A serious drawback to electric vehicles [batteries only] is the idle time needed to recharge their batteries. In this challenge, students can develop ideas and concepts for battery change-out at automotive service stations. Such a capability would extend the range of electric vehicles.

Tabular presentations of student data often hide information about the switches in responses by individual students over the course of a semester. We extend unpublished work by Kanim on "escalator diagrams," which show changes in student responses from correct to incorrect (and vice versa) while representing pre- and postinstruction…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) emphasize the Standards for Mathematical Practice (SMP) that describe processes and proficiencies included in the NCTM Process Standards (NCTM 2000) and in the Strands for Mathematical Proficiency (NRC 2001). The development of these mathematical practices should happen in…

When learning a new math concept, should learners be first taught the concept and its associated procedures and then solve problems, or solve problems first even if it leads to failure and then be taught the concept and the procedures? Two randomized-controlled studies found that both methods lead to high levels of procedural knowledge. However,…

In this article the author describes a problem posed to his class, "How many squares are there on a checkerboard?" The problem is deliberately vague so that the teacher can get the students to begin asking questions. The first goal is to come to an agreement about what the problem means (Identify the problem). The second goal is to get…

Provision of transcripts and certificates at the time of graduation, a normal expectation in higher education in developed countries, was a challenge in the case-study university, which risked affecting stakeholder satisfaction and student enrollment. A group problem-solving method was used to identify the scope of the problem, the goal, and to…

A mathematics classroom that reflects the vision of NCTM's "Principles and Standards for School Mathematics" will have the teacher posing problems, asking questions that build on students' thinking, and encouraging students to explore different solutions. In teaching about area, it is not sufficient to give students the…

Past research has shown that students have difficulty developing a robust conception of function. However, little prior research has been performed dealing with student knowledge of function composition, a potentially powerful mathematical concept. This dissertation reports the results of an investigation into student understanding and use of…

To interpret in detail the meaning-making in the classroom and the corresponding teacher semiotic mediation, we have resorted to Peirce's triadic ign theory, interpreted by Sáenz-Ludlow and Zellweger. We present an example of the use of a few elements of that theory in the analysis of a classroom episode in which meaning is constructed with the…

The purpose of this study is to develop design principles for crafting tasks that will encourage conjecturing and proving in the context of elementary number theory at the undergraduate level. From the analyses of the written work of 46 prospective mathematics teachers on a task designed according to these principles, we think that there is…

In this paper, we discuss the relevance of 'Grundvorstellungen' (GVs), a didactical category to analyze students' mental models in comparison to the intended mathematical meanings in the context of Linear Algebra and Analytic Geometry. Diagnostic tasks were used to reveal students' conceptual understanding in this field of expertise. In…

In this study we investigated how 200 students in seventh grade (mean age = 12.38 years) solved simple addition problems and if the way they performed simple addition was related to their achievement in mathematics. Four performance groups were identified: proficient, almost proficient, inaccurate min counting and accurate min counting. More than…

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…

This study focuses on structured and guided inquiry instruction regarding question asking behaviors and curiosity of elementary students in Turkey. 177 sixth graders in 8 science courses were randomly assigned to treatment groups. Analysis of the data revealed that students in the guided inquiry groups asked higher-cognitive level questions and…

Hospitality students are required to be able to address challenging cases or problems in the work environment. However, traditional lecture- or exam-based instruction leaves a gap between theory and practice. On the other hand, modern youth live and socialise in an increasingly digital environment, and one of their biggest pastimes is playing…