Peg Smith University of Pittsburgh February 15, 2007

Focusing on Challenging Mathematical Tasks: A Strategy for Improving Teaching and Learning
Peg Smith University of Pittsburgh February 15, 2007 Teachers’ Development Group Leadership Seminar on Mathematics Professional Development The work we are going to be talking about today is being done under the auspices of the NSF-funded ESP project in which we are working with mentor teachers (I.e., teachers who serve as cooperating teachers for preservice teachers in our secondary certification program) in helping them develop more inquiry oriented teaching practices. However, we see the approach as being applicable to a range of professional education settings.

Overview Argue for focusing on mathematical tasks
Discuss the components of the task-based model for Professional Development Discuss the role of tools in the model Present evidence of teacher learning Anticipated responses: -traditional curriculum and not knowing how to adapt tasks for greater student learning -knowledge from PD doesn’t translate into the classroom/teachers see a disconnect between PD and practice -getting teachers to see past the reasons they can’t teach in this way -teachers’ beliefs about student learning Transition: You’ve identified a number of challenges that teachers face in reforming their practice, many of which we have noticed with the teachers with whom we have worked. A common theme amongst these challenges is the notion of professional development that both makes contact with teachers’ practice and has the potential to change that practice. One way in which we have attempted to address these challenges is by selecting a focus for professional development that is grounded in research and is fundamental to teacher practice - mathematical tasks. In addition, we have created a set of tools that we feel help teachers to generalize what they learn about tasks and apply those ideas more broadly to their everyday practice.

Why Focus on Tasks? Classroom instruction is generally organized and orchestrated around mathematical tasks The tasks with which students engage determines what they learn about mathematics and how they learn it The inability to enact challenging tasks well is what distinguished teaching in the U. S. from teaching in other countries that had better student performance on TIMSS We have selected a focus on tasks for several reasons: First, classroom instruction is generally organized and orchestrated around mathematical tasks. That is, students’ day-to-day work in mathematics classrooms consists of working on a tasks, activities, or problems. For example, the TIMSS analysis of 100 eighth grade lessons revealed that the delivery of content “was accomplished primarily by working through problems” (NCES, 2003, p. 144) .Second, the tasks with which students engage determines what they learn about mathematics and how they learn it. According to Walter Doyle (1983, p.161), “tasks influence learners by directing their attention to particular aspects of content and by specifying ways of processing information.” Third, in the TIMSS video study involving seven countries including US (all who out performed US on TIMSS) although the percentage of hl tasks used was within range of other countries (17%) NONE of the tasks were enacted at a high level. This research shows that focusing on tasks is promising as it has the potential to impact student learning, and that high-level task implementation is historically lacking in US mathematics classrooms.

The Importance of Mathematical Tasks
“There is no decision that teachers make that has a greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the selection or creation of the tasks with which the teacher engages students in studying mathematics.” Lappan and Briars, 1995 Lappan and Briars make the case that there is NO decision that a teacher makes that is more important in terms of student learning that the tasks that are selected and used.

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” Stein, Smith, Henningsen, & Silver, 2000 My colleagues and I have argued that not all tasks are created equal…

“The level and kind of thinking in which students engage determines what they will learn.” Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human,1997 AND THAT…..

Task-Focused Activities
Distinguishing between high- and low-level mathematics tasks Solving high-level mathematical tasks Analyzing high-level mathematics tasks and work produced by students on these tasks Maintaining the cognitive demands of high-level tasks during instruction Each underlined title is a button that will go to a slide that provides more detail. FIRST Our work related to mathematics tasks consists of 4 different types of activities. These activities are all grounded in the work of teaching in that they are focused on mathematical tasks that can be used in the classroom. They are also closely related to classroom practice - each activity embodies some aspect of the everyday work of teachers and teaching. Then go through each. AT THE END-- All four activities are connected through the use of frameworks and tools Use the arrow button to go to slide 18

Distinguishing between high- and low-level tasks Develop teachers’ capacity to determine the kind and level of thinking required to solve a particular mathematics task Comparing pairs of tasks that focus on the same mathematics content but different with respect to the thinking demands Analyzing a set of tasks that differ with respect to their cognitive demands and task features (e.g., require an explanation, utilize a diagram, provide tools such as calculators) Once title appears, THE goal of distinguishing activities is to ….. Then bring in the next text Specific types of activities in this category include… For the second category of examples, refer folks to the pink sheet which contains a set of tasks that different with respect to cognitive demands. Take a few minutes and review tasks on the pink sheet. These tasks try to make salient that it is not surface features that effect the demands, but rather the thinking required. For example, task D asks for an explanation but it is not high level. The explanation in this case is likely to be procedural in nature. Task F uses manipulatives, but in a procedural way without requiring any thinking. Therefore it is not high level. Task Analysis Guide PURPLE could be used to defend your categorization of each task. [The button takes you back to slide 7 after all discussion of this materials has been completed.]

