# Michael TallmanOklahoma State University - Stillwater | Oklahoma State · Department of Mathematics

Michael Tallman

Doctor of Philoso

## About

28

Publications

12,187

Reads

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177

Citations

Citations since 2016

Introduction

I am an Assistant Professor of Mathematics Education at Oklahoma State University. My primary research interest is in the area of mathematical knowledge for teaching secondary mathematics. In particular, I study the factors that mediate teachers' knowledge and their enacted knowledge.

Additional affiliations

June 2015 - January 2016

August 2010 - May 2015

August 2010 - May 2015

Education

August 2010 - August 2015

May 2008 - August 2010

August 2003 - May 2007

## Publications

Publications (28)

In this study, we developed a three-dimensional framework to characterize post-secondary Calculus I final exams. Our Exam Characterization Framework (ECF) classifies individual exam items according to the cognitive demand required to answer the item, the representation of both the task statement and the solution, and the item’s format. Our results...

The purpose of this article is to describe the development of elementary school teachers’ mathematical knowledge for teaching as they participated in a Modeling Instruction environment that placed heavy emphasis on improving their subject-matter knowledge as a basis for affecting the development of their pedagogical content knowledge. We investigat...

This paper reports the results of a series of task-based clinical interviews I conducted to examine how a secondary mathematics teacher's understandings of angle measure afford or constrain his capacity to bring his mathematical knowledge to bear in the context of teaching. The results suggest that the teacher, David, possessed two complementary bu...

The concept of intellectual need, which proposes that learning is the result of students wrestling with a problem that is unsolvable by their current knowledge, has been used in instructional design for many years. However, prior research has not described a way to empirically determine whether, and to what extent, students experience intellectual...

We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively-distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical fra...

Shulman (1987) defined pedagogical content knowledge as the knowledge required to transform subject-matter knowledge into curricular material and pedagogical representations. This paper presents the results of an exploratory case study that examined a secondary teacher’s knowledge of sine and cosine values in both clinical and professional settings...

This article presents the results of our analysis of a sample of 254 Calculus I final exams (collectively containing 4,167 individual items) administered at U.S. colleges and universities. We characterize the specific meanings of foundational concepts the exams assessed, identify features of exam items that assess productive meanings, distinguish c...

Mathematics anxiety, like all emotions, is an emergent construction, progressively elaborated
and refined through iterative cognitive appraisals of environmental stimuli and somatic states. We synthesize contributions in the areas of emotion, identity, goal theory, and Piaget’s genetic epistemology to propose a theory of the cognitive antecedents o...

We present the results of a teaching experiment designed to foster a pre-service secondary teacher's construction of a scheme for constant rate of change through engendering reflecting and reflected abstractions. Although the research participant developed a productive conception of rate of change as an interiorized ratio, images of chunky continuo...

The undergraduate preparation of preservice teachers requires attention to the factors that enable and constrain a teacher from applying their mathematical knowledge to positive effect in their classroom. In this paper, we examine how the instructional decisions of three in-service secondary mathematics teachers were influenced by individually cons...

This paper reports findings from a study that establishes empirical support for Harel’s (Zentralblatt für Didaktik der Math 40:893–907 2008b) inclusion of mathematical ways of thinking as a component of teachers’ professional knowledge base. Specifically, we examined the role of quantitative reasoning (Smith and Thompson, in: Kaput, Carraher, Blant...

Growing interest in "flipped" classrooms has made video lessons an increasingly prominent component of post-secondary mathematics curricula. However, relatively little is known about how students watch and learn from instructional videos. We describe and use an eye-tracking methodology to investigate attentive fidelity-the degree to which students...

Tallman (2015) argued that pedagogical content knowledge is a form of content knowledge with particular characteristics that endow it with pedagogical utility, and he conjectured that an essential characteristic of a teacher’s content knowledge is her conscious awareness of the mental actions and conceptual operations that comprise her mathematical...

This paper reports findings from a study that explored the effect of a secondary mathematics teacher’s level of attention to quantitative reasoning on the quality and coherence of his instruction of angle measure. I analyzed 37 videos of an experienced teacher’s instruction to characterize the extent to which he attended to supporting students in r...

This paper reports findings from a study that explored the effect of a secondary mathematics teacher's level of attention to quantitative reasoning on the quality and coherence of his instruction of angle measure. I analyzed 37 videos of an experienced teacher's instruction of trigonometric functions to characterize the extent to which the teacher...

I present the results of a study designed to determine if there were incongruities between a secondary teacher's mathematical knowledge and the mathematical knowledge he leveraged in the context of teaching, and if so, to ascertain how the teacher's enacted subject matter knowledge was conditioned by his conscious responses to the circumstances he...

We describe the Algebra and Precalculus Concept Readiness (APCR) instrument and the Calculus Concept Readiness (CCR) instrument, and the reasoning abilities and understandings they assess. We share several tasks from these instruments to illustrate specific reasoning abilities that are needed for understanding precalculus and ideas in introductory...

Teachers must recognize the knowledge they possess as appropriate to employ in the process of achieving their goals and objectives in the context of practice. Such recognition is subject to a host of cognitive and affective processes that have thus far not been a central focus of research on teacher knowledge in mathematics education. To address th...

In this study, we developed a three-dimensional framework to classify post-secondary Calculus I final exams. Our Exam Characterization Framework (ECF) classifies individual exam items according to the cognitive demand required to answer the item, the representational context in which the item is asked, and the format of the item. Our results from u...

We know derivatives are about rates. Why don't our students?

The final exam in a mathematics course is one source of information about the nature and level of student learning that is expected in the course. In this study, a three-dimensional framework was developed to analyze post-secondary calculus I final exams in an effort to determine the skills and understandings that are currently being emphasized in...

## Projects

Projects (4)

The growing interest in progressive instructional formats such as "flipped" classrooms has made video lessons an increasingly prominent component of post-secondary mathematics curricula. However, relatively little is known about how students watch and learn from video lessons. This project involves conducting design research to generate knowledge about how students engage with, make sense of, and learn from videos addressing foundational calculus concepts. In this three-year study, the project team will create, refine, and disseminate materials for creating video lessons for post-secondary introductory calculus courses; collect data to analyze the aspects of the videos that students attend to determine how students make sense of the videos, and identify what students learn from watching the videos; and investigate the impact on student learning of various ways of structuring students' video- watching experience.

The Mathematical Inquiry Project (MIP) is a statewide collaboration among mathematics departments at the 27 public institutions of higher education in Oklahoma to foster sustainable, large-scale reforms to improve learning, applicability, and equity in entry-level mathematics courses.