Aspectos generales

During this study, lessons were conducted in the second-grade classrooms and a computer lab. There were 25 computers in the computer lab, as well as a teacher computer station with a display screen. Every student had their own computer and worked independently in the lab.

The addition pre-test was administered in one day for all three classes. The subtraction pre-test was administered the following day. The lessons for the TCT group started with an introduction to the numeracy topic for the day; this was followed by several mathematical tasks where students used paper and a pencil. Students completed worksheets and teacher-made task sheets that provided practice with the physical manipulatives. At the end of each computer lab and classroom session, the teacher used the last 10 minutes of the class to hold a discussion with the students to elicit thinking and connect ideas that students explored during the sessions.

After these two days, the teacher started a new lesson concept each day followed by a practice exercise. The teacher taught the lesson in each class at their scheduled times. Each assigned class was taught with the use of one treatment application (i.e., VRM, 3DM or TCT).

The teacher explained new concepts on Day 1 and Day 3. On Days 2 and 4, the teacher gave the students' numeracy problems to solve to confirm their understanding. The days (2 and 4) were either spent in the computer lab for Classes A and B or in the classroom for Class C.

The computer lab sessions started with an introduction to the virtual manipulative (VRM or 3DM); this was followed by several mathematical tasks for the students to complete independently. Each day, students received teacher-made task sheets with instructions for using the virtual manipulatives and space to record their work. The teacher modelled how to use the virtual manipulative applets before students worked independently.

Classroom Instructional Settings

The conversational framework by Laurillard (2002) can be used to explain how an active conversation between teachers and students may support student mathematical learning in math classrooms. From this perspective, we based our design of the classroom setting on Laurillard’s conceptual level of actions (Figure ‎4.9). The teacher

helped the students to build their mathematical numeracy knowledge of the concepts through the processes of iterative negotiation.

The class started with the teacher greeting the students and asking them to open their books to that day’s lesson about an addition or subtraction. Similarly, in all classes,

the teacher projected the same page on the screen or board in front of the class. The classroom setting was the same for all groups (Figure ‎4.10). The researcher was present with the teacher in the class at all times to observe without interference.

After introducing the new concept on the screen or board, the teacher solved the examples in each class according to the class-assigned treatment; Class A used the MAVLE application, Class B used the NLVM application and Class C used the paper and pencil method.

Computer-Lab Instructional Settings

Laurillard’s (2002) conversational framework viewed the learning process as a

conversation between the teacher and student. From this perspective, we based the design of the computer lab setting on Laurillard’s experiential level of actions

(Figure ‎4.11). At this level, the teacher sets out practices for the students to improve their understanding of the concepts.

Figure ‎4.11 Laurillard’s ‘Experiential’ level of actions

Class A went to the computer lab with their teacher and the researcher. Each student sat at a desktop computer station and started applying the concepts learned during class at their own pace, with the opportunity to manipulate the exercises freely. The lab setting (Figure 4.12) was the same for the VRM and 3DM groups.

Figure ‎4.12 The computer lab setting

After the teacher explained and solved one example on the computer lab screen, the teacher asked the students to start solving more exercises by themselves to elicit their understanding of the concepts using the assigned treatment (VRM or 3DM) while doing so. The teacher moved around the class to observe the students’ performances.

The same sequence took place with Class B in the computer lab at their scheduled class time.

4.3.4 Data Collection

Data sources included pre- and post-tests used to examine student addition and subtraction content knowledge. The pre- and post-tests had eight questions for both addition and subtraction (Appendices D and E). Table 4.2 provides a list of all the numeracy concepts measured by the pre- and post-tests. Three subject matter specialists

These three subject matter specialists were math teachers in Jeddah—the location of the study. Comments from the subject matter specialists were taken into consideration before the tests were used.

Both pre and post-tests were similar in content. The total grade was out of 28 for each test. Grading systems for each question on the pre- and post-tests were as follows for both addition and subtraction:

 One mark was given for each correct answer in addition or subtraction for any digit (1’s, 10’s and 100’s) and zero for each incorrect answer.

 One mark was given for each correct answer in regrouping concepts (i.e., carry and borrow) and zero for each incorrect answer.

4.3.5 Data Analysis Plan

This section describes the various statistical tests used to analyze and test data. Each research hypothesis were investigated using the collected data for both addition and subtraction numeracy concepts. SPSS Version 17 and Excel 2007 were used to run the statistical tests, which included a paired sample t-test data analysis procedure to determine whether any of the groups (VRM, 3DM and TCT) demonstrated significant improvement from the pre-test to the post-test. An ANOVA was performed on the addition post-tests and the subtraction post-tests to look at the differences in test scores among groups.

The effect size was used to tell if the effect to be tested was weak or strong (Cohen, 1988). The effect size of an ANOVA-type model test is known as partial eta squared (i.e., η2). When the η2 is: 0.1 it assumes that the effect size is small, 0.25 it

assumes that the effect size is moderate and 0.4 it assumes that the effect size is strong. The paired sample t-test data analysis procedure was performed to determine whether any of the groups demonstrated significant improvements from the pre-test to the post- test.

Furthermore, to determine whether significant differences existed among the groups on post-test performance, an analysis of covariance (ANCOVA) was performed with the groups serving as the principal independent variable and the post-test score as the dependent variable; the pre-test score was the covariate. When subjects are randomly assigned to treatment groups and the experimental design includes pre- and post-tests (Schochet, 2008), the ANCOVA are the ideal method for adjusting for possible extraneous variables.

CHAPTER 5 Data Analysis Results

In this chapter, data analysis results are reported separately for the two studies. For each study, the quantitative analysis results, for which data were collected, are reported.

5.1 Study 1: The Impact of Virtual Reality Manipulatives on Student

Performance in Numeracy Concepts

This study examined the delivery of numeracy activities for addition and subtraction, using VRM and 3DM in the computer lab. A comparison was made for the accomplished activities of addition and subtraction and the encountered errors in the place-value and regrouping concepts. The goals of the study were to determine the impact of virtual reality on student performance in numeracy concepts (addition and subtraction) and which manipulatives format, VRM or 3DM, had the greatest effect on student achievement performance and children's behaviours. In this study, data were obtained using a screen-capturing software (CamStudio) that recorded all on-screen interactions performed by each student who used their keyboard and mouse. Data were analysed using descriptive summaries and tests to determine the significant differences among groups, correlations and regression models.

The study specifically attempted to investigate the following research hypotheses:

 The VRM group is predicted to have a significant positive performance outcome (i.e., regarding the number of solving problems for addition and subtraction) than those in the 3DM group.

 The number of errors in place-value concept predicted to be significantly different between VRM group and 3DM group.

 The number of errors in the regrouping concept is predicted to be significantly different between the VRM and 3DM groups.

 The number of errors in the concept of regrouping positively correlates with the number of errors in the concept of place value.

 In the VRM group, a greater number of solving problems correlates with a high level of virtual reality navigation behaviour.