The aim of this study was to analyse preservice elementary mathematics teachers' concept definitions of circle, circular region, and sphere concepts in geometrical terms. The research was conducted during the 2016-2017 academic year with 56 preservice mathematics teachers enrolled within a teacher education programme at a state university in…

Generalization is considered to be an essential part of mathematical reasoning and proving, and it has many definitions in mathematics education research. Despite its centrality, teachers often have difficulty identifying and responding to generalization in students' work. In this study, we focus on preservice teacher's (PTs) ability to describe…

The purpose of this study was to analyze the prompts that preservice secondary mathematics teachers used for the acquisition of mathematics knowledge in dynamic geometry environment tasks. The participants, four preservice secondary mathematics teachers who were enrolled in a computer-supported mathematics education course, designed a dynamic…

In the context of the sociocultural approach, the authors studied the problem of the development of the students' conceptual mental structures in the process of geometry teaching. An educational activity for the development of a generalized ability to solve geometry construction problems in electronic educational environment served as a…

This study aims to analyze how the Mathematics Teacher Candidates (MTCs) define the "prism" and "pyramid" concepts in geometry. The research was carried out in 2017-2018 academic year with 92 MTCs. This test consists of 3 open-ended questions that MTCs can answer conceptually. The first openended question was as "Define a…

Previous research has verified the benefits obtained when learners trace out worked examples with the index finger. Our study conducted two experiments to explore the reasons for this phenomenon and its generalizability. Experiment 1 compared the learning effects among tracing, non-tracing, and cueing methods. The cueing method was included to…

The present paper examines a patterning activity that was organised within a teaching experiment in order to analyse the different uses of variables by secondary school students. The activity presented in the paper can be categorised as a pictorial/geometric linear pattern. We adopted a student-oriented perspective for our analysis, in order to…

Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional…

As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

Two thousand four hundred years ago Socrates gave a remarkable lesson of geometry, perhaps the first detailed record of a pedagogical method in vivo in history [Plato. (2008). "Apologia de Socrates. Menon. Cratilo." Madrid: Alianza Editorial]. Socrates asked Meno's slave 50 questions requiring simple additions or multiplications. At the…

This paper explores how young Indigenous students' (Year 2 and 3) generalise growing patterns. Piagetian clinical interviews were conducted to determine how students articulated growing pattern generalisations. Two case studies are presented displaying how students used gesture to support and articulate their generalisations of growing patterns.…

To examine whether enantiomorphy (i.e., the ability to discriminate lateral mirror images) is influenced by the acquisition of a written system that incorporates mirrored letters (e.g., b and d), unschooled illiterate adults were compared with people reading the Latin alphabet, namely, both schooled literate adults and unschooled adults…

The main purpose of this study is to determine the strategies of using the generalizing patterns of the primary fifth grade students. The practice of this research is conducted on twelve students, which have high, middle and low success levels. Task-based interviews and students journals are used as the tools for data collection. For the analysis…

Used 2 12-year-old children to investigate deductive and inductive reasoning in plane geometry. A LOGO microworld was programmed to measure distances and turns relative to points on the plane. Learning environments like this may enhance formation of inductive geometrical understandings. (Contains 44 references.) (LDR)