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Assessing Problem Based Learning


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Session 79 NCTM 2015 powerpoint for Secondary Mathematics Education

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Assessing Problem Based Learning

  1. 1. Assessing Problem Based Learning Relating Student Work to the Practice Standards Carmel Schettino, Ph.D Deerfield Academy NCTM 2015
  2. 2. Glacial Potholes of shelburne Falls
  3. 3. Overview • Discussion of PBL Classroom Practice – Definitions and Distinctions (PrBL vs. PBL) • Math Practice Standards and Assessment • My view of Assessments in PBL & how PBL fosters the MPS • Types of Assessments I do in my Classroom Practice
  4. 4. What is PBL? • An approach to curriculum and pedagogy where student learning and content material are co constructed by students and teachers through mostly contextually based problems in a discussion based classroom where student voice, experience, and prior knowledge are valued in a non hierarchical environment. Schettino, 2013
  5. 5. Learning Goals of PBL • Master mathematical content • Help students become better problem solvers WDYDWYDKWTD? • Become better mathematical communicators (oral, written, digital, different representations, etc.) • Improve perseverance, creativity, grit, risk-taking, innovation levels • Become better collaborators with their peers
  6. 6. PBL framework Cschettino 2013
  7. 7. PBL Classroom Attribute of PBL Classroom MP Standard Connected Curriculum Decompartmentalized problems, focus on the why Make sense of problems and persevere in solving them Scaffolded problems Reason abstractly Dissolve traditional hierarchy, Construct viable arguments discourse moves that improve equity, valuing risk taking, multiple perspectives Critique reasoning of others Mutliple perspectives Look for repeated reasoning Scaffolded problems Use appropriate tools Student presentation, use of prior knowledge Model with mathematics A circle with radius 5 has an arc from A(5,0) to B(3,4). Find the angular size of the minor Arc AB and then find the coordinates of another arc with the same size.
  8. 8. Key Questions • How do you keep assessment authentic and consistent with the values of the pedagogy? • How do you ensure that your assessment measures the learning goals?
  9. 9. How do the Tests Assess the Math Practices?
  10. 10. Oral Assessment Ongoing monitoring of Classroom Discourse Harkness Diagramming Student Self Assessment Class Contribution & Presentation Student- Authored Norms Teacher feedback Class Contribution Rubric Discussions
  11. 11. Set the tone with clear expectations
  12. 12. Include Student reflections
  13. 13. Written Assessment Formal Written Assessments Problems for Problem Solving Metacognitive Journaling Partner Problem Sets Quizzes for Skill Acquisition Take Home Parts of problem Sets Allow for Corrections? Hand-in Homework
  14. 14. Purpose of Homework? • Review material from past courses • Trigger prior knowledge for an upcoming problem • Inspire construction of new knowledge (give context or connect) • Introduce new technology use • Practice new skill • Challenge more able students • Introduce new terminology/vocabulary • See a familiar topic from a different perspective • Concretize an abstract concept • Have students summarize/generalize a new topic
  15. 15. Assessing Problem Solving
  16. 16. Think about main topic you want to assess Connect with other topic? What is your expectation of what they can do on their own? Put it in a different context
  17. 17. Homework Questions Find two points that are 5 units away from (0,0) on the line x=4.
  18. 18. Other perspectives
  19. 19. Change it up or ask students to • Find two points that are 13 units away from (1,3) on the line y=8.
  20. 20. Give it context
  21. 21. Then we assess...
  22. 22. What good are journals? • Communication form not usually practiced in math classroom, but still a standard (reflection and communication) • Some teachers give prompts – open ended or direct • Some teachers are very clear about the structure other leave it more open i.e “free writing” vs. discussing a problem vs. “the journalist’s questions” vs. “learning log” • Response to other students solutions • Present your initial error/view and reflect on that perspective – describe why it was wrong and correct it. Mid-continent Research for Education and Learning, 2009 ,
  23. 23. “I assumed I needed to do a straight line. I then saw ‘three units’, so I put a point on (5,1), and drew the line y=1. If (5,1) was 3 away, I thought, shouldn’t all the points on the line be 3 away?” “Only 1 point on each of the lines was actually 3. The rest of the points were actually all further than 3 units from the point.” “This, I thought, would cause all points on the line to be 3 units away from point (5,4). However, I was again wrong. The blue line on the diagram shows a point on one of my lines that was more than 3 units from (5,4). The red line shows a point on one of the lines that is less than three units from (5,4). The green lines are points that are 3 units away from point (5,4). I have effectively created a range of lengths from (5,4) opposed to what the question was asking for which was 3 units from (5,4). “It made perfect sense!…Any point from the centerpoint of a circle to any point on the circle was the same length (the radius). I immediately drew the connection. 3 was the radius and (5,4) was the center. the distance between the middle point and any point on the circle was 3!”
  24. 24. Tech & Inquiry Projects
  25. 25. Table of Assessments Type Rubri c? How Often? Type of Feedback Learning Goal Assessed Class Contribution Yes Ongoing Student self- assessment, teacher feedback, self-evaluation Communication, Persistence, perseverance Quiz No biweekly Numerical grade Content Mastery Individual Problem Set No 2-3 weeks Numerical grade, written feedback Content mastery, problem solving Partner problem Set No 1-2 a year Numerical grade, written feedback Communication, collaboration Journal entries Yes biweekly Extensive written feedback, letter grade Communication, problem solving Daily homework Yes Daily Oral Persistence, problem solving, content mastery Homework Hand-in Yes biweekly Written feedback Content mastery, communication
  26. 26. This Slideshow can be found at With all handouts
  27. 27. PD Opportunity • PBL Math teaching summit • July 16 thru 19 • Deerfield, ma • Discussion, sharing and learning all about pbl math • Pick up a flyer
  28. 28. Rate this presentation on the mobile conference app! All presentation surveys are available five minutes before the conclusion of each presentation! Download available presentation handouts from the Online Conference Planner! Join the conversation! Tweet us using the hashtag #NCTMBOSTON
  29. 29. Contact me • • @SchettinoPBL • (for this presentation)