Takashi Kawakami

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• Doctor of Education
• Associate Professor at Utsunomiya University

The difficulty of transferring mathematical and/or extra-mathematical knowledge from one real-world context to another and the lack of established strategies to facilitate student knowledge transfer have long been a gap in educational research involving mathematical modelling. To address this gap, we developed a framework that shows the relationshi...

This study investigates the complex dynamics of factors and their interactions that influence pre-service teachers’ (PSTs) self-efficacy in teaching mathematical modelling. It focuses on influencing PSTs’ self-efficacy through a series of sessions, including international exchanges, experimental teaching, and poster presentations. The central resea...

In light of the complex use of mathematical and statistical models in a data-rich society, their roles in modelling education research merit discussion. This chapter thus clarified the roles of mathematical and statistical models in data-driven modelling (DDM), with an emphasis on social decision-making from a prescriptive modelling perspective. A...

This study focuses on ‘modelling’ and ‘data’ to ensure the effective implementation of STEM education, specifically emphasising the ‘M’ (Mathematics) at its core. While the modelling process is used to develop real-world interdisciplinary problem-solving and concepts in STEM subjects, data are inherently interdisciplinary. In this chapter, we illus...

This study develops and discusses a framework for identifying the role of data in empirical research studies, focusing on the teaching of statistical modelling based on a literature review. A theoretically derived framework that recognises three distinct roles of data in teaching statistical modelling was used to analyse 63 papers. The findings sho...

This study explored secondary school students’ multifaceted perceptions of the role of data from the perspectives of models, modelling, and information, following two or three lessons focused on a data-informed modelling activity with mathematics and statistics at its core. The results showed that half of the students perceived data not only as a w...

Educating pre-service teachers (PSTs) to impart lessons that incorporate a STEAM education approach, which emphasizes the relevance of each STEAM subject and domain in each lesson, is a major challenge in Japan and globally. In this chapter, we aim to address this issue from the perspective of mathematics education by incorporating data modeling an...

This study elaborates on the pivotal roles of mathematical and statistical models in data-driven predictions in an integrated STEM context using the case of Year 4 students: (ⅰ) a descriptive means to describe the features of trends and variability of data and (ⅱ) an explanatory means to explain causal relationships behind data. These roles are lin...

This paper elucidates mathematics pre-service teachers’ perceptions of the role of mathematics in integrated STEM education through a STEM seminar involving data-driven modelling. The results show that their perceptions could be categorised into (Ⅰ) a catalyst for STEM integration; the development of (Ⅱ) twenty-first century skills, (Ⅲ) citizenship...

Mathematics teachers are required to acquire modelling-specific pedagogical content knowledge (MsPCK) to enhance their modelling teaching. We conducted a teacher training where one teacher interpreted and redesigned their modelling lesson, with support from the teacher educator. This training followed the ALACT model, a cyclical process of action a...

Abstract of The 21st International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA21)

This study constructs and illustrates a framework for describing and analysing data-driven modelling in school mathematics from the perspectives of mathematical and statistical models. Based on the constructivist view of models and the perception that they are the subject's deterministic or stochastic interpretation, the framework consists of the t...

Proceedings of the Thirteen Congress of the European Society for Research in Mathematics Education (CERME13) (pp. 1297-1298)

This chapter presents arguments and examples highlighting the similarities and differences between statistics, statistical modelling and mathematical modelling. Based on educational research that focuses on statistical modelling and mathematical modelling, we elaborate on the potentially productive connections for the development of, and research o...

In many countries, incorporating modelling as a part of day-to-day classes has been demonstrated to be a major challenge. This chapter focuses on in-service teachers with less experience in modelling teaching (‘novices’). This chapter aims to describe and analyse the novices’ activities to design modelling tasks based on mathematised tasks. The ana...

Kawakami, T., & Saeki, A. (2022). A framework for describing and analysing data-driven modelling activities in school mathematics: From the perspectives of mathematical and statistical models. Journal of Science Education in Japan, 46(4), 421–437. https://doi.org/10.14935/jssej.46.421 [Abstract] This paper constructs a framework for describing and...

