Amongst important and under-researched questions are how introductory lessons can be designed for teaching initial proofs to junior high school students, and how such lessons enrich students' understanding of proofs. With a view to improving the learning situation in the classroom, in this paper we report on the various functions of introductory…

This is a case study on critical mathematics education lessons in South Korea. This study explores the development of the social consciousness of students via critical mathematics lessons in which students use mathematics as a tool to analyse social issues and to justify their claims about social issues. However, students rarely demonstrated much…

The purpose of this study is to analyze the complex argumentative structure in undergraduate mathematics classroom conversations during problem solving by taking into consideration students' and teacher' utterances in the classroom using field-independent Toulmin's theory of argumentation. Analyzing students' and teacher' utterances in the class…

In the project MultiMa (Multiple solutions for mathematics teaching oriented toward students' self-regulation), we investigated the effects of prompting students to use multiple solution methods while solving real-world problems on their learning. In this quasi-experimental study, we compared three treatment conditions. In one condition, students…

Scholastic tests regard cognitive abilities to be domain-specific competences. However, high correlations between competences indicate either high task similarity or a dependence on common factors. The present rating study examined the validity of 12 Programme for International Student Assessment (PISA) and Third or Trends in International…

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

The Common Core Standards require students to learn content and mathematical practices, and so teachers must have content knowledge and be able to engage in practices themselves. This raises the question of how novice teachers learn to engage in mathematical practices. I investigate pre-service secondary teacher learning of mathematical practices…

This study investigates the impact of teacher characteristics and instructional strategies on the mathematics achievement of students in kindergarten and first grade and tackles the question of how best to use longitudinal survey data to elicit causal inference in the face of potential threats to validity due to nonrandom assignment to treatment.…

It has given importance to the development of 21st century skills in every aspect of life. STEM (Science, Technology, Engineering, and Mathematics) education has played an important role to improve these skills and teachers are expected to be able to organize learning environments accordingly. The purpose of this research is to examine the…

This study examined mathematics and science teachers' perceptions and use of four types of examples, including typical textbook examples (standard worked examples) and erroneous worked examples in the written form as well as mastery modelling examples and peer modelling examples involving the verbalization of the problem-solving process. Data…

Background: The importance of knowledge and skills in mathematics for electrical engineering students is well known. Engineers and engineering educators agree that any engineering curriculum must include plenty of mathematics studies to enrich the engineer's toolbox. Nevertheless, little attention has been given to the possible contribution of…

What is important for citizens to know and be able to do? The OECD Programme for International Student Assessment (PISA) seeks to answer that question through the most comprehensive and rigorous international assessment of student knowledge and skills. The PISA 2015 Assessment and Analytical Framework presents the conceptual foundations of the…

This article presents a designed learning environment intended to engage students in learning about the relationships among multiple representations as they work together on a shared task. Over the course of several extended problem-solving sessions, groups developed several successive alignments of participants and representations as they learned…

The key questions are: is it true that persons with Down's syndrome can study mathematics only at a very elementary level? Might it be possible that their difficulties are mainly restricted to some fields, such as numeracy and mental computation, but do not encompass the entire domain of mathematics? Is the use of a calculator recommended? Is…

Taiwanese students consistently rank near the top on international exams on mathematics and science. In 2007, Taiwan recorded the highest TIMSS math score for eighth grade. The central education agency in Taiwan publishes detailed mathematics curriculum guidelines, which textbooks and national exams follow closely. In May each year, all ninth…