Although research in mathematics education has yielded a great number of results on mathematics teachers' beliefs in recent decades, it is still an open question as to whether these teachers' beliefs are stable or not. However, since mathematics teachers' beliefs are perceived to be the default of their classroom practices, it is important to gain…

Teacher practice is rife with tensions. Tensions around what and how best to teach, how to manage situations with students, and how to manage situations with colleagues, administrators, and parents. These tensions are often seen as pairs of opposing internal and external forces: this assessment is better, but it takes a lot of time. These forces…

We argue that progress in the area of research on mathematics teacher responses to student thinking could be enhanced were the field to attend more explicitly to important facets of those responses, as well as to related units of analysis. We describe the Teacher Response Coding scheme (TRC) to illustrate how such attention might play out, and…

It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…

In this article, the focus is on task construction and the importance of this process to develop and promote classroom communication in mathematics. The students' tests, examination of students' mathematical work, the teachers' lesson plans, and reports of the lessons' instructions are the basic data for this article. The analysis indicated that…

The point of departure in this study is that differences in solving second-degree equations result from differences in what is presented to the students in a learning situation. However, the specified aim is to describe what kind of differences seem to be crucial for learning, and what does seem fruitless. The study is carried out in an upper…

Two heuristic and three rigorous arguments are given for the fact that functions of the form Ce[kx], with C an arbitrary constant, are the only solutions of the equation dy/dx=ky where k is constant. Various of the proofs in this self-contained note could find classroom use in a first-year calculus course, an introductory course on differential…