Responding to Mathematical Thinking: Descriptive Feedback that is Precise and Personalized

1. Responding to Mathematical Thinking: Descriptive Feedback that is Precise and Personalized Connie Quadrini, YCDSB connie.quadrini@ycdsb.ca OAME 2013

2. Acknowledgement This is to acknowledge that today’s presentation builds on: OAME Annual Conference, May 2012 OAME 2012 Leadership Conference Continued… Developing Descriptive Feedback that is Precise and Personalized Connie Quadrini, YCDSB and Shelley Yearley, TLDSB YCDSB Mathematics PA Day, November 2012 A Focus on Assessment for Learning: Developing Feedback that is Precise and Personalized Connie Quadrini, YCDSB YCDSB Grades 4-9 Family of Schools, 2011-13

3. Trapezoid TablesApples & Evergreens Choose a problem. • Grade 8 • Grade 11 Solve the problem in 2 different ways. Be prepared to share your solutions with your group.

4. Session Goals • Identify important characteristics of descriptive feedback in mathematics • Develop descriptive that is precise and personalized based on an intended learning goal.

5. Concept Attainment • Work in groups of 4. • The handout provided contains 3 sets of ‘feedback’ samples. • Identify common characteristics within each set. • Whole Group Share Characteristics that describe set #2: Characteristics that describe set #3: Characteristics that describe set #1:

6. Descriptive Feedback According to Davies (2007), descriptive feedback “enables the learner to adjust what he or she is doing in order to improve.” As the teacher provides feedback, and as the student responds to it, the assessment information gathered is used to improve learning and instruction.(Growing Success, p. 34) …prior to ‘evaluation’

7. Mathematics Teacher Noticing ‘Research on expertise in classroom viewing …shows the importance of skilled viewing…’ (Kevin Miller, 2011; Endsley, 1995)

8. Learning Goal: Grade 8 Patterning & Algebra • Overall Expectation: represent linear growing patterns (where the terms are whole numbers) using graphs, algebraic expressions, and equations • Specific Expectations: • determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation Learning Goal: • Make far predictions for a linear growing pattern by generalizing the relationship between the term number and term value using an equation.

9. Learning Goal: MCR 3U Characteristics of Functions • Overall Expectation: determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications. • Specific Expectation: 2.5 solve problems involving the intersection of a linear function and a quadratic function graphically and algebraically Learning Goal: • Different representations can be used to determine the point of intersection (POI) of two functions. Each representation provides insights into the behaviour of the functions before and after the POI.

10. A Look at the Math • In pairs, examine one of the three student work samples for the problem you selected. • What does the student know / understand? • What does partial understanding / misunderstandings does the student have? • Annotate your observations around the student sample on the chart paper provided. • Rotate the charts for other pairs at your table to review and further annotate.

11. Matching Activity • Review the 3 pieces of descriptive feedback. • Work as a team (3 sets of pairs) to match each piece of descriptive feedback to the student sample that best suits it.

12. Matching Activity • Whole Group Share • What did you notice about the descriptive feedback? • How does this feedback support students in moving their mathematical thinking forward? • What are some implications for providing this type of descriptive feedback to students?

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14. Mathematics Teacher Noticing ‘We conceptualize this expertise (ie. professional noticing of [students’] mathematical thinking) as a set of three interrelated skills: (a) attending to [student’s] strategies (b) interpreting [student’s] understandings (c) deciding how to respond on the basis of [student’s] understandings.’ (Jacob, Lamb, & Philipp, 2010)

15. Descriptive Feedback Choose a new student work sample. • What does the student know / understand? • What partial / misunderstandings does the student have? • What descriptive feedback would you provide this student to move his/her mathematical thinking forward? Learning Goal (Grade 8): • Make far predictions for a linear growing pattern by generalizing the relationship between the term number and term value using an equation. Learning Goal (MCR 3U): • Different representations can be used to determine the point of intersection (POI) of two functions. Each representation provides insights into the behaviour of the functions before and after the POI.

16. Some Final Thoughts • Interconnections • Learning goal • Task • Success criteria • Practice • Professional learning setting • Live classroom • Journey • Professional learning over time

17. References • Descriptive Feedback…Moving to the Next Level PPT. (The Milwaukee Mathematics Partnership, 2008) • Math Expressions: Promoting Problem Solving and Mathematical Thinking through Communication. (Cathy Marks Krpan, 2012) • Learning to Do Mathematics as a Teacher PPT (Deborah Ball, Mathematics Teaching and Learning to Teach (MTLT) Project: NCTM Research Presentation, 2010)

18. All materials from today’s session including artefacts will be posted on the OAME 2011-12 Leadership Conference Wiki (Open Space Technology  OST Descriptive Feedback) Visit http://oame-leadership-conference-2011.wikispaces.com/OST+Descriptive+Feedback Thank You and Enjoy OAME 2013! connie.quadrini@ycdsb.ca