Performance tasks provide effective ways to differentiate mathematics instruction while allowing students to be creative and to incorporate mathematics content that is suitable for their interest and readiness. A project that I have enjoyed assigning to my high school students, Algebra about Me, is designed to introduce, reinforce, and review equation-solving concepts and skills (for a customizable activity sheet, go to www.nctm.org/mt).
Casey Hord, Samantha Marita, Jennifer B. Walsh, Taylor-Marie Tomaro, and Kiyana Gordon
Emotional and contextual support can help students step toward confidence and success with challenging mathematics.
Sherry L. Bair and Edward S. Mooney
Mathematical precision means more than accuracy in computation or procedures; it also means precision in language. The Common Core State Standards for Mathematics states, “Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning” (CCSSI 2010, p. 7). In our recent experience in working with teachers and students, we have noticed a trend toward teachers using informal, and often creative, language and terminology in an effort to connect with students and make mathematical procedures easier to remember.
Reasoning in Algebra Classrooms
Daniel Chazan and Dara Sandow
Secondary school mathematics teachers are often exhorted to incorporate reasoning into all mathematics courses. However, many feel that a focus on reasoning is easier to develop in geometry than in other courses. This article explores ways in which reasoning might naturally arise when solving equations in algebra courses.
Alex Friedlander and Abraham Arcavi
Integrating procedures and thinking processes makes learning more meaningful.
Kristen Lew and Juan Pablo Mejía-Ramos
This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.
Karin E. Lange, Julie L. Booth, and Kristie J. Newton
Presenting examples of both correctly and incorrectly worked solutions is a practical classroom strategy that helps students counter misconceptions about algebra.
Angela Marie Frabasilio
Let students find the connecting thread to create, illustrate, and share word problems to bridge school math and real-life math.
Meghan Riling and Leslie Dietiker
Although new teachers are often prepared to teach using reform practices, they may be given traditional curriculum materials. Learn how these traditional materials can be adapted to reflect reform practices and teaching goals.