With the implementation of the "Common Core State Standards for Mathematics," school administrators expect teachers to teach students on grade-level while preparing them to be college and career-ready. The purpose of this qualitative case study was to understand how secondary mathematics teachers prepare mathematics students from…

States are double scheduling algebra classes; using calculators and virtual manipulative-like algebra tiles; and applying interventions such as Response to Interventions, needs assessments, and various computer graphing technology such as Demos. However, during the school year 2018-2019, 12.9 percent of a state public school students failed to…

We consider here two questions posed by first-year undergraduate students in a statistics tutorial session. These questions are related, and each concerns an aspect of independence in probability. The notion of independence does tend to be a little less intuitive than some of the other elementary probabilistic concepts, thereby providing students…

In this article, we seek to understand how university students learn to use programming as an instrument for 'authentic' mathematical investigations. We use the instrumental approach as a framework, focusing on how the transformation of the programming language into an instrument requires that the user develops or mobilizes multiple schemes at…

Derek Hurrell shares a number of geometry tasks designed to tease out students' reasoning. Concrete materials are used to initiate discussions and develop a culture of reasoning in the mathematics classroom.

In this study, we investigate a sample of in-service teachers' professional noticing of slope. The analysis focuses on which elements of students' statements about slope teachers attend to, and how teachers interpreted those elements. Study results suggest that teachers attended to the vocabulary and mathematical focus of students' statements.…

The Action-Process-Object-Schema (APOS) theory is applied to study student understanding of implicit differentiation in the context of functions of one variable. The APOS notions of Schema and schema development in terms of the intra-, inter-, and trans-triad are used to analyze semi-structured interviews with 25 students who had just finished…

The purpose of the present article is to investigate the definition of matrix multiplication as a central issue in linear algebra courses. Applying both historical and pedagogical approaches, it focuses on the philosophy of generating the usual matrix multiplication, as a special binary operation, with its partly unexpected form compared with the…

In this note, some variants of Cauchy's mean value theorem are proved. The main tools to prove these results are some elementary auxiliary functions.

When teaching a novel mathematical concept, should we present learners with abstract or concrete examples? In this experiment, we conduct a critical replication and extension of a well-known study that argued for the general advantage of abstract examples (Kaminski, Sloutsky, & Heckler, 2008a). We demonstrate that theoretically motivated yet…

In this study, we propose the notion of a socio-mathematical norm to explore the affective aspects of a classroom in the context of problem posing. Our case is a gifted and talented mathematics classroom with twelve students. The primary source of data consists of forty-three mathematics lessons. Our theoretical stance defines two dimensions of a…

This article builds upon a systematic review of 53 articles in international research journals and makes three main contributions. First, it develops a method for identifying motives, values, and assumptions in research by analysing segments of text in journal articles. Second, it represents a reflective account of research within the field of…

This article argues the importance of teaching students about the philosophical and mathematical underpinnings of Australia's superannuation system as an example of a real-world problem context. It also provides a rationale for teaching financial modelling and decision-making in ways that respect the diverse financial realities represented in…

Ciphers based on rotor machines were the state-of-the-art in the mid-1900s, with arguably the most famous being the German Enigma. We have found that students have great interest in the Enigma and its cryptanalysis, so we created our own rotor cipher that is simulated with shifting tables and can be cryptanalyzed. Ours and the historic rotor…

The Enforcement Decree of the Elementary and Secondary School Act (2015) mandates that from 2016 all middle schools in Korea must administer one semester as a free semester (FS), called an exam-free semester or, alternatively, a free learning semester. Consequently, some Korean parents and students have expressed a feeling of anxiety about having…