As part of curriculum changes in South Africa, an introductory programming language, Scratch, must first be taught before switching to the well-established teaching of Delphi. The nature of programming in Scratch is considerably different from that in Delphi. It was assumed that the teaching of Scratch as introductory programming language could…

This article describes a study of how students construct relations of authority during dyadic mathematical work and how teachers' interactions with students during small group conferences affect subsequent student dynamics. Drawing on the influence framework (Engle, Langer-Osuna, & McKinney de Royston, 2014), I examined interactions when…

The purpose of this study was to analyze the effects of schema instruction on the mathematical problem solving of students with emotional or behavioral disorders (EBD). The participants were two fourth-grade students identified with EBD. The intervention package consisted of schema instruction, strategy instruction on problem-solving heuristics…

Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…

The purpose of the study is to reveal the elementary mathematics student teachers' difficulties encountered in the solution of a modelling problem, the strategies to overcome those difficulties and whether the strategies worked or not. Nineteen student teachers solved the modelling problem in their four or five-person groups, and the video records…

For years the text of choice for developing excellence as a teacher of K-12 students with moderate and severe disabilities, this clearly written work has now been revised and updated. Chapters provide step-by-step procedures for designing standards-based individualized education plans and evaluating and enhancing student progress. Methods and…

In this article, we discuss how to use a diagrammatic approach to solve the classic sailors and the coconuts problem. It provides us an insight on how to tackle this type of problem in a novel and intuitive way. This problem-solving approach will be found useful to mathematics teachers or lecturers involved in teaching elementary number theory,…

This article presents the authors' response to Asha K. Jitendra's Response to Xin and Zhang ("The Journal of Educational Research," 2009, Vol. 102, No. 6). The claim of "factual errors, including inappropriate quotes, misrepresentation of information, and inadequate scholarship in Xin and Zhang's text" are not justified. In this rejoinder, the…

Solving word problems is a difficult task for students at-risk for or with learning disabilities (LD). One instructional approach that has emerged as a valid method for helping students at-risk for or with LD to become more proficient at word-problem solving is using schemas. A schema is a framework for solving a problem. With a schema, students…

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

The read-aloud accommodation (RA) is frequently provided to students with high-incidence disabilities to facilitate their access to learning opportunities during instruction and to allow them to demonstrate knowledge and skills during testing. Empirical support for this accommodation has been somewhat mixed, and has primarily focused on…

This paper is essentially about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics. We present a simple numerical procedure for the solution of the equation of motion of the system to…

This case study describes the ways in which problems involving additive differences with unknown starting quantities, constrain the problem solver in articulating the inherent quantitative relationship. It gives empirical evidence to show how numerical reasoning takes over as a Grade 6 student instantiates the quantitative relation by resorting to…

In this paper we examine a commonly suggested proof construction strategy from the mathematics education literature--that students first produce an informal argument and then use this as a basis for constructing a formal proof. The work of students who produce such informal arguments during proving activities was analyzed to distill three…