Math and science textbook chapters invariably supply students with sets of problems to solve, but this widely used approach is not optimal for learning; instead, more effective learning can be achieved when many problems to solve are replaced with correct and incorrect worked examples for students to study and explain. In the present study, the…

The aim of this study is to analyze the mistakes that have been made in the group theory underlying the algebra mathematics. The 100 students taking algebra math 1 class and studying at the 2nd grade at a state university in Istanbul participated in this study. The related findings were prepared as a classical exam of 6 questions which have been…

Topic-specific didactical design research provides means not only to investigate how to learn but also what to learn, i.e., for specifying learning contents by analyzing students' comprehension processes in detail. This important characteristic of didactical design research is exemplarily shown for students' difficulties in finding symbolic…

A vectorial representation of the full sequence of events occurring during the 2D-NMR heteronuclear single-quantum correlation (HSQC) experiment is presented. The proposed vectorial representation conveys an understanding of the magnetization evolution during the HSQC pulse sequence for those who have little or no quantum mechanical background.…

This study proposes a framework for examining ways in which prospective teachers integrate mathematical knowledge acquired in advanced topics courses into explanatory knowledge for school teaching. Participants, all of whom had recently completed coursework in abstract algebra, were asked to explain concepts connected to the school mathematics…

Lesson study, a teacher-led vehicle for inquiring into teacher practice through creating, enacting, and reflecting on collaboratively designed research lessons, has been shown to improve mathematics teacher practice in the United States, such as improving knowledge about mathematics, changing teacher practice, and developing communities of…

Math and science textbook chapters invariably supply students with sets of problems to solve, but this widely used approach is not optimal for learning; instead, more effective learning can be achieved when many problems to solve are replaced with correct and incorrect worked examples for students to study and explain. In the present study, the…

A growing body of research suggests that accounting for student specific variability in educational data can improve modeling accuracy and may have implications for individualizing instruction. The Additive Factors Model (AFM), a logistic regression model used to fit educational data and discover/refine skill models of learning, contains a…

Much literature has presented evidence that supplemental digital resources enhance student performance with mathematics. The purpose of this study was to explore the impact of a web-adaptive digital resource, Think Through Math©, on student performance with state-mandated annual standardized mathematics assessments. This study utilized a…

Creekside High School is a high-performing public high school where students who are not White or Asian face a racialized school environment. This dissertation examines the school's initiative to detrack its ninth grade Algebra class. Detracking is the process of placing students in heterogeneous classes instead of grouping students by ability.…

This study examined the effects of comparison and game-challenge strategies on sixth graders' learning achievement of algebra variable, learning attitude towards algebra variable learning, and meta-cognitive awareness of algebra variable learning. A 2 × 2 factorial design was used, and 86 students were invited to participate in the experimental…

This study examined how a ninth grade teacher improved an Algebra I lesson through a lesson study approach. We used multiple data sources to investigate the improvement of the lesson towards student-centered mathematics instruction, perceived benefits of the teacher, and factors associated with the improvement of teaching. The lesson group…

Understanding how students learn is important for both researchers and teachers. In terms of mathematics, constructing a new mathematical structure depends on conceptual understanding and connection with previous construct and they needs to be consolidated. A construct can be consolidated when the construct is recognized and used in the further…

This study compared the effects of an integrated reform-based curriculum to a subject-specific curriculum on student learning of 19,526 high school algebra students. Using hierarchical linear modelling to account for variation in student achievement, the impact of the reform-based "Core-Plus Mathematics" curricular materials on student…

This study explored the nature of feedback strategies that teachers of Pennsylvania's Keystone courses (Algebra I, biology, and literature) used to prepare their students to meet the minimum proficiency standard on the corresponding Keystone exam, taken at the end of the course. Teachers reported highest usage of the following feedback types:…