In this dissertation, I K-8 mathematics teacher agency and learning within a research-practice partnership (RPP) context. I asked three primary research questions: (a) How is teacher agency enacted within the RPP?; (b) what do teachers perceive they are learning from their participation in the RPP?; and (c) how is teacher agency connected to…

According to the author, the "Australian Curriculum: Mathematics (AC:M) requires primary school students to measure the attributes of angle, time, temperature, length, area, capacity and mass. This article outlines some misconceptions held by primary school students which appear to stem from them not understanding terminology concerning the…

The purpose of this article is to introduce a lesson fondly referred to as the 'Lego Shop' lesson. It stands out as not only the most engaging lesson we've conducted but is also highly adaptable to accommodate a diverse range of learners. Successfully implemented across all year levels, from Foundation to Year 6, this lesson has proven to be…

Mathematical Internet memes are examples of how the creative thrust characterising the Web 2.0 environment reaches the field of mathematics, translating mathematical statements into a new digital form endowed with an epistemic potential that is capable of initiating a process of mathematical argumentation. The research presented in this paper aims…

Inductive reasoning is used when generalizing from particular cases to a general theory. The purpose of this paper is to present some highlights in the history of the problem of induction through notes on a selection of writers from ancient Greece to modern times. These notes contribute to the argument that there is a fundamental problem with…

Translation skills are very important possessed by students, but currently, there are still many students who have difficulty in translating between representations. The purpose of this study is to analyze students' errors in translating from symbolic representations to verbal and graphic representations. This research was descriptive study with…

Psychometric work with young children faces the particular challenge that children's attention spans are relatively short, and therefore, shorter assessments are required while retaining comprehensive coverage. This article reports on three empirical studies that encompass the development and validation of the research-based early mathematics…

The presented paper is devoted to the new teaching model of congruences of computer science students within the subject of discrete mathematics at universities. The main goal was to create a new model of teaching congruences on the basis of their connection with Diophantine equations and subsequently to verify the effectiveness and efficiency of…

In this article, we use a case study to explore the views of first-year university students on the differences between mathematics at school and at university, and on the changes to their study methods as they make the transition to university mathematics. We also consider their views on the differences and affordances of tasks that they encounter…

This article explains how explorations into the quadratic formula can offer students opportunities to learn about the structure of algebraic expressions. In this article, the author leverages the graphical interpretation of the quadratic formula and describes an activity in which students derive the quadratic formula by quantifying the symmetry of…

Using Cultural-Historical Activity Theory, we analyze lecturers' views on the aims and teaching practices of mathematical modelling (MM) education in Norway and England. We aim to expose the tensions that exist within the activity of teaching MM at university, such as those between multiple, sometimes competing, aims for teaching MM, or between…

This article investigates how the recent implementation of programming in school mathematics interacts with algebraic thinking and learning. Based on Duval's theory of semiotic representations, we analyze in what ways syntax and semantics of programming languages are aligned with or divert from corresponding algebraic symbolism. Three examples of…

Young children's symbolic magnitude understanding, or knowledge of how written numerals and number words can be ordered and compared, is thought to play an important role in their mathematical development. There is consistent evidence that symbolic magnitude skills predict mathematical achievement in later childhood and adulthood. Yet less is…

Responding constructively to unexpected events during a lesson is a particularly challenging facet of teaching. This study aimed to investigate how a secondary school mathematics teacher responded to learners' unexpected or unplanned offers in the teaching of algebra. A total of three sequential lessons were video recorded and the quality of the…

In order to enhance students learning environments, mathematics lecturers need to prepare suitable materials in their lessons. So improving the materials in textbooks based on learning theories is so important to enhance the ability of students in mathematics learning through problem solving activities. The purpose of this qualitative case study…