Higher order thinking skills (HOTS) is one of important aspects in education. Students with high level of higher order thinking skills tend to be more successful. However, do this phenomenon also happen in the learning of Mathematics? To answer this question, this research aims to study the relationship between HOTS and students' academic…

Students regularly struggle with mathematical tasks, particularly those concerning non-routine problems in geometry. Although educators would like for their learners to transfer their knowledge to non-routine and real-life situations, students run into a number of difficulties. The goal of this exploratory study was to analyze three participants'…

Statistics pervades everyone's lives, whether it is through media coverage, reading reports, weighing up internal risks or evaluating decisions. Most managers are swamped by endless targets, dashboards and spreadsheets, but few organisations have enough employees with statistical skills to support the requirement for evidence based decision…

The ACT College Readiness Benchmarks are the ACT scores associated with a 50% chance of earning a B or higher grade in selected first-year credit-bearing courses at a typical postsecondary institution. The Benchmarks were established by linking ACT test scores with grades in first-year college courses from the same subject area. Benchmarks were…

This paper investigates the reasoning of first year non-mathematics students in non-routine calculus tasks. The students in this study were accustomed to imitative reasoning from their primary and secondary education. In order to move from imitative reasoning toward more creative reasoning, non-routine tasks were implemented as an explicit part of…

The test instrument GOALS-2 was designed primarily to evaluate the effectiveness of the CATALST curriculum. The purpose of this study was to perform a psychometric analysis of this instrument. Undergraduate students from six universities in the United States (n = 289) were administered the instrument. Three measurement models were fit and…

Few studies on calculus limits have centred their focus on student understanding of limits at infinity or infinite limits that involve continuous functions (as opposed to discrete sequences). This study examines student understanding of these types of limits using both pure mathematics and applied-science functions and formulas. Seven calculus…

The notion of linearity is perhaps the most fundamental idea in algebraic thinking. It sets the transition to functions and culminates with the instantaneous rate of change in calculus. Despite its simplicity, this concept poses complexities to a considerable number of first semester college algebra students. The purpose of this observational…

We studied the linguistic norms of mathematical proof writing at the undergraduate level by asking two mathematicians and five mathematics undergraduate students to read seven partial proofs based on student-generated work and to identify and discuss uses of mathematical language that were out of the ordinary with respect to standard mathematical…

Uri Treisman's model of Collaborative Learning is consistent and supportive of Robert Gagne's learning hierarchy. In order to examine this relationship we must analyze each model individually.

At our Historically-Black University, about 89% of first-year students place into developmental mathematics, negatively impacting retention and degree completion. In 2012, an NSF-funded learning enrichment project began offering the introductory and developmental mathematics courses on-line over the summer to incoming science, technology,…

This paper is based on a large-scale empirical study designed to investigate Calculus I programmes across the United States to better understand the relationship between instructors' concerns about coverage, instructional practices, and the nature of the material covered. We found that there was no association between instructors feeling pressured…

Too often our students submit incomplete homework that is disorganized, unclear, and nonlinear. Typesetting with LATEX, although time consuming for those new to the software, strengthens communication by forcing organization and proper notation required by the precise, formal language of mathematics. In this manuscript we report on a study of 42…

This article is based on data from two major research projects that investigated students involved in mathematically demanding courses during their transition through college and into university. It explores the nature of modelling as a mathematical practice in this important transition phase for students. Theoretical considerations are informed…

A wide body of literature has highlighted how high achievement in mathematics in secondary school does not necessarily motivate students to both choose and succeed on mathematically demanding programmes at post-compulsory level. The recent Enterprising Science project [Archer et al. (2015, "J. Res. Sci. Teach.," 52, 922-948)] and before…