Can designed student responses support teachers to interact with students in a productive way?

This paper introduces the use of pre-designed student responses to unstructured mathematics problems as a possible resource for teachers to develop their capacity of acting contingently in the mathematics classroom in a productive way, whilst teaching. We frame our argument around the notion that contingent moments can be regarded as problem-situations that are, at times, too demanding for the teacher to effectively solve. We provide an unstructured mathematics problem and accompanying designed student responses to illustrate and explain our thinking, considering how this approach has the potential to help teachers flexibly and productively engage with students’ reasoning in-the-moment of instruction. We end the paper with a call for empirical studies to explore these ideas further

Emergent model for teachers' conceptions of argumentation for mathematics teaching

International audienceIn recent years, there has been a growing appreciation of the importance of incorporating argumentation into the mathematics classroom. Whereas considerable research has been done on argumentation, little has specifically focused on teachers’ conceptions. This paper presents an exploratory study as part of ongoing research into teachers’ conceptions of argumentation for teaching mathematics. Drawing on the literature on argumentation and empirical data, we propose an emergent model, presented as a 5-by-2 construct featuring five types of conceptions across two dimensions: structural and dialogic. This paper illustrates the emergent model at this initial stage of the research using an individual case study of a teacher. The overall aim of the research is to theorize a model that can be used to analyze and characterize teachers’ conceptions of argumentation for teaching mathematics

Exploring change in secondary mathematics teachers' noticing of argumentation

This study examined changes in secondary mathematics teachers' noticing of argumentation through experiencing a peer assessment cycle. Sixty-one teachers participated in the cycle comprised of (a) analyzing a written argumentative classroom situation (ACS) by using a report format, (b) collaboratively assessing peers' ACS reports using an ACS rubric format, (c) providing feedback to peers, (d) receiving feedback from peers, (e) individually refining the initial ACS reports, and (f) reflecting on their experience. Analysis of teachers' initial and refined ACS reports revealed changes in teachers’ noticing of various dimensions associated with argumentation. The study provides evidence of the potential of the peer assessment process for teachers' learning to notice key aspects of argumentation

Mathematics as gendered? Views from Palestinian/Arab Israeli high schoolers

In light of a gender-gap in school mathematics favoring girls among Palestinian/Arab Israelis, this study explores 147 high school students’ views of mathematics with respect to gender. We administered a “Who and Mathematics” survey used in a prior study. Findings include gender-neutrality about teacher interactions, parent expectations, and future employment. Negative relations with mathematics were attributed to boys. A broader set of narratives were attributed to girls, including items about caring or worrying about success and finding mathematics interesting. These results challenge an assumption that the social construction of mathematics as masculine is universal and present a picture of how gender shapes and is shaped by mathematics education for Palestinian/Arab Israelis

Transforming critical events through script writing in mathematics teacher education

This paper proposes a teacher education strategy based on a combination of critical events and scripting dialogues. This strategy was used in two teacher education contexts in Israel and Greece with thirty-four prospective teachers (PTs). The PTs identified critical events in the context of their field experiences and transformed them into scripting dialogues with the aim to handle students’ difficulties. The analysis focuses on the adopted pedagogical actions in the critical events and the scripting dialogues. The PTs used general and mathematics-specific actions to address students’ difficulties promoting their conceptual understanding

Predicting Impacts of Offshore Monoculture Farm Expansion in Ultra-Oligotrophic Waters of the Levantine Basin

The aim of this brief research report was to define the consequential shifts in biomass and trophic structure of an ecosystem surrounding an offshore monoculture fish farm in Israel. It attempts to clarify the impact of the industry expansion and input of artificial fish pellets on functional group biomasses. We account for the direct addition of artificial food pellets, the metabolic wastes from the caged fish in a mass-balance food web model (Ecopath), as well as the temporal expansion of the farm’s production capacity to 21,000 t over a 30-year period (Ecosim). In the static mass-balance model of the food web, the addition of the fish cages at its current production size of 1000 t does not adversely affect the system, and trophic energy transfer is still dependent on primary production versus the detrital pathway. The model suggests a semi-stable ecosystem with low trophic interactions. With time, the increase in fish farming at the site is characterized by an increase of all functional group biomasses at the site over the 30-year period. The accumulation in detritus most notably correlates to greater biomass for all benthic functional niches and their secondary consumers. It is, therefore, apt to develop an indicator species list to indicate negative site disturbance. In summary, the sediment column condition will be the main indicator for ecosystem stability, as well as the increase in apex predators that are attracted to the site from the accumulation of discards at the cage botto

Can designed student responses support teachers to interact with students in a productive way?: a report from the Formative Assessment Working Group (2015 ISDDE conference)

This paper introduces the use of pre-designed student responses to unstructured mathematics problems as a possible resource for teachers to develop their capacity of acting contingently in the mathematics classroom in a productive way, whilst teaching. We frame our argument around the notion that contingent moments can be regarded as problem-situations that are, at times, too demanding for the teacher to effectively solve. We provide an unstructured mathematics problem and accompanying designed student responses to illustrate and explain our thinking, considering how this approach has the potential to help teachers flexibly and productively engage with students’ reasoning in-the-moment of instruction. We end the paper with a call for empirical studies to explore these ideas further

Introduction to the papers of TWG21: Assessment in mathematics education

International audienc

Introduction to the papers of TWG21: Assessment in mathematics education

TWG21 met for the second time in Utrecht at CERME11 and in this conference we sought to continue the work started at CERME10. The aim of the previous meeting was to ascertain where the interest of our community is when thinking about assessment, and to maintain the focus firmly on mathematics. At CERME11 we discussed 14 papers and 3 posters which helped defining such interest. We noticed again a variety of focal points: from validation of large-scale assessment instruments, to the affordances and drawbacks of online assessment – especially in the university context - to the details of construction of individualised feedback. As in the previous meeting the papers also presented a variety of methodologies: from large quantitative studies to more nuanced qualitative investigations. Among the submissions we also received papers related to students’ perspectives and teachers’ perspectives on assessment. These themes were not prominent in the past meeting of the group and we welcomed the new perspectives they brought. Finally, we decided to group papers together that indicated the role that mathematics has in the assessment: this is to say papers that focus on the specifics of mathematics, such as assessing proof