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# 数学代写|数学建模代写Mathematical Modeling代考|MATH3290 An Activity-Based Conceptualization of Affect

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## 数学代写|数学建模代写Mathematical Modeling代考|An Activity-Based Conceptualization of Affect

If one wants to study affect in mathematics education, there are many conceptualizations and instruments, but most of these address mathematics holistically. Instead, we wanted to study students’ affect when they engage in an activity, which is different from standard activities of canonical mathematics education. Thus, we sought an activity-based, and not a subject-based conceptualization.

Looking at mathematics from an activity-based perspective goes back to, among others, Freudenthal (1973). He distinguished between mathematics as (1) a wellorganized deductive system, or as (2) a human activity which consists of organizing mathematical patterns when solving problems. The two perspectives are also known as “mathematics as a noun” and “mathematics as a verb”. The first perspective relates to mathematics as a holistic academic discipline, with its own symbols, and its procedures for establishing truth (by creating proofs), and so forth. The second perspective relates to mathematical activities, such as solving non-routine problems and using mathematics to solve problems within non-mathematical contexts, for example within kinematics. Within the first perspective, humans and their activities are less visible than within the second.

An activity-based conceptualization of mathematics also aligns with a sociocultural perspective. One of its advocates, Lerman (2000), describes mathematics as a socio-cultural practice embedded within a community. If embedded within a school institution, mathematics is a practice embedded in a community of a teacher and a group of students. The activities consist, among others, of explanations by the teacher, and work on tasks by the students. This practice differs markedly from mathematics as a practice embedded within a research community, whereby the actors work on problems to which nobody knows an answer. Describing mathematics socio-culturally as a practice embedded within a community entails focusing on the activities undertaken by the actors, which are mediated by language, tools, and so forth. Using an activity-based conceptualization of mathematics enables us to (1) relate affect to activities and not to mathematics as a holistic entity, and (2) distinguish between different kind of activities within different contexts of mathematics education (doing repetitive exercises or an inquiry-based project).
To study students’ affect while they engaged in an activity, one can still focus on different aspects, such as their emotions, their perception of the relevance or meaningfulness of a task, their boredom, their apathy, and so forth. We decided to focus on their perception of being challenged and activated by the activities.

## 数学代写|数学建模代写Mathematical Modeling代考|Methods

In the Spring of 2017 we presented the task described on pages 262-263 to the students of the engineering department (Mechatronics, Electrical Engineering, Renewable Energy, Data Engineering, ICT, and others), as part of the 1st-year physics course. There were 346 students for whom the task was obligatory.

## MATLAB代写

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