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…

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,…

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…

The plight of refugees has recently received considerable media coverage. Yet, little attention is given to groups who are internally displaced. The purpose of this article is to model one way to teach about internally displaced peoples, drawing on the Rohingya crisis as a specific example. We first provide a background of the Rohingya crisis, and…

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,…

Youth involved in 4-H projects have been engaged in science-related endeavors for years. Since 2006, 4-H has invested considerable resources in the advancement of science learning. The new Minnesota 4-H Science of Agriculture Challenge program challenges 4-H youth to work together to identify agriculture-related issues in their communities and to…

A service learning course has been developed through which undergraduate science students create problem-based learning materials for use in high school science classes. Undergraduate students research active learning pedagogies with a specific focus on problem-based learning, create original materials to be used in grades 11 and 12 chemistry and…

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…

When confronted with a challenging problem, many solvers may at first think that not enough information has been provided. If, however, they suspect that the problem is solvable, this feeling typically influences them to persevere as well as monitor and reflect on their efforts. In this article the authors present four nonroutine tasks that they…

Within contemporary developmental science, models derived from relational developmental systems (RDS) metatheory emphasize that the basic process of human development involves mutually-influential relations, termed developmental regulations, between the developing individual and his or her complex and changing physical, social, and cultural…

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…

A well-known optimization problem is the Popcorn Box investigation, which involves a movie theater snack container. The problem has been tailored for classroom investigations by the Ontario Association for Mathematics Education. The exploration was designed for students in grades 9 through 12. A common strategy proposed for algebra students is to…

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?"