Options
The practical worksheet : scaffolding and assessing the problem solving process
Author
Leong, Yew Wah
Supervisor
Tay, Eng Guan
Abstract
Five NIE lecturers recently introduced a new paradigm, the Mathematics Practical, where the process of problem solving was conducted through a ‘Practical Worksheet’ that was premised on a model of Polya’s four phases undergirded with elements of Schoenfeld’s framework (Toh, Quek, Leong, Dindyal & Tay, 2009). This problem solving module was pilot tested in an independent school as an enrichment module with the caveat that the module was to count as part of school assessment. This module was subsequently adopted as part of the Grade 8 mathematics curriculum of the school.
The adoption of the problem solving module by one school begs the question of whether this success could be replicated and without the caveat of it being part of school assessment. The key question for this researcher was whether the success of the Practical Worksheet in scaffolding and assessing the problem solving process could be replicated as only an enrichment module. In addition, the perceptions of the students about the Mathematics Practical were collected for consideration in subsequent reviews of the design of this paradigm.
This study was conducted in an independent school which takes in students of above average ability and the study would leverage on an enrichment module on mathematical problem solving that was conducted for a class of 27 Grade 9 students.
All the worksheets from the lessons and the final assessment were collected for marking. Three worksheets from the end of the module and the final assessment were marked by this researcher as well. End-of-module audio interviews of selected students were also conducted to seek a better understanding of their experience. In addition, pre- and post-module surveys were conducted with the students to find out if there was any change in their attitude and beliefs about mathematics.
The paired-sample t-tests performed on the results of the students in the study showed that there was improvement in the students’ scores despite the fact that the module was not part of school assessment. Chi- square tests on the students’ effective use of the Practical Worksheet showed no significant improvement from class work to final assessment but reflected a surprising finding that the students would attempt all the stages of the Practical Worksheet during a test, unlike what they did for class work.
In comparison, similar tests showed that the students from the pilot project performed better generally. This seemed to suggest that the inclusion of the module as part of school assessment has a relatively strong motivating effect on the students.
Based on the marking done by both the tutor and this researcher, the value of the inter-rater reliability of the scoring rubric of 0.770 (Cohen’s weighted kappa) reflected a good agreement among the two markers, validating the robustness of the scoring rubric.
The interviews of the selected students provided strong feedback that making the module count as part of school assessment would change the way students behave in class. However, the choice of the problems used in the Practical Worksheets and the prior mathematical knowledge of the students were found to be important considerations as well in the design of the module.
The data from the pre- and post- module surveys showed that there was no change in the students’ beliefs about mathematics although the consistently larger variance of their scores observed seemed to point to the students becoming less ‘naïve’ and more aware when filling in the survey after attending the module.
The findings from this study reiterated the significant effect of assessment on the students’ motivation with regards to their learning but the encouraging fact is that there was still significant improvement in the performance of the students despite the lack of this motivating factor of assessment.
The adoption of the problem solving module by one school begs the question of whether this success could be replicated and without the caveat of it being part of school assessment. The key question for this researcher was whether the success of the Practical Worksheet in scaffolding and assessing the problem solving process could be replicated as only an enrichment module. In addition, the perceptions of the students about the Mathematics Practical were collected for consideration in subsequent reviews of the design of this paradigm.
This study was conducted in an independent school which takes in students of above average ability and the study would leverage on an enrichment module on mathematical problem solving that was conducted for a class of 27 Grade 9 students.
All the worksheets from the lessons and the final assessment were collected for marking. Three worksheets from the end of the module and the final assessment were marked by this researcher as well. End-of-module audio interviews of selected students were also conducted to seek a better understanding of their experience. In addition, pre- and post-module surveys were conducted with the students to find out if there was any change in their attitude and beliefs about mathematics.
The paired-sample t-tests performed on the results of the students in the study showed that there was improvement in the students’ scores despite the fact that the module was not part of school assessment. Chi- square tests on the students’ effective use of the Practical Worksheet showed no significant improvement from class work to final assessment but reflected a surprising finding that the students would attempt all the stages of the Practical Worksheet during a test, unlike what they did for class work.
In comparison, similar tests showed that the students from the pilot project performed better generally. This seemed to suggest that the inclusion of the module as part of school assessment has a relatively strong motivating effect on the students.
Based on the marking done by both the tutor and this researcher, the value of the inter-rater reliability of the scoring rubric of 0.770 (Cohen’s weighted kappa) reflected a good agreement among the two markers, validating the robustness of the scoring rubric.
The interviews of the selected students provided strong feedback that making the module count as part of school assessment would change the way students behave in class. However, the choice of the problems used in the Practical Worksheets and the prior mathematical knowledge of the students were found to be important considerations as well in the design of the module.
The data from the pre- and post- module surveys showed that there was no change in the students’ beliefs about mathematics although the consistently larger variance of their scores observed seemed to point to the students becoming less ‘naïve’ and more aware when filling in the survey after attending the module.
The findings from this study reiterated the significant effect of assessment on the students’ motivation with regards to their learning but the encouraging fact is that there was still significant improvement in the performance of the students despite the lack of this motivating factor of assessment.
Date Issued
2012
Call Number
QA63 Leo
Date Submitted
2012