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…

Although the emphases on the importance of proving in mathematics education literature, many studies show that undergraduates have difficulty in this regard. Having researchers discussed these difficulties in detail; many frameworks have been presented evaluating the proof from different perspectives. Being one of them the proof image, which takes…

Undergraduate mathematics instructors often report that students make careless errors or have not previously learned key mathematical ideas and strategies. The purpose of this study is to explore evidence of an alternative explanation that at least some of these "errors" may result from students' application of conceptions developed in…

The aim of this study is to investigate the misanalogical construction of undergraduate students in their cognitive conflict in doing a non-routine mathematical task. Qualitative methods were used in this research. Data were collected from 68 seventh semester undergraduate students of Mathematics Education Study Program, Universitas Negeri Malang…

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Teaching determinants poses significant challenges to the instructor of a proof-based undergraduate linear algebra course. The standard definition by cofactor expansion is ugly, lacks symmetry, and is hard for students to use in proofs. We introduce a visual definition of the determinant that interprets permutations as arrangements of…

In this paper I discuss my experience in using the inverted classroom structure to teach a proof-based, upper level Advanced Calculus course. The structure of the inverted classroom model allows students to begin learning the new mathematics prior to the class meeting. By front-loading learning of new concepts, students can use valuable class time…

Some research has suggested the use of mancala games in mathematics education. The immediate concepts associated with playing mancala games have been limited to counting as well as addition and subtraction, so the potential of mancala has remained limited to primary school education. This proposed adaptation of a mancala game allows for teaching…

Concept inventories have become increasingly common in STEM disciplines as a means of assessing student conceptual understanding on a given topic, and overall they have led to significant reform in the teaching and learning of content in their respective disciplines. In mathematics, the use of the Calculus Concept Inventory seems, anecdotally and…

At the University of Paderborn, the course "Introduction into the culture of mathematics" is required for all first-year students who enter the study program for future mathematics teachers at lower secondary level (grade 5-10). In this inquiry-based transition-to-proof course, we use four different kinds of proofs (the generic proof…

The Mathematics students who perform truth-seeking process upon solving mathematical problems were unique. Therefore, the study deems it necessary to know students' mental structure and mechanism so that they can make the right decision by performing truth-seeking. However, no research has delved into the mental structures and mechanisms of…

This study investigates one Calculus student's meanings for quantifiers in Calculus statements involving multiple quantifiers. The student was asked in a two-hour long clinical interview to evaluate and interpret the Intermediate Value Theorem (IVT) and three other statements whose logical structure was similar to the IVT except for the order of…

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

It is increasingly important for mathematics students to engage in active learning along with discussion of material with their peers. "Slopes" is a mobile application designed to visualize solutions to differential equations and support active learning in the classroom. We implemented group activities using "Slopes" into an…

In this paper, we present a "route of activities" mainly addressed to first and second year engineering students attending the basic mathematics courses. These activities are intended to be a tool both for students and teachers. On the one hand, they should help the students to acquire a deeper understanding of the mathematical ideas and…