Examining individual and collective level mathematical progress

Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle

doi:10.1007/s10649-014-9583-x

Cited by 51 publications

(23 citation statements)

References 24 publications

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“…This approach considers that the mathematical practices emerge from ideas and mathematical norms socially shared in class and expand the mathematical activity of the students to a more advanced level of reasoning. Rasmussen et al (2015) used the construct classroom mathematical practices as an extension of the interpretative framework of Cobb and Yackel (1996) to conceptualize the individual and collective mathematical progress of the students. These authors define classroom mathematical practices as:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…This progress is a construct characterized in the sociological framework of Cobb and Yackel (1996) and their associated works (e.g. Bowers et al, 1999;Cobb, Stephan, McClain & Gravemeijer, 2001;Stephan & Rasmussen, 2002;Rasmussen, Wawro & Zandieh, 2015); it is understood as an evolution of the mathematical reasoning used to solve mathematics tasks (Rasmussen et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…The studies of the collective mathematical progress in reference to the classroom mathematical practices are based on the hypothesis that it is possible to document learning trajectories from instruction (Cobb, 1999;Cobb et al, 2001) focusing on the social productions of ways of reasoning, argumentation and using tools that will eventually be institutionalized and placed beyond justifications (Bowers et al, 1999;Cobb, 1999). Thus, the evolution of the mathematical practices has been analyzed and reported in different classroom contexts and educational levels; for example, elementary school (Cobb, Yackel & Wood, 1992;McClain, Cobb, Gravemeijer & Estes, 1999;Bowers et al, 1999;Cobb et al, 2001), middle school (Cobb, 1999) and higher education (Stephan & Rasmussen, 2002;Rasmussen, Stephan & Allen, 2004;Rasmussen, Zandieh & Wawro, 2009;Rasmussen et al, 2015). However, this research is limited in high school.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Collective Mathematical Progress in an Introductory Calculus Course during the Treatment of the Quadratic Function

Cetina-Vazquez

Cabañas-Sánchez

Moguel

2019

International Journal of Education in Mathematics Science and Technology

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Article HistoryThis study characterizes the classroom mathematical practices that support the collective mathematical progress during the treatment of a quadratic function in an Introductory Calculus course comprised of 15 students from eleventh grade (from 16 to 18 years old). A teaching experiment that discussed two variational situations was designed for the treatment of the quadratic function. This paper only reports data of one these situations. The analysis of the empirical data involved an analytical approach that used Toulmin's model of argumentation and two criteria to inform the classroom mathematical practices. Results correspond with two mathematical practices that supported a collective mathematical progress: 1) analyze and quantify what changes in a variational situation; and 2) generate and interpret representations of how the variable magnitudes change in a variational situation. Three connected elements were identified in the evolution of the mathematical practices: time, structure and mathematics. These elements enabled the establishment of a model of collective mathematical progress based on empirical evidence; this model documents a path students could follow to learn quadratic function. The proposed model has the quality of being explicative and the ability to adjust to interact with other students.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Collective Mathematical Progress in an Introductory Calculus Course during the Treatment of the Quadratic Function

Cetina-Vazquez

Cabañas-Sánchez

Moguel

2019

International Journal of Education in Mathematics Science and Technology

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“…For instance, Stephan and Rasmussen (2002) examined ways of reasoning that become normative through social interaction in an inquiryoriented differential equations class. Rasmussen et al (2015) utilized and elaborated on Cobb and Yackel's (1996) interpretive framework in the undergraduate context to offer a more robust account of the both the social and individual processes that contribute to students' mathematical progress. Lerman (2000) and Valero (2004) posited that considerations and broader acceptance of sociocultural perspectives were in fact motivated by political concerns in mathematics education.…”

Section: A Shift Towards Sociopolitical Perspectivesmentioning

confidence: 99%

Taking the Sociopolitical Turn in Postsecondary Mathematics Education Research

Adiredja

Andrews-Larson²

2017

Int. J. Res. Undergrad. Math. Ed.

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In this paper, we argue for a need to attend to issues of equity in postsecondary mathematics education. In the United States, the broader mathematics education field has begun a shift toward attending to sociopolitical aspects of research, which focus on the interrelatedness of knowledge, identity, power, and social discourses. We argue that explicit uptake of sociopolitical perspectives has the potential to offer new insights to current research and to advance efforts to address inequities in meaningful and theoretically well-informed ways. Situating our argument within the social and political context of the United States, we draw on existing studies that examine inequities in undergraduate mathematics classrooms. We highlight studies that focus on the impact of social discourses and institutional contexts on the negotiations of power and identity in postsecondary mathematics. We end by proposing future research directions and discuss challenges for equity work in postsecondary mathematics education.Issues of equity are becoming increasingly pressing in the political landscape and national discourse in the United States. In particular, various forms of professional and economic opportunity are intertwined with issues related to race and gender. Evidence of these relationships spans contexts ranging from trends in police brutality and incarceration (Chaney and Robertson 2013; Pettit and Western 2004) to pay Int.

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“…Finally, Rasmussen et al (2015) are interested in the investigation of mathematical progress at both collective and individual level. To this aim they expand Cobb and Yackel's (1996) interpretive framework for coordinating social and individual perspectives and offer a set of four constructs for the examination of mathematical progress at a collective and individual level: "disciplinary practices, classroom mathematical practices, individual participation in mathematical activity, and mathematical conceptions that individuals bring to bear in their mathematical work" (p. 259).…”

Section: Theoretical Perspectives and Liaison Of Theoriesmentioning

confidence: 99%