Self-assessment, in the education framework, is a methodology that motivates students to play an active role in reviewing their performance. It is defined as "the evaluation or judgment of 'the worth' of one's performance and the identification of one's strengths and weaknesses with a view to improving one's learning outcomes". The goal…

This paper proposes an experimental path aimed at guiding upper secondary school students to overcome that discontinuity, often perceived by them, between learning geometry and learning algebra. This path contributes to making students aware of how the algebraic language, formalized in the most powerful form by Descartes, grafts itself onto the…

Number talks encourage mathematical discourse and develop students' reasoning about number and operation (Parrish 2011). In a number talk, a teacher presents a purposefully crafted computation problem to solve mentally. Students share their solutions and explain their processes with the teacher facilitating the discussion through strategic…

There are opinions about approaching the proof in mathematics education need to change as providing students to understand the mathematical proof rather than developing formal mathematical proof skills. In this context, proofs without words described as informal proofs can be used in proof teaching. The purpose of this study was to investigate the…

The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students' attention. We present and compare various examples of how…

This study aims to generate the valid and practical PISA-like mathematics problems on uncertainty and data using the football game context of Asian Games. It also aims to see the potential effects of the problems towards the high school students' mathematical ability. This study used a design research methodology with the type of development study…

Purpose: To assess students' problem-solving skills, this study aims to investigate the consistency between self- and peer-ratings in consideration of the teachers' ratings in the process. Method: This study was a descriptive study which examines the mathematical problem-solving skills with the MFRM model concerning self-, peer- and teachers'…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

Suppose that there is an inexhaustible supply of $3 and $5 vouchers from the local supermarket. They may only be exchanged for items that cost an exact number of dollars made up from any combination of the vouchers. What is the highest amount not able to be obtained? This is an interesting problem in mathematical thinking and logic requiring only…

This article describes two heuristic strategies for problem solving: the "use of false assumption" strategy and the "use of double false assumption" strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances…

The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…

This study is to reveal the construction process of student representation in solving of ill-structured geometry problems. The three phases involved in the construction process are interpreting the problem, giving opinions, and concluding. A total of four high school students participated in Surabaya and Sidoarjo in this qualitative study. They…

Teachers use a variety of instructional strategies when they teach various mathematical topics and concepts. Some of these strategies have been found to positively affect the performance of learners while others do not. This study analysed the teacher questionnaire data from the Trends in International Mathematics and Science Studies (TIMSS) 2015…

Conceptual understanding is one of the main concerns of mathematics education. Numerous research have discussed student understanding of algebraic concepts, linear equations in particular. This research was drawn upon in order to develop a new approach for teaching and learning linear equations based on the equivalence concept, one that aims to…

Critical thinking skills are one of the four skills needed in the 21st century. Critical thinking skills are so important that they need to be taught and included in the school curriculum. This research aims to: (1) describe the critical thinking skills of junior high school students in solving mathematical problems and (2) identify the students'…