What do nonroutine algebra problems look like for a second-year algebra course, and where can such problems be found? Starting from the belief that even challenging, nonroutine problems should be solvable with the resources that students possess, Benjamin Dickman proceeded to formulate a small collection of tasks to push students into integrating…

The ties between literacy and numeracy exist in the development of vocabulary and language for understanding mathematical concepts. Research indicates that explicit instruction in mathematics vocabulary supports success with mathematics problem solving (Biemiller 2009; Pierce and Fontaine 2009; Rubenstein and Thompson 2002) for native…

Many ways exist to engage students without detracting from the mathematics. Certainly some are high-tech options, such as video games, online trivia sites, and PowerPoint® presentations that follow the same model as Jeopardy; but sometimes low-tech options can be just as powerful. One exciting way to connect with students is by incorporating…

Since the 1950s, the understanding of how the base 10 system works has been encouraged through alternative base systems (Price 1995; Woodward 2004). If high school students are given opportunities to learn other base systems and analyze what they denote, we believe that they will better understand the structure of base 10 and its operations…

When teaching transformations of functions, teachers typically have students vary the coefficients of equations and examine the resulting changes in the graph. This approach, however, may lead students to memorise rules related to transformations. Students need opportunities to think deeply about transformations beyond superficial observations…

Problem solving is a necessary component of developing a strong mathematics curriculum that will help all students achieve their life goals, regardless of their specific academic plans. What day-to-day instructional decisions do teachers need to make if they believe that problem solving is a vehicle for learning mathematical content? In this…

There is considerable research on the difficulties students have in conceptualising individual concepts of probability and statistics (see for example, Bryant & Nunes, 2012; Jones, 2005). The unit of work developed for the action research project described in this article is specifically designed to address some of these in order to help…

Taking advantage of pedagogical opportunities afforded by new technology requires appropriately designed lessons. This article reports on the use of "lesson study" to research principles for the design of a lesson aiming to take advantage of multiple representations. The lesson, for year 10 students who had personal access to TI-Nspire, focused on…

General Certificate of Secondary Education (GCSE) mathematics assessment previously included a piece of coursework that required learners to develop a general equation to describe the relationship between two groups of numbers on a number grid. In this author's experience, it became clear that Year 10 students often struggled to form a link…

Describes an episode involving conditional statements and the notion of logical equivalence that occurred in a 10th-grade college-preparatory geometry class. Illustrates some of the confusion that can arise in connection with this topic, for both students and teachers. (ASK)

Describes how students in a 10th-grade geometry class discovered relationships that led to the development of conjectures, theorems, and directions of proofs regarding the centroid of a triangle. (ASK)

A large and representative 10% sample of classrooms consisting of 1,587 students from a mid-western province in Canada was administered a standardized achievement test battery. This battery consisted of four tests, Reading, Mathematics, Written Expression, and Using Sources of Information. Gender and rural-urban differences in achievement and…

The ability of tenth grade plane geometry students to structure concepts and relationships from a geometry unit on ratio, proportion and similarity was tested. Analysis of cognitive "maps" of the structural relationships possessed by twenty concrete and twenty formal subjects indicated that formal operational subjects structure subject…

Presents an activity to introduce students to the intrinsic curvature of surfaces using a wide variety of objects. Describes student discoveries, several variations on the project, and possible classroom discussion topics. A reproducible student worksheet and 17 references are included. (MKR)

The Sequential Mathematics Sequence provides an integrated course of study for grades 9-11 in New York City. This document presents lesson plans for part one of the second-year course, designed for 10th grade. The curriculum interweaves algebra, geometry, logic, probability, statistics, and trigonometry, with the emphasis in the 61 lessons in this…