Incorporating modeling activities into classroom instruction requires flexibility with pedagogical content knowledge and the ability to understand and interpret students’ thinking, skills that teachers often develop through experience. One way to support preservice mathematics teachers’ (PSMTs) proficiency with mathematical modeling is by incorporating modeling tasks into mathematics pedagogy courses, allowing PSMTs to engage with mathematical modeling as students and as future teachers. Eight PSMTs participated in a model-eliciting activity (MEA) in which they were asked to develop a model that describes the strength of the magnetic field generated by a solenoid. By engaging in mathematical modeling as students, these PSMTs became aware of their own proficiency with and understanding of mathematical modeling. By engaging inmathematical modeling as future teachers, these PSMTs were able to articulate the importance of incorporating MEAs into their own instruction. 
                        more » 
                        « less   
                    
                            
                            Developing preservice secondary mathematics teachers’ (PSMTs’) mathematical knowledge for teaching (MKT) in content courses
                        
                    
    
            In this paper we present evidence that a) providing opportunities for PSMTs to engage with simulations of practice and b) making connections between advanced perspectives on geometry and 7-12 mathematics allows PSMTs to develop MKT in university mathematics content courses 
        more » 
        « less   
        
    
                            - Award ID(s):
- 1726723
- PAR ID:
- 10072571
- Date Published:
- Journal Name:
- In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, and S. Brown (Eds.), Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education
- Page Range / eLocation ID:
- 826-833
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
- 
            
- 
            null (Ed.)This case study investigated preservice secondary mathematics teachers’ (PSMTs’) developing understanding of formative assessment as a way to leverage mathematical practices for student learning. Qualitative data came from PSMTs’ responses to a learning sequence designed to help them develop nuanced and disciplinary-specific understandings of formative assessment. Analyses suggest a trajectory for PSMTs learning to use formative assessment in problem-solving environments, but also shows how the orientation of one PSMT continued to obstruct her progress. The results suggest that mathematics teacher educators must themselves use formative assessment that supports PMSTs’ developing orientations to currently suggested ways of teaching.more » « less
- 
            In 1908, Felix Klein suggested that to mend the discontinuity that prospective secondary teachers face, university instruction must account for teachers’ needs. More than a century later, problems of discontinuity remain. Our project addresses the dilemma of discontinuity in university mathematics courses through simulating core teaching practices in mathematically intensive ways. In other words, we interpret teachers’ needs to include integrating content and pedagogy. We argue that doing so has the potential to impact teachers’ competence. To make this argument, we report fndings from the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools (MODULE(S2)) project. The results are based on data from 324 prospective secondary mathematics teachers (PSMTs) enrolled in courses using curricular materials developed by the project in four content areas (algebra, geometry, modeling, and statistics). We operationalized competence in terms of PSMTs’ content knowledge for teaching and their motivation for enacting core teaching practices. We examined pre- and post-term data addressing these constructs. We found mean increases in PSMTs’ outcomes in content knowledge for teaching and aspects of motivation.more » « less
- 
            In support of standards for the learning and teaching of mathematics and statistics that advocate for the use of technology to promote reasoning and sense making, and to elicit student thinking, we draw on the use of authentic student work in the form of video case instruction to develop prospective secondary mathematics teachers’ [PSMTs] knowledge of students’ understanding, thinking, and learning with technology in mathematics. Specifically, we draw on the extant literature related to TPACK, video cases as learning objects, and noticing to propose a set of design principles intended to guide the development of materials to support PSMTs’ acquisition of TPACK. Here we explicate six design principles situated in the literature, provide an example of a module designed based on these principles, and share findings from pilot studies utilizing the module.more » « less
- 
            In this article, we present a set of design principles to guide the development of instructional materials aimed to support preservice secondary mathematics teachers (PSMTs) examining student practices in technology-mediated environments. To develop design principles, we drew on the literature related to technological pedagogical content knowledge (TPACK; Niess, 2005), video cases as learning objects (Sherin & van Es, 2005), and professional noticing (Jacobs, et al., 2010). After presenting the design principles, we share a task created using these design principles. Finally, we share PSMTs’ refections about changes in their own understanding after examining students’ practices. Their responses provide insights into the usefulness of the design principles for deepening PSMTs’ mathematical knowledge and knowledge of students’ understanding, thinking, and learning with technology.more » « less
 An official website of the United States government
An official website of the United States government 
				
			 
					 
					
 
                                    