Kyle, a kindergartner from a low-income family, is shown a set of three black dots on a white mat. His teacher then hides the dots with a small box lid and lays down an additional set of two dots. She pushes the two dots under the cover, one at a time. Kyle must now choose the number of dots "hiding" under the box from a set of four…

The branch of biology that studies ecosystems, habitats, their developments, and the equilibrium of species is called conservation biology (Soule 1986). It is important to study this balance of species within an ecosystem, where species might live for a short period of time (such as mosquitoes, the main source of food for frogs) or live for…

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

Engaging students in studies about conservation and sustainability can support their understanding of making environmental conscious decisions to conserve Earth. This article aims to contribute these efforts and direct students' attention to how they can use mathematics to make environmental decisions. Contributors to iSTEM: Integrating…

Textbooks, as well as classroom instruction, tend to present estimation as a stand-alone exercise, ignoring that "the process of estimation depends on the situation itself as well as the estimator." When taught this way, estimation is stripped of its power to help students judge the reasonableness of answers and make sense before,…

Learning through meaningful problem solving is integral in any successful mathematics program (Carpenter et al. 1999). The National Council of Teachers of Mathematics (NCTM) promotes the use of problem solving as a means to deepen understanding of all content areas within mathematics (NCTM 2000). This article describes a first-grade lesson that…

In this article, the author shares how his fourth-grade students' creative thinking concerning a long-standing research problem stimulated changes in his instructional strategies. He begins by providing an example which illustrates that the standard tool of democracy, the plurality vote, suffers serious deficiencies: "The winner can be the voters'…

By following learned rules rather than reasoning, students often fall into common error patterns, something every experienced teacher has observed in the classroom. In their effort to circumvent the developing common error patterns of their students, the authors decided to supplement their math text with two weeklong investigations. The first was…

Traditionally, the first mathematical task for primary grade students to master is addition. Mastering addition facts is truly a positive experience. Then one turns to subtraction. After mastering addition facts, many students think that subtraction facts are a whole new set of facts to learn that have nothing to do with addition facts. They do…

"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…

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…

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…

Connecting mathematical thinking to the natural world can be as simple as looking up to the sky. Volunteer bird watchers around the world help scientists gather data about bird populations. Counting flying birds might inspire new estimation methods, such as counting the number of birds per unit of time and then timing the whole flock's flight. In…

Since 2001, the authors have been working with groups of teachers to investigate students' early algebraic thinking--learning representations, connections, and generalizations in the elementary school grades. They began paying attention to students' explicit remarks about regularities in the number system or what students imply by their…