Discovery learning has long been a part of mathematics teaching in the elementary and middle grades. Since the 1960s and 1970s, based on the work of Jean Piaget, Jerome Bruner, and others, helping students 'discover' or 'construct' their own understandings of mathematical concepts through well-designed activities facilitated by a competent teacher…

In this article, we draw upon the Conceptual Profile Theory to discuss the negotiation of meanings related to the energy concept in an 11th grade physics classroom. This theory is based on the heterogeneity of verbal thinking, that is, on the idea that any individual or society does not represent concepts in a single way. According to this…

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form--where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach…

An equal-armed balance at equilibrium--the bar is horizontal--tips into disequilibrium upon displacing a weight. Equilibrium is restored by reversing that move--putting the weight back where it was, or doing the same on the other side. Piaget adopted the idea of equilibration to describe how the intellect, in relating to the world, develops.…

Research shows that misconceptions are usually detrimental to text comprehension. However, whether misconceptions also impair metacomprehension accuracy, that is, the accuracy with which one self-assesses one's text comprehension, has received far less attention. We conducted a study in which we examined students' (N = 47) comprehension and…

This study focuses on students' understanding of multiple representations of functions. It examines student responses to a task in which calculus students are asked to evaluate the derivative at a point of the cubing function when represented piecewise. Results suggest that attending to the graph of the piecewise function does not improve…

Organic agriculture courses and degrees in higher education have become more common in recent decades. In this article, we characterized instructor priorities for organic agriculture education and identified critical concepts and skills to be included in curriculum. We used interviews and surveys to learn from 19 instructors from universities and…

Meaning and understanding are didactic notions appropriate to work on concept comprehension, curricular design, and knowledge assessment. This document aims to delve into the meaning of school mathematical concepts through their semantic analysis. This analysis is used to identify and establish the basic meaning of a mathematical concept and to…

This paper discusses a game that can be used for introducing the binary representation of integers in an interactive and fun environment. The game is introduced in the way it is presented in an undergraduate Discrete Mathematics class. Variations of the game are discussed, particularly its extension to base-three representation of integers. It is…

Creativity is increasingly considered to be an important goal of education. While creativity can be influenced by many noncognitive factors (eg, personality and motivation), creative thinking remains the most important source of creativity. Creative thinking combines several cognitive processes leading to the generation and selection of new and…

The first day of many mathematics classes is filled with the formalities of the syllabus and a lecture introduction to the course content. Here, an alternative is presented where modeling is placed as the centerpiece to orient students to the work of differential equations; namely, to capture as beautifully and compactly as possible through the…

In this paper we present activities that can help students deepen their understanding of DC circuits and develop practical competences. The students investigate electric properties of commercially available conductive thread and solve a practical design task using the thread. The activities follow the framework of investigative science learning…

In this article, we integrate two constructionist approaches--the theory of constructed emotion and rational constructivism--to introduce several novel hypotheses for understanding emotional development. We first discuss the hypothesis that emotion categories are abstract and conceptual, whose instances share a goal-based function in a particular…

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

This laboratory experiment showcases electroless deposition, an autocatalytic reduction process performed in aqueous solution containing a metal ion in the presence of a reducing agent yielding a coherent metal film. One set of experiments has been performed by second-semester general chemistry students in a 3 h lab session. After preparing an…