Visual Representation Usage Level (VRUL) 1 Description of VRUL

The VRUL (Appendix B) consisted of two sections. The first, Section A: The General Information about Respondent, required students to complete their demographic data: gender, race, major, and the grades that they had obtained for the Mathematics and Additional Mathematics at the SPM level. The distribution of students and their demographic data are as displayed in Table 3.1.

In the second section, Section B: The Visual Representation Usage Level, the students were asked for their views on the use of graphs and diagrams in their daily learning of mathematics. This section is used to address research question 2(i). The instrument consists of 17-Likert scale items that fall under four different constructs :

1) five items on the students’ usage levels of graphs or diagrams in their daily learning behaviour,

2) three items on the usefulness of graphs or diagrams in solving mathematical problems,

3) four items on the students’ difficulty in using graphs or diagrams in solving mathematical problems,

4) five items on the teacher’s behaviours in using graphs or diagrams in teaching mathematics.

In the first category of the students’ usage of graphs or diagrams in their daily learning behaviour, students were asked about their usage of graphs or diagrams and those graphs or diagrams used by their teachers and the textbooks in helping them to solve mathematical problems. An example of the items in the first category is Do you usually use graphs or diagrams in solving mathematical problems?. The second set of items in the second category on the usefulness of graphs or diagrams in solving mathematical problems sought on the students’ efficiency in using graphs or diagrams to assist them in solving mathematical word problems. An example of the items in the second category is Do you think the use of graphs or diagrams is helpful in efficiently solving mathematical word problems?.

The third category of the students’ difficulty of the use of graphs or diagrams in solving mathematical problems looked on the ease of the students to construct graphs or diagrams to help them solving mathematical word problems. An example of the items in the third category is In general, do you know how to construct graphs or diagrams for solving mathematical word problems?. Lastly, the fourth set of items of students’ view on teacher’s behaviours in using graphs or diagrams in teaching mathematics searched for the students’ views on their teachers’ usage and encouragement on the use of graphs or diagrams in solving mathematical word problems. An example of the items in the fourth category is Do your mathematics teachers use graphs or diagrams to explain how to solve mathematical word problems?.

3.4.1.2 Validity and reliability of the VRUL

For the purposes of this study, the content validity of the VRUL was defined as the extent to which the measures or scales, ‘Not at all’, ‘Slightly’, ‘Moderately’, ‘Very much’ and ‘Definitely’, accurately reflected students view on the usage level of graphs and diagrams in the teaching and learning of mathematics. In this study, five

mathematics experts, with at least six years of teaching experiences were consulted on the contexts, language and terminologies that were used in the questionnaire so that students are able to understand and respond to them correctly.

Based on their comments and feedbacks, adjustments were made to suit the students’ understanding on the terminologies. Three feedbacks and actions were taken:

1) The original instrument (permission was requested as in Appendix C) required for the students to rate each item on a five-point Likert scale, with only end points scales with labelled 1 for ‘Not at all’ and 5 for ‘Definitely’. This caused confusion to the students in estimating their answers. Therefore, specific terms of levels were assigned to the instruments. The levels are; 1 for ‘Not at all’, 2 for ‘Slightly’, 3 for ‘Moderately’, 4 for ‘Very much’ and 5 for ‘Definitely’. These were more familiar and ‘clearer’ terms to the students in ensuring that their responses are more accurate.

2) The word ‘image’ brings too vague or too broad meaning. It may take, for example, the form of maps that are very unlikely to be used in the teaching and learning of derivatives. Therefore, since the study focused on the use of graphs, the word ‘image’ in the original instruments was replaced by the word ‘graph’. 3) The two words, ‘difficulty’ and ‘troublesome’ in two of the items triggered the

same meaning to the students, and be regarded as repetitive. The items are ‘How difficult is it for you to make diagrams by yourself for solving mathematical word problems?’ and ‘How troublesome is it for you to use diagrams / graphs in solving mathematical word problems?’. As a result, one of the items, ‘How troublesome is it for you to use diagrams / graphs in solving mathematical word problems?’ was removed due to the fact that students may have the idea that it is seeking for the same concept as the other item. In addition, the word ‘difficulty’,

in the item was replaced with the word ‘easy’ so as to bring consistency on the positivity of the views in the items.

The VRUL was reported to be a reliable instrument to assess the students’ usage levels of diagrams in solving mathematical problems (Uesaka, Manalo, & Ichikawa, 2007). The adapted version of the VRUL was pilot-tested on 50 students to determine the reliability of the VRUL for this study. The students were studying the same programme and with the same education backgrounds, in terms of their academic performance, but not included as participants in the actual study. Table 3.2 shows the reliability estimates as measured by Cronbach Alpha for the overall VRUL and its four main categories. The coefficients ranged from 0.64 to 0.89 for the categories and 0.87 for the overall reliability.

Table 3.2: Reliability coefficients of the VRUL and its categories

Category Alpha Cronbach coefficients

Overall VRUL 0.87

The usage of graphs or diagrams in their daily learning behaviour.

0.74

The usefulness of graphs or diagrams in solving mathematical problems

0.81

The students’ difficulty on the use of graphs or diagrams in solving mathematical problems

0.64

The teacher’s behaviours in using graphs or diagrams in solving mathematical problems.

0.89

3.4.2 Mathematical Visuality Test (MVT)