This contribution has been accepted as Short Presentation in ICTMA20 – the 20th International Conference on the Teaching of Mathematical Modelling and Applications (Online Conference) Würzburg (Bavaria, Germany), Saturday, 24 to Tuesday, 27 September 2022.

In this paper, we develop and discuss a framework for characterising rationales for using statistical modelling from a mathematical modelling perspective based on a systematic literature review. We use this framework to provide an overview of the distributions of these rationales in the analysed studies focusing on statistical modelling. The result...

Kawakami, T. (2022). The role of models in promoting informal statistical inferences of lower grade children: Focusing on data modeling processes. Journal of Science Education in Japan, 46 (2), 125-140. https://www.jstage.jst.go.jp/article/jssej/46/2/46_125/_article/-char/en [Abstract] The need for dealing with uncertainty in today's complex and ch...

The purpose of this paper is to clarify the characteristics of socially oriented data modelling (DM) from a prescriptive modelling (PM) perspective. Some of the social decisions made by a university student through socially oriented DM in the context of COVID-19 were analysed. As a result, the following two points were clarified as the characteris...

This study aims to clarify the dynamic aspects of young children's data modelling processes.

In this paper, we develop and discuss a framework for characterising the rationales of statistical modelling (SM) in educational research from a mathematical modelling perspective. We report some results from a systematic literature review of empirical research on SM departing from the dual rationale of modelling in mathematics education as a means...

This chapter examines ninth-grade students’ data-based modelling to estimate previous and unknown Japanese populations. The results of the students’ productions of group and individual models and their individual use of the group models demonstrated that the data-based modelling approach—which involves putting ‘data’ at the core of mathematical mod...

Most Japanese teachers have little experience of modelling, and little research exists on teacher training of mathematical modelling in Japan. Therefore, we developed a modelling teacher education program starting from the transformation of a mathematised task into modelling tasks. In this paper we describe a framework of the transformation of a ma...

This chapter illustrates how, and to what extent, students (11-12-year-olds) identified a straight-line graph (time-distance graph) as a mathematical model of average speed when making sense of walking situations in relation to technology. The results demonstrated the types of models that students identified explicitly, the phases of identifying su...

This research explores the integration of mathematical modelling into actual learning to see whether it is possible for mathematical modelling to be used as a didactical means for supporting student learning of speed and related mathematical concepts. This study explores modelling for learning in the secondary grades to deepen and expand mathematic...

It is important to understand what and how mathematics teachers learn in mathematics professional development (MPD) programs. In this paper, we examined mid-career teachers' learning in our program wherein participant teachers conducted lesson study and analyzed students' learning by collecting and discussing multiple sources of data. We approached...

Both empirical modelling (EM) and theoretical modelling (TM) are essential in mathematical modelling. This study explored how graduate students promoted teaching competencies for mathematical modelling by conducting EM and TM with the pendulum task. Through the analysis of modelling lessons, we found that the experiences of both EM and TM with the...

With the advent of the era of big data in which we deal with an enormous amount of data and need to build models amid uncertainty, recent research by the ICTMA community etc. has increasingly emphasised the need to extend the idea of models and modelling in mathematics education to statistical domain (e.g. Kawakami, 2017). Data-based modelling emph...

Teachers need the competency to develop and analyse modelling problems in teaching modelling (Borromeo Ferri, 2018). Fostering such competency takes time and careful efforts toward this are needed (e.g. Manouchehri, 2017; Schmidt, 2011). Recent research has proposed transforming a normal mathematical problems or typical math-textbook problems into...

Journal of Japan Society of Mathematics Education, 101, 3, 15-27. This paper reviews the international trends in research on the teaching and learning of statistical modelling from the perspectives of activity type, instructional objectives, and target of practice. As a result, it became clear that there is a trend to emphasize both the constructi...

