The research reported in this article sought to develop a taxonomy of grade 11 students' levels of understanding in algebraic problem-solving tasks. The student sample was from high schools in the province of Ontario in Canada. Problems from four areas in algebra namely, variables, expressions, equations and word problems were chosen to be…

Quadratic equations are a notorious topic for the challenge it provides to students in secondary mathematics. Despite this, there is limited research, particularly in the Australian context, that explains why such challenges persist. This article details the causes of Year 11 students' difficulties in solving quadratic equations. Observing…

Boaler (2016) asserted that problem posing is the "essence of real mathematics", yet many students do not have opportunities to pose and then solve their own mathematical questions. Rather, students spend their time solving tasks someone else posed--often their teacher or textbook. To promote problem posing, the author designed,…

How do scientists make inferences for something they cannot directly observe? The Black Box approach seems ideal to help students understand how scientists work. Black Boxes are sealed units; their interior is not accessible. The effort to determine their possible content (internal structure) demands successive modifications in hypothesis,…

Peter Dunn and Margaret Marshman present the second of their data files articles in which they discuss the statistical investigation cycle which describes the whole process of conducting a statistical research study. [For "The Data Files: A Series of Articles to Support Mathematics Teachers to Teach Statistics," see EJ1259108.]

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…

The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…

Prior research suggests that students' understanding of scientific concepts is pre-determined by their reasoning ability. Other efforts suggest that American students' scientific literacy is in decline. One difficulty Bybee (2009) acknowledges is that there are two divergent philosophical models of scientific literacy. The first describes the…

Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"

Casyopee is an evolving project focusing on the development of both software and classroom situations to teach algebra and analysis at upper secondary level. In this article, we sketch the rationales for the Casyopee project in relationship with the focus on functions in upper secondary curricula. To evaluate Casyopee's contribution, we present…

Although professional learning communities have gained wide acceptance as a way for teachers to support one another's learning, there is less attention paid to the need for principals to meet together to enhance learning and leadership. Three years ago Sterrett (an elementary school principal) and Haas (a high school principal in the same…

This study reports the impact of high sensitivity to early exchange in 11th-grade, CSCL triads solving well- and ill-structured problems in Newtonian Kinematics. A mixed-method analysis of the evolution of participation inequity (PI) in group discussions suggested that participation levels tended to get locked-in relatively early on in the…

Lessons given to a group of mathematically talented eleventh and twelfth graders enrolled in a problem-solving course that provided practice in applying the heuristic strategy of working backward are detailed. Special attention was given to the process of formulating generalizations that represent large problem classes. (MP)

Describes how an 11th-grade English teacher promoted active learning in her class through a hands-on project that required group problem solving, decision making, and technical writing skills. Discusses how the students simulated a toy factory by working collaboratively in teams to design, build, and market a LEGO toy. (RS)

Examines technology education through technological problem solving in real-life contexts. Discusses theoretical framework and presents case studies from Ontario (Canada) elementary and secondary schools: writing and producing a play with grade 1 students, and community projects with grade 10 and 11 manufacturing technology students. Outlines…