skip to main content


Title: Worthwhile problems: How teachers evaluate the instructional suitability of contextual algebra tasks
We investigate the beliefs that influence middle and high school algebra teachers’ appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical features, and connections to the real world. We recorded small-group discussions in which teachers shared their responses to this activity, and qualitatively analyzed their discussions for evidence of beliefs that influenced their appraisals of the tasks. The teachers’ beliefs about contextual problems attended to task authenticity, opportunities for mathematical activity, obligations of tasks, and pedagogy and access. Our preliminary findings can inform future efforts to equip teachers with contextual tasks that develop students’ algebraic reasoning and problem solving.  more » « less
Award ID(s):
2001116
PAR ID:
10508795
Author(s) / Creator(s):
; ; ; ; ;
Editor(s):
Lamberg, Teruni; Moss, Diana L
Publisher / Repository:
University of Nevada, Reno
Date Published:
Journal Name:
Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
Page Range / eLocation ID:
791-799
Subject(s) / Keyword(s):
Teacher Beliefs Algebra and Algebraic Thinking Professional Development
Format(s):
Medium: X Size: 570KB Other: pdf
Size(s):
570KB
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    A growing number of teaching materials invite students to discuss the complex mathematical, contextual and social aspects of data visualizations. Orchestrating such discussions can be difficult, as this requires teachers to balance a variety of learning goals and student perspectives. This paper examines how teachers interact with data visualization discussion tasks—specifically, those that engage visualizations’ social complexities—as they consider using them in their own classrooms. Drawing from semi-structured clinical interviews with six U.S.-based teachers as they reviewed discussion tasks called Data Story Bytes, we explore: How did these teachers envision using these data visualization discussions in their classrooms? And, What mathematical, contextual, and/or social aspects of visualizations did teachers emphasize when engaging with the discussion task materials? We found that all teachers envisioned using data visualization discussions as lesson openers or routine activities, but they differed in their overall emphasis on the visualizations’ mathematical, contextual, or social aspects. Despite these differences, certain types of discussion prompts were associated with particular response patterns across all teachers, suggesting these task structures can help guide teachers to address a shared set of intended baseline goals for all three of these dimensions. Our findings represent a first step in understanding whether and how socially-oriented data discussion materials may be enacted in classrooms, and what additional design features and supports may be needed to help teachers do so productively.

     
    more » « less
  2. Sacristán, A. I. ; Cortés-Zavala, J. C. ; Ruiz-Arias, P. M. (Ed.)
    Mathematics pre-service teachers must learn how to use tools like scientific calculators, Computer Algebra System (CAS), text processors and dynamic mathematical environments. These tools allow users to work with mathematical objects, perform specialized tasks, respond in a defined mathematical way, and transmit mathematical knowledge (Dick & Hollebrands, 2011). To achieve the integration of technology in Mathematics Education, the teacher’s role is very important, since their beliefs and knowledge will dictate how they use technology in the classroom (Julie et al., 2010). The goal of this research is to determine the beliefs and knowledge about technology and its integration into the teaching of mathematics by a group of pre-service teachers at the beginning of their first course of methodology in the teaching of mathematics at the secondary level (N=11). Interviews were conducted, and a questionnaire was administered to determine the profile participants use of technology at their schools and universities. 
    more » « less
  3. 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
  4. This study focuses on a lesson study adaptation for bridging prospective teachers’ experiencesin a methods course and their field experiences in a teacher education program in Puerto Rico. We ask, what opportunities for teacher learning emerge during discussions in lesson study? Two lesson study teams of secondary mathematics prospective teachers, each led by an experienced mentor, planned technology-based lessons. Using the theoretical framework for lesson study by Lewis and colleagues, we analyzed video recordings of the teams’ discussions. The results show learning opportunities in the three dimensions of the framework: teachers’ knowledge and beliefs, the creation of a professional community, and the development of teaching–learning artifacts. The mentors leveraged prospective teachers’ knowledge, built on topics discussed in the methods course, and created a professional learning community. Three resources introduced in the methods course supported the creation of a hybrid space connecting academic and practitioner knowledge: shared language about teaching moves for using technology in math instruction, the mathematical proficiency framework, and a lesson plan template. The mentors drew upon their subject matter and pedagogical knowledge during their facilitation of lesson study. The intervention exemplifies a lesson study adaptation that is feasible in the context of a teacher education program. 
    more » « less
  5. Lamberg, Teruni ; Moss, Diana L (Ed.)
    We investigate teacher beliefs about discourses for equation solving and the challenges these beliefs might pose for the implementation of instructional practices that promote deductive reasoning in algebra. To uncover these beliefs, we recorded three video explanations of solutions to the same linear equation with distinct discursive characteristics and analyzed seven secondary mathematics teachers’ small-group critical discussions of these explanations. Three prevalent themes surfaced in our thematic analysis. Teacher beliefs about discourse for equation solving specified different roles and potential benefits of deductive explanations, estimated students’ capacity to understand deductive explanations, and hypothesized differences between teachers' and students' potential to understand deductive reasoning. We discuss implications of these beliefs for opportunities to engage all learners in conceptual thinking about equations. 
    more » « less