Mathematics needs to take on a real-world quality, and students need to be able to identify and connect the value of what they are learning within the classroom to life outside the classroom. Creating a connection between the mathematics learned within a classroom and its value to life in the outside world is critical to effectively engage…

The benefits of rich tasks, project-based learning, and other inquiry-based approaches in terms of student understanding and engagement with mathematics are well documented. Such pedagogies are consistent with the development of mathematical proficiencies as described in the "Australian Curriculum: Mathematics" (Australian Curriculum…

Computer-supported collaborative learning (CSCL) is an approach to learning in which learners can actively and collaboratively construct knowledge by means of interaction and joint problem solving. Regulation of learning is especially important in the domain of CSCL. Next to the regulation of task performance, the interaction between learners who…

"A Framework for K-12 Science Education" identifies eight science and engineering practices for K-12 classrooms. These practices, along with core ideas and crosscutting concepts, define the nation's learning goals for science. The practices outlined in the framework are: (1) Asking questions and defining problems; (2) Developing and using models;…

"Research studies show that when students discover mathematical ideas and invent mathematical procedures, they have a stronger conceptual understanding of connections between mathematical ideas." Flewelling and Higginson state that inquiry, investigations, and problem solving "give students the opportunity to use their imagination…

Parson's programming puzzles are a family of code construction assignments where lines of code are given, and the task is to form the solution by sorting and possibly selecting the correct code lines. We introduce a novel family of Parson's puzzles where the lines of code need to be sorted in two dimensions. The vertical dimension is used to order…

In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

Problem-based learning (PBL) is an instructional approach that is organized around the investigation and resolution of problems. Problems are neither uniform nor similar. Jonassen (1997, 2000) in his design theory of problem solving has categorized problems into two broad types--well-structured and ill-structured. He has also described a host of…

The authors' primary aim was to investigate a potential causal relationship between spatial ability and math ability. To do so, they used a pretest-training-posttest experimental design in which children received short-term spatial training and were tested on problem solving in math. They focused on first and second graders because earlier studies…

The purpose of this study was to investigate the advantages of an approach to instruction using current problems and issues as curriculum organizers and illustrating how teaching must change to accomplish real learning. The study sample consisted of 41 preservice science teachers (13 males and 28 females) in a model science teacher education…

Investigations in Number, Data, and Space[R], published by Pearson Scott Foresman, is an activity-based K-5 mathematics curriculum designed to help students understand the fundamental ideas of number and operations, geometry, data, measurement, and early algebra. The curriculum encourages students to use prior knowledge to develop an understanding…

In 2006, the authors began a project to understand what happens in middle school technology education classrooms in order to document the goals that technology education teachers pursue, the instructional strategies they use to teach children to meet these outcomes, the measures they use to assess achievement of these goals, and the learning…

With student numbers decreasing and traditional teaching methods having been found inefficient, it is widely accepted that alternative teaching methods need to be explored in tertiary physics education. In 2006 a different teaching environment was offered to 244 first year students with little or no prior formal instruction in physics. Students…

A simplified model of an industrially relevant fluid-particle flow system is analyzed using linear stability theory. Instabilities of the uniform state of a fluidized bed are investigated in response to small flow perturbations. Students are expected to perform each step of the computational analysis, and physical insight into key mechanistic…