Constructing mathematical proofs is a fundamental yet challenging skill in secondary school geometry. While technology has been used to scaffold different aspects of the proving process, existing approaches often separate inquiry and conjecturing from formal proof or focus on structural and technical assistance without addressing students' initial…

This executive summary highlights findings from the full report (published separately) which analyzes construct and predictive validity of a Social and Emotional Learning (SEL) Competency Survey. Students' SEL skill ratings were correlated with other measures of SEL skills and other outcomes of interest. A separate research brief also was…

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

This research brief highlights findings from the technical report (published separately). Student-level analyses were conducted with the SEL Skills Survey and the Student Climate Survey to determine if a single measure of students' SEL skill acquisition and perceptions of school climate is possible. [For the Technical Report, see ED629195.]

The objective of this paper is to discuss the didactic potential offered by the use of a Dynamic Geometry System (DGS) in introducing students to theoretical thinking and specifically to the practice of proof. Starting from a discussion about what constitutes the general objective in developing students' sense of proof, the notion of Theorem is…

One of the great pleasures of being a mathematics teacher lies in experiencing that very special buzz in the classroom that occurs when every single student is thoroughly engrossed in the task the teacher has set them. The teacher knows that in those precious moments genuine learning is taking place, however noisy and chaotic it may appear to an…

In the era of globalization, the trend towards learning Chinese as a foreign language (CFL) has become increasingly popular worldwide. The increasing demand in learning CFL has raised the profile of the Chinese proficiency test (CPT). This study will analyze in depth the inadequacy of current CPT's utilizing the common European framework of…

A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics.…

This article describes the development and two studies on the construct validity of the Academic Emotions Scale (AES). The AES is a French self-report questionnaire assessing six emotions in the context of school learning: enjoyment, hope, pride, anxiety, shame and frustration. Its construct validity was studied through exploratory and…

In the framework of a long term teaching experiment we present an Educational approach based on the use of a dynamic geometry software and a symbolic manipulator. Here we present the general ideas of the followed approach focusing on how meanings can originate from phenomenological experience and evolve under the guidance of the teacher. In…