In this article, Lindsey Fowler describes how an animal rhyme--that she shared with her fifth-grade students with the intention of assisting them with the concept of metric conversions--made fostering the Standards for Mathematical Practice (SMP) more difficult. The addition of animals, which added an extraneous element that students mistakenly…

The sandwich problem described in this article would likely be considered more appropriate for third grade or above. However, as members of the research team for a lesson study involving teachers from kindergarten through fourth grade, the authors saw kindergarten students rise to the challenge. The authors invite readers to review two scenarios,…

One of the most important jobs mathematics teachers have is supporting students and helping them to develop confidence in their own capabilities as mathematical thinkers. Children who do not believe in themselves are unlikely to share their ideas, persevere through challenges, or take risks that lead to new insights. Yet many students have no…

The twenty-first century has seen an increased call to train students to craft mathematical arguments. The third of the Common Core's (CCSS) Standards for Mathematical Practice (SMP 3) (CCSSI 2010) calls for all mathematically proficient students to "construct viable arguments" to support the truth of their ideas and to "critique…

Children's intuitive understandings of mathematical ideas--both correct, generalizable strategies alongside misconceptions--showcase the complexity of their thinking. However, recognizing children as complex thinkers is one thing but it is another thing altogether to leverage their ideas to plan for and carry out mathematics instruction. The…

Eliciting student thinking is paramount to effective mathematics teaching and learning. Although one can use many strategies and techniques to promote student thinking, technology is one resource that is often underutilized. Whether it is the informed use of calculators or an interactive website, technology can be leveraged to promote mathematical…

Understanding the decimal system is challenging, requiring coordination of place-value concepts with features of whole-number and fraction knowledge (Moloney and Stacey 1997). Moreover, the learner must discern if and how previously learned concepts and procedures apply. The process is complex, and misconceptions will naturally arise. In a…

Students' success with fourth-grade content standards builds on mathematical knowledge learned in third grade and creates a conceptual foundation for division standards in subsequent grades that focus on the division algorithm. The division standards in fourth and fifth grade are similar; but in fourth grade, division problem divisors are only one…

Is anything more refreshing than going for a nice, long swim? The math scenarios presented in this article will take the reader back to hot summer days and remind the reader what a cool dip in the water feels like. Solving these problems is enjoyable and encourages the solver to think of the many ways that math is all around--even in the middle of…

Communication is a critical skill for students to possess in preparation for college and their future careers. One way for students to communicate their ideas in all content areas is through writing. The English language arts portion of the Common Core State Standards (CCSSI 2010a) specifically states that students need to understand perspectives…

Teachers use the word assessment to describe any method of gathering information about student learning. Whether it be formative assessment (intended to guide instructional decisions) or summative assessment (a reflection on the entirety of student learning from prior instruction), teachers are constantly working to identify what their students…

In a classroom teaching experiment, we explored fifth graders' ability to identify relationships in and between two patterns--what we may refer to as functional relationships. Conventional functions curricula are dominated by defining relationships between two patterns via a rule, describing how to find y or f(x) given a particular value for x…

After teaching the concept of division with remainders for many years, Vanessa Battreal, Vanessa Brewster, and Juli Dixon noticed that interpreting remainders in contextualized problems is particularly challenging for elementary school students. To effectively interpret remainders, students must attend to problem context and consider carefully…

A "repeating pattern" is a cyclical repetition of an identifiable core. Children in the primary grades usually begin pattern work with fairly simple patterns, such as AB, ABC, or ABB patterns. The unique letters represent unique elements, whereas the sequence of letters represents the core that is repeated. Based on color, shape,…

Based on a study with six elementary school teachers and 115 students in grades 3, 4, and 5, this article discusses ways that teachers might support an understanding of variable as students explore pattern-finding activities. The practices emerged from interviews with teachers and a yearlong observation of teaching algebraic thinking during an…