Researchers have been interested in students' transition to calculus since the early 1900s. One line of inquiry highlights students' understandings of high school mathematics as impeding or supporting their successful transition to university mathematics. This paper addresses an underlying question in this line of inquiry: does school mathematics…

In this paper we examine changes to the national calculus curriculum of South Korea, where mathematics performance often serves as the mark of academic excellence. We describe relevant cultural traditions of mathematics education in South Korea, including the history of curricular changes in calculus at the secondary level. We then investigate how…

Many studies have reported on the influence of teachers' conceptions of variability on different aspects of their professional knowledge for teaching statistics and their classroom practices. However, research on these kind of conceptions is still scarce, particularly in Latin American countries like Venezuela. In an effort to help fill this gap,…

This paper analyzes the content and tasks involving quadratic equations in eight mathematics textbooks published during the period 2000-2012 at the uppersecondary level in Sweden. The study applies the theoretical "hypothetical learning trajectory" (HLT) framework combining "conceptual" and "procedural" knowledge. The…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

Suppose that there is an inexhaustible supply of $3 and $5 vouchers from the local supermarket. They may only be exchanged for items that cost an exact number of dollars made up from any combination of the vouchers. What is the highest amount not able to be obtained? This is an interesting problem in mathematical thinking and logic requiring only…

Past definitions of statistical literacy should be updated in order to account for the greatly amplified role that data now play in our lives. Experience working with high-school students in an innovative data science curriculum has shown that teaching statistical literacy, augmented by data literacy, can begin early.

In this paper, research on some problematic aspects high school students have in learning trigonometry is presented. It is based on making sense of mathematics through perception, operation and reason in the case of trigonometry. We analyzed students' understanding of trigonometric concepts in the frame of triangle and circle trigonometry…

This article describes two heuristic strategies for problem solving: the "use of false assumption" strategy and the "use of double false assumption" strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances…

The paper focuses on four upper secondary students' collaborative small-group mathematical reasoning (MR) with respect to a sinusoidal function. The students were collaboratively engaged in a process of MR regarding the relationships between mathematical theoretical descriptions of parameters in the algebraic expression of the sinusoidal function…

The main purpose of this chapter is to document the reasoning of three students, two with disabilities and one with mathematical difficulties, as they participated in and contributed to the classroom mathematical practices established by a seventh-grade class during integer instruction. The integer instructional sequence was designed to support…

Two content topics will be described. One deals with geometric measurement: length, area, and volume. These are important topics and they have not been learned very well. In particular, what types of relations can one consider when dealing with these three aspects of geometric measurement? The second topic is fractions, and different views of what…

We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to…

The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…

The divide between those who do and those who do not excel in mathematics is patterned in problematic ways. Women and people of color are typically underrepresented in Science, Technology, Engineering, and Math (STEM) and other quantitative fields (ex. Finance) where mathematics plays gatekeeper. However, mathematics is not a subject these groups…