Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

Science is of critical importance to daily life in a knowledge society and has a significant influence on many everyday decisions. As scientific problems increase in their number and complexity, so do the challenges facing the public in understanding these issues. Our objective is to focus on 3 of those challenges: the challenge of reasoning about…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

In the authors' examination of various instructional programs, they observed that most provide all the necessary data to solve proportion problems, employ compatible numbers that are usually unrealistic, present numbers (data) in the order in which they are to be manipulated, discuss contexts that cannot be easily replicated, and present…

Describes a framework for identifying and classifying students' alternative conceptions and unscientific patterns of reasoning within a particular scientific domain. Provides a basic system for indicating how much researchers know about students' non-scientific conceptions and reasoning. Suggests how the framework may prove useful for…

Science classes are full of abstract or challenging concepts that are easier to understand if an analogy is used to illustrate the points. Effective analogies motivate students, clarify students' thinking, help students overcome misconceptions, and give students ways to visualize abstract concepts. When they are used appropriately, analogies can…

The challenge for education in today's knowledge age is developing students' capacity for sustained creative work with ideas. Although even the youngest students don't fear the abstract, working to improve ideas is an acquired disposition. Creative production is a progressive design process. Software is described in which students, as a community,…

Two astronomy professors, using the Decoding the Disciplines process, help their students use abstract theories to analyze light and to visualize the enormous scale of astronomical concepts. (Contains 5 figures.)

Reviews a monograph which addresses children's higher-order thinking skills. Suggests the following for teaching problem solving: identify and develop content-independent and content-dependent problem-solving skills, connect developed skills through workshop-style activities to subject discipline, and help students identify and reconstruct their…