The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners' procedural and conceptual knowledge of…

The Pearson correlation coefficient can be recovered from the two least squares regression lines y[with circumflex] = b[subscript 0] + b[subscript 1]x and x[with circumflex] = a[subscript 0] + a[subscript 1]y without any data. This can be done both algebraically and geometrically. This can be done without data even when the scales of the variables…

Numbers and variables often follow the same principles of arithmetic operations, yet numbers can be computed to a value whereas variables cannot. We examined the effect of symbols--numbers versus variables--on middle school students' problem-solving behaviors in a dynamic algebra notation system by presenting problems in numbers (e.g., 3+5-3) or…

This quantitative causal-comparative study was conducted to determine if or to what extent a statistically significant difference existed in academic achievement between early college high school (ECHS) and traditional high school for Black males as measured by standardized test scores in English and math. Dependent variables, State of Texas…

The shift across developmental education from prerequisite to corequisite remediation has left students underprepared for college-level mathematics in need of additional support. Typically, this support takes the form of content remediation, but what happens when this extra help is reframed in terms of student learning skills and confidence?…

Over the years, many special education trends have emerged and faded, each claiming to be the solution to providing students with special needs a greater chance for success. Each year, new requirements for graduation and new educational legislation are introduced to try and correct old problems of ensuring students with special needs are properly…

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…