Do your students think a triangle can be constructed from any three given line segments? Do they believe that a transformation affects only the pre-image--not the whole plane? Do they understand that examples--no matter how many they find--cannot prove a conjecture but one counterexample is sufficient to disprove it? "What tasks can you…

A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulations of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In the The Xs and Whys of Algebra: Key…

Multiple-choice testing is an educational reality. Rather than complain about the negative impact these tests may have on teaching and learning, why not use them to better understand your students' true mathematical knowledge and comprehension? Maryann Wickett and Eunice Hendrix-Martin show teachers how to move beyond the student's answer--right…

The classic experiment presented in this problem-solving test was designed to identify the template molecules of translation by analyzing the synthesis of phage proteins in "Escherichia coli" cells infected with bacteriophage T4. The work described in this test led to one of the most seminal discoveries of early molecular biology: it dealt a…

"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…

Provides a method to help students understand problem-solving techniques used in introductory physics courses. (MVL)

Notes that when using the screw as a simple machine, the pitch of the screw is important in the amount of force that will be produced. (MVL)

Identifies the misunderstandings and problem-solving strategies of secondary students when solving stoichiometry problems. (Author/CCM)

Fact-filled textbooks that stress memorization and drilling are not very good for teaching students how to think mathematically and solve problems. But this is a book that comes to the rescue with an instructional approach that helps students in every grade level truly understand math concepts so they can apply them on high-stakes assessments,…

When permitted, children frequently devise approaches to solving problems that are distinct from those typically used by adults. Presents examples of children's thinking from Project IMPACT which illustrate the crucial interplay between a teacher's instructional decisions and children's thinking while confronting mathematical misconceptions.…

Explains the concept of mole and presents a teaching approach in which students can experiment with atoms and develop an understanding of mass ratios. Presents 10 examples of chemistry problems involving moles and unit conversations. (YDS)

Focuses on the importance of building from mistakes in mathematics instruction to develop better reasoning and problem-solving abilities. (Contains 11 references.) (YDS)

Discusses and provides an example of reflectivity approximation to determine whether reflection will occur. Provides a method to show thin-film interference on a projection screen. Also applies the reflectivity concepts to electromagnetic wave systems. (MVL)

A discussion of what E=mc2 means and other issues associated with the equation are presented. The differences between matter, mass, and energy, a derivation of the equation, the history of the word mass and examples of how it is used, misconceptions surrounding the equation, and a discussion of uranium fission are included. (KR)