This study is based on two different, but overlapping, areas of knowledge: 3D-visualization and mathematics in compulsory school. Digital visualization has great potential as an enabler for learning and teaching. To achieve this potential, opportunities and limitations for technology and the content of the visualization must be understood. It is important to understand the interaction between information, technology and recipients (Skolforskningsinstitutet, 2017). New digital learning materials are based on different types of visual pedagogy. But what do we know about these teaching materials? Do children learn better through them? How do teachers handle these learning materials? How do teachers and students experience the work with visual pedagogy? And, which designs and theoretical frameworks have been the base for research?  

In order to be able to concretize this study within a school subject, we have chosen mathematics since students’ knowledge has declined during the last 15 years, both nationally and (OECD, 2018; Skolverket, 2017). Increasing interest in students' results in mathematic is of the highest national priority. Research on mathematics didactics has become increasingly interesting as Swedish students' results in mathematics have declined.

Previous research in 3D and school subjects  shows different results, possibly depending on the type of 3D teaching materials that are used; 3D-pictures, 3D-animations or 3D-interactive animations (Bamford, 2011; Hylén, 2013; Presmeg, 2006). Empirical studies focusing on the learning effects of 3D visualizations in school contexts are so far rare and inconsistent according to Korakakis et al. (2012). Differences in results can also depend on different software, quality of software, differences in the designer's design and chosen subject matter (Elentari, 2017). Researchers point out that the real value of new digital tools in the classroom could and should be verified through controlled evaluations (Andersson, Wiklund & Hatakka, 2016).  This problem area, including differences between girls and boys regarding results and attitudes when learning geometry, comparing traditional teaching and teaching augmented with a visual learning component, were therefore the focus of this study.

The overall purpose of the study was to explore the effect of a digital visualization learning material on learning outcomes in geometry through a quasi-experimental mixed method study. The research questions were:

a)     Does digital 3D visualizations have an impact on students’ results or attitudes when learning geometry in grades 6 and 8, and

b)     Are there gender differences in results or attitudes when using 3D visualizations when learning geometry in grades 6 and 8?

In this study, we analyzed the results using two comprehensive frameworks for the integration of technology support in learning, Substitution, Augmentation, Modification Redefinition (SAMR) (Puentedura, 2006) and Technological Pedagogical Content Knowledge (TPACK) (Koehler & Mishra, 2009). The former framework contributed with a taxonomy in the discussion of how well the technological possibilities were utilized in teaching materials and in learning activities. The latter, TPACK, can be valuable in analyzing the teachers´ didactic use of the visualization software. Above all, teachers’ technical subject competence and technical-pedagogical competence play a part in how the performance of the lessons will ultimately be, and in what way the visualizations will benefit the students. The concept of affordance becomes interesting when analyzing students' actions or behaviors that were not planned or foreseen by the teacher. The latter framework, SAMR, is useful for a discussion of the didactic issues with a focus on the role of technology. The model can primarily serve as a basis for discussion as to what the transition to digital learning resources used in schools actually entails, and to discuss the design of the learning activities in which the students have participated.

The study is based on a quasi-experimental design where students in a control and experimental group process the same knowledge area but tackle it in different ways. The students’ knowledge was tested both before and after the work in geometry. A number of statistical analyzes of the collected data material were carried out. Basic descriptive statistics for both test and attitude surveys were calculated. The test questions were analyzed using classical test theory to estimate the degree of difficulty and the ability of discrimination. The test result was analyzed for differences between different subgroups by t-test significance testing. The attitudinal questionnaire was tested for reliability using Cronbach's alpha and any differences between subgroups were significance tested using t-test. The subgroups that were compared were control and experimental groups, grades, boys and girls, as well as combinations of these subgroups. In addition, interviews were conducted with teachers. The interviews were based on themes that were about teaching, learning and the content area of the software in relation to the school's curriculum. In addition, one teacher in sixth grade collected reflections. These reflections were in a diary-like form throughout the three-week teaching period. . The qualitative data was analyzed by inductive content analysis (Mayring, 2000). In this study, an embedded mixed method design that is common in school research (Creswell, 2014) has been used. In this case, this means that qualitative data collection with both convergent and sequential elements has been combined with the overall quasi-experimental design, i.e. a parallel component in the form of diary entries and observations from teachers, and partly a follow-up part consisting of interviews with the teachers. The basic motive for using multi-method research, mixed-method, is to combine the strengths from quantitative methods with the strengths of qualitative methods and at the same time compensate for the weaknesses with each respective method (Punch & Oancea, 2014).

Concerning students' results, one of the major research questions in the study, we found no significant differences between traditional teaching and teaching with the visualization teaching material (3D). Regarding students' attitudes to geometry, the attitudes in the control group for grade 6 improved significantly, but not in grade 8. Regarding the results and attitudes of girls and boys, the girls in both grades had stronger content knowledge than the boys and in grade 6 the girls were more positive about geometry than the boys in the control group. In addition, we cannot discern any significant differences. Other important findings in the study were that the difficulty level and composition of the test were not optimal and that the time of day for test administration had a large impact on test scores. The results of the qualitative analysis point toward positive attitudes and behaviors of the students in the work on the 3D teaching material. Students' collaboration and communication improved during the lessons. Furthermore, the teachers pointed out that when using the 3D teaching material, more opportunities were given to stimulate several different senses during the learning process. One conclusion is that the 3D teaching material is an important complement in teaching, but cannot be used completely by itself. We cannot rely on 3D visualization to be superior to teaching resources for students' results or to those researchers who warn of its effects on students' cognitive overload. Our results are more in line with the conclusions of Skolforskningsinstitutet (2017), namely that teaching with digital teaching aids in mathematics can have positive effects, but equally effective teaching can possibly be designed in other ways. However, the results in our study point toward a number of disturbances that may have affected possible results and the need for appropriate technology and well-developed software.

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