Research focused on learning mathematics in a 2nd language is generally located in individual 2nd-language contexts. In this ethnographic study, I investigated mathematics learning in 4 different second-language contexts: a mainstream classroom, a sheltered classroom for Indigenous students, a welcome class for new immigrants, and a…

The effects of prior encodings of manipulatives (red and blue plastic chips) on children's ability to use them as representations of quantity were tested. First graders (N = 73) were assigned to four conditions in which the encoding of plastic chips was experimentally manipulated. All children then participated in an addition activity that relied…

The sequence in which problems of different concepts are studied during instruction impacts concept learning. For example, several problems of a given concept can be studied together (blocking) or several problems of different concepts can be studied together (interleaving). In the current study, we demonstrate that the 2 sequences impact concept…

Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This "flexible procedural knowledge" distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students' flexible use…

Peer feedback is a useful strategy in teaching and learning, but its effectiveness particularly in introductory courses can be limited by the relative newness of students to both the body of knowledge upon which they are being asked to provide feedback and the skill set involved in providing good feedback. This paper applies a novel approach to…

Pupils' difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils' knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in…

Due to the shift of civilization from the Industrial Age to the Information Age, mathematical literacy has become a necessity in the twenty-first century. However, in order to learn and contribute to the mathematical community, one has to be in a state of good mental health. Where "good mental health," is defined as one who has developed…

Research tells us much about the effects of primary and lower-secondary schooling on skills inequality, but we know less about the impact of the next stage of education. This article uses a differences-in-differences analysis of data on literacy and numeracy skills in PISA 2000 and SAS 2011/12 to assess the contribution of upper-secondary…

We developed an intervention based on the learning by teaching paradigm to foster self-regulatory processes and better learning outcomes during complex mathematics problem solving in a technology-rich learning environment. Seventy-eight elementary students were randomly assigned to 1 of 2 conditions: learning by preparing to teach, or learning for…

We have created an inventory to characterize the teaching practices used in science and mathematics courses. This inventory can aid instructors and departments in reflecting on their teaching. It has been tested with several hundred university instructors and courses from mathematics and four science disciplines. Most instructors complete the…

In recent decades, the dropout rate in Abitibi-Témiscamingue is a worrying phenomenon. An analysis of ministerial examination results identifies that students in Abitibi-Témiscamingue have specific difficulties with mathematical problem solving tasks. Among the activities that develop those skills, the daily routines in mathematics seem to be a…

Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school…

The purpose of the present study was to examine factors that influence strategic flexibility in computational estimation for Chinese- and Canadian-educated adults. Strategic flexibility was operationalized as the percentage of trials on which participants chose the problem-based procedure that best balanced proximity to the correct answer with…

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…

In this article, we outline the findings of a Canadian survey study (N = 302) that focused on the extent of computer algebra systems (CAS)-based technology use in postsecondary mathematics instruction. Results suggest that a considerable number of Canadian mathematicians use CAS in research and teaching. CAS use in research was found to be the…