This study examined whether learning with heuristic worked examples can improve students' competency in solving reality-based tasks in mathematics (mathematical modeling competency). We randomly assigned 134 students in Grade 5 and 180 students in Grade 7 to one of three conditions: control condition (students worked on reality-based tasks),…

Carbon cycle pool-and-flux reasoning is a critical facet of climate literacy. This article begins with discussion of why this type of reasoning is both challenging and important. Results from two studies are reported. The first describes students' approaches to carbon cycle pool-and-flux reasoning. The second describes and reports results from an…

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

Michèle was hurrying to class. How, she thought, could she offer the students in her African American English in Society and Schools class a method of understanding, comparing, and abstracting the studies they had been reading in class? The heuristic described in this study evolved from a desire to capture aspects of several seminal studies that…

The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content…