Interleaved practice combined with comparison prompts can better foster students' adaptive use of subtraction strategies compared to blocked practice. It has not been previously investigated whether all students benefit equally from these teaching approaches. While interleaving subtraction tasks prompts students' attention to the different task…

Not-knowing is an underexplored concept defined as an individual's ability to be aware of what they do not know to plan and effectively face complex situations. This paper focuses on analyzing students' articulation of not-knowing while completing geometric reasoning tasks. Results of this study revealed that not-knowing is a more cognitively…

This study answers two research questions: (1) How do 12- and 13-year-old students respond to metacognitive questions posed during a complex task in mathematics or in science and (2) Do these responses differ by discipline? Content analysis was applied to responses collected from 92 students from a French-speaking Belgian school. The results…

Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires…

Trigonometry is an important part of secondary school mathematics, but it is usually challenging for students to understand and learn. Since trigonometry is learned and used at a university level in many fields, like physics or geodesy, it is important to have an insight into students' trigonometry knowledge before the beginning of the university…

We explored primary pre-service teachers' beliefs about challenging mathematical tasks and the role they perceived their initial teacher education played in influencing those aspects. Fifty-seven pre-service teachers completed an online questionnaire, and four participants were individually interviewed. Results showed that most participants…

This study investigated the effectiveness of using a sequence of worked examples as part of the feedback cycle. Worked examples were either presented as full worked examples or partial worked examples (single-step and completion formats). In two experiments, grade 8 students completed a learning phase on a mathematics topic, which was immediately…

Although trigonometry is an important section in secondary school mathematics curricula, many teachers find it challenging to teach as a result of insufficient pedagogical content knowledge (PCK). Therefore, the aim of this article was to report on how PCK on trigonometry manifests itself in teachers' practice. This exploratory case study was…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

Several studies related to mathematical proof have been done by many researchers on high-level materials, but not yet examined on the material of transformation geometry. The aim of this research is identification learning obstacles pre-service teachers on transformation geometry. This study is qualitative research; data were collected from…

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…

Instruction can be made relevant to students when it draws upon and utilizes their interests, experiences, and "funds of knowledge" in productive ways to support classroom learning. This approach has been referred to as "context personalization." In this paper, we discuss the cognitive basis of personalization interventions,…

Purpose: A growing body of research has focused on the topic of inclusive education for ethnic minorities in Hong Kong. At the same time, few scholars have explored the role technology can play in enhancing inclusivity within the context of quality education. This study examines how the differentiated use of technology that takes into account…

This study examined the effectiveness of an integrated context approach to the instruction of basic compass-and-straightedge construction. The formulation of a perpendicular bisector of a segment was used as a knowledge module to guide students from the pre-attention level to the elaboration level of information processing. The students were…

Mathematics curricula are frequently rich with visuals, but these visuals are often not designed for optimal use of students' limited cognitive resources. The authors of this study revised the visuals in a mathematics lesson based on instructional design principles. The purpose of this study is to examine the effects of these revised visuals on…