# Teaching-Focused Articles

In this section, you will find articles from journals written specifically for teachers, supervisors, administrators, and others in mathematics education. These readings are often based on research, but are written to focus on practical information to support mathematics instruction.

#### Updated August, 2015

Aisling, L. M., Friel, S. N., & Mamer, J. D. (2009). It’s a fird!: Can you compute a median of categorical data? *Mathematics Teaching in the Middle School, 14*(6), 344-351.

Beaudrie, B. P., & Boschmans, B. (2013). Transformations and handheld technology. *Mathematics Teaching in the Middle School, 18*(7), 444-450.

Bieda, K. (2010b). Stuck in the concrete: Students’ use of manipulatives when generating proof. *Mathematics Teaching in the Middle School, 15*(9), 540-546.

Bouck, M., Keusch, T., & Fitzgerald, W. (1996). Developing as a teacher of mathematics. *The Mathematics Teacher, 89*(9), 769-73.

Breyfogle, M. L., & Lynch, C. M. (2010). Van Hiele revisited. *Mathematics Teaching in the Middle School, 16*(4), 232-238.

Brucker, E. L. (2008). Journey into a Standards-based mathematics classroom.* Mathematics Teaching in the Middle School, 14*(5), 300-303.

ABSTRACT: A standards-based approach to mathematics involves using story problems to allow students to investigate a solution. This approach emphasizes an understanding of concepts and processes and assumes mastery of basic computation skills. This article will encourage teachers to continue teaching standards-based mathematics and to take advantage of available training to produce students who are better prepared in mathematics and who enjoy the process.

Camenga, K. A., & Yates, R. B. J. (2014). Connecting the dots: Rediscovering continuity. *The Mathematics Teacher*, 108(3), 212–217.

Chapin, S. H. (2003). Crossing the bridge to formal proportional reasoning. *Mathematics Teaching in the Middle School, 8*(8), 420-425.

Choppin, J. M., Callard, C. H., & Kruger, J. S. (2014). Interpreting Standards as Sense-Making Opportunities. *Mathematics Teaching in the Middle School*, 20(1), 24-29.

Description: “The authors are a team of two teachers and a researcher who for several years have studied the teachers’ enactment of Accentuate the Negative, a unit on rational numbers that is part of the Connected Mathematics Project (CMP) curriculum (Lappan et al. 2006). We show how allowing students to create algorithms provided opportunities for them to reason about rational number addition and subtraction.”

Choppin, J. M., Cancy, C. B., & Koch, S. J. (2012). Developing formal procedures through sense-making. *Mathematics Teaching in the Middle School, 17*(9), 552-557.

Collins, A. M. (2000). Yours is not to reason why. *Education Week, 20*(1), 60.

Cross Francis, D. I., Hudson, R. A., Lee, M. Y., Rapacki, L., & Vesperman, C. M. (2014). Motivating Play Using Statistical Reasoning. *Teaching Children Mathematics*, 21(4), 228-237.

Description: One of the activities (Figure 3) is an adaptation of a CMP2 activity.

Danielson, C. (2015). They'll Need it for Calculus. *Mathematics Teaching in the Middle School*, 20(5), 260-265.

Description: “This article focuses on the big question of what it means to be ready for calculus; it also explores the role of the middle school curriculum in preparing students to study calculus later.” Specific to CMP, this article cites the bike shop problems from Variables and Patterns and finite difference problem(s) in Frogs, Fleas, and Painted Cubes as examples of middle school tasks that give students opportunities to think about rates of change, exposure to which may help students prepare for similar ideas in calculus.

Edwards, C. M., & Townsend, B. E. (2012). Diary of change: Shifting mathematical philosophies. *Mathematics Teaching in the Middle School, 18*(3), 174-179.

Friel, S. N. & O’Connor, W. T. (1999). Sticks to the roof of your mouth? *Mathematics Teaching in the Middle School, 4*(6), 404–11.

ABSTRACT: Part of a special issue on teaching and learning the concepts of data and chance in the middle school. An activity that involves students comparing data sets by using data about 37 brands of peanut butter and their quality ratings is presented. The testing of the peanut butter, the graphing of the data, the determination of outliers, and the extension of the data analysis are discussed.

