Mathematics for Teaching Category: Algebra

Category: Algebra

Assessing understanding of graphs of functions

Problems about graphs of functions can be grouped into interpretation or construction tasks. The tasks may involve interpreting individual points, an interval, or the entire graph. The same may be said about construction tasks. It may involve point-plotting,  a part of the graph, or constructing the whole graph. Tasks involving constructing graphs are considered more difficult than interpreting…

Evolution of the definition of function

How do you define function? Do you teach relation first before teaching function?  Does knowing about relation a pre-requisite to function understanding? The concept of function “was born as a result of a long search after a mathematical model for physical phenomena involving variable quantities” (Sfard, 1991, p. 14). In 1755, Euler (1707-1783) elaborated on…

Solving systems of equations by elimination – why it works

Mathematical knowledge is only powerful to the extent to which it is understood conceptually, not just procedurally. For example, students are taught the three ways of solving a system of linear equation: by graphing, by substitution and by elimination. Of these three methods, graphing is the one that would easily make sense to many students. Substitution, which…

What is algebraic thinking?

In my post Arithmetic and Algebra, I wrote that it’s how you solve a problem that tells whether you are doing algebra or arithmetic, not the problem itself. Here’s a description of algebraic thinking that I think teachers in elementary school mathematics might find useful especially when they are teaching about numbers and number operations:…

Levels of understanding of function in equation form

There are at least three representational systems used to study function: graphs, tables and equations. But unlike graphs and tables that are used to visually show the relationships between two varying quantities, students first experience with equation is not as a representation of function but a statement which state the condition on a single unknown quantity.  Also,…