Create homework assignments that both engage middle-grades students and strengthen their mathematical understandings and skills.
Rob Wieman and Fran Arbaugh
Ben Freeburn and Fran Arbaugh
Read about ways to determine how your students are thinking, and then implement NCTM's mathematical teaching practices as students work on a task.
Professional development opportunities for mathematics teachers are abundant in the United States. School-and district-based workshops, college and university courses, summer institutes, and local, state, and national meetings for K–12 mathematics teachers all combine to provide numerous opportunities for professional growth. Individual teachers often return from these types of experiences with new activities to use in their classrooms and new ideas about teaching mathematics. What is often missing from many of these types of professional development experiences is the opportunity for teachers to build ongoing and collaborative learning relationships with mathematics teachers in their own school buildings.
Dustin Jones and Fran Arbaugh
Clearing up the Confusion over Calculator Use in Grades K-5
Barbara J. Reys and Fran Arbaugh
Since the publication of NCTM's Principles and Standards for School Mathematics in April 2000, considerable discussion has taken place about “key messages” of the document. The breadth of the content of Principles and Standards may hamper attempts to identify messages about particular topics. In addition, many of the fundamental messages are not easily distilled into short phrases. In fact, when such messages are too succinctly articulated, the danger of oversimplification and misunderstanding arises. This misapprehension can be seen in a question that often emerges in discussions about elementary school mathematics and Principles and Standards. That is, what does Principles and Standards say about calculator use in elementary school?
Fran Arbaugh, Carolyn Scholten and N. Kathryn Essex
“Spotlight on the Standards” focuses on the grades 6–8 content and process standards found in NCTM's Principles and Standards for School Mathematics (2000). The articles compare NCTM's Curriculum and Evaluation Standards for School Mathematics, published in 1989, with the Principles and Standards relating to the middle grades and suggest ways that teachers might incorporate Standards-based practices into their instruction.
Shiv Karunakaran, Ben Freeburn, Nursen Konuk and Fran Arbaugh
Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.
Fran Arbaugh, Duanne Graysay, Nursen Konuk and Ben Freeburn
In the last decade, mathematics teacher educators have begun to design learning opportunities for preservice mathematics teachers using a pedagogies-of-practice perspective. In particular, learning cycles provide a structure for engaging PSTs in learning to teach through the use of representations, approximations, and decompositions of practice (Grossman et al., 2009). In this article, we provide details of one learning cycle designed to support secondary mathematics preservice teachers' learning to elicit and use evidence of student thinking and pose purposeful questions (National Council of Teachers of Mathematics, 2014). Through qualitative analyses conducted on learning reflections, we provide evidence of the impact on engagement of this cycle through the lens of the Framework for Learning to Teach (Hammerness et al., 2005).
Kathryn B. Chval, John K. Lannin, Fran Arbaugh and Angela D. Bowzer
Educators who can elicit preservice teachers' beliefs about teaching mathematics can effectively challenge and change unrealistic expectations.
John K. Lannin, Fran Arbaugh, David D. Barker and Brian E. Townsend
Give me a productive error over a boring, mundane, and unproductive fact any day.