Grandau, L., & Stephens, A. C. (2006). Algebraic thinking and geometry.* Mathematics Teaching in the Middle School, 11*(7), 344–349.

ABSTRACT: This article describes how two middle school teachers incorporated algebraic thinking into their textbook-based geometry lessons. One teacher embedded algebraic concepts within an existing textbook lesson while the other teacher elicited algebraic thinking by extending a textbook lesson.

Herbel-Eisenmann, B. A. (2002). Using student contributions and multiple representations to develop mathematical language. *Mathematics Teaching in the Middle School, 8*(2), 100-105.

ABSTRACT: Describes a way to introduce and use mathematical language as an alternative to using vocabulary lists to introduce students to mathematical language in mathematics classrooms. Draws on multiple representations and student language.

Herron-Thorpe, F. L., Olson, J. C., & Davis, D. (2010). Shrinking your class. *Mathematics Teaching in the Middle School, 15*(7), 386-391.

Huntley, Mary Ann. (2008). A framework for analyzing differences across mathematics curricula. *National Council of Supervisors of Mathematics Journal, 10*(2), 10-27.

Jackson, K. J., Shahan, E. C., Gibbons, L. K., & Cobb, P. (2012). Launching complex tasks. *Mathematics Teaching in the Middle School, 18*(1), 24-29.

Keiser, J. M. (2000). The role of definition. *Mathematics Teaching in the Middle School, 5*(8), 506–511.

ABSTRACT: The writer examines the role that mathematical definitions can play in the middle grades math classroom, focusing on the concept of angle as it was introduced to sixth-grade students.

Keiser, J. M. (2010). Shifting our computational focus. *Mathematics Teaching in the Middle School, 16*(4), 216-223.

ABSTRACT: Through professional development activities involving action research, middle-grades teachers at this author's school learned how to honor students' prior knowledge and experience by finding out about their K-5 computational development. Rather than complaining about what their students did not know, they learned to appreciate results from their K-5 instruction. These results seem to indicate more conceptual understanding, a strong number sense, and increased computational flexibility than they had seen in the past. In this article, the author shares the data and the process that middle-grades teachers undertook to learn about their students. She describes how middle-grades teachers used the Connected Mathematics Project (CMP) for mathematics instruction. Overall, the process of learning about the computational knowledge that students bring to middle school has highlighted the importance of flexibility.

Keiser, J. M. (2012). Students’ strategies can take us off guard. *Mathematics Teaching in the Middle School, 17*(7), 418-425.

Kim, O. K., & Kasmer, L. (2007). Using "prediction" to promote mathematical reasoning. *Mathematics Teaching in the Middle School, 12*(6), 294-299.

ABSTRACT: This article introduces prediction as a useful tool to promote mathematical reasoning. First, the article addresses prediction expectations in state standards and gives examples. It also provides a classroom example and activities to illustrate what prediction can look like and how it can serve as a building block for the development of students' reasoning abilities. Second, the article suggests some ideas to teachers that promote reasoning when prediction is incorporated into mathematics lessons. (Contains 1 table and 3 figures.)

Kim, O. K., & Kasmer, L. (2009). Prediction as an instructional strategy. *Journal of Mathematics Education Leadership, 11*(1), 33–38.

Kladder, R., Peitz, J., & Faulkner, J. (1998). On the right track. *Middle Ground, 1*(4), 32-34.

Lambdin, D. V., Lynch, K., & McDaniel, H. (2000). Algebra in the middle grades. *Mathematics Teaching in the Middle School, 6*(3), 195-198.

ABSTRACT: The writers describe a weeklong series of lessons with their sixth graders that used bicycle racing as both a motivator and a context for thinking about rate of change and the shapes of graphs.

Lepak, J. (2014). Enhancing Students' Written Mathematical Arguments. *Mathematics Teaching in the Middle School*, 20(4), 212-219.

Description: The article shares how one teacher used peer-review activities involving rubrics to support students’ arguments and justifications for the Pool problem in Say it With Symbols, among other tasks.

