The More A-More B intuitive rule has become a research hotspot in the field of mathematical education in recent years. The intuitive rule of More A-More B is often reflected in students' responses to comparison tasks. In such tasks, students are asked to compare 2 objects that differ in a certain salient quantity A (where A[subscript 1] >…

In this study we investigated word-problem (WP) item characteristics, individual differences in text comprehension and arithmetic skills, and their relations to mathematical WP-solving. The participants were 891 fourth-grade students from elementary schools in Finland. Analyses were conducted in two phases. In the first phase, WP characteristics…

Intelligent learning environments can be designed to support the development of learners' cognitive skills, strategies, and metacognitive processes as they work on complex decision-making and problem-solving tasks. However, the complexity of the tasks may impede the progress of novice learners. Providing adaptive feedback to learners who face…

In this article we examine 4th and 5th grade Portuguese students' performance on problems of structuring 2D rectangular arrays of squares, which was analyzed and categorized into the five levels of sophistication described by Battista, Clements, Arnoff, Battista, and Borrow (1998). In general, the results suggest that students in the higher-grade…

This study aims to analyze the correlation of the student's progress in solving a given problem with the logic of the teacher in the layout of the questions asked. The research was conducted in the government's secondary schools and colleges in the district of Abidjan and involved 453 participants, including 423 student and 30 teachers. The data…

The aim of this research is to determine the misconceptions among 6th, 7th and 8th grade students about the order of operations in line with arithmetic expressions and posing and solving problems related to arithmetic expressions. The research has a mixed-method research design with concurrent-triangulation design. The study group for the research…

Complexity is one of the major demands of adolescents' future life as adults. To investigate adolescents' competence development in applying problem-solving strategies in complex environments, we conducted a 2-wave longitudinal study in a sample of Finnish adolescents (11-17 years old; N = 1,959 at Time 1 and N = 1,690 at Time 2, 3 years later).…

Maker-centered learning is a creative hands-on educational strategy that uses a variety of tools and materials to support the iterative design of physical or digital artifacts. It involves the "messy" process of trial and error; therefore, authentic integration of maker-centered learning requires teachers to embrace ambiguity. This…

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…

This collaborative inquiry between an academic (James Russo) and two school-based practitioners (Jessie McCosh and Travis Hewish) explores student attitudes towards learning mathematics through problem solving in a medium sized primary school in regional Victoria.

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…

National mathematics achievement results show that elementary students in the United States are not increasing in cognitive ability or critical thinking skills (NAEP, 2020). For this increase, mathematically promising students require more opportunities for cognitively demanding mathematics instruction. As a result, this descriptive study focused…

Background and Context: Subgoal labeled worked examples have been extensively researched, but the research has been reported piecemeal. This paper aggregates data from three studies, including data previously unreported, to holistically examine the effect of subgoal labeled worked examples across three student populations and across different…

A previous study found that task shifting and fluid intelligence, but not working memory capacity (WMC) and prior knowledge, influenced the worked example effect (Schwaighofer, Bühner, & Fischer, 2016). To increase confidence in these findings, we report a preregistered extended replication study of Schwaighofer et al.'s investigation.…

Students in upper secondary education encounter difficulties in applying mathematics in physics. To improve our understanding of these difficulties, we examined symbol sense behavior of six grade 10 physics students solving algebraic physic problems. Our data confirmed that students did indeed struggle to apply algebra to physics, mainly because…