Education experts argue that using rich mathematical tasks in student-centered classrooms is especially conducive to student learning (NCTM 2000). That said, they also acknowledge that using complex tasks and developing student-centered classrooms can be intimidating and challenging for teachers (Chazan and Ball 1999). One difficulty associated…

A picture is worth a thousand words. This statement is especially true in mathematics teaching and learning. Visual representations such as pictures, diagrams, charts, and tables can illuminate ideas that can be elusive when displayed in symbolic form only. The prevalence of representation as a mathematical process in such documents as…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

Recent research suggests that it is not simply experiencing anxiety that affects mathematics performance but also how one responds to and regulates that anxiety (Lyons and Beilock 2011). Most people have faced mathematics problems that have triggered their "run response." The issue is not whether one wants to run, but rather…

Multidimensional mathematics teaching, as discussed in this article encourages the use of context in mathematics teaching and learning to help teachers better recognize and build upon the cultural and social resources students bring to the classroom. Such efforts can impact students' performance and can help students make sense of decisions…

In the authors' examination of various instructional programs, they observed that most provide all the necessary data to solve proportion problems, employ compatible numbers that are usually unrealistic, present numbers (data) in the order in which they are to be manipulated, discuss contexts that cannot be easily replicated, and present…

The game of Plinko offers students an exciting real-world example of the applications of probability and data analysis. The Common Core State Standards for Mathematics (CCSSI 2010) and the Guidelines for Assessment in Statistics Education (GAISE) (Franklin et al. 2007) suggest that students in grades 6-8 be given ample opportunities to engage in…

Middle school is a crucial transition period for students as they move from concrete to algebraic ways of thinking. This article describes a sequence of instruction geared toward helping prospective middle school instructors teach the topic of percentages.

Dot arrays provide opportunities for students to notice structures like commutativity and distributivity, giving these properties an image that can be manipulated and explored. These images also connect to ways that we organize discrete objects in everyday life. This article describes how the authors developed an array of dot tasks that have been…

Geometry is a major area of study in middle school mathematics, yet middle school and secondary students have difficulty learning important geometric concepts. This article considers Alexis-Claude Clairaut's approach that emphasizes engaging student curiosity about key ideas and theorems instead of directly teaching theorems before their…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

A renewed emphasis was placed on ratio and proportional reasoning in the middle grades in the Common Core State Standards for Mathematics (CCSSM). The expectation for students includes the ability to not only compute and then compare and interpret the results of computations in context but also interpret ratios and proportions as they are…

Students' success in solving problems involving proportional reasoning is an indication that they have moved beyond additive thinking to multiplicative thinking. However, classroom work indicates that many students do not reason proportionally in many practical contexts. The authors discuss a particular task that reveals students'…

Mathematics teachers are constantly looking for real-world applications of mathematics. Aerospace education provides an incredible context for teaching and learning important STEM concepts, inspiring young people to pursue careers in science, technology, engineering, and mathematics. Teaching mathematics within the context of aerospace generates…

Recent research suggests that high-impact activities in science and math classes promote positive attitudinal shifts in students. By implementing high-impact activities, such as designing a school and a skate park, mathematical thinking can be linked to the engineering design process. This hands-on approach, when possible, to demonstrate or…