Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task…

SCILAB is a lesser-known program (than MATLAB) for numeric simulations and has the advantage of being free software. A challenging software-based activity to analyze the most common linear reversible inhibition types with SCILAB is described. Students establish typical values for the concentration of enzyme, substrate, and inhibitor to simulate…

Over the course of her teaching career, this author learned to create environments in which both the teacher and learners embrace understanding. She introduced new concepts with a general question or word problem and encouraged students to find solutions with a strategy of their choice. By using this instructional method, she allowed her students…

In this article, fourth grade Upper Allen Elementary School (Mechanicsburg, Pennsylvania) teacher Jeffrey Smith describes his exploration of the Playing Basketball activity. Herein he describes how he found the problem to be an effective way to review concepts associated with the measurement of elapsed time with his students. Additionally, it…

When students begin work with fraction division in fifth grade or sixth grade, they bring with them experiences from whole-number division. Many students think that a division problem should lead to a quotient that is smaller than the dividend. It is also common for students to believe that the dividend should be larger than the divisor. Many, if…

This study aims to describe how the learning study model can be used to improve lesson design and children's learning outcomes by enabling them to perceive and define the critical aspects of the object of learning, guided by variation theory. Three lesson designs were used with three groups of children (A = 24, B = 13, C = 14) from two schools.…

In this paper we present the main lines of a course on the history of mathematics for prospective secondary school (students' age range 14-19) mathematics teachers, enrolled on a 2-year postgraduate teacher preparation program. In order to integrate the historical objectives with the educational objectives of the program we adopted the…

For years, anchor charts have been commonly used in literacy instruction. They also can be a powerful tool for learning mathematics. Anchor charts help create excitement for learning, establish real-world connections, and furnish a reference during work time as well as a solid foundation for later lessons. In this article, the author explores…

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI…

The purpose of this study is to examine whether there is a difference in students' understanding of the core concepts in Pre-calculus after integrating student group presentations into teaching versus the teacher-led traditional classroom setting. The results of the analysis indicated that student group presentations do increase student retention…

Shulman's notations of subject matter knowledge (SMK) and pedagogical content knowledge (PCK) have been very influential in education research on teachers' knowledge for teaching. However, there is little empirical evidence in support of these as separate analytical constructs. Furthermore, attempts to distinguish SMK and PCK highlight the complex…

This study is part of a larger research program aimed at studying mental mathematics with objects other than numbers. It concerns operations on functions in a graphical environment with Grade-11 students. Grounded in the enactivist theory of cognition, particularly in problem-posing, the study aims to characterize students' mathematical activity…

This study uses lesson study to investigate what mathematics teachers notice about students' mathematical reasoning during the planning of a lesson on fractions. Most research examines teaching noticing during or after a lesson, and focuses on the specificity of what teachers notice as a characteristic of noticing expertise. In this paper I…

The Alabama State Department of Education (ALSDE) was grappling with several issues including: (1) A respectable rate of growth in student achievement for both fourth- and eighth-grade math in the state of Alabama, as measured by the National Assessment of Educational Progress (NAEP), but below the national average; and (2) A growing concern about…