Mathematics for Teaching

This site is NOT about making mathematics easy because it isn't. It is about making it make sense because it does.

Tips for Teaching Proofs and Proving

I propose here ideas teachers need to know and pay attention to when teaching mathematical proofs and how to prove.

A. What is a (mathematical) proof?

I define proof as a relational network of claims (propositions and conclusions), substantiation (established knowledge that makes the claim legitimate) and appropriate connectives so sequenced to justify why the conclusion is a logical consequence of the premises. Continue reading “Tips for Teaching Proofs and Proving”

Variables, Constants and Parameters

Whether a mathematical notation is a variable,  parameter, or constant depends on what you mean by it.

  • If you intend to represent the value of a quantity whose measure varies within a situation, then you are using that notation as a variable.
  • If you intend to represent the value of a quantity whose measure is the same within all situations (e.g., pi), then you are using that notation as a constant.
  • If you intend to represent the value of a quantity that is constant in a particular situation, but which can vary from one situation to another, then you are using that notation as a parameter.

Continue reading “Variables, Constants and Parameters”

Teaching the derivative function

Most Grade 10 syllabus do not yet include the concept and calculation of derivative. At this level, the study of function which started in Year 7 and Year 8 on linear function is simply extended to investigating other function classes such as polynomial function to which linear and quadratics belong, the exponential function and its inverse, rational function etc. There is no mention of derivative. This should not prevent teachers from deriving functions based on the properties of the function students already know. Continue reading “Teaching the derivative function”

How to select and sequence examples in math lessons

In my previous post about examples, I described different uses of examples in teaching mathematics. In this post I’ll give a series of examples for us to be conscious about sequencing examples in our lesson. What are the things do you consider when you think of an example in a math lesson? And how do you sequence them? I’ll give an example to answer the questions I posed. Continue reading “How to select and sequence examples in math lessons”