Promoting Student Learning and Productive Persistence in Accelerated

  • Slides: 50
Download presentation
Promoting Student Learning and Productive Persistence in Accelerated Mathematics Courses: High Impact Practices in

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

Today’s Session § Overview – The Carnegie Pathways Instructional System – The Learning Opportunities

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

A New Way: Coherent, Intensive, Accelerated Learning Quantway 1 Quantway 2 or College Level

A New Way: Coherent, Intensive, Accelerated Learning Quantway 1 Quantway 2 or College Level QR Course Statway Elem Alg Semester 1 Int Alg Semest er 2 College Math Credit Bridge to STEM College Math Credit College Math Semeste r 3 College Math Credit 3

Effective Pathway through College Level Math Increase the percentage of Developmental Math students achieving

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

Pathways Instructional System Learning Opportunities Productive Struggle Explicit Connections Deliberate Practice Ambitious learning goals

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

What Do We Want Our Students to Learn? § Flexible vs. routine expertise (Hatano

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

Research Indicates Three Critical Learning Opportunities To achieve flexible expertise, students need recurring and

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

Productive Struggle (Hiebert & Grouws, 2007) We use the word struggle to mean that

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.

Thinking Hard

Thinking Hard

The Power of Connections Few Connections B B C A H C A D

The Power of Connections Few Connections B B C A H C A D F G Many Connections D F E G H E

Deliberate Practice § Different from repetitive practice § Constantly increasing variation, complexity, challenge §

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

Learning Opportunities Explicit Connections − + − Step-By. Step Procedures Well. Formed Lecture +

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

Learning Opportunities Deliberate Practice ✪ ✪ ✪ Explicit Connections − + − Productive Struggle

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

Creating Learning Opportunities: Easier Said than Done! Teacher Actions Instructional Practices/Routines - Collaborative Learning

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

Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion

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

Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion

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.

Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion

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.

Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion

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).

Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (whole class) Conclusion:

Problem Cycle Launch (whole class) Working the Problem (group work) Discussion (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.

Pathways Instructional System Learning Opportunities Productive Struggle Explicit Connections Deliberate Practice Statway/Qua ntway Curricula

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

A student, upon completing a diagnostic assessment in a developmental math course: “I am

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

Promising Ideas Exist § In Research and Psychology – Brief and inexpensive interventions with

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

23

23

Productive Persistence Aim: Students continue to put forth effort during challenges and when they

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

Students? § Based on survey with developmental math students. § Categorized students as “at

Students? § Based on survey with developmental math students. § Categorized students as “at risk” or not in terms of the four drivers during week 1 Low risk (0 risk factors) High risk (4 risk factors) 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Moderate risk (2 risk factors) 78% 61% 45% 42% 21% Below-median Baseline Math Knowledge 63% 55% 37% 28% 13% Failed Mid-Course Failed End-of. Assessment Course Assessment 42% 21% Overall Course Success (B- or better and passed both exams) 25

Can we change students’ beliefs and attitudes in three weeks? 1 0. 8 Cohen’s

Can we change students’ beliefs and attitudes in three weeks? 1 0. 8 Cohen’s D 0. 6 0. 4 0. 2 0 -0. 2 -0. 4 -0. 6 Effect Size -0. 8 -1 Interest in Math 0. 34 Belief that math Relevance of Confidence Math Anxiety math in course intelligence is fixed 0. 21 0. 48 -0. 65 -0. 47 Stereotype Threat -0. 22

“Being a 'math person' or not is something about you that you really can't

“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. "

Students believe they are capable of learning. Mindsets About Ability Fixed mindset (intelligence is

Students believe they are capable of learning. Mindsets About Ability 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

Students believe they are capable of learning. 29

Students believe they are capable of learning. 29

Students believe they are capable of learning. “Most people don’t know that when they

