In mathematics education, researchers often contrast conceptual and procedural teaching approaches, although labels and conceptualizations often vary across studies. Prior research has extensively examined empirical relationships between the two teaching approaches and mathematics achievement. In our study, we aimed to extend this research by…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with textbooks either containing the original practice problems or in which a portion of those problems were converted into a combination…

This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in a task inspired by the Elkonin and Davydov curriculum. The analysis showed that the mathematical reasoning was mainly anchored in mathematical properties related to fractional or algebraic…

This research focuses on the retention of students' algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3-5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly…

This research focuses on the retention of students' algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3-5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly…

Knowledge representations that result from practicing problem solving can be expected to differ from knowledge representations that emerge from explicit verbalizing of principles and rules. We examined the degree to which the two types of learning improve problem-solving knowledge and verbal explanation knowledge in classroom instruction. We…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

This paper examines the implementation of an instructional module on preservice elementary teachers' professional noticing of children's mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic…

Algebra I is a crucial course for middle and high school students for successful STEM-related coursework. A key issue is whether students should take Algebra I in Grade 8 versus Grade 9. Large-scale policy studies show conflicting results, and there are few (particularly longitudinal) individual difference studies. In the study, 53 students were…

Cara, a seventh-grade student with learning disabilities (LD) in mathematics, believes that the ratio 2:3 is equivalent to 4:5 because there is a difference of one between the two numbers in each ratio and there is a difference of two between corresponding numbers in the two ratios (2 + 2 = 4 and 3 + 2 = 5). This misconception affects her ability…

Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

Objective: This article examines the effectiveness of remediation for community college students who are identified as having the lowest skills in math. Method: We use transcript data from a state community college system and take advantage of a regression discontinuity design that compares statistically identical students who are assigned to the…

Language is often depicted as the sine qua non of mathematical thinking, a view buttressed by findings of language-of-training effects among bilinguals. These findings, however, have been limited to studies of arithmetic. Nothing is known about the potential influence of language on the ability to learn rules about the relations among variables…

Numeracy needs of nursing students are often underestimated by students when they enter university. Even when students are aware of the mathematics required, students underestimate or overestimate the skills they have. Research has highlighted the mathematics and numeracy skills required of nurses and nursing students and numerous studies have…

Students who fail algebra are significantly less likely to graduate on time, and algebra failure rates are consistently high in urban districts. Identifying effective credit recovery strategies is critical for getting students back on track. Online courses are now widely used for credit recovery, yet there is no rigorous evidence about the…