Summary in English
Within the frame of the research project ARK&APP (2013–2015) two quantitative surveys and 12 qualitative case studies are conducted. The present case study is the third of three case studies in Mathematics, and the 11th of 12 case studies in total. Three research questions have guided the study:
- How are educational resources used in teaching practices?
- What role do various educational resources play in interactions between students and their teacher?
- How do educational resources foster engagement and learning among students?
The study here presented was conducted in December 2014 in a Norwegian primary school. Our researchers observed one teacher and one group of 23 5th grade students (11 boys and 12 girls) in all of their Mathematics lessons for three consecutive weeks. The topic was Algebra.
The data collected includes pre- and post-tests evaluating student learning outcome, observations and video recordings of various forms of classroom interactions as well as interviews with focus group students and their teacher. The textbook used, Matemagisk published byAschehoug publishing house, was the main teaching resource throughout the three weeks of observed teaching. The students spent considerable time working individually with textbook tasks. The textbook’s digital resource for interactive whiteboards, gave basis for exploratory conversations in full-group teaching. Algebra computer games were introduced as means to create methodical variation In particular, our analysis focus on 1) the use of digital educational resources on an interactive whiteboard, and the role of these resources in interactions between students and teacher in full-group conversations, and 2) the use of two different algebra computer games (“Symbolenes Verden” from Salaby and “Bike Racing Math Algebra Game” from Math Nook), and the role these games played in the interaction between students collaborating in pairs. We have used Kilpatrick, Swafford, & Findell’s (2001) model for mathematical proficiency as framework for the analysis. Mathematical proficiency has five strands (conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition) that are interwoven and interdependent in the development of proficiency in mathematics.
In our study, the observed teacher facilitated students’ conceptual learning by creating a safe environment for full-group conversations where students were encouraged to explain, to ask questions, and also given some time to ponder. Furthermore, we observed that the full-group conversations were centred on visual representations projected onto an interactive whiteboard, which the students found engaging. Last, but not least, the teacher had an explicit focus on central concepts in algebra, such as variable and equivalence, and most of the visual representations, as well as the discussions, were related to these concepts. The teacher promoted a deeper and more connected understanding of algebra, making algebraic manipulations more meaningful.
The two algebra computer games used in the case clearly created enthusiasm among the students, and the alternative representations stimulated curiosity as well as engagement in the activity. The students collaborated closely when working together in pairs on the computer. In the motorbike-game from Math Nook, the students practiced procedural skills, first and foremost procedures they were already familiar with. An element of competition and time pressure left no opportunities for reasoning or discussing alternative solutions. In the Salaby-game, however, mathematical reasoning was a central element. Our data suggest that the alternative representations combined with the interactive possibilities gave the students opportunities for a deeper conceptual understanding of variables, and for structures and procedures where those variables are included.
The students performed significantly better on the post-test than they did on the pre-test. Since most of the test-items emphasised conceptual understanding, we can assume that important learning has occurred during the three weeks of observed algebra teaching. This case illuminates how central elements of mathematical proficiency – conceptual understanding, adaptive reasoning, procedural fluency and productive disposition – can be practiced by using different teaching methods and educational resources, hence providing insights into how algebra in school can become a more meaningful activity than what has been documented as traditional practice.