# Teaching Algebra

LUDWIG WITTGENSTEIN, Philosophical Investigations

Before we talk about Algebra and teaching Algebra, I think we should address the elephant in the room...

## So, what exactly is Algebra?

This is not an easy question for sure. You can take a look at the Wikipedia entry on algebra by clicking here. Algebra is a huge field of mathematics and the term Algebra is used in many contexts. This articles refers to the beginnings of Algebra sometimes refer to as Elementary Algebra or Algebra that is typically taught to secondary school students (grades 7-12), building on their understanding of arithmetic. Note that this is a different use of the word as that of more advance treatments such as Modern or Abstract Algebra, Linear Algebra, Commutative Algebra, Algebraic Combinatorics and so on.

An attempt at defining Algebra could be something like this: **Algebra** is the fundamental language of mathematics from which we: create a mathematical model of a situation, provide mathematical structure to use in a model, link numerical and graphical representation, condense large amounts of data into efficient statements, analyze change, understand functions and variables (understand the idea and the variety of uses), interpret mathematical statements and, create and move fluently between multiple representations for data. Note that more of a definition, this is just a description of the different **uses** of Algebra, which will be in line with the spirit of the famous Austrian-British philosopher Ludwig Wittgenstein (see quote at the top of this page).

## So, how are we as teachers going to effectively teach algebra?

Although algebra as a concept is hard to clearly define, we can all agree that there are certain features worth pointing out. How many features and which are more important, is also a complicated question. However, the following topics surely make it into the list. These are important features or ways of thinking about algebra that can greatly benefit students' understanding and development of the subject.

- Developing algebraic habits of mind
- Meaningful use of symbols
- Mindful manipulation
- Reasoned solving
- Connecting algebra with geometry
- Linking expressions and functions

This is by no means an exhaustive list. In fact, I encourage you to reflect on what other aspects of algebra are worth pointing out explicitly. A good way to start thinking about these issues is to think on ways you would use Algebra.

## So, are there any more Algebra resources available?

**Yes!**, in fact there are plenty of resources. In this section I will try to provide links to an array of resources that will be of great use for your own algebraic thinking and for preparation of lesson plans. Enjoy!

- Annenberg Learner: Teacher resources and professional development across the curriculum
- NLVM: National Library of Virtual Manipulatives

It is hard for me to find ALL available resources. That is why I ask you to contribute. If you find a resource on the web that you think is useful and relevant for teaching Algebra, do not hesitate to contact me. You can do so in two ways: you can comment on the facebook plugin below or you can write me an email at . Thanks for your collaboration!