The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

This article describes five representations and the connections between and among them. It also describes how to use multiple representations to support students' mathematical understanding.

In the renewed "Primary Framework for Mathematics" for England, great emphasis is given to calculation and its prerequisites (DfES, 2006). Expectations are increased for calculations and the recall of number facts, with mental calculation owning a higher profile, while progression in written calculation is clarified. The greater focus on…

Across the U.S., teachers are encountering students who are in the process of learning English as a second language. In the past two decades, this student population, known as English-language learners (ELLs), has more than doubled. Because of the linguistic demands of social studies content, ELLs may have particular difficulty understanding this…

Discusses the organization and retrieval of information. Describes the tip-of-the-tongue state during mathematics problem solving. Provides five rules for a deep level of processing of new concepts. (YP)

Reports on a study of four Australian 11th-grade biology students that used stimulated recall to evaluate student thinking processes.The study confirmed the complexity of the teaching-learning process. (MD)

Describes five writing activities and assignments designed to help students understand the content of social studies and the process of writing. These include student journals, biographical poems, elaborate word games, and creative writing exercises. Illustrative examples relate these to social studies issues. (MJP)

This book brings a philosophical perspective to the topic of children's thinking. It attempts to answer the questions of what it is to think and understand, and how children do so. The book provides an introduction to the philosophy of education as it relates to children's understanding, and is careful not to assume any previous philosophical…

This article discusses the importance of questions as a means for hearing-impaired students to acquire and clarify information and develop independent learning processes. The article also discusses the difficulties faced by hearing-impaired students in comprehending question forms (especially WH-question forms) and offers strategies for diagnosing…

Disjunction between what law teachers mean and how students interpret what is being taught explains why a significant number of law students are not learning or performing at their capability levels. The comments of diverse students at nine law schools can help teachers understand what creates barriers to learning and what helps students learn.…

Asserts that a primary goal of social studies is to prepare students to make informed decisions on public and political issues. Maintains that the most effective approach to teaching critical thinking is through infusion--teaching thinking skills in the context of subject matter. (CFR)

Discusses the uses and benefits of Narrative Assisted Instruction (NAI). This technique uses a story or narrative to illustrate specific content instruction thereby increasing student motivation, comprehension, and memory of the material. Uses NAI to illustrate these concepts by recounting the story of the Wild Boy of Aveyron. (MJP)

Discusses the importance of instruction in metacognition, the mental process of observing, evaluating, and making adjustments in one's own thinking behavior to enhance comprehension during a learning activity. Reviews educational programs which have taught metacognitive behaviors and charts a model instructional approach for use in the college…

The Learning in Science Project (Primary)--LISP(P)--was designed to examine problems and difficulties in primary science and to explore ways of overcoming these problems. Early research led to a proposal that children's questions and explanations could form the basis of an alternative teaching approach. However, several issues were raised which…

Stresses the importance of metacognitive skills (knowledge of one's own cognitive processes) in mathematical performance. Discusses the differences between metacognitive thinking and metacognitive experiences and the ways they each influence performance. Describes how accurate metacognition improves students' mathematical performance, and outlines…