Posted in Teaching mathematics

Math Knowledge for Teaching

The mathematics that engineers, accountants, etc and teachers of mathematics know are different. They should be. There are some engineers, accountants, chemists, etc who become very good mathematics teachers but I’m sure it is not because they have ‘math knowledge for engineering’ for example but because they were able to convert that knowledge to ‘math knowledge for teaching’.

What is math knowledge for teaching?

It includes knowledge of mathematics but on top of that according to Salman Usiskin, it should also include knowledge of:

  1. ways of explaining and representing ideas new to students;
  2. alternate definition of math concepts as well as the consequences of each of these definitions;
  3. wide range of application of mathematical ideas being taught;
  4. alternate ways of approaching problems with and without calculator and computer technology;
  5. extensions and generalizations of problems and proofs;
  6. how ideas studied in school relate to ideas students may encounter in later mathematics study; and,
  7. responses to questions that learners have about what they are learning.

appreciating teachersI don’t know why some people especially politicians think teaching is easy. Surely college preparation is not enough to learn all these. You certainly need to be a practicing teacher to even start knowing #1 and #7.  Teachers need more support in acquiring these knowledge when they are already in the field than when they are still in training.

I started this blog to contribute towards helping teachers to acquire the seven listed by Mr. Usiskin. After 250 posts, it looks like I have not even scratched the surface 🙂

More posts: teaching mathematics and levels of teaching mathematics

Posted in Humor

Things you learn in math education forums

You always get good ideas from forums (or fora), whatever form they are. If you want great insights about math and science education, try attending a PhD forum or seminar. I’ve just been to one. Following are some of the things I learned from the spirited discussion during the question and answer portion from these serious educators.

  1. We complain that our learners are not doing well in their Maths especially in secondary schools. These students are now engineers, doctors, lawyers, and politicians. We trust them anyway (except the politicians).
  2. It is only in math that 1+1 = 2. In real-life, it doesn’t work that way. For example, when two churches combine, you get 3 – the new one and the two old ones. This also applies to political parties.

    number theory
    number theory
  3. On the question of the relevance of your PhD to science education. Short answer by the speaker: I am now relevant to the science education. They now have one learned participant in the science education discourse.
  4. Why do we always expect the teachers to know all their Maths? Answer: It is probably because of our experience of our teachers in first grade as all-knowing. We believe everything teacher say and it was important for us then to have believe them. I think we need to grow up.
  5. Tell me, “Do you know of a mathematician who know all their mathematics?” Why should a math teacher know all their math? This is not fair to teachers. Do you complain in the media when a doctor misdiagnose your illness?math teachers
  6. “My conclusion in my review of literature why, despite the extent of research about teaching and learning algebra we still have not solved the difficulty of learning it, is that because algebra is a moving target.”
  7. “I initially thought to explore the reasons of students absenteeism in lectures. But then I thought, why should they when they can find great lectures in the net. Now I do not know how to proceed from here. Will anybody suggest a research question that’s not in the net?”
  8. “In my interview with teachers, most of them said that they don’t really know why students are not getting the test. When they teach them, they seem to understand everything they are discussing and solving. My interview with students confirms this. The students said that they understand everything during the lectures but they couldn’t answer the same questions and problems in the test.”
Posted in Algebra, Math blogs

Math Teachers at Play at Math Mama

Math Teacher at Play (MTAP) #51 is now live in Math Mama Writes …. Really great collection of 51 posts from teachers, lecturers, professors, bloggers, … in the following categories: Arithmetic, Patterns and Logic, Visual Math, Algebra-Geometry-Trigonometry, Puzzles and Games, Notations and Logic, and Breaking News, and may favorite, Teaching Mathematics.  I even got two posts in the carnival. Thanks Sue.

The next MTAP carnival will be hosted in Let’s Play Math. Submit your post first week of July using the MTAP submission form.

Posted in Math blogs

Math Teachers at Play blog carnival #50 – submission

Hello  bloggers and teachers. This blog is hosting the 50th edition of Math Teachers at Play (MTAP) blog carnival this 18th of May 2012. Promote your favorite posts/articles by submitting the links using the MATP submission form before the 18th.

  1. Do you have a game, activity, or anecdote about teaching math to young students? Please share!
  2. What is your favorite math club games, numerical investigations, or contest-preparation tips?
  3. Have you found a clever explanation for math concepts and procedures? E.g. how to teach bisecting an angle, or what is wrong with distributing the square in the expression (a + b)^2.
  4. How do you make an upper-level (high school) math topics come alive?
  5. What is your favorite problem? (I hope not the students:-))
  6. What kind of math do you do, just for the fun of it?

Click here to see past editions of MTAP Carnivals.

Don’t be shy — share your insights! If you do not have a blog, just send your ideas and short articles at mathforteaching@gmail.com. I’ll find a way to publish it in the carnival.

The last math blog carnival I hosted was Math and Multimedia Carnival #17.