Effects of Spreadsheet Towards Mathematics Learners’ Problem Solving Abilities

Abstract

This paper reports the findings of a study exploring the effects of using spreadsheet towards preuniversity students’ problem solving abilities. The sample of this quasi-experimental study comprised 64 preuniversity students from a private college in Malaysia. The experimental group was taught the topic limits using a spreadsheet module while the control group was taught using the traditional module. Observation was done throughout the treatment, and data about problem solving abilities was collected, analysed and transcribed for differences in both groups. The results revealed the following differences between both groups: (a) number of correctly solved problems, (b) problem solving strategy, (c) preference in problem and solution presentation and (d) priority in problem solving.

Appendix: Content of Spreadsheet and Traditional Module

W	Learning outcome	Problem to be solved
1	Judge the validity of limits with reference to the formal definition	Lina and John are arguing with the limit of ${a}_n=\frac{1}{n}$ as n becomes large. Lina says that the limit is 0 but John claims that the limit could be 1. Whose statement do you think is correct? Why?
2	Identify the significance and relationship of ɛ and N in the formal definition	In the previous task, Lina and John were arguing with the limit of ${a}_n=\frac{1}{n}$ as n becomes large. Lina said that the limit should be 0 but John said that the limit could be 1. From the activity, you saw that Lina’s statement is “more correct” due to more TRUE. However, there is no TRUE for Lina when ɛ = 0.1. Do you think that Lina’s statement is still correct? Why?
3	Prove the implication that if the limit of a sequence exists and is known, then the limit is the horizontal line clustered by infinitely many points	What can you say about the relationship between the limit of a sequence a n and the clustered value of its scatter plot?
4	Predict the limit of a sequence geometrically	Explain how the limit of a sequence a n can be obtained from its scatter plot?
5	Prove the implication that if there exists no horizontal line of clustered points, then the limit does not exist	From previous activities, we know that if the limit of a sequence is A, then the horizontal line y = A would be clustered by infinitely many points. How about if we are not able to identify a horizontal line of clustered points, can we say that a limit does not exist? Why?
6	Disprove the implication that if y = A is a horizontal line of clustered points, then the limit of the sequence is A	From previous activities, we know that if the limit of a sequence is A, then the horizontal line y = A would be clustered by infinitely many points. How about if y = A is a horizontal line of clustered points, can we say that the limit of the sequence is A? Why?
Let {x n } and {y n } be two sequences of real numbers in such a way that $\underset{n\to \infty }{ \lim }{x}_n=X$ and $\underset{n\to \infty }{ \lim }{y}_n=Y$ where $X,Y\in \mathrm{R}.$ Is the following statement true? Why?
7	Prove the distributivity of sum of limits	$\underset{n\to \infty }{ \lim}\left({x}_n+{y}_n\right)=X+Y$
8	Prove the distributivity of scalar product of limits	$\underset{n\to \infty }{ \lim}\left(l{x}_n\right)=lX$ where $l\in \mathrm{R}$
9	Prove the distributivity of difference of limits	$\underset{n\to \infty }{ \lim}\left({x}_n-{y}_n\right)=X-Y$
10	Prove the distributivity of product of limits	$\underset{n\to \infty }{ \lim}\left({x}_n\cdot {y}_n\right)=X\cdot Y$
11	Prove the distributivity of quotient of limits	$\underset{n\to \infty }{ \lim}\left(\frac{x_n}{y_n}\right)=\frac{X}{Y}$, where Y ≠ 0