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Moving Beyond Implementation: Challenges and Possibilities

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

2 Today’s 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 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?

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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 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 Having worked with a number of districts as they implemented CMP I have been able to observe fairly consistent, sometimes dramatic, growth patterns in student achievement that run for several years following successful implementation. I have also noticed that these growth pattern began to level off somewhere around 5 or 6 years out. This project is a joint effort to work with teachers in districts who have used CMP for several years to try to understand and address this Implementation plateau phenomenon. After some playing around with some ideas in , we began our first full year May 2003 are familiar with the structure and philosophy of curriculum know where the ideas appear, in what order, and which problems give better access to some mathematical ideas have a sense of comfort with activities and sometimes develop a shorthand for talking about it (What will I do in the Launch? I started with the Reflections; I assigned the ACE problems, etc…).

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 District’s resources no longer available Furthermore, since no other program change in their experience has needed attention and resources for this length of time Teachers feel generally confident, but still do not feel fully competent especially as it concerns the facilitation of the open-ended tasks. They typically are not able articulate what aspect of practice they need to address and this makes working on it problematic. Plateau appears at a vulnerable time for districts who have made the change to standards-based programs as concerns about change reemerge. Districts/educators are not prepared to describe with any specificity the work that still remains to fully utilize these new resource materials. Also, the timing of the plateau occurs at a point where the district’s resources have been expended on the first few years of program implementation. Having worked with a number of districts as they implemented CMP I have been able to observe fairly consistent, sometimes dramatic, growth patterns in student achievement that run for several years following successful implementation. I have also noticed that these growth pattern began to level off somewhere around 5 or 6 years out. This project is a joint effort to work with teachers in districts who have used CMP for several years to try to understand and address this Implementation plateau phenomenon. After some playing around with some ideas in , we began our first full year May 2003

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

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

11 The Goals of the BIFOCAL Project
Understand the implementation plateau Assist teachers and schools Level IV: Refinement & Building Local Capacity

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 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 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 Instructional practice focus Professional development model

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 Looking more closely at this new skill set , one notices that embedded in this over arching work of facilitating learning in the context of problem solving lurks a diverse range of instructional decisions. This quote from the teaching principal described in the 2000 NCTM Standards suggest generally what this might include. There is a growing research base that suggests that eliminating or reducing the mathematical challenge for students may be a particularly important variable in the equation of increasing student achievement. Since our goal was to address the plateau effect this seemed like a reasonable place to focus our work.

16 BIFOCAL: Background in a Nutshell
Supporting Frameworks/Perspectives : “Practice-based” approach (Ball, Smith) Mathematical Task Framework (QUASAR) Case Analysis & Discussion Lesson Study Instructional practice focus Professional development model

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

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 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 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 Lesson Study

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 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?” The last session we chose to sample for you comes from February Our goals for this session, were to sustain teacher’s attention on the identification and use of a lesson’s mathematical goals and also on the use of multiple solutions strategies to support learning. This was a topic we began working on during the January session. In addition, this session was designed to give us the opportunity to take up what were then “new” issues around anticipating student thinking when planning a lesson and attending to student thinking during class. First, the focus questions we used as we worked on the mathemtics from the case. This is a proportional reasoning task that is similar to the problem used in the January session. [In this problem students can see the drawing of a bag of candy containing Jollyranchers and Jawbreakers. The question for students is Given that you have the same ratio of Jollyranchers to Jawbreakers as are currently in the bag, how many Jawbreakers would you have if there are 100 Jollyranchers? How many of each kind of candy would you have if the jar contained 720 candies?] Focus on attending to (during class) and anticipating student thinking (lesson planning) (strategies, errors, misconceptions, current knowledge) around the mathematical goals.

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 Marie’s 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 Then as we explored the case, the questions continue to provoke thinking about the same instructional delemas. To understand the last question it will helpful to know that In the case of Marie Hanson her students explore several proportion problems and generate a variety of solutions. Text includes a focus on Marie’s approach to the lesson and the dilemmas she faced in dealing with her students’ multiple solutions. The focus questions opperate at two levels…. One they make visable and available for analysis the issues of instruction that our teachers were grappling with as-well-as drawing attention to new instructional strategies offered in the case, and two, they ask teachers to… Adopt analytic stance toward teaching, to practice making claims based on evidence rather than opinion, they direct their Attention toward instructional goals and issues (the teachers decision points throughout the lesson), in a context that brings the analysis of teaching to the level of a lesson. ------ The role of facilitation in this case discussion is vital in that…link case to their practice Notice the connections between the questions used with the task, those used with the case (issue of confusion with multiple solutions up for students to look at)