Lowe, P. (2004). A new approach to math in the middle grades. *Principal, 84*(2), 34-39. ABSTRACT: Part of a special section on mathematics teaching and learning. Suggestions for implementing reform programs such as Connected Mathematics Project in the middle grades are provided. The advantages and disadvantages of such research-based reform programs are also discussed.

Meyer, M., Dekker, T., & Querelle, N. (2001). Contexts in mathematics curricula. *Mathematics Teaching in the Middle School, 6*(9), 522 527.

Miller, J. L., & Fey, J. T. (2000). Proportional Reasoning. *Mathematics Teaching in the Middle School, 5*(5), 310-313.

ABSTRACT: Proportional reasoning has long been a problem for students because of the complexity of thinking that it requires. Miller and Fey discuss some new approaches to developing students' proportional reasoning concepts and skills.

Moore, A. J., Gillett, M. R., & Steele, M. D. (2014). Fostering student engagement with the flip. The Mathematics Teacher, 107(6), 420–425.

Polly, D. & Orrill, C. (2012). CCSSM: Examining the critical areas in grades 5 and 6. *Teaching Children Mathematics, 18*(9), 566-573).

Raymond, A. (2004). “Doing math” in Austin. *Teaching Pre K-8, 34*(4), 42-45.

ABSTRACT: Since 1990, the January issue of "Teaching Pre K-8" has highlighted a school visit by the president of the National Council of Teachers of Mathematics. This article discusses Cathy Seeley's visit to a 6th grade classroom at the J. E. Pearce Middle School in Austin, Texas, where she participated in a math activity from the Connected Mathematics Project, a complete middle school mathematics curriculum for grades 6, 7, and 8. Funded by the National Science Foundation between 1991 and 1997, the program includes eight units for each grade, "built around mathematical problems that help students develop understanding of important concepts and skills in number, geometry, measurement, algebra, probability and statistics."

Reinhart, S. C. (2000). Never say anything a kid can say! *Mathematics Teaching in the Middle School, 5*(8), 478-483.

ABSTRACT: Reinhart discusses teaching mathematics to middle school students. To help students engage in real learning, Reinhart asks good questions, allows students to struggle, and places the responsibility for learning directly on their shoulders.

Rubenstein, R. N., Lappan, G., Phillips, E., & Fitzgerald, W. (1993). Angle sense: A valuable connection. *Arithmetic Teacher, 40*(6), 352-358.

Sjoberg, C. A., Slavit, D., Coon, T., & Bay-Williams, J. (2004). Improving writing prompts to improve student reflection. *Mathematics Teaching in the Middle School, 9*(9), 490-495.

ABSTRACT: The teaching of mathematics continues to move away from a sole focus on correctness and a finished product to include a focus on process, context, and understanding. Writing tasks can be ideal tools for supporting student expression of ideas as a learning activity.

Smith III, J. P., & Phillips, E. A. (2000). Listening to middle school students’ algebraic thinking. *Mathematics Teaching in the Middle School, 6*(3), 156-161.

Star, J. R., Herbel-Eisenmann, B. A., & Smith III, J. P. (2000) Algebraic concepts: What's really new in new curricula?. *Mathematics Teaching in the Middle School, 5*(7). 446-451.

ABSTRACT: Examines 8th grade units from the Connected Mathematics Project (CMP). Identifies differences in older and newer conceptions, fundamental objects of study, typical problems, and typical solution methods in algebra. Also discusses where the issue of what is new in algebra is relevant to many other innovative middle school curricula.

Stauffer, T. C. (2011). More of sixth graders flip for breakfast. *Teaching Children Mathematics, 18*(5), 328-330.

ABSTRACT: A coin-flipping activity is meant to show students that a small number of trials may produce a wide variation in results.

Umbeck, L. M. (2011). Navigating classroom change: A renegotiated classroom culture results in students learning to participate in new ways. *Mathematics Teaching in the Middle School, 17*(2), 88-95.

Wasserman, L. (2008). A Marriage Made in Math Class. *Teacher Magazine, 2*(1).

Zawojewski, J. S., Robinson, M., & Hoover, M. V. (1999). Reflections on mathematics and the Connected Mathematics Project.* Mathematics Teaching in the Middle School, 4*(5), 324-30.