An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, award-winning researcher Dr. Nicole Fonger addresses the issue of how to support all learners to experience algebra as meaningful. In a highly visual approach, the book details four research-based lenses with examples from 9th-grade…

This article explains four kinds of inquiry exercises, different in purpose, for teaching advanced-level high school and college students the hypothetico-deductive (H-D) method. The first uses a picture of a river system to convey the H-D method's logic. The second has teams of students use the H-D method: their teacher poses a hypothesis…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

A color-blot exercise is described as a way of getting students involved in abstract thinking by a low risk, confidence-building activity. Students are asked to combine poetry and art. (CL)

Discusses how elementary school children perceive abstract art and describes activities used to increase their appreciation of abstract art. Students draw dinosaurs and discuss the variations in their drawings. Two movement activities which reinforce concepts about abstraction are described. (AM)

Argues the benefits of introducing S. I. Hayakawa's "abstraction ladder" to students. Discusses its implications for developing good writing and thinking skills and ways to use it with students. (RAE)

Includes a dandelion poem that is designed to stimulate elementary students' creativity and abstract-thinking skills. Offers several exercises to go with the poem: creating mental pictures, drawing first images, and performing for better understanding. A reproducible for creating a dandelion-shaped poem is included. (SM)

Discusses the level of knowledge, understanding, and ability relative to mathematics for the college graduate in the 21st century. Focuses on mathematical literacy and abstraction such as the definition of abstraction, difficulties in addressing abstraction, and one approach to helping students learn to address abstraction. (Contains 12…

Discusses three problems preschool teachers should consider when aiming to facilitate children's mathematical activity: (1) How may young children relate to the necessarily abstract basis of mathematics? (2) When is a child's activity mathematical? (3) How may "mathematical" language, concepts, and experiences be appropriately defined?…

Describes the mathematical processes that occur during problem solving, reasoning, and communication. Provides examples from mathematics education research with preschoolers. (ASK)

Proposes that technical writing teachers have a special responsibility to use their subject matter to advance the critical reasoning processes required in the composing process, the disciplines, and the professions. Suggests 10 critical thinking skills to encourage in technical writing courses. (MS)

Described is an exercise that will help college-level psychology students learn abstract and relational thinking skills. The exercise will provide students with a new way to handle compare-and-contrast questions. (RM)

Encourages teachers to listen more carefully to what students say. Discusses two modes of reasoning in an effort to understand more deeply what students hear and the styles of reasoning that they might use in mathematics. (Contains 12 references.) (ASK)

Reacts to the publications "Curriculum Guidance for the Foundation Stage" and "National Numeracy Strategy: Framework for Teaching Mathematics from Reception to Year 6" published by the Department for Education and Employment in Great Britain. Makes the case for the marrying of formal and informal, abstract and concrete…

Shows how a teacher's questions and responses have positive impact on student comprehension. (MKM)