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. ” 30

Course Dropout in Dev Math Students Who Withdrew 20% 9% 10% 0% Control (Brain

Course Dropout in Dev Math Students Who Withdrew 20% 9% 10% 0% Control (Brain Facts) Growth Mindset Students believe they are capable of learning. 51% decrease ~40 minutes $0 In collaboration with: Greg Walton, Dave Paunesku, Carol Dweck, Carissa Romero, Roberta Carew, & www. perts. net N = 288, Z = 2. 87, p =. 004

Productive Persistence Aim: Students continue to put forth effort during challenges and when they

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

Belonging Uncertainty Students feel socially tied to peers, faculty, and the course. (Walton &

Belonging Uncertainty Students feel socially tied to peers, faculty, and the course. (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, 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

Interviews with Students feel socially tied to peers, faculty, and the course. Examples of

Interviews with Students feel socially tied to peers, faculty, and the course. 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. ”

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

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

Trust Students feel socially tied to peers, faculty, and the course. § Trust is

Trust Students feel socially tied to peers, faculty, and the course. § 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)

Student Group Noticing Routine

Student Group Noticing Routine

Student Group Noticing Routine Attendance (By Day) 120% Percent of Student in Attendance 100%

Student Group Noticing Routine Attendance (By Day) 120% Percent of Student in Attendance 100% 80% 60% 40% 20% 0% 8/26/2013 9/2/2013 9/9/2013 9/16/2013 9/23/2013 9/30/2013 10/7/2013 10/14/2013 10/21/2013 10/28/2013 11/4/2013

Productive Persistence Survey Data 39

Productive Persistence Survey Data 39

Pathways Instruction in Practice • Statway 2. 1. 1 • Quantway 2. 3

Pathways Instruction in Practice • Statway 2. 1. 1 • Quantway 2. 3

Let’s get ready to collaborate! Instructions: 1. Form groups of 4 - preferably with

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.

The Statway Cohort Contract By signing below, I agree to fulfill the following requirements

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 a positive attitude, and will be willing to try out new learning strategies and study skills. Printed Name: ___________Signature: _____________Date: ____

NBA's New Ball Gets Bounced by Commissioner By Ivan Carter Washington Post Staff Writer

NBA's New Ball Gets Bounced by Commissioner By Ivan Carter Washington Post Staff Writer Tuesday, December 12, 2006 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. 43

Quantway 2. 3: Measuring Change In your small groups, work together on problems 1

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?

Quantway 2. 3: Measuring Change In your small groups, read Problem Situations #2 and

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?

Please Sign-In Enter into your browser: cfdn. at/NISOD 15 Thank you!

Please Sign-In Enter into your browser: cfdn. at/NISOD 15 Thank you!

www. carnegiefoundation. org pathways@carnegiefoundation. org

www. carnegiefoundation. org pathways@carnegiefoundation. org

Statway: Time to Complete a College Level Math Course 2 Years 1 Year 15%

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

Statway colleges have maintained success rate during period of expansion 50% 4500 52% 48%

Statway colleges have maintained success rate during period of expansion 50% 4500 52% 48% 4000 48% 3500 40% 3000 Enrollment Percent Correct (C or Better) 60% 2500 30% 2000 16% 15% * 14% 1000 10% 0% 1500 0 2011 -2012 Statway 2012 -2013 Comparison 2013 -2014 Enrollment *Estimate – 11% success after one year, predicted 15% at two years

College Math Success by Race/Gender 2013 -2014 Non-Statway 109200% 85800%80400% 49500% Female Hispanic Black

College Math Success by Race/Gender 2013 -2014 Non-Statway 109200% 85800%80400% 49500% Female Hispanic Black White Multi 858 804 1092 389 203 178 241 97 n ow nk n th er O ti ul 68% U Female Number of Students Non-SW Statway M hi te W k ac Bl c is p an i n 42% H U nk n ow th er O ti ul M W Bl ac k c an i 54% 48% 0%50% H is p 61% hi te 43% 36% 38900% 22400% 15400% 55% 50% 47% 44% Male Other Unknown Hispanic 224 154 495 52 24 122 Black 481 111 Male White Multi 755 224 166 41 Other Unknown 172 79 44 50 22