Inquiry-based instruction is a student-centered approach to teaching that focuses on active learning (Barron and Darling-Hammond 2008) in which students engage with "tasks that promote reasoning and problem solving" (NCTM 2014). Specifically, such tasks encourage a variety of solution strategies and stimulate use of the NCTM Process…

The Puppy Love problem asked fifth and sixth grade students to use their prior knowledge of measures of central tendency to determine a data set when given the mean, mode, median, and range of the set. The problem discussed in this article is a task with a higher level of cognitive demand because it requires that students (1) explore and…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Students' experiences with statistics and data analysis in middle school are often limited to little more than making and interpreting graphs. Although students may develop fluency in statistical procedures and vocabulary, they frequently lack the skills necessary to apply statistical reasoning in situations other than clear-cut textbook examples.…

Emperor penguins, the largest of all the penguin species, attain heights of nearly four feet and weigh up to 99 pounds. Many students are not motivated to learn mathematics when textbook examples contain largely nonexistent contexts or when the math is not used to solve significant problems found in real life. This article's project explores how…

Engineering-based modeling activities provide a rich source of meaningful situations that capitalize on and extend students' routine learning. By integrating such activities within existing curricula, students better appreciate how their school learning in mathematics and science applies to problems in the outside world. Furthermore, modeling…

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

Numerous research articles and curricula standards maintain that learning is optimized when students are actively involved in the learning process by assimilating information and constructing their own meanings. The authors' experience with teaching probability concepts has shown that students struggle with concepts of counting. These…

This article describes how a sixth-grade teacher's "missing word" task uncovered higher-level thinking and engaged her students in the Standards for Mathematical Practice. The role and selection of the task promotes higher-level thinking and connects to the Common Core State Standards for Mathematics. The task required students to apply…

This article describes "modeling" as the act of creating an "idealized version of a real-life situation" that has been "translated into mathematical terms." By exploring an open-ended investigation involving proportional reasoning, sixth grade students were able to walk through both problem solving and modelling. The…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Much attention has been devoted in the literature to students' struggles with fraction division. With regard to the traditional invert and multiply algorithm, researchers and educators have examined such areas as typical errors, how to help students understand why this method works, and what alternatives are available that might be more intuitive.…

Mr. Carter is about to start a two-day lesson on subtraction of integers with his sixth-grade prealgebra students. He plans to use contextualized problems that will allow his students to develop an interpretation of subtraction that involves the idea of "difference." This article outlines one way to teach students develop number line…

Playing mathematical games enables middle school students to engage their minds while discovering and using meaningful strategies. Blokus[R] is one such game. While playing, students exercise spatial awareness, analyze attributes of two-dimensional shapes, compare patterns, and use logic--all of which encompass NCTM's Content Standards. Students…