The aims of this study were to synthesize and evaluate the learning model in gamification environment together with cartoon animation media to promote students' creative problem-solving skills. This study was divided into three phases, (i) synthesized and evaluated the appropriateness of learning model (ii) developed cartoon animation and (iii)…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

Representation is widely viewed as central to mathematical problem solving, while online scaffolding is considered helpful in supporting learners' progress from actual to potential developmental levels of mathematics understanding. Therefore, this study investigated the effectiveness of employing online single vs. multiple representational…

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance,…

This paper aims to discuss the use of Brousseau's Theory of Didactical Situations in mathematics (TDS) for eighth-graders to explore the concept of triangle inequality in Euclidean geometry. Data sources included observation notes, video recordings of lessons, and students' written work. Data analysis was done through a deductive content analysis…

Ferris wheel is one amusement playground that resembles a giant spinning wheel. Many students are familiar with the Ferris wheel in the mini version of it at night market festivals. This is the potential for learning mathematics. Furthermore, there is a mathematical learning approach called Indonesian Realistic Mathematics Education (IRME) where…

In the present study, we tested the hypotheses that: a) there are individual differences in secondary students' conceptual and procedural fraction knowledge, and b) these differences are predicted by students' approach (deep vs. surface) to mathematics learning. We used two instruments developed and evaluated for the purposes of the study which…

Open learning model as well as conventional learning model is a learning model that is able to enable students in acquiring knowledge and learning experiences. The purpose of this research is to know the difference of learning result between students taught by using model of open matter problem and conventional learning model on the subject of…

This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and…

Intuitive knowledge seems to influence human decision-making outside of consciousness and differs from deliberate cognitive and metacognitive processes. Intuitive knowledge can play an essential role in problem solving and may offer the initiation of subsequent learning processes. Scientific discovery learning with computer simulations leads to…

Flexibility in transforming algebraic expressions is recognized as fundamental for a rich procedural knowledge. Here, flexibility in-depth is proposed as the ability to apply one strategy to a wide range of unfamiliar expressions. In this study, design experiments with four groups of students were conducted to support students' flexibility…

This study compared students' learning in troubleshooting and problem solving activities. The troubleshooting activities provided students with solutions to conceptual problems in the form of refutation texts; namely, solutions that portray common misconceptions, refute them, and then present the accepted scientific ideas. They required students…

Mathematical representation is an important skill in mathematics learning that enables students to interpret and solve problems with ease. However, building confidence in such a skill can be difficult for some students, especially for those who lack self-motivation skills. Therefore, this study examines the effects of the think-talk-write strategy…

Mathematical problem solving typically involves manipulating visual symbols (e.g., equations), and prior research suggests that those symbols serve as diagrammatic representations (e.g., Landy & Goldstone, 2010). The present work examines the ways that instructional design of student engagement with these diagrammatic representations may…

This article seeks to substantiate the need for the prognostic assessment of the degree to which school students are prepared to master new types of activity, which underlie their design of an individual learning route at an appropriate senior stage of learning. The authors discuss the concept of project competence as an integral characteristic of…