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1 Moving Beyond Implementation: Challenges and Possibilities NCSM April 24 - 26, 2006 Edward A. Silver, Valerie Mills, Lawrence Clark, Geraldine Devine,

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Presentation on theme: "1 Moving Beyond Implementation: Challenges and Possibilities NCSM April 24 - 26, 2006 Edward A. Silver, Valerie Mills, Lawrence Clark, Geraldine Devine,"— Presentation transcript:

1 1 Moving Beyond Implementation: Challenges and Possibilities NCSM April , 2006 Edward A. Silver, Valerie Mills, Lawrence Clark, Geraldine Devine, Hala Ghousseini

2 2 Todays Session: An Overview The Implementation Plateau The BIFOCAL Project Background The Mathematics Task Framework & Levels of Cognitive Demand Design Principles and Structural Features Instructional Issues Addressed in BIFOCAL The Case of Giselle Questions and Discussion

3 3 A Common Dilemma School District USA, introduced a problem- based, reform-oriented mathematics instructional program in the middle grades (i.e., CMP) about four years ago. Student achievement increased steadily for three years, but appears to be leveling off. Why? What can be done to support teachers and sustain growth?

4 4

5 5 Comments on Video Clip Teachers discuss case in relation to their classroom experiences implementing a problem-based curricula Issues of curriculum materials are not the focus Issues of instructional refinement emerge How to manage multiple solutions How to reach all students in the classroom

6 6 Implementation Plateau Characterized by teachers who participated in curriculum centered professional development during the implementation of a standards-based mathematics program Teachers are familiar and confident using new program features such as: new lesson format designs, Student tasks that require eliciting and evaluating student s written mathematical explanations, and Investigations that utilize various grouping structures in the classroom Teachers are generally committed to their own use of the new materials

7 7 Implementation Plateau After the first year, student achievement on various standardized measures typically improves steadily for three to five years, then growth appears to level off. Teachers feel generally confident, but …not fully competent and unable to articulate the problem Vulnerable time for districts as concerns reemerge Districts resources no longer available

8 8 Implementation Plateau The curriculum implementation plateau is a stage when teaching and learning appear to bog down; there is a need to refine instructional practices established during implementation, to continue building local capacity, and to maintain growth in student performance through sustained, long-term teacher engagement and the provision of a space for guided reflection on the instructional issues they currently face.

9 9 Processes Associated With Implementation of Standards-based Mathematics Curricula Level I: Awareness Level II: Selection & Adoption Level IV: Refinement & Building Local Capacity Level III: Implementation (St. John, Heenan, Houghton, & Tambe, 2001) PLATEAU

10 10 The Role of the BIFOCAL Project Level I: Awareness Level II: Selection & Adoption Level IV: Refinement & Building Local Capacity Level III: Implementation (St. John, Heenan, Houghton, & Tambe, 2001) PLATEAU BIFOCAL

11 11 The Goals of the BIFOCAL Project Understand the implementation plateau Assist teachers and schools

12 12 The BIFOCAL Project Beyond Implementation: Focus on Challenge and Learning Project Team Edward Silver, Valerie Mills, Alison Castro, Charalambos Charalambous, Lawrence Clark, Gerri Devine, Hala Ghousseini, Melissa Gilbert, Dana Gosen, Jenny Sealy, Beatriz Font Strawhun, & Gabriel Stylianides

13 13 The BIFOCAL Project The following organizations provide funding for various aspects of BIFOCAL: The National Science Foundation (via CPTM) The University of Michigan The Mathematics Education Endowment Fund The Oakland Intermediate School District

14 14 BIFOCAL: Project History Year One 12 teacher leaders (experienced CMP users) 10 full-day sessions Year Two 12 teacher leaders and 48 teachers (Ele., MS, HS) 6 full-day sessions 6 school-based sessions lead by teacher leaders Year Three Similar design to Year Two Focus on assessment for learning

