It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing the appearances of history of mathematics in curriculum materials. This framework consists of four formats that are entitled speck, stamp, snippet, and story. Characteristic properties are named for each format, in terms of size, content, location, and function. The formats are related to four ascending levels of cognitive demand. We describe how these formats, together with design principles that are also derived from the history of mathematics, can be used to raise the cognitive level of existing tasks and design new tasks. The combination of formats, cognitive demand levels, and design principles is called the 4S-model. Finally, we advocate that this 4S-model can play a role in mathematics teacher training to enable prospective teachers to reach higher cognitive levels in their mathematics classrooms.
A primary teacher needs mathematical problem solving ability. That is why Dutch student teachers have to show this ability in a nationwide mathematics test that contains many non-routine problems. Most student teachers prepare for this test by working on their own solving test-like problems. To what extent does these individual problem solving activities really contribute to their mathematical problem solving ability? Developing mathematical problem solving ability requires reflective mathematical behaviour. Student teachers need to mathematize and generalize problems and problem approaches, and evaluate heuristics and problem solving processes. This demands self-confidence, motivation, cognition and metacognition. To what extent do student teachers show reflective behaviour during mathematical self-study and how can we explain their study behaviour? In this study 97 student teachers from seven different teacher education institutes worked on ten non-routine problems. They were motivated because the test-like problems gave them an impression of the test and enabled them to investigate whether they were already prepared well enough. This study also shows that student teachers preparing for the test were not focused on developing their mathematical problem solving ability. They did not know that this was the goal to strive for and how to aim for it. They lacked self-confidence and knowledge to mathematize problems and problem approaches, and to evaluate the problem solving process. These results indicate that student teachers do hardly develop their mathematical problem solving ability in self-study situations. This leaves a question for future research: What do student teachers need to improve their mathematical self-study behaviour? EAPRIL Proceedings, November 29 – December 1, 2017, Hämeenlinna, Finland
Social robots have been introduced in different fields such as retail, health care and education. Primary education in the Netherlands (and elsewhere) recently faced new challenges because of the COVID-19 pandemic, lockdowns and quarantines including students falling behind and teachers burdened with high workloads. Together with two Dutch municipalities and nine primary schools we are exploring the long-term use of social robots to study how social robots might support teachers in primary education, with a focus on mathematics education. This paper presents an explorative study to define requirements for a social robot math tutor. Multiple focus groups were held with the two main stakeholders, namely teachers and students. During the focus groups the aim was 1) to understand the current situation of mathematics education in the upper primary school level, 2) to identify the problems that teachers and students encounter in mathematics education, and 3) to identify opportunities for deploying a social robot math tutor in primary education from the perspective of both the teachers and students. The results inform the development of social robots and opportunities for pedagogical methods used in math teaching, child-robot interaction and potential support for teachers in the classroom
