On entering Mr. Wilson's seventh-grade classroom, the authors immediately noticed the students talking about mathematics and their teacher listening to them. To create an interactive learning environment that would stimulate and perpetuate discourse, Wilson discussed two main issues with his students: (1) What the students and teacher would do in…

Considerable literature has documented both the pros and cons of students' use of empirical evidence during proving activities. This article presents an analysis of a classroom episode involving in-service middle school, high school, and college teachers that demonstrates that learners need not be steered away from empirical investigations during…

Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…

Many students will need remedial work in mathematics during their high school years. Some sort of help will be needed to fulfill the National Council of Teachers of Mathematics' (NCTM's) (2000) vision of a mathematics classroom that involves students having access to mathematically rich problems and being engaged in solving them. The high school…

The Teacher Education and Development Study in Mathematics (TEDS-M) of 2008 focused on how teachers are prepared to teach mathematics in primary and lower-secondary schools in 17 countries. The main results were published in 2012, and the associated public-use database provides a valuable source for secondary analysis of the collected data. The…

Although student attrition and retention are researched all over the world, there is no final formula available to ensure academic success for selected students. The purpose is to share research undertaken at the Tshwane University of Technology (TUT) in order to investigate the role of mathematics in student achievement and retention in National…

The integration of digital technology confronts teachers, educators and researchers with many questions. What is the potential of ICT for learning and teaching, and which factors are decisive in making it work in the mathematics classroom? To investigate these questions, six cases from leading studies in the field are described, and decisive…

We investigate interpersonal difficulties that student teachers and cooperating teachers may experience during the teaching internship by exploring the tension between one high school mathematics student teacher and his cooperating teacher. We identified seven causes of this tension, which included different ideas about what mathematics should be…

Professional learning communities and teacher efficacy are at the core of many of the current educational reform models. The intention of this dissertation was to identify the correlation between professional learning communities and collective teacher efficacy for math data teams in the six Kaua'i Complex Area secondary schools, as measured by…

Are sequences functions? What can't the popular "vertical line test" be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? Helping high school students develop a robust understanding of functions requires…

"Core-Plus Mathematics" is a four-year curriculum that replaces the traditional sequence with courses that each feature interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. The first three courses in the series provide a common core of broadly useful mathematics,…

In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…

Games can be a valuable tool for a mathematics teacher. Students who dislike mathematics and are not engaged in class never get to experience the exhilaration that accompanies hard work and real accomplishment in mathematics; they usually experience only the frustration that accompanies enforced and futile effort. Game playing is a way to engage…

Students at all levels often generate ideas that are not obviously right or wrong, and, when they do, it is productive to take time to explore the ideas as a group. Some of these ideas are really strange. Occasionally, they are so strange that even the teacher might not know what to think of them. This is the story of what Cosby's rule is, how it…

In this sequence 1/1, 7/5, 41/29, 239/169 and so on, Thomas notes that the sequence converges to square root of 2. By observation, the sequence of numbers in the numerator of the above sequence, have a pattern of generation which is the same as that in the denominator. That is, the next term is found by multiplying the previous term by six and…