The traditional method of teaching math--showing students how to do a procedure, then assigning problems that require them to use that exact procedure--leads to adults who don't know how to approach problems that don't look like those in their math book. Seeley describes an alternative teaching method (upside-down teaching) in which teachers give…

Being able to find the correct answer to a math problem does not always indicate solid mathematics mastery. A student who knows how to apply the basic algorithms can correctly solve problems without understanding the relationships between numbers or why the algorithms work. The Common Core standards require that students actually understand…

Many students in U.S. schools have trouble understanding fractions and Algebra II, the one difficultly occurring at the end of elementary school, the other in high school. One reason is that schools generally focus on one aspect of mathematics--calculation--and often fail to address the second aspect--interpretation. Also responsible is the…

Using play learning and real-world problem solving, an alternative Arizona program is cultivating confidence and love of learning in bilingual first-graders. Children learn by using their own language (Spanish), learning styles, and thought processes. Besides problem-solving, the "cube train" teaches estimation, number relationships,…

Outlines two mathematics teaching strategies: the exploration/discovery approach to mathematical concepts, and the use of pair group problem-solving. These require teachers to shift from the traditional role of lecture/demonstrator to a role demanding new skills in planning and facilitating student work. Includes 10 references. (MD)

Presents research on cognitive skills demanded by elementary and secondary school mathematics textbooks, based on an original 10-level classification of thinking activities; reports a general decline both in the amount of material demanding student involvement and in the percentage of that material requiring higher-order thinking. (MCG)