Summary in English
Two quantitative surveys and 12 qualitative case studies will be conducted in the research project ARK&APP (2013–2015). The present study is the first of three case studies in mathematics. Three research questions guide this case study:
- How are educational resources used in teaching practices
- How do educational resources foster engagement and learning among students?
- How do various educational resources function in interactions between students and teachers?
In this case study, we follow a teacher and a group of 75 students in lower secondary school (13 year olds) who work with various educational resources in algebra. Students were divided into two classes where they had identical instruction by their teacher before 37 students worked with Kikora on computers, while 38 students worked with DragonBox on iPads. Kikora is a digital learning resource in mathematics available through the school's digital learning platform. It presents algebra in a similar way to mathematical textbooks. DragonBox is an award-winning app for iPad that enables students to play with designed symbols and mechanisms that represent arithmetic operations in algebra. All students received the same instruction by the same teacher, thus the difference in working with algebra was in the use of Kikora and DragonBox.
The students were observed for a total of 9 school periods (480 minutes in total) over two weeks. The data in this case study consisted of pre-and post-tests for identifying variations in students' learning outcomes, videotapes of various forms of classroom interaction and engagement, and interviews with selected students and their teacher. With this setup, we were able to distinguish the impacts of the two different digital learning resources on engagement and learning outcomes, as well as explore the variations in interaction between students, and between the teacher and the students.
The results of the case study show varied use of educational resources and teaching methods. The textbook is the main structuring resource when teaching, but the teacher also makes use of various digital learning resources organized by his teacher team. The two dominant forms of work in the case study were whole-class interaction and group work. More than half of the time was used for group work with Kikora and DragonBox. On the one hand, we observed that teachers and students experienced DragonBox as being far more engaging than Kikora. It is rare to find that all students remained focused throughout a school period, as they were when they used DragonBox. On the other hand, in terms of learning outcomes, the analysis of pre-and post-tests shows that the students who used Kikora performed much better than those using DragonBox. The qualitative analysis in this case study indicates that the reason that students who used Kikora performed better than those using DragonBox is that the latter deprives students and teachers of a standard language for problem solving in mathematics. In situations using DragonBox where students need help, it is difficult for students and teachers to make use of established practices in mathematics, because DragonBox's symbols and mechanisms do not transfer easily to notebooks or whiteboards. In contrast, Kikora uses a standardized mathematical language and formal methods that give the teacher a larger repertoire when he helps students who are stuck when solving algebra problems.
The implication of this case study is that it is demanding to introduce new symbolic representations and operations that break with the established practices that the students encounter in textbooks and tests. Although the change to new symbolic representations and operations may be engaging, it may be at the expense of students' opportunities to practice a formal mathematical language and their understanding of mathematical concepts and methods.