This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

Using a Mixed Methods approach, this study investigated changes in levels of self-efficacy among elementary preservice teachers following a semester course on teaching elementary students' mathematics. Participants in this study included 347 preservice elementary teachers at a mid-size regional university who had just completed an elementary…

The objective of this paper is to present attitudinal and cognitive beliefs of two preservice secondary mathematics teachers about teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised ten task-based interviews, a series of five each with two participants, senior undergraduate preservice mathematics…

In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a "real-world" scenario. Even though the school values students' ideas, the reaction of the teacher to one student's alternative modelling of the problem suggests that he was expecting a particular answer to be…

In this proposal, I introduce a method for modeling the dynamics of a sixth-grade student's accommodation of his fractions scheme to include a disembedding operation (Steffe & Olive, 2010). I will describe a three-part approach consisting of a constructivist teaching experiment, retrospective analysis, and stochastic modeling of the student's…

This action research study explored a constructivist, flipped classroom approach to teaching developmental mathematics. This study was developed in response to a concern regarding a lack of success in developmental mathematics. Throughout the study, adult developmental learners were required to watch video lectures prior to attending class. Class…

This study explored the effectiveness of a unique math intervention program in a local school district in Orange County, California in terms of academic achievement and student perceptions about their math abilities as a result of their experiences in the program. As the predominate instructional approach, the program provided students with…

High school mathematics students often complete homework and study for unit tests without support to consider how these actions could contribute to their mathematical learning. Learning to learn mathematics invites students to bring into view how they learn mathematics. The constructivist grounded theory study reported in this presentation…

This study of "Preservice Secondary Mathematics Teachers' Beliefs about Teaching Geometric Transformations (GTs) using Geometer's Sketchpad (GSP)" aimed to explore the beliefs hold by preservice secondary mathematics teachers about teaching geometric transformations with Geometer's Sketchpad. In this study, I applied three methodological…

The purpose of this study is to determine elementary school teachers' and school principals' views on physical learning environments of schools where teachers are expected to implement the constructivist philosophy/approach. In this qualitative study, the researcher interviewed 48 elementary school teachers and 6 school administrators working in…

This study examined the influence of a researcher-conjectured learning trajectory instructional approach toward the enhancement of teachers' technological pedagogical content knowledge (TPACK). The study provides a rich description of how a learning trajectory, situated within a "social metacognitive-constructivist" instructional…

A learning center in the southeastern part of the United States used the Singapore mathematics curriculum (SMC) to support student learning of a wide range of mathematics skills. However, a study had yet to be conducted to gain an understanding about the administration and implementation of the program. This case study was conceptually based on…

The quality of mathematics teaching in Lesotho primary education remains one of the vexing problems in the education system. The study investigated how teachers viewed the impact of instruction on enhancing their knowledge of teaching. Data for the study were elicited from the second-year students enrolled for a Bachelor of Education in the…

This study addresses the problem of mathematics teachers' resistance to problem-solving models that align with constructivist perspectives because they feel pressure to utilize more teaching approaches that focus on preparing students for high-stakes tests. The purpose of this qualitative study was to explain how ninth grade mathematics students…

This article explores junior high school students' views regarding what it takes to be successful in mathematics. Qualitative and quantitative methods were employed to collect and analyse data, describe and interpret junior high school students (12-14 years) perceptions about what it takes to be successful in mathematics. 22 students from four…