1. Carnegie’s Pathways: Facilitating Active Learning with Games and Choir Ann Edwards, Carnegie Foundation Wioleta Jaworska, Borough of Manhattan Community College AMATYC 2014 Nashville, TN

2. Today’s Session What is Quantway? What mathematics we want students to learn What kinds of experiences they need to learn these things How to create these experiences in the classroom Promoting students’ productive persistence Demonstration of innovative teaching strategies in Quantway classroom

3. Today’s Session What is Quantway? What mathematics we want students to learn What kinds of experiences they need to learn these things How to create these experiences in the classroom Promoting students’ productive persistence Demonstration of innovative teaching strategies in Quantway classroom

4. Today’s Session What is Quantway? What mathematics we want students to learn What kinds of experiences they need to learn these things How to create these experiences in the classroom Promoting students’ productive persistence Demonstration of innovative teaching strategies in Quantway classroom

5. Today’s Session What is Quantway? What mathematics we want students to learn What kinds of experiences they need to learn these things How to create these experiences in the classroom Promoting students’ productive persistence Demonstration of innovative teaching strategies in Quantway classroom

6. What is Quantway? Quantitative reasoning-based developmental math course First term of two-term pathway leading to college level mathematics credit

7. Quantway Instructional System Mathematical learning goals that are powerful and relevant Research-based pedagogy supporting Learning Opportunities – Productive Struggle – Deliberate Practice – Explicit Connections Supports for non-cognitive factors – Productive Persistence – Mindset – Social Belonging – Value and relevance of mathematics – Study skills 7 Quantway at BMCC

8. What Do We Want Our Students to Learn? Flexible vs. routine expertise (Hatano & Inagaki) What is flexible expertise? – Procedural fluency – Conceptual understanding – Disposition to think/make sense of mathematics – Ability to nimbly bring knowledge to bear across a wide array of new situations

9. Research Indicates Three Critical Learning Opportunities To achieve flexible expertise, students need recurring and sustained opportunities for: Productive struggle – with important mathematics Explicit connections – between concepts, procedures, problems, situations Deliberate practice – increasing variation and complexity over time

10. Productive Struggle (Hiebert & Grouws, 2007) We use the word struggle to mean that students expend effort to make sense of mathematics, to figure something out that is not immediately apparent. We do not use struggle to mean needless frustration or extreme levels of challenge created by nonsensical or overly difficult problems. We do not mean the feelings of despair that some students can experience when little of the material makes sense. The struggle we have in mind comes from solving problems that are within reach and grappling with key mathematical ideas that are comprehendible but not yet well formed.

11. Confucius I never enlighten anyone who has not been driven to distraction by trying to understand a difficulty or who has not got into a frenzy trying to put his ideas into words. When I have pointed out one corner of a square to anyone and he does not come back with the other three, I will not point it out to him a second time ( 不愤 不启, 不悱不发. 举一隅不以三隅反, 则不复也.) (Lau, 7:8)

12. QW Lesson 2.3 (draft) Consider problems 1-3: – What might your students do with these problems? – What would they productively struggle with? – What might they unproductively struggle with? – What might you do to help them to struggle productively? 12

13. Thinking Hard

14. The Power of Connections Few ConnectionsMany Connections A E D F G H B C A E D F G H B C

15. Example: Struggle to Make Connections ⅓ ¼ ⅓ ½ What fraction of the rectangle is shaded brown? (a) (b) SOURCE: Deborah Ball (2013)

16. Deliberate Practice Different from repetitive practice Constantly increasing variation, complexity, challenge With feedback Staving off premature automaticity

17. Learning Opportunities Step-By- Step Procedures Well- Formed Lecture Discovery Learning ✪ Explicit Connections Productive Struggle − + − +− +

18. ✪ Learning Opportunities Step-By- Step Procedures Well- Formed Lecture Discovery Learning ✪ Explicit Connections Productive Struggle − + − +− + ✪ ✪ ✪ ✪ Deliberate Practice Maintaining struggle and connections through time

19. Creating Learning Opportunities: Easier Said than Done! Teacher Actions Learning Opportunities Flexible Expertise

20. Implications for Instruction Teaching moves – Clarify/refine understanding learning goals – Study student thinking to find gaps in understanding – Vary the task or problem: what variations will fine tune challenge and connections? – Ask questions: what questions will force students to engage in the hard work of connecting a problem/situation to important concepts? – Provide explanations: what can I say to help students understand connections? Teaching is planned but improvised experience!

21. Productive Persistence 21 I am embarrassed by how stupid I am and suddenly feeling very discouraged … I can't even tell which fraction is bigger than another, or where they should fall on the number line. I feel like crying. I’m embarrassed to be at community college because high school teachers said I would end up at community college because I’m lazy I don’t have any friends here. In between classes, I sit in my car and see everyone talking to others and I wonder: how did everyone else make friends?

