Performance due to Tasks and Boxes

The performance scores were dependent on the problem (Section 5.5.2, p.144).

Students performed well in Problem 2, which was an application problem. The scores

for the other application problem (Problem 1) and abstract problem (Problem 3) were

lower than that of Problem 2. Students may perform better in the application problems;

however, the experimental design did not allow an exhaustive look at the abstract and

application problems. Further, it was found that whilst mathematics confidence did not

influence how students performed in Problem 2, it did influence the performance in

Problems 1 and 3, where students with higher mathematics confidence were more likely

to do better. Therefore, students with higher mathematics confidence should mostly

perform better than lower mathematics confidence students as expected but there may

be problem types where mathematics confidence may not always influence

Performance was also found to be associated with tasks (Section 5.5.2, p.144).

The scores obtained for the interpretive and constructive tasks corroborated the

prediction and results of Galbraith and Haines (2000a) that students performed better in

interpretive tasks than constructive tasks. The study by Galbraith and Haines was based

on students solving these two task types with pen and paper. In the current study where

there is a technology-enabled environment, students performed better in the interpretive

tasks than in the constructive tasks. Although students had access to technology to solve

the procedural part of the constructive task, this did not provide any advantage to the

students, possibly as knowing what to do with the software box rather than being able to

use the software box played an important role in the performance of the constructive

task.

A comparison of scores obtained by Galbraith and Haines for their

undergraduate students solving tasks in polynomial algebra showed that their students

scored 37% less in the constructive task than in the interpretive task. In the present

study, the students performed even worse as they scored 60% less in the constructive

task than the interpretive task. This probably is because the two studies were in two

different mathematical domains or possibly because Galbraith and Haines used more

tasks (6 each).

The scores obtained for the interpretive and constructive tasks also varied with

Problem, where students performed better in the interpretive tasks for Problems 2 and 3.

The suggested reason for this was because the answers for these two interpretive tasks

had to be deduced from previously calculated values and these required interpreting or

reading off the variables carefully. For the constructive tasks, students all performed

significantly different on each problem, performing best on Problem 2’s constructive

problem type for the constructive task, with the students performing better on the

applications problems than the abstract problem.

Task types were also found to be affected by mathematics confidence with

students who had higher mathematics confidence performing better in the interpretive

tasks, whilst performing equally well in the constructive task regardless of mathematics

confidence. This probably meant that since interpretive tasks required conceptual

understanding that these students with higher mathematics confidence compared to

lower mathematics confidence students were more likely to make connections between

the answers ascertained from the mechanical task and then deduce what they meant,

such as in the cases of Problems 2 and 3.

It was interesting that the students regardless of mathematics confidence

performed the same in the constructive task, as this required finding relationships

between procedural and conceptual knowledge and then applying them together. It was

expected that the higher mathematics confidence students were probably more poised to

do these tasks since they had a higher likelihood of undertaking a deep processing level

and connecting their procedural and conceptual knowledge.

Now, looking at the first research question, that is:

Does the students' performance in solving the three task types depend upon the

software box they have access to?

What has been noted was that performance was dependent on task type but this

was already known from Galbraith and Haines. Now, was performance on the tasks

influenced by the software boxes? A cautionary yes is put forward. Performance on

either the interpretive or the constructive tasks was not significantly dependent on the

software boxes, although the difference in performance scores between the interpretive

dependent on the software boxes (Section 5.5.2, p.144). In particular, students using the

black-box software had the smallest disparity in their scores compared to the students

using the glass and open-box software. Further, marginal significance showed that

students using the glass-box software were doing better in the interpretive tasks than

those students in the black-box. Although there was no statistical significance, graphical

trends indicated that students using the black-box were performing best in the

constructive task. This suggested that for the constructive tasks, students using the

black-box software were more likely to grasp the conceptual-procedural knowledge

connection required for solving constructive tasks and perhaps the black-box software

influenced the ease in which the students were able to make this connection.