Negotiating different disciplinary discourses: biology students’ ritualized and exploratory participation in mathematical modeling activities

Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary

the interplay of rationality and identity in a mathematical group work

This contribution originates from a joint work aimed at networking theoretical tools and employ them to better understand teaching and learning episodes, with a special focus on mathematical group work. In a socio-cultural perspective, two theoretical lenses are combined: the construct of rational behavior, initially developed by Habermas and adapted in mathematics education, and that of identity. In this paper we propose a general description of our approach and present the main findings emerged after investigations in grade 6 (group work on negative numbers) and grade 4 (arithmetics problem solving). The networked analysis sheds light into mathematical group works: the students' mathematical identities turn into prevailing dimensions of rational behavior and the interplay of dimensions of rationality affects the participation into the group activity. Moreover, the teacher is shown to have a role in students' identifying process, affecting indirectly the students' participation

Mathematical Learning Difficulties and Dyscalculia

Terms such as “Mathematical Learning Disability,” “Developmental Dyscalculia (DD),” but also “Mathematical Learning Disorder” and “Mathematical Learning Difficulty”1 are originated in the field of cognitive psychology in order to investigate the development of basic number processing. These terms are introduced referring to atypical situations, defined as a presence of various cognitive deficits in a student’s processing of numerical information that lead to persistent and pervasive difficulties with mathematics. The issues of diagnosis of a Mathematical Learning Disorder and instruction for the students with a positive diagnosis are getting increasing research attention; however research in this area is still lagging behind compared with other academic subjects such as reading. Generally, the clinical context lacks attention toward the important theoretical perspectives that should guide any form of educational support aimed at prevention or remediation of MLD. In the following sections, we will introduce the main perspectives, other than the purely cognitive ones, taken in mathematics education to study MLD, focusing in particular on findings on prevention and remediation. We will conclude with considerations on the possibility of fostering more constructive collaboration across the research communities studying MLD

Attitudes, beliefs, motivation and identity in mathematics education:an overview of the field and future directions

Abstract Research on mathematics-related affect is varied in theories and concepts. In this survey we record the state of the art in this research through short sections from leading experts in different areas. We describe the historical development of the concept of attitude and different ways it is defined. Research on student self-efficacy beliefs in mathematics is summarized. There is reflection on the dialectic relationship between teacher beliefs and practice as well as on how their beliefs change. One section records the emerging research on student and teacher mathematical identities over the last two decades. Finally, mathematical motivation is explored from the perspectives of engagement structures, social behaviors, and the relationship between individual factors and social norms

Ritualisation in early number work

In this paper, we propose a way of thinking about ritual that is new to mathematics education research and that challenges the more common approaches to ritual that dichotomise thinking and acting. We argue for a material, monist conceptualisation of ritual, which we refer to as ritualisation. In the context of early number work, we show that ritualisation can be seen as meaningful—and not simply as rote repetition lacking mathematical sophistication—particularly in relation to a symbolically structured environment. We argue that ritualisation practices can allow entry into new fields of activity and discourse, without going through a phase of merely un-thinking performance.</p