15 15 Teaching with Challenging Mathematics Tasks Teachers must decide what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask to challenge those with varied levels of expertise, and how to support students without taking over the process of thinking for them and thus eliminating the challenge. NCTM, 2000, p.19

16 16 BIFOCAL: Background in a Nutshell Supporting Frameworks/Perspectives : Practice-based approach (Ball, Smith) Mathematical Task Framework (QUASAR) Case Analysis & Discussion Lesson Study

17 17 BIFOCAL: Practice-Based Approach Professional development experiences situated in authentic teaching practice allow the everyday of teaching to become the object of on-going investigation and inquiry Build around professional learning tasks (Smith, 2000; Ball & Cohen, 1999)

18 18 The Mathematical Task Framework Tasks as set up by teachers Tasks as they appear in curricular materials Tasks as enacted by teacher and students Student learning Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000)

19 19 MTF - The Bottom Line Tasks are important, but teachers also matter! Teacher actions and reactions … influence the nature and extent of student engagement with challenging tasks, affect students opportunities to learn from and through task engagement.

20 20 Some MTF-Related Challenges Facing All Teachers of Mathematics Resisting the persistent urge to tell and to direct; allowing time for student thinking Knowing when/how to ask questions and to provide information to support rather than replace student thinking Helping students accept the challenge of solving worthwhile problems and sustaining their engagement at a high level

21 21 BIFOCAL: Background in a Nutshell Motivation: Implementation plateau phenomenon Supporting Frameworks/Perspectives : Practice-based approach (Ball, Smith) Mathematical Task Framework (QUASAR project) Case Analysis & Discussion Case Analysis & Discussion Lesson Study Lesson Study

22 22 A Typical Year One BIFOCAL Session Case Analysis and Discussion (CAD) Solve mathematical task Read, analyze/discuss teaching cases (text, video, student work samples) Modified Lesson Study (MLS) Discuss lesson enactment from previous session Select target lesson Use structured set of questions to guide collaborative planning

23 23 Feb 2004 Marie Hanson Case: The Candy Jar Task What mathematical goals might a teacher using this task have for students? What kinds of thinking/reasoning might we anticipate students using with this task? What student misconceptions or errors might we anticipate with this task?

24 24 Feb 2004 Marie Hanson Case What inferences might you draw about these students understanding or misunderstanding? (cite line numbers to support your conclusions) What did Marie do to assess student understanding or misunderstanding? (cite line numbers to support your conclusions) Identify Maries instructional decisions in this segment and: indicate how these moves either helped to maintain or undermine the demand of the tasks speculate on the rationale Marie may have used to inform her use of multiple student solution approaches and its relationship to the mathematical goal of the lesson

25 25 Feb 2004 Modified Lesson Study - Adapted TTLP Selecting and Setting up a Mathematical Task What are your math goals for the lesson? What are all the ways the task can be solved? How will you introduce students to the activity so as not to reduce the demands of the task? Supporting Students Exploration of the Task As students are working independently or in small groups Sharing and Discussion the Task Which solution paths do you want to have shared during the class discussion in order to accomplish the goals for the lesson? What will you see or hear that lets you know that students in the class understand the mathematical ideas or problem-solving strategies that are being shared?

26 26 A Mathematics Professional Development Synergy Modified Lesson Study Case-Based Professional Development Curriculum-Based Professional Development

27 27 Blending CAD and MLS as the Professional Development Evolves Modified Lesson Study (1) Case Analysis and Discussion(1) Case Analysis and Discussion (2) Modified Lesson Study (2) Case Analysis and Discussion (3) Modified Lesson Study (3) Instructional Issue X Instructional Issues XY Instructional Issues XYZ

28 28 Instructional Issues Available for Refinement at the Implementation Plateau Identifying mathematical goals, short-term and long -term Considering multiple solution strategies Scaffolding student thinking in ways that support the cognitive demands of the mathematics task Assessing student understanding of mathematical ideas Deciding how to support students without taking over the process of thinking for them and thus eliminating the challenge of the task Anticipating student misconceptions

