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Anticipates Student Strategies The instructor anticipates student strategies for solving a given mathematical task and effectively facilitates participant learning and application of these strategies

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

A. 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

B. 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)

C. Analyzes participant responses and compares to anticipated responses

- Reflects afterward on how the anticipated students compared/contrasted with what emerged during the session


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- 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)


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

- Passing: The instructor lists the grade level, domain, and task.

§ 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? - Passing: The instructor lists at least five anticipated student strategies, solution paths, or

misconceptions and the resources used to generate the list.

§ What categories did you select ahead of time for the sequencing/sorting activity? - Passing: The instructor lists two ways in which the participants can sort/sequence the student

work and the math content-focused learning goal (math goal) for each.

§ 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? - Passing: The instructor lists at least three anticipated participant misconceptions and how s/he

plans to address each.

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

“Yes” “Almost” “Not Yet” “Not Observed”

Uses the Three-Phase Lesson Structure to demonstrate the before, during and after phases for task-based learning (1)

The instructor plans a demonstration lesson using the Three-Phase Lesson Structure; the completed sheet indicates that all three parts were effectively planned and presented

The instructor plans a demonstration lesson using the Three-Phase Lesson Structure; the completed sheet indicates that two of the three parts were effectively planned and presented

The instructor plans a demonstration lesson using the Three-Phase Lesson Structure; the completed sheet indicates that one of the three parts was effectively planned and presented

The instructor does not submit a Three-Phase Lesson Structure sheet OR the completed sheet indicates that none of the parts were effectively planned and presented

Demonstrates selection of students for presentation as participants interact with the task (1)

The instructor effectively demonstrates how to select two to four students to present their tasks to the group, providing direction and rationale as described in the Three-Phase Lesson Structure

The instructor does not effectively demonstrate how to select two to four students to present their tasks to the group

Provides opportunity for participants to share

The instructor provides opportunity for the selected participants to

The instructor provides opportunity for the selected participants

The instructor provides opportunity for the selected participants to

The instructor does not provide opportunity for the


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multiple strategies/solution paths (1)

share their strategies/solution paths, effectively asking guiding questions as needed OR no guiding questions are necessary, as described in the Three-Phase Lesson Structure

to share their strategies/solution paths, asking questions that fail to effectively guide the conversation, as described in the Three-Phase Lesson Structure

share their strategies/solution paths but interrupts or takes over the presentations, as described in the Three-Phase Lesson Structure

selected participants to share their strategies/solution paths, as described in the Three-Phase Lesson Structure

Facilitates brainstorming of possible strategies, misconceptions, and solution paths for the given task (2)

The instructor effectively facilitates brainstorming of possible strategies, misconceptions, and solution paths for the task at hand, recording the brainstorming on a prepared anchor chart; the instructor guides participants to look at anchor charts from previous sessions (except on Day 1)

The instructor effectively facilitates brainstorming of possible strategies, misconceptions, and solution paths for the task at hand, recording the brainstorming on a prepared anchor chart; the instructor does not guide participants to look at anchor charts from previous sessions

The instructor facilitates a brainstorming of possible strategies, misconceptions, and solution paths for the task at hand; the instructor fails to guide participants when poor or incomplete examples are given; the instructor may fail to record the brainstorming on a prepared anchor chart

The instructor does not include brainstorming

Facilitates participants in sequencing or sorting of strategies based on the math content-focused learning goal (math goal) (3)

The instructor effectively engages participants in the planned sequencing or sorting activity; the participants use student examples and the determined math content-focused learning goal (math goal) to justify their thinking

The instructor effectively engages participants in the planned sequencing or sorting activity; the participants use student examples to justify their thinking

The instructor attempts to engage participants in the planned sequencing or sorting activity, but participants do not sort/sequence appropriately, and the instructor does not correct them

No sequencing or sorting activity is attempted

Stays within the given time frame (~20 minutes) (1)

The task-based learning segment lasts no longer than 20 minutes

The task-based learning segment lasts longer than 20 minutes

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)? - Passing: The instructor compares and contrasts the planned strategies with the strategies listed

during class.


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§ What misconceptions or gaps in prior knowledge did you observe with your participants? How did this compare to your prediction? - Passing: The instructor describes at least three participant misconceptions/missing knowledge and

compares this to the 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? - Passing: The instructor describes the sorting/sequencing of strategies and how these were

referenced later in the day to enhance the content knowledge of the participants.