Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth grade students' answers to a word problem, accompanied by diagrams, involving generalization in an algebraic functional context. In this research, we jointly addressed two objectives: (a) to determine the strategies deployed by students to generalize and (b) to…

It is known that teacher noticing skills improve through different interventions such as video clubs, lesson study, and short-term professional development programs. However, it is not known whether this improvement is permanent and whether teachers can transfer their noticing skills into the classroom. It is extremely important to provide an…

Generalisation is a skill that enables learners to acquire knowledge in general, and mathematical knowledge in particular. It is a core aspect of algebraic thinking and, in particular, of functional thinking, as a type of algebraic thinking. Introducing primary school children to functional thinking fosters their ability to generalise, explain and…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

Background & aims: In recent years, there has been an increased interest in analyzing the mathematical performance of students with learning difficulties in order to provide them with teaching methods adapted to their needs. In particular, the importance of studying the type of informal strategy that students use when solving problems has been…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

This paper explored the following: (1) teachers' ways of attending to students' written responses in pattern generalization tasks and (2) differences in the ways of attending to students' responses associated with different factors. A questionnaire was developed to classify teachers' ways of attending to students' written responses. The…

We conducted a comprehensive synthesis of computer-assisted instruction (CAI) research that aimed to facilitate the learning of mathematical word problem solving involving elementary and secondary school students with learning disabilities or difficulties in mathematics. We examined a total of 13 studies under the four instructional categories:…

Linear pattern is the primary material in learning number patterns in junior high schools, but there are still many students who fail to generalize the linear pattern. The students' failure in generalizing the pattern occurred when the students ended to view the problems globally without breaking them into the constructors' components such as the…

Self-regulatory interventions have demonstrated numerous benefits for helping improve the academic performance of students. The purpose of this review was to report on the effectiveness and focus of academic self-regulation interventions for children and adolescents with emotional and behavioural disorders. Thirty-six studies published in 35…

Jeff McQuillan offers case studies of intermediate level language learners who read young adult and adult fiction successfully as an argument against explicit vocabulary instruction. Case studies provide useful insights into whatever is being investigated but may not always be generalizable. However, McQuillan's reference to case studies has made…

Research Findings: Naturalistic instruction is the intentional use of strategies embedded within typical activities of the environment to create learning opportunities for children. We used multilevel modeling to analyze data from this single-case design study that focused on improving teachers' use of naturalistic language strategies and…

Educators aim to equip students with learning strategies they can apply when approaching new problems on their own. Teaching design-thinking strategies may support this goal. A first test would show that the strategies are good for learning and that students spontaneously transfer them beyond classroom instruction. To examine this, we introduce…

This paper presents protests from academically successful students who privately conveyed to the researchers their feelings of personal discontent with schools. The criterion to select this "sample" was that these students, dissatisfied with school but having good marks, would reveal what others, academically less successful, could not…