Concretising factorisation of

Many secondary mathematics teachers find it a challenge to teach factorisation of quadratic expressions to students who have weak foundations in algebra. This paper is a sharing of a project we embarked on to help students who have been generally unsuccessful in the topic to gain greater proficiency in the concepts and skills involved with quadratic factorisation. Concretising factorisation of quadratic expressions

Background of project

The way quadratic factorisation was usually taught to students in Bukit View Secondary (as well as other secondary schools in Singapore) was through the familiar "cross-method". An illustration of this method in the example of [x.sup.2] 3x 2 is shown in Figure 1.

[FIGURE 1 OMITTED]

However, some teachers felt that a significant number of students could not use the method effectively even after careful demonstration through repeated examples. As such, a Lesson Study (1) team was formed comprising the authors in this paper with the aims of identifying students' difficulties and devising ways to help them improve in their proficiency. We targeted the secondary Normal (Academic) (2) students in the school. A pre-test was administered to find out the extent of students' difficulties. The results confirmed the hunch that a majority of students was unable to factorise quadratic expressions correctly. This finding strengthened the resolve to devise another approach to teaching the topic.

After discussion, the team identified possible problems that students might experience regarding quadratic factorisation. These included:

* students' common conception of algebra as being "abstract" and thus beyond them;

* students' lack of pre-requisite algebraic skills (such as simplification of like terms);

* students' perception of the "cross method" as arbitrary, and the subsequent failure to make sense; and

* factorisation seen as an isolated skill to be learned without a broader context.

The team agreed that a reworking of another approach must address the concerns listed above. In addition, the team was convinced that for a teaching method to work practically in the classroom, it had to take Jimmy Choo Bags Replica into consideration realistic constraints of the classroom such as time constraints, large class sizes, and usefulness in actual test situations. In other words, the team was not working towards ideal pedagogies that could theoretically bring about radical changes in students' abilities; rather, we were targeting a realistic pedagogy that was useable in actual day-to-day lessons that could bring about improvements in students' learning of the topic. In response to these concerns and constraints, we decided that a new approach to teaching quadratic factorisation should satisfy the following criteria; that it would:

* appear concrete to the students;

* require minimum prerequisite algebraic skills;

* be perceived as sensible and non-arbitrary to the students;

* connect to the broader context of factorisation as reverse expansion;

* be useable directly by students as a method for Juicy Couture test situations.

Exploring possibilities: Algebra discs and algebra tiles

We first explored Algebra Discs developed by the Ministry of Education, followed by Algebra Tiles (3). For the reader who may not be familiarReplica Watches
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