Healthy lifestyles are increasingly emphasized these days. This month the authors begin a series of mathematical problems that also address physical activity. They hope that these problems offer opportunities to investigate mathematics and also reinforce the desire to lead a healthy life. In their first problem of the academic year, students…

Proportional reasoning is perhaps one of the most important types of mathematical thinking for elementary school students to develop. It includes aspects of rational numbers, spans the entire mathematics curriculum, and is a significant foundation for mathematical proficiency. Understanding students' use of proportional reasoning is a basis on…

When the author recently turned her attention to the National Council of Teachers of Mathematics (NCTM) "Principles and Standards," she was startled to see communication as key. She adjusted her teaching to meet the NCTM Communication Standard and promote communication in her classroom by providing a safe environment, developing discourse and…

Ms. Beyer's first graders have been working for several weeks on solving problems that encourage the use of such multiple representations as ten frames and number lines. The class is using Math Trailblazers, a National Science Foundation-supported elementary school math curriculum developed to reflect recent reform efforts in mathematics…

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…

Mathematics educators promote student engagement in the Process Standards and create problem-solving tasks and facilitate discussions to help their students develop strengths in explaining their methods, using and interpreting multiple representations, and making connections between topics. They are excited and encouraged when they see students…

One mathematical focus for third graders is to develop deep understanding of fractions and fraction equivalence, including comparing fractions through use of models and reasoning strategies. Before reading further, consider how you might solve the following problem: Which fraction is greater, 14/24 or 17/36? The initial impulse of many adults is…

"Help! I'm stuck!" How many times have you heard a student make a similar plea? What do you consider when deciding how to respond? What reasoning is most productive? As part of a large research project, the authors explored these questions with 131 prospective and practicing teachers and found patterns in their reasoning. They began their project…

"The World Is Flat" (Friedman 2005) describes the globalization that advances in technology have imposed on the world economy in recent decades. For the U.S. to maintain its stature in the world, future citizens must be prepared to problem solve and apply their skills to new situations. These future citizens are sitting in elementary school…

The "flat" world described by Friedman (2006) is one of global supply chains and economic networks, outsourcing, international personal entrepreneurial opportunities, and nearly unlimited, universal information availability. American children will inherit a world in which their competition and opportunities are international. In light of these…

Elementary school teachers are responsible for constructing the foundation of number sense in youngsters, and so it is recommended that teacher-training programs include an emphasis on number sense to ensure the development of dynamic, productive computation and estimation skills in students. To better prepare preservice elementary school teachers…

Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…

Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

Too often the professional development provided for teachers of mathematics is a short-term, one-shot effort. Today's shrinking budgets, increasing class sizes, and growing demands on teachers' time present further challenges. For the past six years, staff development efforts in the author's district have focused on language arts with little…

As young children make sense of mathematics, they begin to see with new eyes. What once was uncertain may now be determined. Objects become countable; fingers become tools; and numbers become more than just names. Educators revel in such developments--which mark significant progress toward more sophisticated understanding of number--and work…