- Professor Jill Adler: Revisiting resources as a theme in mathematics education
- Professor Jinfa Cai: Mathematical Problem Posing, Curriculum Development, and Professional Learning
- Professor Birgit Pepin: Mathematics (E-)Textbooks: Help or Hindrance for Innovation?
- Professor Susanne Prediger: Enhancing and understanding students’ processes of mathematization and active knowledge organization - Didactical Design Research for and with textbooks in the KOSIMA-Project
Professor Jill Adler
(University of the Witwatersrand, South Africa; King’s College London, UK)
Revisiting resources as a theme in mathematics education
The idea of interrogating resources and their use in school mathematics practice was mooted some twenty years ago, arguing for an extension of the notion of a resource beyond the physical and material, and examination of their use in practice (Adler, 2000). In this time extensive related work has evolved. In this presentation I will revisit the early work, the trajectory of selected related developments, including relevant work on textbooks, and reflect on its current salience
Professor Jinfa Cai
(Changjiang Scholar, China Ministry of Education, Southwest University; University of Delaware, US)
Mathematical Problem Posing, Curriculum Development, and Professional Learning
Recent years have seen an increased effort to incorporate problem posing into school mathematics at different educational levels around the world. Curriculum has historically been viewed as a powerful agent for instructional change. Given the potential positive impact of including problem-posing activities in mathematics classrooms, it is useful to consider how curriculum might support such activities. In this plenary, I will first present a historical analysis of mathematical problem-posing activities in both China and the United States over the past several decades. Unfortunately, this analysis shows that only a very small proportion of the mathematical activities included in Chinese and U.S. curricula were problem-posing activities. Thus, the call to integrate problem-posing activities in mathematics classrooms is not well aligned with existing curricular resources and there is a need to help teachers develop problem-posing resources and implement problem posing in mathematics classrooms. I will then present findings from a longitudinal study investigating the impact of teachers’ learning to teach mathematics using problem posing on students’ thinking and affect. I will end by discussing methodological issues related to historical analyses of curricula and a longitudinal study of teachers’ professional learning.
Professor Birgit Pepin
(Eindhoven University of Technology, The Netherlands)
Mathematics (E-)Textbooks: Help or Hindrance for Innovation?
Textbooks may help education innovation as they can efficiently steer and support many teachers to enact renewed curriculum intentions in classroom processes. At the same time textbooks may also hinder real innovation as they reduce the opportunities of teachers to (re)design the curriculum, or to develop curriculum design capacity, by an overdose of detailed scripts that reduce teachers to technical slaves. E-textbooks are heralded to be interactive and to support teachers in their everyday classroom practices, as well as in their curriculum (re-)design, and innovative and collaborative work with colleagues. However, access to useful subject-didactical resources does not always lead to curriculum renewal and innovative practices.
In this presentation I suggest a promising middle road: educative materials, focusing on a limited number of essential characteristics for curriculum renewal. Such materials may:
- help teachers to orientate on and practice with new elements in their teaching repertoire;
- guide teachers in role taking experiences that exemplify new pedagogical approaches;
- create opportunities for shared reflection by teachers that may challenge also their beliefs about appropriate teaching.
It is argued that such educative materials are best designed and piloted by small teams of mixed composition: teachers, teacher educators, curriculum designers, and researchers. The development process is said to be iterative, with gradually shifting emphasis in quality criteria: from relevance, to consistency, practicality, and effectiveness.
Professor Susanne Prediger
(TU Dortmund University, Germany)
Enhancing and understanding students’ processes of mathematization and active knowledge organization - Didactical Design Research for and with textbooks in the KOSIMA-Project
When textbook research is conducted as design research, two aims are systematically combined: (a) research-based design of teaching-learning arrangements and (b) design-based research for a deeper understanding of the initiated learning processes. In the Kosima-project, 18 years were spent on enhancing and understanding students’ learning processes, with a specific focus on mathematization and active knowledge organization. Initiating rich processes of mathematization is a central aim for all mathematics education. However, many obstacles appear for these processes to generate solid and sustainable mathematical knowledge. By Didactical Design Research, obstacles in students’ learning pathways can be systematically identified in the Kosima-project and then overcome.