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…

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…

To be able to support meaningful mathematical experiences, preservice elementary school teachers (PSTs) must learn mathematics in deep and meaningful ways (Ma 1999). They need to experience investigating and making sense of the mathematics they will be called on to teach. To expand their own--often limited--views of what it means to teach and…

To support students' development of concepts in mathematics, the use of technology is often encouraged (Common Core State Standards Initiative [CCSSI] 2010). Technology can contextualize learning and provide a meaningful setting for mathematical ideas. Most teachers are supportive regarding the use of technology to encourage learning and…

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

In this article, the authors discuss a special type of multiplication-and-division-of-fractions problem that elementary school teachers can use to promote children's understanding of fractional quantities and their relationships. These problems are accessible to students working at different levels of fraction understanding, and they can be solved…

Elementary school mathematics is increasingly recognized for its crucial role in developing the foundational skills and understandings for algebra. In this article, the author uses a lesson to introduce the concept of "rates"--comparing two different types and units of measure--and how to graph them. Described is the lesson and shared…

As teachers seek activities to assist students in understanding division as more than just the algorithm, they find many examples of division as fair sharing. However, teachers have few activities to engage students in a quotative (measurement) model of division. Efraim Fischbein and his colleagues (1985) defined two types of whole-number…

In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…

The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, the…

Because fractions and percentages can be difficult for children to grasp, connecting them whenever possible is beneficial. Linking them can foster representational fluency as children simultaneously see the part-whole relationship expressed numerically (as a fraction and as a percentage) and visually (as a pie chart). NCTM advocates these…

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…

Students from thirteen fifth-grade classrooms from six different elementary schools investigate the preferred escape routes of cockroaches. These identified routes of 90-, 120-, 150-, and 180-degrees are the research findings of Paolo Dominici, an Italian scientist. The students used rubber cockroaches and lizards to map out these escape routes.…