Date of Award
5-1-2018
Degree Name
Doctor of Philosophy
Department
Curriculum and Instruction
First Advisor
Becker, Jerry
Abstract
The purpose of this research is to explore preservice teachers’ attitudes and beliefs towards mathematics, mental and written computations, and mental computation anxiety, to investigate their use of different mental computation strategies using different approaches (i.e., Direct Teaching (DT) and Open-Approach (OA)) among the three different groups, and to identify how the use of preservice teachers’ mental computation strategies affects their flexibility regarding mental computation. The participants were preservice teachers (PTS). Three classes were used for this study: two classes in a mathematics class (Course A) for experimental groups and one class for the control group. One class from professional education courses was selected. A mixed methods design was used, more specifically, the Mathematics Attitude Survey (MAS) was administrated before and after intervention to examine PTS’ attitudes towards mathematics, mental and written computation, and mental computation anxiety. In addition, to determine whether there is any statistically significant difference among the three groups, the one-way analysis of variance (ANOVA) was used. Then, the MAS was analyzed descriptively. Next, a pre-and post-Mental Computation Test (MCT) was given to investigate PTS’ mental computation knowledge in relation to whole numbers, integers, and rational numbers (i.e., fractions, decimals, and percentages). A one-way analysis of covariance (ANCOVA) was conducted to determine if there were significant differences in mental computation performance among the three groups (i.e., DT, OA, and Control) with different instructions. Further, before and after intervention, face-to-face interviews were given to both the experimental and control groups to identify how they arrived at their answers. During interviews, 38 interviewees in the pre-interviews and 36 in the post-interviews for all groups participated. The interview items were selected from the pre-and post-MCT problems. Three levels of problems (i.e., high, medium, and low difficulty) for each operation were selected. The results of the MAS showed that with respect to the attitudes towards mathematics, PTS were generally shown positive attitudes towards learning mathematics and were aware of the importance of learning mathematics; however, in reality, about half of them did not want to spend time on learning or studying mathematics. In terms of PTS’ attitudes towards mental and written computation, PTS were aware that learning mental computation is more useful in real life situations and provides benefits in their mathematics learning. However, they do not feel comfortable and safe when using mental computation because of their lack of confidence and teaching abilities. For the mental computation, PTS showed slightly higher anxiety levels from pre-to post-tests. The findings of Mental Computation Test (MCT) revealed that there was a statistically significant difference in post-MCT scores between the different instructional groups when adjusted for pre-MCT scores. In particular, PTS using Open-Approach (OA) performed better than the PTS in the group using Direct Teaching (DT). The PTS in the control group performed worst. Significant differences between pre-and post-MCT performance were found among the three groups in solving multiplication, fraction, and decimal operations. The results of interviews suggest that there was an association between each interviewee’s quintile level and their flexibility in the use of the mental computation strategies. Regarding the whole number operation strategies, the results revealed that the interviewees in the middle and upper quintiles in both DT and OA used more than two different strategies with higher accuracy and were more likely to use the strategies. Interviewees in the middle and upper quintiles for the DT and OA groups were more likely to use the strategies that reflect efficient number facts or number-sense (e.g., Adding by place, Decomposing, & Compensation). The mental image of the Traditional method was frequently observed in the OA group. In contrast, for the lower quintiles, alternative strategies were not provided for both groups. The interviewees in the control group offered the smallest range of strategies. For the integer and rational operations, the interviewees in the DT group showed strategies that focused more on conceptual understanding. Surprisingly, the interviewees in the OA group were more likely to apply teacher-taught methods, including the Traditional method. The control group was not able to provide any alternative strategies. Plans for future research are set forth to add to the body of knowledge that exists regarding mental computation.
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