How can we make sense of what we learned today?" This is a question the author commonly poses to her algebra students in an effort to have them think about the connections between the new concept they are learning and concepts they have previously learned. For students who have a strong, expansive understanding of previously learned topics,…

One of the foundational topics in first-year algebra concerns the concept of factoring. This article discusses an alternative strategy for factoring quadratics of the form ax[superscript 2] + bx + c, known as "factoring for roots." This strategy enables students to extend the knowledge they used when the leading coefficient was 1 and…

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

As teachers working with students in entry-level algebra classes, authors Amy Nebesniak and A. Aaron Burgoa realized that their instruction was a major factor in how their students viewed mathematics. They often presented students with abstract formulas that seemed to appear out of thin air. One instance occurred while they were teaching students…

The American educational landscape is changing rapidly, and so are the students in American mathematics classrooms. In the New York City public schools, one of every four students is an English language learner (ELL) (New York City Department of Education 2014). Mathematics teachers find themselves teaching either in a classroom that contains all…

According to the National Center for Education Statistics (2016), the number of public school students in the United States who were English learners (ELs) was estimated at 4.5 million. However, in 2005, the national standardized testing scores (Fry 2007) show that about 51 percent of eighth-grade EL students were behind other students in reading…

In this article, the authors introduce the value of "e" by building on students' prior knowledge of slope and using their abilities to analyze, approximate, and interpret rates of change using graphs, symbols, and numerical data. This approach allows students to construct and interpret the value of "e" while laying the conceptual foundation for…

The social and educational status of black male youth in the United States has been receiving increasing attention. In February 2014, President Barack Obama announced a new national initiative--My Brother's Keeper--for helping black boys and male youth or, to speak more generally, boys and young men of color, to "stay on track; providing the…

Effective instruction is multifaceted, dependent largely on the context and, consequently, on numerous variables. Although "effective instruction" is difficult to define, in the author's experience--and as the work of mathematics education specialists and researchers indicates--three key features of quality instruction stand out: (1) Teaching…

The fun thing about teaching measurement topics is allowing students to create three-dimensional objects from cardboard or paper and then to use them to calculate volume and surface area. The project described in this article is one that author Shafer has used for many years at the high school and college levels to reinforce the concepts of volume…

A mathematical problem is solved using the extension-reduction or build it up-tear it down tactic. This technique is implemented in reviving students' earlier knowledge to enable them to apply this knowledge to solving new problems.

NCTM's Principles and Standards for School Mathematics advises that school mathematics experiences at all levels should include opportunities to learn about mathematics by working on problems arising in contexts outside of mathematics. Students should be given the opportunity to learn mathematics by building on their understandings of how the…