1. Promoting Student Learning and Productive Persistence in Accelerated Mathematics Courses: High Impact Practices in the Carnegie Pathways Instructional System Rachel Beattie, Carnegie Foundation Ann Edwards, Carnegie Foundation Michelle Brock, American River College CADE 2015 June 26, 2015 Costa Mesa, CA

2. Today’s Session  Overview – The Carnegie Pathways Instructional System – The Learning Opportunities – Productive Persistence  Statway Teaching – Statway 2.1.1 – Discussion  Quantway Teaching – Quantway 2.3 – Discussion  Q&A 2

3. 3 Statway Quantway 1 Quantway 2 or College Level QR Course Elem AlgInt Alg College Math Credit College Math Credit Semester 1 Semester 2 Semester 3 College Math Credit College Math Credit College Math Credit College Math Credit A New Way: Coherent, Intensive, Accelerated Learning Bridge to STEM

4. Increase the percentage of Developmental Math students achieving college math credit within one year of continuous enrollment Quality System of Instruction Support Faculty Development Effective Pathway through College Level Math Focus on Productive Persistence

5. 5 Statway/Qua ntway Curricula Pathways Pedagogy Learning Opportunities Productive Struggle Explicit Connections Deliberate Practice Language & Literacy Supports Productive Persistence Research-based collaborative and student-centered pedagogical practices that support deep and long lasting understanding Ambitious learning goals and curricular materials designed around authentic and relevant problem situations Pathways Instructional System

6. 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

7. 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

8. 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.

9. Thinking Hard

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

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

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

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

14. Creating Learning Opportunities: Easier Said than Done! Teacher Actions Learning Opportunities Flexible Expertise Instructional Practices/Routines - Collaborative Learning - Problem Cycle Routine

15. Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion (whole class) Designed to support productive struggle Collaborative learning is critical component Makes student thinking/reasoning visible Builds key mathematical ideas from student thinking Leaves students with key takeaways from problem

16. Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion (whole class) Problem Launch: The purpose of the launch is to prepare students for productive struggle -- to create a shared understanding of the problem to be worked on, make clear why solving it is important, and stimulate a variety of ways to think about the problem.

17. Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion (whole class) Working the Problem: The purpose of the working phase is to engage students in productive struggle with the problem and the concepts and to study students’ ways of thinking to prepare for the discussion. The purpose of this phase is NOT to ensure that all students get the correct answers.

18. Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion (whole class) Discussing the Problem: The purpose of discussing the problem is to make public students’ ways of thinking (correct and incorrect), encourage students to learn new ways of thinking by understanding each other, and connect their thinking to the key concept(s).

19. Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion (whole class) Conclusion: The purpose of the conclusion is to concisely highlight the key concepts drawn from students’ thinking, express the concepts with appropriate notation and representations, and explicitly connect the lesson concept(s) with the course organizing concepts.

20. 20 Statway/Qua ntway Curricula Pathways Pedagogy Learning Opportunities Productive Struggle Explicit Connections Deliberate Practice Language & Literacy Supports Productive Persistence Pathways Instructional System

21. A student, upon completing a diagnostic assessment in a developmental math course: 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.”

22. Promising Ideas Exist  In Research and Psychology – Brief and inexpensive interventions with large and enduring effects from K-12 and 4-year settings.  In the Field – Effective faculty interventions exist but are not widely tested and shared. 22

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24. 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. 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 Primary Driver (Drivers of the solution)

25. 25 Do These Drivers Matter for College Students?  Based on survey with developmental math students.  Categorized students as “at risk” or not in terms of the four drivers during week 1

26. Can we change students’ beliefs and attitudes in three weeks?

27. “Being a 'math person' or not is something about you that you really can't change. Some people are good at math and other people aren't." Survey data from Carnegie Foundation Statway, N ~ 1,100

28. 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. 28 Mindsets About Ability Students believe they are capable of learning.

29. 29 Students believe they are capable of learning.

30. 30 Students believe they are capable of learning. “Most people don’t know that when they practice and learn new things, parts of their brain change and get larger, a lot like the muscles do. This is true even for adults. So it’s not true that some people are stuck being “not smart” or “not math people.” You can improve your abilities a lot, as long as you practice and use good strategies.”

31. Course Dropout in Dev Math Students Who Withdrew N = 288, Z = 2.87, p =.004 51% decrease ~40 minutes $0 In collaboration with: Greg Walton, Dave Paunesku, Carol Dweck, Carissa Romero, Roberta Carew, & www.perts.netwww.perts.net Students believe they are capable of learning.

