Three mathematics education researchers discuss their findings on the use of diagrams in math instruction for English language learners. The authors show how diagrams can help students who are English learners better develop mathematical thinking and communicate their mathematical understanding.

How can the best of mathematical problem-based learning be applied toward literature classes? Daniel Sussman, an English teacher at Moorestown Friends School in New Jersey, discusses how he uses problem solving tactics to encourage close, critical reading of fiction texts in his Jewish literature and poetry classes. He explores the challenges of…

In some math classrooms, students are taught to follow and memorize procedures to arrive at the correct solution to problems. In this article, author Mike Flynn suggests a way to move beyond answer-getting to true problem solving. He describes an instructional approach called three-act tasks in which students solve an engaging math problem in…

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…

In one Colorado fifth grade classroom, math period begins with Mathematician's Chair, an activity allowing students to share their problems with entire class. Using this technique, students became adept at writing math problems, solving their own and peers' problems, using math-related writing as important medium of social discourse, and making…

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…

This article describes a mathematics lesson taught by a 5th grade teacher who engages her class in an in-depth examination of one student's incorrect solution to a problem. Because the teacher consistently asks her students to devise alternative calculation strategies and explain how those strategies work, the students have come to expect that…

Recent research suggests that knowledge is stored in the learner's head as a network of concepts or constructs. Children's mathematical problem-solving strategies become increasingly abstract as they are able to engage in more abstract thinking. An experimental study using an alternative Cognitively Guided Instruction approach is described.…

Because of the complex interaction between economic class and learning, improving mathematics education for all while narrowing achievement gaps is no simple task. As a young teacher, the author conducted action research to determine how low-SES and high-SES 7th graders responded to a problem-centered mathematics curriculum. To her dismay, she…

Mathematics portfolios need not be limited to problem-solving efforts. When California algebra teacher asked students what portfolio contents would show their effort and learning, they suggested daily notes, personal budget and lottery projects, scale drawing, their best and worst tests, weekly problems, daily class notes, and homework. Students…

Except for its relationship to science, mathematics is the forgotten cousin in interdisciplinary teaching and learning. In the Journeys in Mathematics project, teachers engage children in imaginative activities that inspire them to identify patterns and relationships, solve problems, and communicate accurately, using Jonathan Swift's…

The Martin Luther King School in Boston and nine other Massachusetts public schools used a grant from the Massachusetts Department of Education to expand their school days by at least two hours. Each school lengthened the time students spent in reading and math instruction. Farbman focuses on the Martin Luther King School's foray into an extended…

A Maryland middle-school teacher can no longer imagine a math classroom without computers, word processing programs, graphing calculators, graphic design programs, and colored printers and monitors. Aided by these devices, her students made great leaps toward the 21st-century technology goals spelled out by the Department of Education in 1995.…

To help future graduates cope with a twenty-first century era dominated by computers, worldwide communication, and a global economy, mathematics teachers must change their curricula, teaching methods, and assessment techniques. Students must learn to value mathematics, reason and communicate mathematically, solve problems, and develop confidence.…