Scaffolding small groups’ mathematics learning
Sharon Calor |
Scaffolding small groups’ mathematics learning, thesis
UvA, 10 april 2024, 14:00 S. M. Calor. (2024). Scaffolding small groups’ mathematics learning (PDF), FacultyFaculty of Social and Behavioural Sciences (FMG) (pp. 198). Amsterdam: University of Amsterdam. |
Abstract
This dissertation addresses how teachers can guide student collaboration in mathematics. Group discussions in mathematics contribute to student learning. However, when groups get stuck, some kind of content help is needed to get the discussion back on track. Teachers tend to find supporting these small groups difficult. Consequently, this dissertation aimed to develop and test a tool designed to help teachers provide scaffolding on the level of the group, i.e., adapt their support according to group needs. The main research question was the following: What is the effect of small-group scaffolding on the quality of mathematical discussions, and does it raise the mathematical knowledge level of students in seventh-grade early algebra classes? The first study focused on designing early algebra lessons to evoke mathematical discussions. Subsequently, a small-group scaffolding tool (SGS-Tool) was developed in the second study. In particular, this SGS-Tool assists teachers in deciding whether to give content support (when a group gets stuck) or process support, i.e., stimulating the group to continue the discussion among themselves. The effectiveness of this tool was tested in a quasi-experimental design. The results showed that the use of the SGS-Tool improved the teachers’ group scaffolding. Finally, another quasi-experimental study evaluated the effect of small-group scaffolding at the group level. The results revealed that small-group scaffolding not only improved the quality of mathematical discussions but also enhanced students’ mathematical knowledge. This dissertation demonstrates that the SGS-Tool is a powerful tool that can help teachers effectively scaffold student groups at the group level.
Research question
What is the effect of small-group scaffolding on the quality of mathematical discussions, and does it raise the mathematical knowledge level of students in seventh grade early algebra classes?
Method
Four four quasi-experimental studies were conducted in three phases. The first phase (study 1, chapter 2) was a preparatory phase in which we investigated the effect of shift-problem lessons (lessons that invite student groups to discuss a mathematical problem) for seventh-grade early algebra. The aim was to develop qualitatively good shiftproblem lessons that could be used in the subsequent phases of this research. In the second phase (study 2, chapter 3), we developed a tool for small-group scaffolding (SGS-Tool) and investigated whether teachers were able to apply this tool and whether teachers’ small-group scaffolding behavior improved. In the final phase, we investigated the effect of small-group scaffolding, i.e., teachers applying the SGS-Tool, on the quality of mathematical discussions (study 3, chapter 4) and the mathematical knowledge of students (study 4, chapter 5) and determined whether the quality of mathematical discussions mediated the effect of smallgroup scaffolding on the mathematical knowledge of students (study 4, chapter 5).
Conclusions
Study 1 – Shift-problem lessons elicited more and qualitatively better mathematical discussions in seventh grade but that applying shift-problem lessons may be a necessary but not sufficient condition to improve mathematical level raising.
Study 2 & 3 – We concluded that the SGS-Tool helped teachers support small groups that discussed mathematics, offered teachers support regarding whether content or process support was appropriate and helped them return responsibility for learning to the group when a group could continue their discussion independently.
We concluded that guiding seventh-grade students with the SGS-Tool elicited qualitatively better mathematical discussions.
Study 4 – The conclusion was that small-group scaffolding positively affected students’ mathematical knowledge level and the quality of discussions. However, the quality of mathematical discussions did not play a mediating role.
Our main research question is answered as follows: This research showed that smallgroup scaffolding improves the quality of mathematical discussions and enhances the mathematical knowledge levels of students.
Abstract (een van de deelstudies, 2021)
| Background | Supporting students during collabora- tive learning in mathematics is challenging for tea- chers. We developed the Small-Group Scaffolding Tool (SGS-Tool) to assist teachers regarding how and when to offer support. The tool is based on three characteristics of scaffolding small groups at the group level: contingency to the group, phasing out content support when the group can continue inde- pendently, and transferring responsibility for learning to the group. |
| Method |
We investigated whether the scaffolding behavior of teachers using the SGS-Tool was more adapted to the group level than that of teachers not using the tool. Participants were four teachers and their seventh grade classes. The topic was Early Algebra. We analyzed teachers’ scaffolding behavior with one group during five lessons. Findings: The SGS-Tool offered teachers support when the groups discussed mathematics, but adapta- tions of the tool are needed. Overall, the SGS-Tool seems to be a promising tool for supporting mathe- matics teachers in scaffolding groups at the group level. |
| Contribution | Our study provides insight into what scaffolding small groups at the group level entails and how teachers can apply it. |
Verwijzingen
- S. M. Calor. (2024). Scaffolding small groups’ mathematics learning (PDF), FacultyFaculty of Social and Behavioural Sciences (FMG) (pp. 198). Amsterdam: University of Amsterdam.
- Calor, S. M., Dekker, R., van Drie, J. P., & Volman, M. L. L. (2022). Scaffolding small groups at the group level: Improving the scaffolding behavior of mathematics teachers during mathematical discussions. Journal of the Learning Sciences, 31(3), 369–407. https://doi.or g/10.1080/10508406.2021.2024834
- S. Calor, R. Dekker, J. P. Van Drie and M. L. L. Volman. (2021). Scaffolding small groups at the group level: Improving the scaffolding behavior of mathematics teachers during mathematical discussions (PDF) Journal of the Learning Sciences, 2022(1-39) doi:10.1080/10508406.2021.2024834.
- Calor, S. M., Dekker, R., van Drie, J. P., Zijlstra, B. J. H., & Volman, M. L. L. (2020). “Let us discuss math”; Effects of shift‐problem lessons on mathematical discussions and level raising in early algebra. Mathematics Education Research Journal, 32(4), 743–763. https:// doi.org/10.1007/s13394-019-00278-x
- Webinar van Sharon Calor uit 2022
- Scaffolding