29 29 The Case Of Giselle Background information Openness in voicing concerns and sharing dilemmas Tracing her learning trajectory with respect to: Questioning techniques-supporting student work without doing the thinking for them Sharing multiple solutions

30 30 The Case Of Giselle May 2003 October 2003 November 2003 March 2004 January 2006

31 31 May 2003 The kids [in Davids class] were talking with each other. There were a couple of instances where he was not even doing the questioning. They were excited to ask the questions. The first thing I thought about was Wow, they are really confident! I dont get enough of that in my room. I am usually the questioner.

32 32 Giselleinvolve another student and another idea. I would want the kids interacting more Giselle: […] Bring the other students in. I would want to involve another student and another idea. How quickly? I dont know. But I know I would want the kids interacting more. Learning In Transition: October 2003 Giselle a lot of questions I do ask a lot of questions Giselle: I noticed right off the bat that he [Randy Harris] asked a lot of questions. [...] I didnt think it was as appropriate there. He was trying to get her up to where he thought she should be. This is something I would do. If my students are not all there I do ask a lot of questions and I dont think that is always the right thing to do […] His question was far too specific and [the student] wasnt doing any higher level thinking… He walks her through what it should have been step by step […] She gives all the right answers, but she wouldnt have gotten there without the questions. Facilitator Facilitator: So what would you do?

33 33 I am really concerned about their cognitive development. Are they really getting anything out of it as they should be? Or am I just holding their hand and walking them one on one? You know what I mean? I wanted them to be successful, so I came to find to sacrifice something. Its a little bit of cognitive demand, definitely. Cause I wanted them to be motivated. Learning In Transition: November 2003 At first you are reminding them […] pull out from previous stages, look for something that would help you, how can you draw the lines, how can you make a triangle, all that. But eventually they need to do that independently. You know, you are not always going to be in their hip pocket. They have to know what they are looking for.

34 34 I would look at what they were doing and what they were not getting at all and I would ask them things that would generate relationships, like what is the relationship between the height of the tallest man and this tree. Learning in Transition: March 2004 You can prepare questions beforehand but you have to look at what the kids are doing and it changes. […]I got them to get with a partner and compare statements, and see if there were errors before we got together and shared. In terms of questions, I really ended up coming up with them as we worked through,

35 35 Still Learning: January 2006 Giselle helps another teacher realize the idea of using assessment for learning Giselle helps another teacher realize the idea of using assessment for learning. Instead of just telling the kids what they did wrong and then showing them the right way to do it, we wanted them to brainstorm together on what was wrong in that approach.

36 36

37 37 Implementation Plateau The curriculum implementation plateau is a stage when teaching and learning appear to bog down; there is a need to refine instructional practices established during implementation, to continue building local capacity, and to maintain growth in student performance through sustained, long-term teacher engagement and the provision of a space for guided reflection on the instructional issues they currently face.

38 38 Instructional Issues Available for Refinement at the Implementation Plateau Identifying mathematical goals, short-term and long -term Considering multiple solution strategies Scaffolding student thinking in ways that support the cognitive demands of the mathematics task Assessing student understanding of mathematical ideas Deciding how to support students without taking over the process of thinking for them and thus eliminating the challenge of the task Anticipating student misconceptions

39 39 Teaching with Challenging Mathematics Tasks Teachers must decide what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask to challenge those with varied levels of expertise, and how to support students without taking over the process of thinking for them and thus eliminating the challenge. NCTM, 2000, p.19

40 40 Instructional Issues Available for Refinement at the Implementation Plateau As you talk with and observe teachers who are poised on the implementation plateau, what aspects of practice do you believe teachers would value an opportunity to explore? What feels challenging about professional development at this stage of implementation? What feels compelling about professional development at this stage of implementation?

41 41 Thanks for being such an attentive audience… Contact Information: Valerie Mills Edward Silver


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