The purpose of this study was to investigate a high school Algebra I program through an examination of potential relationships among teachers' beliefs about teaching and learning mathematics, teachers' instructional styles, students' academic self-concept in mathematics, and students' mathematics achievement in an Algebra I course. While a…

The achievement gap that exists in K-12 education between Latino student students and other races is not only evident but profound. To bridge this gap, underlying factors needed to be explored. One such factor that has affected overall student performance is math anxiety. Researchers have determined that math anxiety has had a tremendous impact on…

This discussion explored the integration of creative thinking pedagogy and the anthropological theory of didactics in university-level algebra education, emphasizing the importance of understanding the perspectives of both learners and teachers. The work began by highlighting the necessity of considering these viewpoints to create effective and…

In this article we illustrate how one teacher used PhET cannonball simulation as an instructional tool to improve students' algebraic reasoning in a fifth grade classroom. Three instructional phases effective to implementation of simulation included: Free play, Structured inquiry and, Synthesizing ideas.

Like terms are usually defined for variables with numerical coefficients. While the definition is sufficient to combine polynomial terms, it does not help the students to combine radical, logarithmic, or trigonometric terms. The purpose of this paper is to propose a lesson that introduces a broader definition of like terms and trialed with a group…

Evidence is emerging that technology-based curricula and adaptive learning systems can personalize students' learning experiences and facilitate development of mathematical skills. Yet, evidence of efficacy in rigorous studies for these blended instructional models is mixed. These studies highlight challenges implementing the systems in…

At present, a new generation of students is studying at universities with their specific abilities and skills. In addition to hard skills, potential employers also require significantly developed soft skills from their employees. The school, and not just the university, is entering this process in a different position than in the past due to the…

Our field has generally reached a consensus that active-learning approaches improve student success; however, there is a need to explore the ways that particular instructional approaches affect various student groups. We examined the relationship between gender and student learning outcomes in one context: inquiry-oriented abstract algebra. Using…

This paper focuses on the emergence of abstraction through the use of a new kind of motion detector--WiiGraph--with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their…

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, log (MN) = log (M) log (N)) with bidirectional…

The mathematics curricula of countries such as the United States, Singapore, Australia and New Zealand have started to incorporate the teaching of algebra in early childhood education. From this perspective, our study has two objectives: (a) to design a learning trajectory and teaching itinerary introducing patterns for children between the ages…

Facilitating productive mathematical argumentation is challenging; it is critical to develop a specific guiding vision of practices to help teachers learn to teach argumentation. However, what counts as acceptable classroom-based mathematical argumentation remains an open question. In this study, building on Habermas' theory of communicative…

Evidence is emerging that technology-based curricula and adaptive learning systems can personalize students' learning experiences and facilitate development of mathematical skills. Yet, evidence of efficacy in rigorous studies for these blended instructional models is mixed. These studies highlight challenges implementing the systems in…

Tracking in education is a process that started in the early 1900s. What started as a tool to help migrant students, evolved into a discrete form of segregation. Tracking normally negatively affects marginalized students. It often separates students by socioeconomic status and race. Black and Hispanic students normally make up a small percentage…

This research compares the use of triadic dialogue and translanguaging in two multilingual grade seven classrooms where algebra is taught in a foreign language. Ten lessons in one classroom that involve teaching properties and seven lessons in another classroom that involve teaching conventions were video- and audio-recoded and then transcribed.…