We adopted Brown's (1987) conceptualisation of metacognition to examine how student teachers can be taught metacognitive control while solving mathematical problems. In addition, tasks given to these student teachers were in-built with opportunities for them to be aware of the need for metacognition. We describe the use of the Practical Worksheet…

We describe an attempt by a former mathematics teacher to read an undergraduate mathematics proof aided by discussions with a mathematician using the language of mathematical problem solving. The literature on successful approaches to reading mathematics is scarce at the secondary and undergraduate levels. Shepherd, Selden and Selden (2012)…

We report on a long-term study which was executed in a German secondary school with 128 eights graders (ages 14 to 15) in four different classes. Two of these classes served as control groups. The mathematics lessons of the other two classes (treatment groups) were frequently enriched by distinguished phases in which structured argumentation and…

We encounter ratios on a daily basis. They also play an important role as a basic construct of thinking in many areas of school mathematics. For example, a fraction can be interpreted as the ratio of a part to the respective whole. Many children appear to have difficulties with fractions and although the concept of ratios is crucial for this…

Despite their apparent simplicity, the concepts of square numbers and square roots are problematic for high school students. I inquired into students' understanding of these concepts, focusing on obstacles that students face while attempting to solve square number problems. The study followed a modified analytic induction methodology that included…

Background: A potential problem of low-stakes large-scale assessments such as the Programme for the International Assessment of Adult Competencies (PIAAC) is low test-taking engagement. The present study pursued two goals in order to better understand conditioning factors of test-taking disengagement: First, a model-based approach was used to…

In order to achieve the present study's goal--to understand better the phenomenon of mathematical giftedness--we performed a multidimensional examination of the mental processing in students who exhibited mathematical expertise (EM) at the secondary school level. The study included participants from the three groups: students who excelled in…

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an…

This longitudinal study examines the relative importance of counting ability, additive reasoning, and working memory in children's mathematical achievement (calculation and story problem solving). In Hong Kong, 115 Chinese children aged 6 years old participated in 2 waves of assessments (T1 = first grade and T2 = second grade). Multiple regression…

To create a learning experience which replicates the process by which consultants, systems developers and business end users collaborate to design and implement a business application, a cross-functional student team project was developed and is described. The overall learning experience was distinguished by specific components and characteristics…

In this study, dynamic testing principles were applied to examine progression of analogy problem solving, the roles that cognitive flexibility and metacognition play in children's progression as well as training benefits, and instructional needs of 7- to 8-year-old gifted and average-ability children. Utilizing a pretest training posttest control…

Design in educational contexts is a relatively new topic. The basic idea of design and design-driven education is that students and teachers participate together in the planning, implementation and evaluation of learning projects. However, how design-driven education should be carried out in practice is yet to be established. Therefore, the aim of…

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

Purpose: This paper aims to discuss issues related to science, technology, engineering and mathematics (STEM) education. It is emphasized that the need to prepare students with twenty-first-century skills through STEM-related teaching is strong, especially at the elementary level. The authors present selected previous experiences, publications,…

With regard to the growing interest in developing teacher education to match the twenty-first-century skills, while many assumptions have been made, there has been less theoretical elaboration and empirical research on this topic. The aim of this article is to present our pedagogical framework for the twenty-first-century learning practices in…