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…

In this article, the author shares the Menu Writing project, designed to promote a meaningful, real-world connection to mathematics with the lives of students. The rationale for developing this project was two-fold: (1) to connect school mathematics to students' lived experiences to encourage and sustain students' interest, motivation, and…

"Drawing Conclusions" explores the use of juxtaposed visual representations (JVRs) to help preservice teachers grapple with abstract concepts, theories, or complex controversies in education. Acting as both a learning tool and an intellectual spark, JVRs are two simple contrasted sketches that students produce on a divided sheet of…

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.

Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra…

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…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) propose a new vision for the mathematics classroom with updated content standards and Standards for Mathematical Practice (SMP). These practices are founded on NCTM processes (Problem Solving, Reasoning and Proof, Communication, Representation, and Connections) and abilities…

The social studies curriculum travels through time and space and is bigger on the inside than it is on the outside. To an outsider, the social studies curriculum is a single line on a program of studies, 45 minutes of a student's school day. Those on the inside, however, know that the field covers history, geography, civics, economics, and much…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

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…

Within a group of advanced learners, the variety of abilities, talents, interests, and learning styles can be formidable. For the first time, this book connects the unique learning differences among gifted students to the specific teaching methods used to tailor their educational experiences. Differentiated instruction for gifted and talented…

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…

Presents a developmental approach to teaching programing at all educational levels which stresses concepts rather than syntax; provides motivation, relevant examples, and activities; proceeds from concrete to pictorial to abstract according to age and experience of learners; and utilizes increasingly complex activities building upon and extending…

Describes the use of chess instruction to develop abstract thinking skills and problem solving among gifted students. Offers suggestions for starting school chess programs, teaching and evaluating chess skills, and measuring the success of both student-players and the program in general. (PB)