Problem-solving ability was one of the competencies that students had to have, but it became more important when learning mathematics. Quite a lot of research has studied this ability, but not much has studied how to optimise it, especially using didactical design research based on lesson study. Participants in this research were 10 students…

Empirical evidence demonstrates the effect of productive failure (Kapur, 2008) on disciplinary knowledge. However, there is no clear theoretical explanation for why this is the case. Empirical evidence on argumentation and education shows the impact of curricular embedded deliberative argumentation on learning. However, these two trends of…

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…

Project-based learning (PBL) aims to foster students' problem-solving ability and collaboration by engaging them in completing a project in teams. Researchers have indicated the importance of guiding students to make comparisons and reflection during the process of project-based learning. Therefore, the present research proposed a peer…

The phenomenon of teachers designing their own instructional materials is gaining more attention in research. Different aspects of this enterprise have been examined--its potential to reveal the complexity of teachers' instructional planning considerations, the design principles employed by teachers to realise instructional goals, among others. In…

Creativity, one of the cornerstones of students' 21st-century skills, is regarded as an important learning outcome of science, technology, engineering, arts, and mathematics (STEAM) education. Meanwhile, problem-based digital making (DM), which combines the child-friendly programming activities of DM with problem-solving elements, is an emerging…

At an unrivaled and enduring pace, computing has transformed the world, resulting in demand for a universal fourth foundation beyond reading, writing, and arithmetic: computational thinking (CT). Despite increasingly widespread acceptance of CT as a crucial competency for all, transforming education systems accordingly has proven complex. The…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

As the core element of classroom teaching, questions play an essential role in constructing students' knowledge systems and cultivating their ability to discover, explore, analyze, and solve problems. Therefore, the design and application of appropriate questions is the key to the success of classroom teaching. Teaching based on protocol-guided…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

The study aims to investigate prospective middle school mathematics teachers' mental actions related to debugging, which is one of the computational thinking skills in the modeling process. The study was conducted with a single-case embedded model. The collaborative working group consisted of three prospective mathematics teachers selected by…

One challenge facing the fields of mathematics education and special education is how to design instruction on fraction concepts that can meet the needs of diverse learners. An innovation that shows promise is to base instructional design upon well-established trajectories of students' fraction learning. However, little research has been done to…

More research is needed on how to best use analytics to support educational decisions and design effective learning environments. This study was to explore and mine the data captured by a digital educational game designed for middle school science to understand learners' behavioral patterns in using the game, and to use evidence-based findings to…

Productive Failure (PF) facilitates students' conceptual knowledge by delaying instruction until after problem solving. While PF is well investigated in middle and high school students, little is known about its effectiveness in younger students. Studies in younger samples, which implemented delayed instruction designs similar to those used in PF…

Learning the content of entrepreneurship arithmetic is an extension of social arithmetic that focuses on mathematical calculations in business or creative economy. Most teachers do not link students' daily activities to classroom teaching and learning on traditional markets around the environment. This significantly affects the interest in…