire true number sense, then they find out they are good at math after all.

Sometimes we reward unthinking compliance (as when kids memorize the tricks and shortcuts) and punish the thinkers for whom the tricks and shortcuts do not make mathematical sense.


  1. I saw this post about a week after it appeared, and so I was prepared to prove MY 7th grade pre-algebra students would not make such mistakes.

    Equation-solving did them in, with this as a solution: -5¼ + 2½ = -3¾.

    I had previously showed them how illogical such a thing was, and how it didn't make "number sense", yet the method error persisted.

    I appreciate your posts a great deal.

  2. Thank you for your comment. It became the basis of a new post.