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…

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…

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)

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

Describes a week-long activity for general to honors-level students that addresses Hubble's law and the universal expansion theory. Uses a discrepant event-type activity to lead up to the abstract principles of the universal expansion theory. (JRH)

Mathematical games designed for children from kindergarten to grade five using buttons as counters are described. Each game description includes a brief discussion of the number and mathematical concepts it teaches. (JD)

Argues that writing instruction is most effective when instruction focuses on inquiry which includes: utilizing concrete data, solving problems by using thinking strategies inherent in various writing tasks, focusing on student-centered problems, and encouraging student interaction with a minimum of teacher lecture. (JAD)

Describes 15 types of analogies, their facilitating function in mental processing, the kinds of knowledge for which they are most effectively employed, and their applicability across subject matter. Eight steps for constructing and presenting analogies and types of analogical relationships are included. Prevention of misconceptions is discussed.…

Describes a vocabulary/spelling development guessing game in which students must deduce a secret letter by process of elimination, with as few guesses as possible. (HTH)

Suggests having students write short summaries using the principles of the journalistic news "lead" to help them sharpen their abstraction skills. Includes samples of data blocks from which students would compose their summaries, kernel sentences from the samples, "kernel" kernel sentences, first draft summaries, and 30-word…

Discusses students' inability to make the connection between manipulative materials and pencil-and-paper calculations in mathematics instruction. Outlines the development of mathematical ideas through the concrete, representational, and abstract phases of instruction. An annotated bibliography listing teacher resources for representational-level…

Simple graphing activity helps primary students make the jump from counting concrete objects to understanding abstract symbols. As part of the activity, students vote for their favorite season, then stand up and become a graph of the data they collect. The activity requires the Graph Club Classroom Kit software program. (SM)

Argues that phonemic awareness in young readers may be knowledge that is constructed in the unique situation of trying to match speech to an alphabetic orthography. Stages of learning about print, teaching children about written language, and the roles of alphabet recognition and perceptual-motor skills in learning to read are discussed.…

Specific teaching strategies to help hearing-impaired secondary students comprehend abstract concepts include (1) pinpointing facts and fallacies, (2) organizing information visually, (3) categorizing ideas, and (4) reinforcing new vocabulary and concepts. Figures provide examples of strategy applications. (DB)