22. 22 Productive Persistence Tenacity + Good Strategies

23. Students have skills, habits and know- how to succeed in college setting. Students have skills, habits and know- how to succeed in college setting. Students believe they are capable of learning math. Students believe the course has value. Students believe the course has value. Students feel socially tied to peers, faculty, and the course. Students feel socially tied to peers, faculty, and the course. Faculty and college support students’ skills and mindsets. Aim: Students continue to put forth effort during challenges and when they do so they use effective strategies. Productive Persistence

24. Fixed mindset (intelligence is fixed)  “If I have to try hard, I’m clearly not smart.”  No point in trying if one is not a “natural”  If “dumb,” have to rely on “luck” Growth mindset (intelligence is malleable)  “Trying harder makes you smarter.”  Obstacles can be overcome through effort, help from others, and use of improved strategy  Note: It’s NOT just about effort. Also strategy and help. 24 Mindsets About Ability Students believe they are capable of learning math.

25. Belonging Uncertainty (Walton & Cohen, 2007) People may commonly question their belonging in new social and academic settings – Especially when they are targeted by stigma and negative stereotypes This uncertainty makes the meaning of negative social events more ambiguous – After each negative event, they have to ask: “Do I belong here or don’t I?” 25 Students feel socially tied to peers, faculty, and the course. Students feel socially tied to peers, faculty, and the course.

26. Research on Relevance Coursework isn’t objectively relevant Strategies that enlist students in generating reasons why something is relevant to them, personally, can be highly effective at: – Promoting short-term interest – Promoting deeper learning and commitment 26 Students believe the course has value.

27. Skills, Habits, and Know-How Many students often study long hours, but continue to fail because they are using ineffective strategies Shallow learning strategies, like highlighting or rereading, should not be the only strategies used by students Deeper learning strategies that involve metacognition lead to longer retention of information 27 Skills, Habits, and Know-How to Succeed

28. Learning Our Way Into Innovations Supporting Productive Persistence Targeted Psychological Interventions Will they work for community college students, and if so, how? Targeted Psychological Interventions Will they work for community college students, and if so, how? Expert Practitioner Knowledge How can we build an evidence base for effective instructional practices? Expert Practitioner Knowledge How can we build an evidence base for effective instructional practices? Learning from Network Data How do we improve outcomes related to difficult drivers we know are important? Learning from Network Data How do we improve outcomes related to difficult drivers we know are important?

29. The Ecology of Teaching: Leveraging the Community Teacher: Knowledge, Skill, Judgment Learning Goals Assessments Tasks/Approa ches Productive Persistence Interventions Questions Represent- ations

30. Mathematics -- Music to My Ears: Choir Repetition and Non- Competitive Game Methods Wioleta Jaworska Borough of Manhattan Community College

31. Goals and Benefits Goals of Choir-Repetition and Non-Competitive Games – Limit non-cognitive obstacles to active and sustained learning – Enhance collaborative learning and productive struggle, explicit connections and deliberate practice. – Ensure equity of access to quality learning opportunities and support consistent engagement Choir-repetition method developed from music school experience in voice harmony and music memorization – Rote Learning – Questioning Focus on critical thinking (open-ended questions) Focus on norms of collaborative learning (more closed questions) (Hess Cognitive Rigor Matrix: www.nciea.org)

32. Outcomes Reduce anxiety about eloquence and academic sophistication Increase self-efficacy Develop growth mindset and belief in course value Reduce math anxiety Develop skills, habits, and know-how to succeed in college Develop effective math learning strategies Improve students’ engagement in the cooperative learning and critical thinking Improve teachers’ understanding of students thinking and opportunities to promote effectively support student learning

33. And the mathematical music begins… Work in your table groups (“group cluster”) on problems 1 and 2 on the handout. – Think like your students! – Time how long it takes for each of the problems. Wait for further instructions…

34. Choir Repetition Questions Lower level questions How many times faster was your “group-cluster’ on the second question in comparison to the first one? Not faster 2 times faster Many times faster Specific times faster (calculated) Are the dimensional analysis rules on fractions very different from all rules on fractions you learnt so far? Higher level questions How did you have to think differently in these two questions? Why is this important? If you answered yes, different in what way? If you answered no, what is the umbrella concept you learned?

35. Choir Repetition Method: Discussion What questions do you have? What benefits and challenges do you see with the method? 35

36. Non-competitive (team) Games Promote student engagement and collaborative learning Provide public and safe environment for showing mathematical thinking All groups get credit for participating but “extra points” are given for presentation and correctness. 36

37. Let’s try a game! Take 2 mins to read problem 3 on the handout. As a team, write a solution on the paper provided. Show all work and justify your answers. Be prepared to share your work publicly with the class. 37

38. Non-competitive Games: Discussion What questions do you have? What benefits and challenges do you see with the method? 38

39. edwards@carnegiefoundation.org pathways@carnegiefoundation.org wjaworska@bmcc.cuny.edu