Promoting teacher training for the teaching of mathematical modelling is an urgent issue in Japanese mathematics education. This study analysed primary school teachers’ initial changes, and extending perspectives on math-textbook problems from the viewpoints of the real world and the mathematical world as essential elements of mathematical modellin...

https://iase-web.org/Conference_Proceedings.php?p=ICOTS_10_2018

The need to overcome the boundaries between statistics education and models and modelling approaches has been increasingly emphasised. These approaches spotlight children’s models and the process to create, modify, and apply these models to real-world contexts. This study illustrated how models and modelling approaches encourage young children (age...

In the new Japanese curriculum of mathematics for primary and secondary schools, which will be implemented successively from 2020, statistics education has been strongly emphasized. One of the big targets of new statistics education in Japan is to incorporate statistical-inquiry process in usual lessons. This paper illustrates two Japanese lessons...

This study addressed some aspects of secondary teachers' construction of perspectives on developing modelling problems. A pilot study of teacher training on teaching modelling which comprised three lessons was designed and implemented for two Japanese in-service teachers of secondary schools and for a Japanese pre-service teacher. Through the anal...

This chapter illustrates how students combined distribution-related models using a case study involving 31 Year-5 students (10–11 year olds) in a Paper Helicopter Experimentation. Through the experimental activities that included conjecturing and validation, the students grasped relevant statistical and/or contextual elements from models of real di...

The aim of this study was to investigate how 23 students from one Year 6 class in an Australian primary school engaged with two modelling tasks using the dual modelling cycle framework. This framework is designed to assist students who do not find a solution to a modelling task by introducing a second similar yet simpler modelling task in a second...

In learning mathematics through mathematical modelling, students’ activities of mathematically making sense of real-world situations, in which they elicit and identify mathematical objects, are crucial. Several research have pointed out that technology plays an important role in supporting the activities. It is well known that the speed concept is...

Integrating task context with mathematics is an indispensable pedagogical issue in the teaching and learning of mathematical modelling. This paper provides two case studies in different instructional situations, one Year 5 classroom from Japan and one Year 6 classroom from Australia, analysing how students dealt with contexts and the mathematics re...

Modelling ideas are now emphasised in the teaching and learning of statistics (e.g., Kawakami, 2015). This presentation reports on a case study examining how Year 9 students (14-15 year olds) created and utilized data models in estimating and predicting Japanese population by 5-year age group. The analysis illustrated that the students perceived th...

Distribution is at the heart of statistics, hence it is an important objective to develop students' notions of distribution in school statistics curricula. Modelling is highlighted as a powerful vehicle for developing students' statistical ideas (e.g., Lesh, 2010). Statistical investigation requires developing ideas and models with statistical and...

The purpose of this chapter is firstly to show how students who could not solve an initial task by themselves shared and refined models through dual modelling teaching, and secondly to derive suggestions for dual modelling teaching. Through examining students’ worksheets and protocols of video and audio records of the lessons, it was shown that uns...

The purpose of this paper is firstly to illuminate the development of Year 1 children’s informal views of distributions through model creating and sharing as features of models and modelling and secondly to derive some suggestions for quality teaching and learning of statistics in the early years of schooling. For this purpose, a teaching experimen...

The aim of this study is to compare how Japanese and Australian teachers utilise opportunities to promote students' switching between mathematical modelling cycles based on the dual modelling cycle framework (DMCF).This study found that teachers need to change how they assist students when transitioning from one modelling cycle to another not only...

The aim of this study was to investigate the use of the dual mathematical modelling cycle framework as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an Oil Tank Task that required them to develop two models in order to solve the t...

The aim of this paper is to propose and verify modelling teaching based on 'dual modelling cycle framework' corresponding to diversities of modellers. Research methods are to design the experimental lessons using an initial modelling task and a similar modelling one, to implement the lessons for 5 th graders and to analyse them. As a result of expe...

We focus on individual constructing and simplifying/structuring process related situation model in the modelling cycle (Blum & Borromeo Ferri, 2009; Blum & Leiß, 2007). In this paper, we introduce a case study for elementary school pupils. At first, pupils tackle modelling tasks as the first test. At next, the teacher instructs mathematical modelli...