Use of teaching aids in class

Last week, we have looked at the use of teaching aids in algebra. We first started with alge disc and alge tiles in term of expansion and factorisation and then four pan balance for solving linear equations. These tools do help us to bring in the concepts of operations thus let the students understand the underlining meaning of each step we do. However, once reached the negative values or fractions, it may be tough to use these tools. Actually I felt that we should not force the students to use the teaching aids to solve the complex questions but rather let them use the embedded concepts to solve them. By doing so, we can get them smoothly transit to abstract thinking which is very important in upper secondary and pre-u level as some of the topics cannot be taught using models. For example, for quadratic manipulations we can use a 2d model and for cubic manipulations, we can use 3d model but it is more difficult. However, when we start to talk about higher powers or fraction powers, we cannot really use them any more. Thus it is important to use the models for conceptual learning and also ensures that the students think about what they are doing as abstract mathematical manipulations at the same time.