Information was obtained through various instruments such as questionnaires, tests, classroom observations, journals and informal interviews.
3.4.1 Questionnaires
The same questionnaire was given to both the control and experimental groups before and after intervention. It consisted of seventeen questions that were divided into four sections.
(See appendix C).
Section A: Consisted of two fill in questions about gender and age of learners.
Sections B and C: Consisted of multiple- choice questions about learners’ attitudes to mathematics in general and problem solving (word problems) in particular.
Learners chose responses from the following five options:
(a) False (b) Partially false (c) Don’t know (d) Partially true (e) True
Section D: This section consisted of an open-ended question. Learners were given one mathematical problem stated in both numerical form and in words. They were required to say, with reasons, which of the two problems they enjoyed solving. This question was posed to determine learners’ attitudes towards word problems.
3.4.2 Pre- and Post-tests
The pre-test was given to both groups before the intervention. It consisted of eight contextual problems. The questions were taken from different sources, such as,
articles, books and Olympiads. Some of the questions were taken directly from the sources, whilst others were modified. The problems used were chosen for the following reasons:
They were non-routine
They can be solved through a variety of strategies
They were challenging yet of reasonable difficulty (mathematics required in solving them was within their syllabus).
The pre-test was given to learners on the first week of February 2005. It was written during study time at school. The researcher marked it manually using the rubric shown in Table 1.
The post-test was given to both the experimental and control groups after the intervention. The questions in the post-test were very similar to those in the pre-test. This test was administered during one study period on the third week of March 2005. Just like the pre-test, it was also marked manually with the same rubric that was used for the pre-test.
The rubric was used to assess the learners’ achievement. The rubric enabled the researcher to quantify the problem solving processes of the learners. In using the rubric, the emphasis was placed not only on the correct answer, but also on the understanding of the problem and the solution processes that learners used to solve the problems. The rubric catered for the different strategies that learners used. By using this rubric every effort that the learner has put in trying to solve the problem is recognized. For the above reasons, it was considered appropriate for assessing problem solving.
Number of
points Observed characteristics of the student’s solution
0
• Blank paper
• Numbers from problem recopied-no understanding of problem evidenced
• Incorrect answer and no work shown
1 • Inappropriate strategy shown-Problem not shown • Approach unsuccessful-different approach not tried • Attempt failed to reach a sub goal
2
• Inappropriate strategy-but showed some understanding of the problem
• Appropriate strategy used-did not find the solution or reach a sub goal but did not finish the problem
• Correct answer and no work shown 3
• Appropriate strategy but
o -ignored a condition in the problem o -incorrect answer for no apparent reason o -thinking process unclear
4 • Appropriate strategy or strategies • Work reflects understanding of the problem
• Incorrect answer due to a copying or computational error 5 • Appropriate strategy or strategies • Work reflects understanding of the problem
• Correct answer
Table 1 Rubric for marking problem solving tests
In both tests learners were expected to write answers in the spaces provided in their question papers. Learners were strongly requested not to write answers only but to show all the working details that led to their answers. They were also advised to use the sheets of paper provided where the spaces were not enough. Those sheets were then stapled to their answers.
3.4.3 Classroom observations
The learners were observed daily as they solved the problems. The observations were recorded as comments on how the learners were progressing during problem solving and these comments / observations were then reviewed after every lesson. The observations assisted the researcher to identify areas that needed improvements before the next lesson. They also indicated learners’ progress on a daily basis.
Classrooms observations concentrated on the following areas: What learners do first when confronted with a problem. Whether appropriate strategies are used.
What learners do when the chosen strategy fails.
Whether learners in a group are free to express their opinions during discussions.
Whether learners were able to explain their solutions to each other in the group and the whole class.
What learners do after they have solved the problem.
In order to gain as much information as possible during observations, the researcher had to move around and interview (informally) learners as they solved problems. From these informal interviews the researcher wanted to detect the thinking processes of learners during problem solving. Learners’ responses during the interview were also recorded.
3.4.4 Learners’ journals
Learners were advised to use the back of their exercise books as journals. They were requested to record their feelings about the lessons, difficulties encountered as well as their progress as often as they can. They were also free to note down questions they would like to ask in the next lesson. Although the researcher could have used some of the information from these journals for her research, these were mainly for learners’ benefit.