Framing mathematics ability as innate or intimately connected to someone's intelligence is common. Have you ever heard a parent or colleague say something akin to, "Jonathan can really write, but I don't know what happened in math!"? Unfortunately, this framing not only narrowly describes how mathematics learning occurs but also raises…

In this article the author describes a problem posed to his class, "How many squares are there on a checkerboard?" The problem is deliberately vague so that the teacher can get the students to begin asking questions. The first goal is to come to an agreement about what the problem means (Identify the problem). The second goal is to get…

"Classroom number talks," five- to fifteen-minute conversations around purposefully crafted computation problems, are a productive tool that can be incorporated into classroom instruction to combine the essential processes and habits of mind of doing math. During number talks, students are asked to communicate their thinking when presenting and…

How can a teacher use the practice of reflection to create rich mathematical learning environments that are engaging to students? In such environments, one can hear and see a seamless integration of Problem Solving, Reasoning and Proof, Communication, making mathematical Connections, and Representation (the NCTM Process Standards) through Number…

The classic Chickens and Pigs problem is considered to be an algebraic problem with two equations and two unknowns. In this article, the authors describe how third-grade teacher Maria is using it to develop a problem-based lesson because she is looking to her students' future needs. As Maria plans, she considers how a series of problems with the…

Problem solving lies at the heart of mathematical learning. Children need opportunities to write, discuss, and solve problems on a regular basis. The problems must incorporate grade-appropriate content and be "accessible and engaging to the students, building on what they know and can do." Teachers also play a key role in establishing a classroom…

Fourteen fifth-grade students gather at the front of the classroom as their summer school instructor introduces Jonathan Bostic as the mathematics teacher for the week. Before examining any math problems, Bostic sits at eye level with the students and informs them that they will solve problems over the next four days by working individually as…

Encouraging children to think--independently and publicly--is possibly one of any teachers' most challenging and rewarding responsibilities. Young children's less-developed language and listening skills further complicate teachers' work at the early elementary level. Yet, the author has been fortunate to work with many teachers who have embraced…

Can a rich problem-solving task challenge a diverse range of students? How would students across various grade levels, from elementary school to secondary school, respond to the same task? These were the questions five different teachers in different schools wanted to explore in their respective classes, ranging from first grade through ninth…

Although English Language Learners (ELLs) quickly acquire basic interpersonal communication skills, most struggle for several years with reading and writing academic content in English. In particular, in English-only mathematics classes, children are likely to have difficulty reading and comprehending text, reading word problems, and giving…

This article reports on the use of a unique number system to facilitate teachers' understanding of the concepts of place value. Teachers' mastery of base-ten may hinder their recognition of the difficulties students have with place value, so the authors created a number system that used five symbols to represent values. Using this system, teachers…

Describes a literature-based approach to helping primary students become more proficient problem solvers in mathematics. Literature-based activities were chosen to develop a sense of community in the classroom. This enabled students to develop the self-confidence to share thoughts and feelings while problem solving in small-group and class…

Five classroom situations in Japanese elementary schools are described and interpreted from perspective of first four standards in the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards. Concludes that Japanese children do so well in mathematics because Japanese teachers embody essence of the standards in…