1. Project Pathways Marilyn P. Carlson Michael Oehrtman Dawn Teuscher Arizona State University

2. Goals of Project Pathways Realize substantive shifts in the quality of secondary mathematics and science instruction towards more conceptually oriented and inquiry based teaching Establish and sustain highly effective professional learning communities Improve learning and performance of secondary mathematics and science students Create new knowledge of the processes and tools needed to support teachers in providing quality math and science instruction. 8/24/2015 Project Pathways

3. Research and development cycles generated Refined 4-course sequence (Carlson & Oehrtman, in press) Refined content-based professional learning community model – Our research revealed central attributes of a highly effect PLC facilitator (Carlson, Moore, Bowling, Ortiz, 2007) – developed PLC facilitator training model Identified 4 key practices (RULES of ENGAGEMENT) that were needed for quality discourse in Pathways courses and PLCs – Speak with meaning – Engage in sense making; make sense of content and other’s thinking – Respect the learning process of colleagues – Exhibit intellectual integrity—don’t pretend to know when you don’t, offer up conjectures that are logical to you. (Clark, Carlson, Moore, 2007) 8/24/2015Project Pathways

4. Pathways Impact Realized significant gains in content knowledge of over 300 mathematics and science teachers (PCA, FCI) Established professional learning communities (PLCs) in over 40 schools Realized significant gains in some teachers’ classroom practices as measured by the Reform Teaching Observation Protocol (RTOP) 8/24/2015Project Pathways

5. P HOTO E NLARGEMENT T ASK 1.A photographer has an original photo that is 6 inches high and 10 inches wide and wishes to make several copies differing in size. When told the desired width in inches of any copy, the photographer wants to know how to determine the height, also in inches, so that the new photo is not distorted. a.How might students approach this problem? b. What does it mean for two quantities, (in this case height and width) to be proportional? a.How might a teacher relate proportionality to linearity so that the ideas are meaningful to students? 10″ 6″ ? 25″ 5Copyright ©2010 Carlson and Oehrtman W#3

6. C ONSTANT M ULTIPLE & S CALING h is related to w by a constant multiple. h = (c) (w) ″ 6 If we scale w by some factor, we should also scale h by the same factor. The quantities h and w always remain in a constant ratio. Why? Copyright ©2010 Carlson and Oehrtman W#3

7. width height w2w2 w1w1 h1h1 h2h2 h1h1 h2h2 w2w2 w1w1 If we scale the image to a larger size, how are the new measurements represented? How will measurements of small photographs be represented? Why? What about larger images? How do we represent the measurements of all possible scaled images? 7Copyright ©2010 Carlson and Oehrtman W#3

8. Obstacles to Widespread and Lasting Shifts in Many Schools The principal and/or the department chairs did not support Pathways philosophies School curriculum did not support conceptually focused, inquiry based instruction State and local tests had a strong procedural orientation, with teacher pay being tied to students’ performance on district exams Many teachers had low expectations for students 8/24/2015Project Pathways

9. Began a New Cohort of Teachers Principal and department chairs supported Pathways philosophies School based and content focused PLCs required by all math and science teachers within a school (principal mandated) Summer workshops 2 course sequence for mathematics and science teachers (23 of 39 teachers) Monthly 4-hour workshops for other teachers 8/24/2015Project Pathways

10. Year One Shifts Significant shifts in teachers’ content knowledge (PCA) Modest shifts in teachers’ beliefs about the methods of mathematics Modest (but significant) shifts in some aspects of teachers’ classroom practices; integration of STEM content, questioning Teacher interviews revealed that: – The majority of teachers believed their curriculum and instruction needed improvement, but they: felt ill-equipped to make changes Expressed concern about district exams – Most teachers valued the PLCs and expressed a strong desire to continue them – The principal’s and department chairs’ enthusiasm for Pathways interventions escalated 8/24/2015Project Pathways

11. Year 2 Summer 2009: Pathways faculty led a one week workshop focused on issues of understanding and learning key ideas of algebra I through precalculus (rate of change, exponential growth, trig functions). Teachers spent 4 weeks with Pathways staff revising their curriculum in one course Fall 2009: Teachers implemented newly developed curriculum into their classrooms (alg II, trig, geometry, biology, physics, chemistry). School based PLCs continued; School leaders and Pathways staff continued to meet weekly for 3 hours to reflect on classroom practices and adapt or create new curriculum One teacher (Colleen) piloted research based precalculus curriculum 8/24/2015Project Pathways

12. Results Semester one (Fall, 2009): -Significant shift in RTOP scores -Level of enthusiasm for continued work to improve curriculum is high, although the time commitment for PLC facilitators has been extensive -Newly developed worksheets were well received by most teachers—teachers report that the tasks and scaffolding (in the worksheets) supported them in raising the content expectations, level of student engagement and conceptual orientation of classroom discussions. -Colleen experienced dramatics shifts in one semester 8/24/2015Project Pathways