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? The Modified Lesson Study design was refined over the course of the year. In particular our use of the TTLP which was introduced after the first session and is quite lengthy, we quickly learned to adapted for each session. That is we selected and used only the questions from the TTLP that paralleled the issue(s) of practice that would be highlighted in the case discussion. This worked to strengthen the transfer of ideas generated during the case analysis into the planning and enactment of the Lesson Study. So for example you can see that for the Feb session the lesson planning template we used contained the questions from TTLP that relate to supporting student learning with challenging tasks, anticipating and assessing student thinking and working with multiple solutions strategies to support learning. Each of these questions echoed ideas raised in the discussion of the mathematics and the case. --Using this approach to lesson study meant that we need to pay careful attention to selecting a lesson for the lesson study in which the targeted issues of practice were likely to appear. One other note about the case analysis and discussions, it was incumbent upon the facilitator to open the link between the case classroom and teachers classrooms.

26 A Mathematics Professional Development Synergy
Modified Lesson Study Case-Based Professional Development Curriculum-Based Lots of discussion recently about grounding professional development in the practice of teaching. That is using teacher’s work as targets of inquiry and investigation. But how do you structure that work over time? Where do you start? What might it look like? Curriculum materials provide a good starting point, but may not be sufficient to bring about the changes in practice we are after. Of particular interest in this session will be the way in which the project’s “practice-based” professional development approach combines elements of lesson study with the analysis of narrative cases. We will illustrate this combined approach and describe some outcomes across one and one-half years of the project. Participants will view and discuss artifacts from project sessions and video clips illustrating teachers’ activity in the project. In addition to fostering discussion concerning ways to help teachers improve their effectiveness using innovative curriculum materials and to help school districts build local capacity to accomplish this goal, we will engage session attendees with the conceptual issues that lie at the heart of our work. Particular attention will be given to the ways in which lesson study and case analysis complement each other to achieve a powerful synergy.

27 Blending CAD and MLS as the Professional Development Evolves
Modified Lesson Study (3) Instructional Issues XYZ Case Analysis and Discussion (3) Case Analysis and Discussion (2) Modified Lesson Study (2) Instructional Issues XY These examples were intended to demonstrate the ways in which Case Analysis Bended with Modified Lesson Study allows us to work on a variety of instructional issues in both an iterative and adaptive way over time. For teachers, this professional development model allowed them to take up these Issues of practice, repeatedly exploring and analyzing them first from a position outside the pressures and particulars of their own practice, and then from within the context of their own classrooms with each additional conversation offering teachers the opportunity to take up new teaching strategies, deepen and solidify their understanding . Modified Lesson Study (1) Instructional Issue X Case Analysis and Discussion(1)

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 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 We now turn to a teacher and illustrate how the synergy between lesson planning and case discussion offered her significant opportunities to reflect on certain aspects of her teaching. When she first joined the Bifocal sessions (i.e., 3 years ago), Giselle had already been teaching mathematics at middle grade for four years. She had also had some experience with CMP. What distinguished her from the other participants was her openness in voicing her concerns and sharing her dilemmas, something that offered us a window to her thinking. In tracing her trajectory, we focus on two issues both of which help us illustrate this synergy of lesson planning and case discussion. In particular, we examine Giselle’s engagement with the issue of questioning techniques --the questions that a teacher poses to students, and particularly, the importance of maintaining the cognitive demand- and the issue of multiple solutions.

30 The Case Of Giselle October 2003 May 2003 January 2006 March 2004
November 2003 Two remarks should be made here: First, in tracing her trajectory, we are again using this spiral diagram to emphasize that the sessions offered Giselle recurring opportunities to reflect on certain issues. And second, we are using different colors: starting from light colors at the bottom and moving to darker as we move to the top. The reason for doing this is to underscore that Giselle’s thinking with respect to these two instructional issues was gradually becoming more nuanced. October 2003 May 2003

31 May 2003 The kids [in David’s 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 don’t get enough of that in my room. I am usually the questioner. In the first session, back in May 2003, our teachers discussed the case of Catherine and David. Let me remind you that this is a case of two teachers who enacted the same lesson in different ways. The case offers several stimuli for reflection on different instructional issues. Let us see what Giselle chooses to focus on. It is obvious that Giselle elaborates on an issue that was pertinent to her own teaching, an aspect of her teaching that she considered somewhat problematic. So, she uses David and the way he enacted his lesson to talk about her own practice. And what are the issues that she raises? Notice that she feels quite uncomfortable for being the questioner. She wants to minimize the questions that she asks and offers students more space for interaction. She wants to facilitate than lead the discussion, and she realizes that she needs to pose fewer questions. Therefore, at this point she views the issue of posing questions from a rather quantitative perspective. She also wants students to ask questions to each other– and she considers this as evidence of self-confidence.

