Gabriel T Matney

Curriculum Clearings as Being-With-Mathematics Experiences: Authentic Learning through a Heideggerian Lens

This question has haunted both of us as we have wrestled with helping our students experience their worlds in mathematical ways. The more we have thought about authentic experiences as related to mathematical explorations, relationships, and understandings, the more we have come to realize there is a gap in the literature as well as our own understandings of what it means to have authentic experiences in mathematics classrooms. Further questions plagued us: How and when do authentic experiences occur? Who has these experiences? And ultimately, why do (or don’t) these experiences occur for some students rather than others? These questions infer a delicate dynamic among individuals, how they experience their world, and disciplinary content such as mathematics. They also create a shadow over the mathematics curriculum, for learning, if connected with authentic experiences, cannot be predicted, controlled, or manipulated. In exploring our questions of authenticity and experience, we engage in critical curriculum pedagogy, challenging the notion that the mathematics curriculum is a set body of knowledge or facts. In our exploration of authentic mathematical experiences we find we are engaging in an aspect of curriculum theorizing as described by Bill Pinar in his book: What is Curriculum Theory? (Pinar, 2004).

Effects of Minute Contextual Experience on Realistic Assessment of Proportional Reasoning.

Abstract This mixed methods study describes the effects of a minute contextual experience on students’ ability to solve a realistic assessment problem involving scale drawings and proportional reasoning. Minute contextual experience (MCE) is defined to be a brief encounter with a context in which aspects of the context are explored openly. The study looked closely at what happened during an instructional unit examining proportional reasoning. Students completed a pretest and posttest involving items characterizing a novel context, and data were analyzed to determine the effects of the MCE. Students were interviewed to gather their perspectives on the problem and their own solutions. Pretest results indicated that instruction in which students demonstrated growth in understanding had little effect on students’ ability to solve a novel problem in which they had difficulty associating their everyday mundane knowledge with the realistic context. The students demonstrated a significant increase in ability to solve the novel problem after a MCE. Furthermore, students explicated that the MCE aided their ability to visualize the context, and this helped them apply instructional learning to solve the problem. A discussion of the complexities involving the assumptions of students’ familiarity with contexts and their abilities to draw upon their mundane everyday experiences to solve proportional reasoning problems is shared.

Peer mentoring professionalism among pre-service mathematics teachers: Safe spaces for community teaching practice

ABSTRACT The study described here is a longitudinal qualitative case study conducted on a mathematics pre-service teaching program at a university in Southeast Asia. The university program of study required all pre-service teachers of mathematics to be involved in an alternative form of field experience in which the pre-service teachers would enact mathematics camps for college freshmen and for K–12 students. The pre-service teachers were expected to take on increased responsibility for the success or failures of the mathematics camps as they matriculated through the program. Constant comparative analysis revealed a peer mentoring professionalism among the pre-service teachers as they negotiated the challenges of teaching mathematics during these alternative field experiences. Description of the construct of peer mentoring professionalism as well as explanation of its derivation from the study are given. Implications and applicability across mathematics teacher education programs are discussed.

Research projects and secondary mathematics pre-service teachers’ sense of efficacy

ABSTRACT This two-year study investigated the differences in the level and amounts of change in teaching efficacy of secondary pre-service mathematics teachers who completed one of two different research projects during a methods course. The first type, field research, involved a three day trip to an urban school to investigate successful mathematics teaching and learning from engaging directly with practitioners. For the second type, text-based research, participants remained on campus and investigated successful mathematics teaching and learning through text-based literature. Pre-service teachers were separated into two self-selected groups based on the type of research project they completed. The two types of research projects were focused and grounded one source of self-efficacy: vicarious experience. Within the possible vicarious experiences that inform pre-service teachers’ sense of efficacy, two are readily applicable for teacher educators: watching others teach followed by discussing results (field research) and reading professional literature followed by discussions of enacting those ideas (text-based research). Data revealed that pre-service mathematics teachers showed improved teaching efficacy. Those who did field-based research had a higher level and greater increase on measures of teaching efficacy compared to peers completing text-based research. Implications for mathematics teacher educators are discussed.

A validation process for observation protocols: Using the Revised SMPs Look-for Protocol as a lens on teachers’ promotion of the standards

ABSTRACT The Standards for Mathematical Practice (SMPs) describe mathematical behaviors and habits that students should express during mathematics instruction. Thus teachers should promote them during classroom-based mathematics instruction. The purpose of this article is to discuss the validation process for an observation protocol called the Revised SMPs Look-for Protocol. An implication of this study is that users with a robust understanding of the SMPs may feel confident using the protocol as a validated and reliable tool in research and school-based settings. We discuss opportunities and challenges for mathematics teacher educators engaging in classroom observations, in light of this observation protocol.