13. Quote from Principal of Transforming School A “I’ve been trying to improve mathematics and science instruction in schools for over 30 years—I visit 2 classes per day and have witnessed stand and deliver instruction year after year in most math and science classrooms—I was bored to tears, so I’m sure the students were too. Project Pathways has changed our school’s approach to teaching mathematics and science—when I visit classrooms now, kids are engaged and are being challenged to think—they appear to be enjoying it. This is the first project in my 30 years of being a principal that has made a difference in what happens in classrooms. What I didn’t understand before was that there are no quick fixes. Substantive improvement require high commitments and hard work.” 8/24/2015Project Pathways

14. Background on Colleen Precalculus mathematics teacher who has taught for 10+ years. Completed 2 mathematics courses that were focused on understanding central ideas algebra I through precalculus Currently is using a research-based mathematics curriculum designed to focus on students conceptual understanding of key ideas of precalculus from a quantities and co-variation perspective. 8/24/2015Project Pathways

15. Teacher shifts RTOP: Reformed Teacher Observation Protocol Five constructs with a total of 20 points total for each area: – Lesson Design – Propositional Knowledge – Procedural Knowledge – Classroom Climate – Student/Teacher Relationship First observation was completed in April 2008 and completed 4 more observations through September 2009. 8/24/2015Project Pathways

16. Teacher Data Gains made by Colleen from the first to the last observation. Lesson Design: Increased 5 points Propositional Knowledge: Increased 4 points Procedural Knowledge: Increased 3 points Classroom Climate: Increased 1 point Student/Teacher Relationship: Increased 1 point 8/24/2015Project Pathways

17. Anecdotal Evidence of Shifts 8/24/2015Project Pathways MKT/PCK attributes BeforeAfter Questioning Looking for the right answer Listening to students, trying to identify what they understand or do not understand. Curriculum Used the textbook as if it was the authority – no ownership for what she was teaching Used the textbook and tasks to generate discussion among students and herself in learning mathematics. Preparation Used the materials, as the map of how her class should go. Used the materials to help her learn mathematics and make connections among concepts. Content Knowledge Weak – relied heavily on the instructor notes and observers in her classroom for help. Stronger – has the confidence to design and implement a lesson for her students on the number e because they did not understand it the day before with the lesson in the curriculum.

18. Student Background 34 students in two precalculus courses – 15 students completed Trigonometry – 18 students completed Algebra 2 Honors – 1 student completed Algebra 2 (Used Holt and Larson & Stuart textbooks for prerequisite courses.) Typical course sequence at this school is: Algebra 2H, Precalculus, AP Calculus AB or Algebra 2, Trigonometry, Precalculus 8/24/2015Project Pathways

19. Student PCA Results NMean Std. Deviationtp Pre PCA3411.793.77 17.771*0.000 Post PCA3419.442.87 8/24/2015Project Pathways *Students’ Post PCA mean score were significantly higher than Pre PCA mean score. Precalculus Concept Assessment (PCA) is a 25 item assessment tool to gauge students understanding of functions. PCA is multiple choice with distracters that are common misconceptions that students have about functions.

20. An Example PCA Item A ball is thrown into a lake, creating a circular ripple that travels outward at a speed of 5 cm per second. Express the area, A, of the circle in terms of the time t (in seconds), that have passed since the ball hit the lake. a)A = 25 t b) A = r 2 c) A = 25 t 2 d) A = 5 t 2 e) None of the above 8/24/2015Project Pathways

21. A PCA Item The model that describes the number of bacteria in a culture after t days has just been updated from to. What implications can you draw from this information? a) The final number of bacteria is 3 times as much of the initial value instead of 2 times as much. b) The initial number of bacteria is 3 instead of 2. c) The number of bacteria triples every day instead of doubling every day. d) The growth rate of the bacteria in the culture is 30% per day instead of 20% per day. e) None of the above. 8/24/2015Project Pathways

22. Student PCA results 8/24/2015Project Pathways Function Concept # of PCA items Mean (S.D.) tp Pre PCAPost PCA Function Evaluation 7 3.766.62 10.943*0.000 (1.62)(0.60) Rates of Change 6 2.293.79 8.098*0.000 (1.31)(1.17) Function Composition 7 3.125.68 11.415*0.000 (1.37)(1.17) Function Inverse 7 2.184.76 9.56*0.000 (.38)(1.33) * Post PCA mean scores for each function concept were significantly higher than Pre PCA mean scores.

23. What Next? Lesson-study cycles being implemented this semester in each PLC Continued curricular refinements this summer (2010) Recruit more teachers to use research-based precalculus curriculum; study shifts in teachers’ classroom practices, track shifts in students’ problem solving behaviors and learning of key concepts Continue to investigate the role of school culture, curriculum, teacher beliefs and teacher knowledge in transforming teacher classroom practices. 8/24/2015Project Pathways