32 Learning In Transition: October 2003
Giselle: I noticed right off the bat that he [Randy Harris] asked a lot of questions. [...] I didn’t 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 don’t think that is always the right thing to do […] His question was far too specific and [the student] wasn’t 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 wouldn’t have gotten there without the questions. So, let’s now move to October. To help us better understand how her thinking about the issues of questioning techniques and the use of multiple solutions gradually becomes more nuanced, we are using two different colors. Blue and underlined utterances mirror her thinking about these issues when she entered the Bifocal sessions. Utterances colored in orange correspond to other dimensions of these issues that Giselle started considering as a result of the case discussion and the lesson planning. So, in October 2003 teachers discussed the case of Randy Harris. In this case, Randy selects a rich mathematical task, that asks students to draw connections between decimals, fractions, and percents. Yet, to his dismay, the students seemed unable to engage in this deep-level of thinking. Randy employs different strategies to help students make sense of the task. What does Giselle focus on? What do we notice here? First, once more Giselle raises the issue of the number of questions posed. She is again concerned with her posing so many questions. But she moves a step forward. Capitalizing on the MTF discussed in the June session, Giselle now also pays attention to the issue of cognitive demand. She remarks that the questions that Randy posed walked the student to the answer of the problem. Hence, it was him who did the thinking and not the student. Notice that then the facilitator prompts her to reflect on her own practice. However, Giselle misses a good chance to further elaborate the idea of maintaining the level of cognitive demands, and again reverts to the idea of having students interacting with each other. Facilitator: So what would you do? Giselle: […] Bring the other students in. I would want to involve another student and another idea. How quickly? I don’t know. But I know I would want the kids interacting more.

33 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. 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. It’s a little bit of cognitive demand, definitely. Cause I wanted them to be motivated. In November 2003, we used a video case of a Japanese lesson on geometry. During this discussion, Giselle supported that the teacher also needs to pose what she identified second level questions – not just questions that ask for recalling fact and applying ideas. Being prompted to elaborate this argument she proposed that student be asked to find alternative solutions to a given problem or generalize their answer to a new situation. Let’s see how she justified the need for adopting such an approach. Additionally, in her end of session reflections she wrote… What we now see is that her focus has now been shifted a little bit. In addition to talking about students being confident, she now emphasized the need to help her students become independent thinkers. Notice also that how Giselle appropriates /assimilates the ideas discussed in the sessions. She is now well aware of the importance of this issue of cognitive demands. But she also wants to ensure that her students will also be motivated and successful. What is also important to notice during this session is that Giselle started reflecting more deeply on this issue of questioning techniques and cognitive demands. In fact, she started putting some ideas in practice- however, it is one thing to endorse an idea and another thing to incorporate it in your teaching- especially if this idea seems to contradict existing practices. Therefore, during the lesson planning part of the session Giselle shares one of her instructional dilemmas: So, how does one go with this issue of cognitive demands, when some students have already found the answer, whereas others are still struggling? You never know how far to go with that when you are trying to maintain your cognitive demand.

34 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, 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. The March session was devoted to having teachers share the lessons that they planned in the previous session and enacted in the meantime. So, in this session the cases of analysis were the lessons that teachers taught. In sharing her lesson, Giselle again revisits this issue of questioning techniques. Notice now, that although she prepared some questions in advance, she was flexible and improvised a lot, to respond to how her students themselves were responding to the stimuli she was providing. Also notice this idea of asking questions to generate relationships. This idea definitely indicates that Giselle has started focusing more on the quality of the questions that a teacher poses, compared to the quantity of these questions, which was her main concern at the first session. This idea did not came out of the blue. In the previous session, teachers discussed the case of Marie Hanson, in which this teacher purposefully posed certain questions to help students link the multiple solutions that presented to a problem.

35 Still Learning: January 2006
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” . Just to illustrate how her thinking evolved over time, we now shift to the January 2006 session during which Giselle helped a colleagues of her put into practice the idea of using assessment as a means for further fostering student learning rather than solely as a means of getting an idea of student learning. This is the emphasis of the third year of the project. In sharing this experience, Giselle notes that contrary to what she used to be doing before – just going over the test and pointing to students’ mistakes, this time she decided to have students take a more active role. Just a brief remark on what we saw: (a) note what questions she posed- open ended questions that would help her students draw connections (not how many but what kind of questions), (b) note also how she organizes the activity to give students the opportunity to pose questions to each other– coming full circle, doesn’t this sharing reminds you how she started? I want my students to be like the students in David’s class.

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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 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 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 Looking more closely at this new skill set , one notices that embedded in this over arching work of facilitating learning in the context of problem solving lurks a diverse range of instructional decisions. This quote from the teaching principal described in the 2000 NCTM Standards suggest generally what this might include. There is a growing research base that suggests that eliminating or reducing the mathematical challenge for students may be a particularly important variable in the equation of increasing student achievement. Since our goal was to address the plateau effect this seemed like a reasonable place to focus our work.

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


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