Martha’s Carpeting Task The Fencing Task
Distinguishing Martha’s Carpeting Task The Fencing Task Refer participants to the blue sheet -- which contains these two problems. Give participants a few minutes to review the problems and to indicate how they are different or how the same. Get at the fact that content same - processes required to solve are different. We call these high level vs. low level tasks.

Martha’s Carpeting Task
Martha was recarpeting her bedroom which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase? Stein, Smith, Henningsen, & Silver, 2000, p. 1

The Fencing Task Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen in which to keep the rabbits. If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? How long would each of the sides of the pen be if they had only 16 feet of fencing? How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it. Stein, Smith, Henningsen, & Silver, 2000, p. 2

Comparing Two Tasks Both require prior knowledge of area Area problems
Way in which the area formula is used The need to generalize The amount of thinking and reasoning required The number of ways the problem can be solved The range of ways to enter the problem Way in which area formula is used -Martha’s Carpeting can be solved by knowing and using the area formula but this formula alone is not sufficient to solve the Fencing Task - Martha’s carpeting does not lead to a generalization but the Fencing Task does The amount of thinking and reasoning required - Martha’s Carpeting requires limit thinking and reasoning while the Fencing Task can’t be solved without it

Importance of Distinguishing
Low-Level Tasks High-Level Tasks There are 2 types in each category NEXT SLIDE

Low-Level Tasks memorization procedures without connections High-Level Tasks procedures with connections doing mathematics Memorization -- times tables - Procedures with/out connections - Martha’s Carpeting P w/C - Using pattern blocks to explain why 1/2 x 1/3 = 1/6 Doing math - Fencing Task Point out here that initially, we hope that teachers will simply make the determination between low and high… as their understanding progresses, the distinctions between the four subcategories become more clear. Next slide

Low-Level Tasks memorization procedures without connections (e.g., Martha’s Carpeting Task) High-Level Tasks procedures with connections doing mathematics (e.g., The Fencing Task) [Button goes back to Distinguishing]

Solving high-level mathematical tasks Develop teachers’ understanding of mathematical ideas, processes, and tools that support learning Solving challenging mathematical tasks that focus on developing understanding of key ideas, that use a range of tools, that feature different representational forms, and that connect procedures with meaning Multiplying binomials using algebra tiles Using rectangular grids to make sense of the connections between fractions, decimals, and percents Exploring visual patterns and determining the connection between the physical and symbolic representations As the material comes up, indicated the activity category -- solving The goal - develop teachers’…. Specific activities that are used to achieve goal [Mention something here about the idea that teachers should be able to solve tasks in multiple ways and make connections, which is frequently novel to them] Use the example of the fencing task -- show different solutions and talk about how to make connections between and among them [Button goes back to slide 7 - the 4 activities]

Analyzing high-level mathematics tasks and work produced by students on these tasks Develop teachers’ ability to identify the mathematical potential of a task and to determine what students’ responses communicate about their current mathematical understandings Specifying what mathematical ideas could be learned from engaging with a particular task and what standards could be addressed Analyzing students’ written responses and determining what students appear to understand about mathematics, and developing questions to assess and advance student thinking As the material comes up, indicated the activity category -- analyzing The goal - develop teachers’…. Specific activities that are used to achieve goal Note that there are two goals here: one related largely to planning and the other largely to implementation. The planning goal is for teachers to determine the math ideas that could be learned from a task - this can occur either with or without student work and may aid in the selection and positioning of tasks. The second goal is more dynamic - to give teachers tools for analyzing in-progress student work, which in some sense represents emergent student thinking, and develop a means for better understanding the student’s thinking as well as a means for moving such thinking forward. [Talk about the fencing task & what might come out of an analysis of the task.] We consider these together here because we have found it particularly useful to use the particular mathematical idea or ideas that we wish for students to develop through their engagement in a task as a lens through which to examine the student work. Your YELLOW SHEET has an example of an activity in which we engaged with teachers related to assessing and advancing questions. By considering the task first, through solving and then identifying the goal, teachers then had the opportunity to focus their questioning on the key understandings they wished for their students to develop. [button goes back to slide 7]

