Comics in teaching mathematics: A design experiment
Toh Tin Lam
National Institute of Education, Nanyang Technological University, Singapore
Abstract. Education theories and practices have pointed to the advantages of teaching academic subjects through lessons that use comics for instruction. This lecture shares the author’s experience in a series of research projects carried out in Singapore schools on using comics for instructions for mathematics lessons for low progress learners in Singapore schools. The research uses design experiment as the backbone of the development phase of the research projects. We test the theory on the use of comics for mathematics instruction, conceptualizes a design to test the theory and implement it in the authentic school context. Based on the findings on the research phase, the design was fine-tuned to further address the shortcomings of the initial design and perform a second iteration of the implementation. The lecture will present details of both the development and research phases, and implications of the research findings will be discussed.
Using design-based research to promote interdisciplinary secondary mathematics and science teaching through real-world tasks: A cross-national study in Australia and Indonesia
Wanty Widjaja https://orcid.org/0000-0002-7288-6088
Abstract. There is a pressing need to find ways for adopting an integrative approach in teaching science and mathematics. The central argument for adopting this approach in teaching science and mathematics is motivated by the intention to enable students to see and make links between mathematics and science and engage them in meaningful and deeper learning. The use of real-world tasks, modelling and representation construction are central to this approach. However, different structures, history and pedagogical traditions, and lack of common language between science and mathematics in science and mathematics proved to create barriers for teachers to cross the boundaries between the two disciplines. Using design-based research (DBR) methodology, this study designed learning environments where teachers from both disciplines work together to design real-world tasks that meaningfully engage and challenge students to use skills from both conceptual areas. Video data of science and mathematics lessons and interview data with teachers from the two countries will be discussed. The findings indicated the importance of engaging teachers first-hand with ways to connect real-world tasks to their understanding of the disciplines. It is vital to provide opportunities for science and mathematics teachers with time to plan collaboratively with a pedagogical approach that allows for individual disciplines to be integrated.
About the D in Sea-DR
Freudenthal Institute for Science and Mathematics Education, Utrecht University, Utrecht, The Netherlands
Abstract. Mathematics investigations are challenging for students, teachers, and researchers. That is good; no one likes boring tasks, and doing mathematics should surely be exciting. As bare problems and word problems are not really supporting the growth and development of children, we will need to design great math investigations that fit the situation of the students in our class and that support their ongoing development. In my talk, I will discuss the characteristics of a good investigation and I will show examples of good investigations and of students and teachers at work.
Teachers’ mathematics content knowledge about the meaning of fractions
Department of Mathematics Education, Faculty of Teacher Training and Education, Sanata Dharma University
Abstract. In Indonesia, there are currently two Teacher Professional Program (TPP), namely in-service paths for teachers and pre-service pathways for undergraduate program graduates who want to become teachers. The aims of this study were (1) to design a hypothetical learning trajectory (HLT) of a workshop using the realistic mathematics education (RME) approach for junior high school mathematics teachers who take part in in-service TPP to help them to understand the fraction meaning and represent the fraction meaning and (2 to describe their understanding about the fraction meanings and their fraction meanings representation. The type of research was the Cobb and Gravemeijer models design research. The research subjects were 29 junior high school mathematics teachers who took part in in-service TPP in 2019. The methods of data collection were to make field notes and tests Data analysis followed three stages of qualitative research data analysis. After the teacher participated in the workshop, the conditions of the teachers were as follows: (1) there were five meanings and representations of 3/5 that the teacher was able to make correctly, and (2) 51.72% the teacher was able to explain two meanings of 3/5 and represent meaning correctly.
Task sequence theories for curriculum design to develop mathematical thinking
CRICED, University of Tsukuba, Japan
Abstract. This lecture explains the task sequence for designing mathematics curriculum and textbook. Freudenthal, H (1973) proposed mathematization under the reinvention principle against set and axiom manner on New Math. He explained mathematization by the reorganization of mathematical experience and as for curriculum design he extended van Hiele levels to explain mathematization and he explained that it is not the same as the horizontal and vertical mathematizations (Treffers, 1987; Freudenthal, 1991) which are the background of the model of situation and the model for form on the RME theory, a theory for the task sequence by Freudenthal Institute. Japanese emended Mathematization into the textbook since 1943 and currently called it by the Extension and Integration Principle since 1968. Isoda, M. proposed two design theories for task sequence under Freudenthal’s mathematization and Japanese principle which is no contradict with Freudenthal’s mathematization and RME theory. First theory is the representation theory (1990) which explains a long term sequence. Second theory is the conceptual and procedural knowledge theory (1992) which explains a short term sequence. On the lecture, those two theories are explained by using the Bahasa Indonesia edition of Japanese textbooks which will be published from the ministry of education, Indonesia.