Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

Natural disasters often receive massive media attention. The headlines can engage students to think mathematically and scientifically about the world around them. 'Principles and Standards for School Mathematics' explicitly encourages instruction where students "recognize and apply mathematics in contexts outside of mathematics" (NCTM…

This article details a high school classroom activity in which algebra tiles are used to help students gain a conceptual understanding of completing the square. The activity utilises the eight elements of effective mathematics education suggested in the National Council of Teacher of Mathematics' (NCTM's) "Principles to action: Ensuring…

Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…

In today's differentiated classroom, each individual student receives from their teacher student-centered instruction and customized assignments to reflect their skills and knowledge. Teachers differentiate their assignments so each of their students may access the Common Core State Standards, interact with complex nonfiction texts, integrate…

The most recent Kindergarten Common Core Mathematics State Standards include an emphasis on teaching geometry skills, such as recognizing, describing, naming, and composing shapes. This article provides five effective ideas for teachers of young children as they introduce and teach shapes.

The Common Core State Standards were created with college and career readiness in mind to help prepare students to succeed upon graduation from high school. In this article, I examine college readiness as it has been described by both university mathematicians and educational researchers to precisely discern what will foster success in collegiate…

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…

Financial skills, like mathematical ones, must be built on a firm foundation. Whether one is putting money in a piggy bank or a 401(k), and purchasing a toy car or a real one, everyone needs the understanding of financial issues and math skills necessary for making sound decisions. The elementary classroom is the perfect place to introduce…

The authors recently conducted a randomized controlled trial that showed a significant impact of teachers' lesson study, supported by mathematical resources, on both teachers' and students' understanding of fractions. The research and mathematical resources are described in the second part of this article. First the authors examine some of the…

In 2001, Kilpatrick, Swafford, and Findell proposed a new way to look at what it means for students to be mathematically proficient. They described mathematical proficiency as comprising five intertwined strands: procedural fluency, conceptual understanding, adaptive reasoning, strategic competence, and productive disposition. The vision is that…

Building physical models is a natural activity for children and provides a context for lessons on two-dimensional (2D) and three-dimensional (3D) shapes. However, children do not think of their models as prisms, cylinders, and pyramids. Their creations are spaceships, tunnels, castles, and nets on the floor. Creating these types of shapes with…

With rigor outlined in state and Common Core standards and the addition of constructed-response test items to most state tests, math constructed-response questions have become increasingly popular in today's classroom. Although constructed-response problems can present a challenge for students, they do offer a glimpse of students' learning through…

Many students with and/or at risk for emotional and behavioral disorders have academic deficits that affect their performance in mathematics. In addition, these students' behavioral issues may interfere with their academic achievement. For these students, it makes sense for teachers to consider implementing research- and/or evidence-based…