responding to mathematical thinking: descriptive feedback that is precise and personalized connie...
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Responding to Mathematical Thinking: Descriptive Feedback that is Precise and Personalized Connie Quadrini, YCDSBconnie.firstname.lastname@example.org
AcknowledgementThis is to acknowledge that todays 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 2012A Focus on Assessment for Learning: Developing Feedback that is Precise and PersonalizedConnie Quadrini, YCDSB
YCDSB Grades 4-9 Family of Schools, 2011-13
Trapezoid TablesApples & EvergreensChoose a problem. Grade 8 Grade 11
Solve the problem in 2 different ways.
Be prepared to share your solutions with your group.
Session GoalsIdentify important characteristics of descriptive feedback in mathematics
Develop descriptive that is precise and personalized based on an intended learning goal.
Concept AttainmentWork in groups of 4.
The handout provided contains 3 sets of feedback samples.
Identify common characteristics within each set.
Whole Group ShareCharacteristics that describe set #1:Characteristics that describe set #2:Characteristics that describe set #3:
Descriptive FeedbackAccording 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
Mathematics Teacher NoticingResearch on expertise in classroom viewing shows the importance of skilled viewing
(Kevin Miller, 2011; Endsley, 1995)
Learning Goal: Grade 8Patterning & AlgebraOverall Expectation: represent linear growing patterns (where the terms are whole numbers) using graphs, algebraic expressions, and equationsSpecific Expectations: determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equationLearning Goal: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 3UCharacteristics of FunctionsOverall 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.
A Look at the MathIn 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.
Matching ActivityReview 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.
Matching ActivityWhole 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?
Mathematics Teacher NoticingWe conceptualize this expertise (ie. professional noticing of [students] mathematical thinking) as a set of three interrelated skills:
(a) attending to [students] strategies(b) interpreting [students] understandings(c) deciding how to respond on the basis of [students] understandings.
(Jacob, Lamb, & Philipp, 2010)
Descriptive FeedbackChoose 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.
Some Final ThoughtsInterconnectionsLearning goalTaskSuccess criteriaPracticeProfessional learning settingLive classroomJourneyProfessional learning over time
ReferencesDescriptive FeedbackMoving 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)
All materials from todays session including artefacts will be posted on the OAME 2011-12 Leadership Conference Wiki (Open Space Technology OST Descriptive Feedback)
Thank You and Enjoy OAME 2013!
Set #1: evaluative or motivationalSet #2: deficit model: descriptive; tell approachSet #3: asset mode; descriptive; questioning to evoke and expose thinking / reasoning; requires active thinking / reflecting
As part of assessment for learning, teachers provide students with descriptive feedback and coaching for improvement. (Growing Success, p. 28)Providing descriptive feedback that moves learners forward (i.e., outlining what was done well, what needs improvement, and how to improve) (Growing Success, p. 32)Descriptive feedback helps students learn by providing them with precise information about what they are doing well, what needs improvement, and what specific steps they can take to improve. The focus of the feedback is to encourage students to produce their best work by improving upon their previous work... Ongoing descriptive feedback linked specifically to the learning goals and success criteria is a powerful tool for improving student learning and is fundamental to building a culture of learning within the classroom. (p. 34)
Descriptive feedback sample #1 page 14 (S), Descriptive feedback sample #2 page 12 (S), Descriptive feedback sample #3 page 5 (S),
Precise and personalized feedback, matched to the mathematical thinking demonstrated in the student work sampleMoves student towards the learning goal, in a scaffolded wayRequires teacher to unpack students mathematical thinking; students need to respond to descriptive feedback; may require 1+ additional rounds of descriptive feedback; prior to evaluationExamining Mathematical Knowledge for Teaching in Secondary and Post-Secondary Contexts, Natasha Speer, University of Maine & Karen King, New York UniversityCommon Content Knowledge:mathematical knowledge of a kind used in a wide variety of settings [e.g. every day life] in other words not unique to teaching; these are not specialized understandings but are questions that typically would be answerable by others who know mathematics (Ball, Hoover Thames, & Phelps, p. 399)Specialized Content Knowledge:the mathematical knowledge entailed by teaching in other words, mathematical knowledge needed to perform the recurrent tasks of teaching mathematics [e.g. how mathematical ideas are related, being able to unpack a student solution] to students (Ball, Hoover Thames, & Phelps, p. 399)Horizontal (Horizon) Content Knowledge:an awareness of how mathematical topics are related over the span of mathematics [e.g. continuum of learning] included in the curriculum (Ball, Hoover Thames, & Phelps, p. 403).
New samplesHave participants tape to chart paper and annotate like previous activity