This article describes how to play two abstract strategy board games: (1) "Blokus" which uses polyominoes--plane geometric figures formed by joining one or more equal squares edge to edge; and (2) "Gemblo" which uses translucent, colored pieces, each of which is made up of one to five hexagons.

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.

When presented with a problem in mathematics class, students often function as problem performers rather than problem solvers (Rigelman 2007). That is, rather than understanding the problem, students focus on using an operation to complete it. Students' tendencies to act as problem performers can prevent them from suggesting problem-solving…

"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…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

Legal reasoning is a type of problem solving, and is situated within thinking skills, one of the six threshold learning outcomes established under the auspices of the Australian Learning and Teaching Council's Bachelor of Laws Learning and Teaching Academic Standards Statement. The threshold learning outcomes define what law graduates are…

Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Describes an earlier study on the main characteristics and background of undergraduate students' difficulties when trying to solve mathematical tasks. Focuses on and extends part of an earlier study that concerned task solving strategies. Indicates that focusing on what is familiar and remembered at a superficial level is dominant over reasoning…

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

The author suggests that teaching may be enhanced as more insights are gained about how each student responds to the teaching/learning process and how learning style and teaching style are interrelated. Four learning styles are compared and four teaching styles are examined. (CT)

This paper presents two puzzles that have emerged in a series of completed and ongoing studies at Queen's University, Ontario. These puzzles concern teachers' professional knowledge, a term used to refer to the non-propositional forms of knowledge assumed to be of importance to professional action. This research assumed that the professional…

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.)

An inquiry attempted to build an agenda for research that would result in a cognitive theory of instruction capable of informing educational practice and extending the limits of knowledge about how people learn and develop. What would such a theory look like, how close are we to having one, and what directions must be followed to further its…

An analysis is presented of the latest findings from psychology and education on how children acquire complex thinking skills and learn to reason, and how the schools can teach such skills more effectively. This paper reviews previous research, highlights successful learning strategies, and makes specific recommendations about problems and…