32. 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. 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. Primary Driver (Drivers of the solution) Aim: Students continue to put forth effort during challenges and when they do so they use effective strategies. Productive Persistence

33. 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 (Goffman, 1963; Cohen & Steele, Steele, 1997; Steele, Spencer, & Aronson, 2002)  This uncertainty makes the meaning of negative social events more ambiguous (Crocker et al, 1991; Cohen, Steele, & Ross, 1999) – After each negative event, they have to ask: “Do I belong here or don’t I?” 33 Students feel socially tied to peers, faculty, and the course. Students feel socially tied to peers, faculty, and the course.

34. Interviews with Students Examples of Student Quotes:  “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?” “ I felt that if I stopped coming no one would even notice.” Students feel socially tied to peers, faculty, and the course. Students feel socially tied to peers, faculty, and the course.

35. “How often, if ever, do you wonder: ‘Maybe I don't belong here?’”

36. Trust  Trust is a “cognitive leap” (Bryk et al., 2002; Cohen et al., 1999; Gambetta, 1988) – An assumption that another party’s intentions are good – An expectation that one will be dealt with fairly  Trust frames the meaning of ambiguous interpersonal treatment (Asch, 1957) Students feel socially tied to peers, faculty, and the course. Students feel socially tied to peers, faculty, and the course.

37. Student Group Noticing Routine

39. Productive Persistence Survey Data 39

40. Pathways Instruction in Practice Statway 2.1.1 Quantway 2.3

41. Let’s get ready to collaborate! Instructions: 1.Form groups of 4 - preferably with people you do not know. 2.Create a team name. 3.When you are in your group, introduce yourselves and then work together to find three non-obvious things that you have in common. 4.Then, each group member needs to share one unique fact about themselves.

42. The Statway Cohort Contract By signing below, I agree to fulfill the following requirements for participation in Statway course, and acknowledge that I understand the requirements for continued enrollment. Specifically: ●I commit to successfully completing Statway course with the members of my cohort. ●I commit to helping all of my cohort members understand statistics and complete Statway course. ●I will come to class everyday prepared to participate in all classroom activities. ●I will contribute to creating a productive classroom atmosphere that supports everyone learning. ●I will keep an open mind and a positive attitude, and will be willing to try out new learning strategies and study skills. Printed Name:______________________Signature:_________________________Date:________ Printed Name:______________________Witness: __________________________Date: _______

43. NBA's New Ball Gets Bounced by Commissioner By Ivan Carter Washington Post Staff Writer Tuesday, December 12, 2006 43 The NBA has decided to go back to a traditional leather basketball, the league announced yesterday, ending an experiment with a new synthetic ball this season that has been roundly criticized by players. The old ball, which was used for 35 seasons, will return Jan. 1. "Our players' response to this particular composite ball has been overwhelmingly negative and we are acting accordingly," NBA Commissioner David Stern said in a statement. The league sent a memo to its teams yesterday, telling them that the change would be made for the remainder of the 2006-07 season. Both balls are manufactured by Spalding but the new one is made of microfiber composite materials. It was supposed to provide a superior grip and allow for better ball handling, but players wasted no time complaining about it when training camps opened in early October. Washington Wizards guard Gilbert Arenas said the new basketball gets slippery when it comes into contact with even small amounts of sweat. Teammate Antawn Jamison said he had trouble palming the new ball while driving to the basket. Miami Heat center Shaquille O'Neal said it "feels like one of those cheap balls that you buy at the toy store." Some players, including league MVP Steve Nash, recently began complaining that the new ball was producing small cuts on their hands. The players' union filed an unfair labor practice charge with the National Labor Relations Board on Dec. 1 because it was upset that the league switched to the new ball without consulting players. It was one of two complaints the union filed with the labor board that day; the other involved a new league rule cracking down on players' complaints to referees during games.

44. Quantway 2.3: Measuring Change In your small groups, work together on problems 1 - 3. Consider: What do you want your students to struggle productively with in these problems? What do you think your students might struggle unproductively with?

45. Quantway 2.3: Measuring Change In your small groups, read Problem Situations #2 and #3 (but don’t do the problems) Consider: How do these problems help students understand absolute and relative change? How do they support students to extend and practice what they’re learning?

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47. www.carnegiefoundation.org pathways@carnegiefoundation.org

48. Traditional Sequence Statway Statway: Time to Complete a College Level Math Course 1 Year 2 Years Triple the success rate in half the time. 6% 51% 15%

49. Statway colleges have maintained success rate during period of expansion * *Estimate – 11% success after one year, predicted 15% at two years

50. College Math Success by Race/Gender 2013-2014 50 Number of Students FemaleMale HispanicBlackWhiteMultiOtherUnknownHispanicBlackWhiteMultiOtherUnknown Non-SW858804109238922415449548175522417279 Statway203178241975224122111166414422