Posted in Algebra

Different conceptions of algebra

The kind of task we ask our learners to engage in algebra communicates particular notions of algebra and with it particular use of variable. There are at least four conceptions of algebra embedded in the curriculum. These are reflected in the tasks in textbooks and in our lessons. Zalman Usiskin proposed the following conceptions of algebra in school mathematics. These are present in the curriculum in varying degrees. Continue reading “Different conceptions of algebra”

Posted in Algebra

What is a variable (in mathematics)?

A variable is often talked about in mathematics class as  a symbol that stands for numbers. As Prof Zalman Usiskin reminds us, a variable need not only stand for numbers. In Geometry it could stand for a point in Logic, a proposition, in Analysis, a function, in Linear Algebra, a matrix or a vector and even an operation in Higher mathematics.  Continue reading “What is a variable (in mathematics)?”

Posted in Algebra, Calculus

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”

Posted in Algebra

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”