This study explores how a problem-solving based professional learning community (PLC) affects the beliefs, knowledge, and instructional practices of two sixth-grade mathematics teachers. An interview and two observations were conducted prior to beginning the year-long PLC in order to gather information about the participants' beliefs,…

This study examined prospective middle grade mathematics teachers' knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It…

This paper presents the results of a study that aimed at increasing students' problem-solving skills. Polya's (1985) heuristic for problem solving was used and students were required to articulate their thought processes through the use of a structured diary. The diary prompted students to answer questions designed to engage them in the phases of…

Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge…

This theoretical paper explores the decision-making process involved in modelling and mathematizing situations during problem solving. Specifically, it focuses on the authority behind these choices (i.e., what or who determines the chosen mathematical models). We show that different types of situations involve different sources of authority,…

Graphing calculators facilitate learners' ability to build cognitive links between mathematical representations by providing quick access to multiple representations. This exploratory study investigated the effects of technology-enhanced instruction on student achievement, perceptions of technology use during instruction, problem-solving success,…

Many empirical investigations concerning the use of computer algebra systems (CAS) and symbolic calculators (SC) are restricted to a period of only a few weeks. They do not show long-term effects on students understanding. Therefore, a long term project (2003-2012) was started to test the use of symbolic calculators in Bavarian…

This article presents material that has been used as a classroom activity in a calculus-based probability and statistics course. The application was used in the first few lessons of this course. Students had three previous semesters of math, including calculus (single and multivariable), differential equations, and a course in mathematical…

An nth-term problem involves a sequence. Students must determine which expression will allow them to calculate the nth position of the sequence. To solve such problems, students are to find "a rule that determines the number of elements in a step from the step number." These types of problems help students develop concepts of functions, variables,…

Proportional reasoning is perhaps one of the most important types of mathematical thinking for elementary school students to develop. It includes aspects of rational numbers, spans the entire mathematics curriculum, and is a significant foundation for mathematical proficiency. Understanding students' use of proportional reasoning is a basis on…

This article analyzes the experiences of prospective secondary mathematics teachers during a teaching methods course, offered prior to their student teaching, but involving actual teaching and reflexive analysis of this teaching. The study focuses on the pedagogical difficulties that arose during their teaching, in which prospective teachers…

In 2010, the William and Flora Hewlett Foundation's Education Program has established the Deeper Learning Initiative, which focuses on students' development of deeper learning skills (i.e., the mastery of core academic content, critical-thinking, problem-solving, collaboration, communication, and "learn-how-to-learn" skills). Two test…

This article discusses the conditions under which all solutions to x[double prime] + q(t)b(x) = f(t) are bounded on [0, [infinite]]. These results are generalizations of the linear case. A short discussion of the properties of bounded oscillatory solutions for both the linear and nonlinear cases when f(t) = 0, xb(x) greater than 0 and b[prime](x)…

Three distinct points A = (a, 0, 0) B = (0, b, 0) and (c, 0, 0) with abc not equal to 0 are taken, respectively on the "x", "y" and the "z"-axes of a rectangular coordinate system in R[superscript 3]. Using the converse of the theorem of Pythagoras, it is shown that the triangle [delta]ABC can never be a right-angled triangle. The result seems to…

The Mathematics Performance Expectations (MPE) define the content and level of achievement students must reach to be academically prepared for success in entry-level, credit-bearing mathematics courses in college or career training. They were developed through a process that involved faculty from Virginia's two- and four-year colleges and…