The recent push for more problem solving in elementary school mathematics classrooms intimidates many teachers. Anyone can look at the arguments--that problem solving deepens knowledge, provides real-world context, allows for multiple entry points, and so on--and see their logic and potential (Lester and Charles 2003). But teachers tend to think…

Tasks that develop spatial and algebraic reasoning are crucial for learning and applying advanced mathematical ideas. In this article, the authors describe how two early childhood teachers used stories as the basis for a unit that supports spatial reasoning in kindergartners and first graders. Having mathematical experiences that go beyond…

The Common Core State Standards in Mathematics (CCSSM) are, at the same time, promising and problematic. Some educators hope that the adoption and implementation of this document can result in a deeper, more coherent curriculum for all students. Others are concerned that it will push schools and teachers to be even more focused than they have been…

According to the author, much of their math teaching is through pictures and words. They write number sentences, they draw geometric figures, and they talk about math. The representations they use--numbers, shapes, operators, and mathematics vocabulary--make it possible for them to learn and communicate mathematical ideas. These representations…

This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…

The author's teaching goal is always to make certain that his students, children and adults alike, have some reason for joining him on his mathematical journeys. The lesson he describes in this article provides him with the unusual opportunity to call attention to strategies that have had a long history and remarkable results. With careful…

As elementary educators across the country begin to interpret the Common Core State Standards for Mathematics (CCSSI 2010) and put them into practice, this article takes a look at this latest set of mathematics standards from a historical viewpoint. The author discusses how educators might use a historical perspective to make the outcome of…

Kolby is a four-year-old, identified on the autism spectrum as having sensitivity issues, attention challenges, and limited verbal language abilities. Next to Kolby sits Melanie, a reserved four-year-old with visual, fine-motor, and gross-motor challenges. Amy rounds out the group as one of the peer models in the inclusive classroom setting. Mrs.…

During the winter of 2011, the author faced an instructional dilemma: Should she teach the concept of adding and subtracting fractions with unlike denominators using a "quick trick" for the sake of staying on schedule, or should she try something different in hopes that her students would gain understanding through their own methods? The latter…

Elementary school teachers in Seattle, Washington, are encouraged to adapt differentiated instructional practices in math to accommodate the particular students in their own classrooms. Seattle Public Schools is a large, urban district serving 47,000 students who speak over a hundred languages. More than a third receive free or reduced lunch. The…

Young students, new to formal mathematics, come to school with various number experiences. To meet their needs, teachers must understand each student's thinking and tailor instruction appropriately. Differentiation is a vehicle for making this possible. According to Tomlinson (2001), differentiated instruction is student-centered; rooted in…

Moving beyond physical interactions with materials is a significant mathematical step for students that is often difficult to take. Persistent tally-mark use, for example, among older children is a testament to this challenge. For many students, shifting away from tangible tools begins a precarious journey; teachers should support it with…

All good teachers recognize their students' varying learning needs and strive to meet them. So differentiation is certainly not a revolutionary idea. In fact, Tomlinson and Eidson describe differentiated instruction as "really just common sense" (2003, p. 1). In practice, however, offering such opportunities for students is challenging. In this…

One of the many challenges teachers face is trying to differentiate instruction so all students have equal opportunities to participate, learn, and engage. To provide guidelines for differentiated instruction in mathematics, staff from the Madison Metropolitan School District in Wisconsin created a pedagogical framework for teaching called…

Math Workshop offers differentiated instruction to foster a deep understanding of rich, rigorous mathematics that is attainable by all learners. The inquiry-based model provides a menu of multilevel math tasks, within the daily math block, that focus on similar mathematical content. Math Workshop promotes a culture of engagement and…