Key Method

The instructor demonstrates an understanding of multiple student strategies, misconceptions, and/or solution paths for solving a given mathematical task by investigating and listing them beforehand. The instructor also facilitates interactions where participants anticipate possible student strategies to look for when their students interact with the assigned task. In addition, participants should sort or sequence the strategies in a way that highlights the math content-focused learning goal (math goal), typically moving from least to most sophisticated based on a given criteria (e.g., concrete to abstract, representations vs. thinking strategies, etc.) and connect these strategies to other activities throughout the day.

Method Components

The intention of this competency is to examine the degree to which the instructor knows and effectively transfers understanding of multiple student strategies that may be used to solve a given mathematical task, both through planning ahead of time and by providing opportunities for participant learning. A logical place to demonstrate this competency would be during the “New Student Task” segment, but that is not necessarily the only point where this competency can be demonstrated.

Components for Demonstrating Understanding of Multiple Strategies/Solution Paths

1. Anticipates student strategies/solution paths to be explored during planning
• Uses multiple resources to generate a list of possible student strategies and misconceptions for the given concept/task
• Selects the categories for how the strategies might be sequenced or sorted based on the math content-focused learning goal
• Anticipates participant misconceptions and/or missing background knowledge and ways to address them

2. Facilitates group discussion around student strategies
• Uses the Three-Phase Lesson Structure to demonstrate the before, during, and after phases for task-based learning
• Demonstrates selection of student strategies for presentation as participants interact with the task
• Provides opportunity for participants to share multiple strategies/solution paths
• Facilitates brainstorming of possible strategies, misconceptions, and solution paths for the given task
• Facilitates participants in sequencing or sorting of strategies
• Stays within the given time frame (~20 minutes)

3. Analyzes participant responses and compares to anticipated responses
• Reflects afterward on how the anticipated students compared/contrasted with what emerged during the session
• Reflects afterward on how the anticipated misconceptions/gaps in prior knowledge compared/contrasted with what emerged during the session.
  

Supporting Research

• Ball, D. L., Thames, M.H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 59, 387-407.

• Borko, H. (2004). Professional Development and Teacher Learning: Mapping the Terrain. Educational Researcher, 33(8), 3–15.)

• Carpenter, T. P., et al. (1989). Using Knowledge of Children’s Mathematics Thinking in Classroom Teaching: An Experimental Study. American Educational Research Journal, 26(4), 499-531.

• Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. b. (1999). Children’s Mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann.

• Loucks-Horsley, S., Stiles, K. C., Mundry, S., Love, N., & Hewson, P. W. (2010). Designing Professional Development for Teachers of Science and Mathematics (3rd ed.). Thousand Oaks, CA: Corwin.

Resources

• National Governors Association for Best Practices & Council of Chief State School Officers. (2010). Common core state standards—Mathematics. Washington DC: Author.

• Progressions Documents for the Common Core Math Standards (2011).
  http://math.arizona.edu/~ime/progressions/

• The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children’s cognitive development and by the logical structure of mathematics.

• Rimbey, K. A. (2013). From the Common Core to the Classroom: A Professional Development Efficacy Study for the Common Core State Standards for Mathematics.
  http://hdl.handle.net/2286/R.I.18088

• Standards for Mathematical Practice: Commentary and Elaborations for K–5 (2014).
  http://commoncoretools.me/wp-content/uploads/2014/02/Elaborations.pdf

• Van de Walle, J. A., et al. (2014). Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K-2. Pearson.

• Van de Walle, J. A., et al. (2014). Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5. Pearson.

• Van de Walle, J. A., et al. (2014). Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8. Pearson.

Submission Guidelines & Evaluation Criteria

The items in this following section detail what must be submitted for evaluation. To earn the micro-credential, you must receive a passing evaluation for each question in Parts 1 and 3, and a “Yes” each component in Part 2.

Part 1. Overview Questions

(300-word limit for each response)

Part A

• What grade level, mathematics domain, and task were discussed in the New Student Task segment?

• What student strategies did you anticipate for this task? What resources did you use to inform your own understanding of the possible strategies/solution paths for this concept?

• What categories did you select ahead of time for the sequencing/sorting activity?

• What participant misconceptions and/or missing background knowledge did you anticipate beforehand? How did you plan to to address each? What resources did you use to inform your anticipations?

Part 2. Work Examples/Artifacts

Instructor must submit photo(s) of the student strategy list generated in class, demonstrating anticipation of student strategies. The rubric in this section will focus on the comparison between the instructors’ anticipated strategies and the participants’ anticipated strategies and ways in which the instructor addressed misconceptions or gaps in prior knowledge.

Part B
To view the rubric associated with this part, please download the requirements doc at the bottom of the page.

Part 3. Educator Reflection

(300-word limit for each response)

Part C

• How did your planned student strategies list match up with your participants’ strategies list(s)?

• What misconceptions or gaps in prior knowledge did you observe with your participants? How did this compare to your prediction?

• How did your participants respond to the sequencing/sorting of the anticipated strategies? How did you connect these strategies to the content segments that took place later in the day?

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