While proof has been studied from different perspectives in the mathematics education literature for decades, students continue to struggle to build proof comprehension. Complicating this, the manner in which proof comprehension is assessed largely remains to be the definition-theorem-proof format in which students are asked to reproduce proofs or…

This dissertation focused on mathematics instruction in early grades (Pre-K-3rd grade) by exploring teachers' beliefs about mathematics teaching and the teaching practices of one teacher. I specifically examined teachers' beliefs and one teacher's practices that reflect asset-based views of students and support mathematics learning with…

Mathematics assessment is integral in enabling teachers to implement specially designed instruction for students with disabilities. This article presents an overview of an underutilized form of assessment, the clinical interview. A type of diagnostic assessment, clinical interviews are critically important when designing individualized instruction…

Brief experimental analysis (BEA) is a methodology of rapidly implementing interventions and observing the effect each has on student performance. Extensive research exists demonstrating the utility of BEA in identifying effective reading interventions for students, but comparatively little research exists regarding BEA and mathematics. The…

Writing skills are essential for success in the 21st-century school and workplace, but most classrooms devote far more time to reading instruction, with writing often addressed in isolation or excluded. In this insightful professional development resource and text, leading researchers discuss why and how to integrate writing and reading…

The Association for the Advancement of Computing in Education (AACE) is an international, non-profit educational organization. The Association's purpose is to advance the knowledge, theory, and quality of teaching and learning at all levels with information technology. "E-Learn 2019: World Conference on E-Learning" took place in New…

The purpose of the research is to evaluate the games prepared by pre-service classroom teachers within the scope of "Mathematics Teaching 1" and "Mathematics Teaching 2" courses, which are included in the undergraduate classroom teaching programs in Turkey, and to make predictions on the game design skills of pre-service…

Classic stock portfolio analysis provides an applied context for Lagrange multipliers that undergraduate students appreciate. Although modern methods of portfolio analysis are beyond the scope of vector calculus, classic methods reinforce the utility of this material. This paper discusses how to introduce classic stock portfolio analysis in a…

In this paper, we propose the mathematical cognitive technology noticing framework for examining how mathematics teachers evaluate, select, and modify mathematical cognitive technology to use in their classrooms. Our framework is based on studies of professional and curricular noticing and data collected in a study that explored how secondary…

This mixed-methods study explores changes over time in assessment strategies and identifies variables that facilitate that change by examining assessment practices of 11 teacher candidates enrolled in a one-year postbaccalaureate teacher education program that prepares for teaching in rural and urban settings of Alaska. Analyzing multiple data…

Random forests are presented as an analytics foundation for educational data mining tasks. The focus is on course- and program-level analytics including evaluating pedagogical approaches and interventions and identifying and characterizing at-risk students. As part of this development, the concept of individualized treatment effects (ITE) is…

It is understandable that misuse of the terms "specially designed instruction" (SDI), "high-leverage practices" (HLPs), "explicit instruction" (EI), and "intensive instruction"(II) has bred confusion among professionals, and this confusion may lead to miscommunication and misunderstandings in the field.…

This qualitative exploratory case study focused on the achievement gap in mathematics that exists in one urban North Carolina middle school and the strategies used by school personnel to narrow this gap. The goal of this research was to determine effective instructional strategies and best practices used to engage students in learning that will…

The objective of this study is to demonstrate that the criteria of didactical suitability, proposed by the theoretical framework known as the Onto-Semiotic Approach (OSA) of mathematical knowledge and instruction, are powerful tools for organizing the reflection and assessment of instruction processes carried out by mathematics teachers. To this…

Since teachers always teach area and perimeter together--and they are both introduced soon after the definition of a rectangle--it is not surprising that students mix up the notions of area and perimeter. Changing the investigation on maximising the area of a fixed perimeter from the traditional, but boring, "Sheep pens" to the much more…