Teaching English language learners has long presented challenges for teachers tasked with bringing these students to a level of language comprehension comparable to that of native speakers. These challenges and issues can lead to difficulty comprehending core academic topics for those learning the English language. "Optimizing Elementary…

Significant instructional changes in mathematics will be achieved only if each educator involved with school mathematics engages in a personal rethinking of various aspects of mathematics instruction and identifies some concrete ways in which his or her current practice could be modified to reflect the results of such rethinking. This book is…

Explores first-year students' understanding of fundamental calculus concepts using written tests and interviews. Analysis of the written and verbal responses to the test items revealed significant misconceptions on which students' mathematical activities were based. Describes some of those misconceptions and errors relating to students'…

Demonstrates ways students think about decimals and how this changes as students get older. Presents a test teachers can use to help diagnose the mistakes students make. (MKR)

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.…

Considers teaching strategies to help children overcome misconceptions and difficulties with the mathematical concept of angles. (ASK)

One of the biggest hurdles in teaching statistics is convincing students that the area under curves has anything to do with all the samples, histograms, and various other indicators to which they have been exposed. Presents two examples to illustrate this phenomenon. (ASK)

Discusses the integration of assessment into instruction using a four-step framework: planning the activity, gathering evidence, interpreting evidence, and using evidence. (MKR)

Expands upon the popular belief that mirrors cause the left-right reversal of objects placed in front of them. The image-location rule and image-symmetry rule are applied throughout the article to help summarize some important properties of mirror images. (ZWH)

Dispells five myths in mathematics education related to the standards and reform efforts. Contains 19 references. (ASK)

Explores misconceptions that students hold about sampling techniques on surveys. Highlights students' thinking and instructional implications from two studies that examined upper-elementary students' written and oral explanations as they responded to survey situations. (ASK)

Discusses how students fail to recognize the underlying equivalence when the same set of points is represented by a graph or an equation or a table. Presents activities in which more than one form of representations of the same information are included. (ASK)

Identifies common misconceptions about polygons. Discusses current practices used to teach geometry to search for the source of misconceptions, and describes ways to help students avoid these misconceptions. (ASK)

Presents an activity in which students must arrange five fractions represented by dominoes in ascending order and justify their reasons for the ordering. Representing common fractions with dominoes helps identify students' misconceptions about fractions. (ASK)

Examines correct and incorrect student-developed criteria for parallelograms. (MKR)