Colleges and universities cannot ignore the increasingly diverse student population in their classrooms, and how a focus on equity, diversity, and inclusion across disciplines trains students in the intercultural awareness they will need in competitive job markets. Yet while faculty may be aware of a need to understand EDI goals in relationship to…

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…

Almost every child has experienced the sniffly, stuffy, and achy congestion of the common cold. In addition, many have encountered the "old wives tales" that forge a link between personal actions and coming down with this common respiratory infection. Much of this health folklore has been passed down from generation to generation (e.g., getting a…

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Gary Rubinstein doesn't buy the adage that rules--for students or for teachers--must be stated positively, without don'ts or nots. So he lists 10 rules for things teachers must not do in their first years. Tops on his list is "Don't try to teach too much in one day," which Rubinstein says is a common mis-step because teacher preparation programs,…

People who live in poverty consider life in different ways than those who have adequate basic resources. Many educators tend to see the world through their middle-class worldview. Because of this, they do not understand these significant and often rational differences. They may misinterpret behavior they see and ascribe negative connations to how…

The aim of developing students' understanding of the nature of science [NOS] has been considered an important aspect of science education. However, the results of previous research indicate that students of various ages and even teachers possess both inaccurate and inappropriate views of the NOS. Such a failure has been explained by the view that…

Middle school is a crucial transition period for students as they move from concrete to algebraic ways of thinking. This article describes a sequence of instruction geared toward helping prospective middle school instructors teach the topic of percentages.

"Formative assessment is a powerful learning tool that is too seldom, too haphazardly, and too ineffectively used in the United States," Pendred E. Noyce writes in the introduction to this volume. "The purpose of this book is to delve into why this is so and how it can be changed." Formative assessment involves constantly monitoring student…

The mathematical topic of inverse functions is an important element of algebra courses at the high school and college levels. The inverse function concept is best understood by students when it is presented in a familiar, real-world context. In this article, the authors discuss some misconceptions about inverse functions and suggest some…

Over the past three decades, more than a quarter of a million children have become citizens of the United States through international adoption. Kindergarten teacher Jane Katch recently found herself with three such children in her class: Katya, born in Russia, Jasper, from Cambodia, and Caleb, from Romania. Each child had spent early years in an…

Formative assessment probes are used not only to uncover the ideas students bring to their learning, they can also be used to reveal teachers' common misconceptions. Consider a process widely used in inquiry science--developing hypotheses. In this article, the author features the probe "Is It a Hypothesis?", which serves as an example of how…

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…

In addition to meeting National Science Education Standards (NSES) related to the history and nature of science (NOS), reading or hearing about real scientists helps students connect with science emotionally. The authors have even noticed increased student interest in science concepts during history of science discussions. Toward these efforts,…