The aim of this study is to examine possible sources of negative math attitudes as well as some possible effects. The main body of this dissertation are three stand-alone chapters that are designed to be stand-along academic article. Chapter 2 uses data from the High School Longitudinal Study (HSLS) and lagged-dependent variable and school fixed…

The value of some university mathematics courses gets characterized within a liberal arts course of study in terms of supporting "critical thinking skills" or some other phrase for generally improved reasoning. This can be seen as an application of the millennia old "Theory of Formal Discipline" that claims that mathematics…

This theoretical, methodological, and empirical networking study investigated the potential of inferentialism to contribute to the study of meaning and collective argumentation in mathematics. I carefully attended to my worldview and explicated my philosophical process for identifying inferentialism as my theory of choice. I then drew on Prediger…

Polyiamonds are the 'and so on' when unit-squares are replaced with unit-equilateral triangles. Polyiamonds are used to play the satisfying Blokus variant, Blokus Trigon, where the playing grid is also hexagonal, and the playing pieces are all the polyiamonds from mono- to hex. This article discusses the use of polyiamonds in puzzles.

With the proliferation of video-based professional development (PD) courses for mathematics teachers, understanding the role of the facilitators of these courses has become an emerging field of theoretical and empirical study. The purpose of this article is to address some of the challenges and opportunities that facilitation of discussions…

Prior research has revealed robust and consistent relations between spatial and mathematical skills. Yet, establishing a causal relation has been met with mixed effects. To better understand whether, to what extent, and under what conditions mathematics performance can be improved through spatial training, we conducted a systematic meta-analysis…

Using data from the Applied Problems subtest of the Woodcock-Johnson Tests of Achievement (Woodcock & Johnson, 1989/1990, "Woodcock-Johnson psycho-educational battery-revised. Allen, TX: DLM Teaching Resources") administered to 1,364 children from the National Institute of Child Health and Human Development (NICHD) Study of Early…

A clear relationship exists between the consistent selection and implementation of cognitively demanding tasks and students' conceptual understanding of mathematics. However, mathematics teachers often struggle to maintain the cognitive demand of implemented tasks, with a number of factors identified as contributing to this decline. As many…

We further conceptualize the work of responsive teaching by contrasting it with a type of teaching we call endorsing. We define responsive teaching as a type of teaching in which the teacher: (a) ensures students' ideas are the genesis of ways of reasoning that are eventually taken up by the classroom community; and (b) continually assesses and…

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K-Grade 12 to develop flexibility in students' mathematical understanding and to provide them…

Two previous studies mapping university mathematics students' summative assessment diet in the UK revealed a clear picture. In general, there was a dominance of closed book examinations with a strong relationship to departmental league table position. The decade since then has seen many changes in higher education in the UK, particularly in the…

Students identified with emotional or behavioral disorders (EBD) display deficits across academic content areas, most notably in mathematics. We reviewed research on student-mediated math interventions for students with EBD. A total of 19 studies published between 1968 and 2019 met inclusion criteria, with 24 of 32 cases meeting the What Works…

Toulmin's argumentation model is an effective tool in the description of one step of an argument. However, there is a need to consider more than this model to portray a comprehensive argumentation process. The purpose of the study is to investigate types of global argumentation structures that emerged while prospective middle school mathematics…

Many mathematics educators believe a goal of instruction is for students to obtain conviction and certainty in mathematical statements using the same types of evidence that mathematicians do. However, few empirical studies have examined how mathematicians use proofs to obtain conviction and certainty. We report on a study in which 16 advanced…

The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical…