This study investigated preservice secondary mathematics teachers' difficulties with and understanding of graphs of two-variable inequalities with the lens of the APOS theory. The analysis showed that most teachers understood inequality graphs as actions, at best, and used informal rules to construct graphs. They also had difficulty justifying…

For this brief, EdTrust and Just Equations partnered to explore differences in patterns of math course enrollment for high school students using data from students who participated in the 2009 High School Longitudinal Study (HSLS:09). Like other research has shown, the authors find that high-achieving Black and Latino students and students from…

Background: Persisting after experiencing difficulty allows students to work in the upper ends of their zones of proximal development, where most learning occurs (Ventura et al., 2013; Vygotsky & Cole, 1978). Digital educational games promote productive persistence by allowing students to repeat the same or similar problems until they reach…

We investigate teacher beliefs about discourses for equation solving and the challenges these beliefs might pose for the implementation of instructional practices that promote deductive reasoning in algebra. To uncover these beliefs, we recorded three video explanations of solutions to the same linear equation with distinct discursive…

Teaching in ways responsive to the cultures of our students is vital towards enhancing equity of access to mathematics achievement and putting educational policy into practice. New Zealand has the largest group of Pasifika people in the Western world, a multi-ethnic group of indigenous people from Pacific Island nations who have differing cultural…

The aim of this paper is to analyse the reasoning and symbolisations used by sixth grade Moroccan students in solving a task based on figurative patterns. Our analysis aims at identifying the systems of actions elaborated by the students to give the general expression of the sequence, according to their perceptions of the sequence of its patterns.…

Literature has established that some learners encountered difficulties solving first order ordinary differential equations (ODEs). The use of error analysis in teaching ODEs is believed to make essential contribution towards calculus knowledge development. This paper therefore focuses on analyzing pre-service teachers' (PSTs) errors and…

This article describes a modeling project the author did with his algebra, geometry, and applications students in grades 9, 10, and 11 as an enrichment and exploration of an extremely relevant real-world phenomenon and introduction to the adult profession of epidemiologist. With discussion and exploration, this project consumed two periods of 88…

This research study compares the use of two different online asynchronous discussion technologies in hybrid algebra classes at an urban community college. One of the technologies is the discussion board, which utilizes text commenting, and the other technology is VoiceThread, which allows users to interact with audiovisual commenting. Students…

This paper constructs an overview of the historical development of the International Journal for Technology in Mathematics Education (IJTME) during the period 2004- 2018. The titles of the published papers in this period are examined, focusing on what technological tools were studied, and what theoretical ideas were used to study the teaching and…

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to regression and correlation analysis to increase student understanding of the concepts and methods in elementary statistics courses and in courses at the college algebra/precalculus level that…

Successful mathematical problem-solving relies on choices about how best to represent and solve problems. In this article, a range of methods and strategies are presented for solving a single mathematical problem, including novel methods posed by in-service teachers at one Australian university. The variety of problem-solving strategies rely on…

There is a compelling need to develop an algebra teacher self-efficacy instrument (ATSEI) as algebra continues to be considered a gatekeeper course for postsecondary educational and career opportunities, which is seen as a crucial piece in closing the achievement gap. This paper reports on the development and validation of the ATSEI, an instrument…

Teaching determinants poses significant challenges to the instructor of a proof-based undergraduate linear algebra course. The standard definition by cofactor expansion is ugly, lacks symmetry, and is hard for students to use in proofs. We introduce a visual definition of the determinant that interprets permutations as arrangements of…

Proving is a process that has important roles in terms of learning and teaching in almost all the areas of mathematics. Because the process of proof constructions an extensive process that includes skills as mathematical thinking, reasoning and making connections. Reasoning is one of the most important components of this process. However, most…