Maintaining the cognitive demands of high-level tasks during instruction Develop teachers’ awareness of how high-level tasks “play out” in the classroom and the factors that support and inhibit students engagement at a high level Solving tasks and reflecting on and discussing how the facilitator supported their learning Analyzing narrative cases and identifying what the teacher featured in the case did to support or inhibit her students’ learning of mathematics As the material comes up, indicated the activity category -- maintaining The goal - develop teachers’…. Following teachers’ work in solving tasks, we took time to explicitly discuss what moves the facilitator made that supported their learning, as a way of highlighting general pedagogical moves that could be applied to any task in their own classroom. In this way, we endeavored to emphasize the notion that it isn’t the specific task that we want them to take back into their classrooms, but the general lessons learned that can apply to their teaching more broadly. With respect to the nature of the moves we identified, we know from research on mathematical tasks that when tasks work out as planned (or when they don’t) there are a set of factors at play. Most teachers, regardless of what stage they are in their career, are skilled at assessing whether a lesson went well or not after the fact, but often times the reasons for that “sense” are unarticulated or hidden from view. By highlighting these factors that emerged from their own solving of the task, and then identifying those factors in a narrative case that depicts classroom teaching, teachers gained a context for how the factors impact classroom processes, and can “be on the look out” for these in teaching more generally. Refer to the Light gold Factors [button goes back to slide 7]

Consider and Discuss How do you help teachers apply the ideas that emerge in professional development sessions in their own classrooms? Anticipated responses: Observing their classroom practice and providing feedback Creating assignments that connect to their classroom practice Having them bring in student work and analyze it Transition: We’ve identified a number of ways to try to press teachers to use the ideas they’ve learned in a professional development setting in ways that make contact with their classroom practice. We know from experience that the level of impact that these sorts of activities might have on teachers’ classroom practice can vary greatly. Sometimes there’s tremendous uptake of the ideas in their use of mathematical tasks in the classroom; sometimes, the impact is more subtle, or perhaps there is no impact at all. Next, we’d like to share a perspective that we have found useful in considering how to help these ideas travel into teachers’ classroom practice.

Distinguishing Solving Maintaining Using TOOLS Analyzing Ultimately, what we would hope to see as a result of PD is a change in teachers’ classroom practice; specifically, a change in their ability to USE HL tasks. The activities in the PD setting are situated in practice, with artifacts from teaching at the core. But the artifacts are not from TEACHERS’ OWN PRACTICE. Teachers begin by coming to understand what HL tasks are, what SL looks like, and how to support students’ learning. Understanding these ideas has the potential to impact teachers’ use of HL tasks during instruction. [Jump to next slide; read rest of notes when we return to this slide] In order for teachers to change their classroom practice, two things need to happen. First, teachers need to see a value to changing their practice - in this case, in creating a more inquiry-oriented, student-centered pedagogy through the selection and implementation of high-level tasks. This primarily occurs in the PD setting; by using materials that are practice-based, teachers come to see a value as they analyze and explore what students come to know and understand from their engagement in HL tasks. The second thing that needs to happen is teachers need to be able to generalize the ideas seen in the PD and apply them to their own practice. This is where the framework and tools come into play. BRING IN TOOLS ARROW The framework frames the task-based activities in a setting that’s recognizable as the flow of classroom instruction. The tools facilitate teachers in applying these ideas in their own classrooms with content relevant to them. Practice-based Professional Development Classroom Teaching

Using Cycle of Teaching Reflecting Planning On Practice Classroom
The green sheet provides an example of the types of activities in which we engage teachers that are intended to connect the ideas from the session to their own teaching practice. Take a minute and read through a few of the activities. What do you notice about these activities? (use of tools that have been developed, limited focus on any one activity, accountability to do something, activities become more fine-grained) [Jump back to Slide 19 using button and complete notes] “Scaffolded field experiences”

Frameworks and Tools provide a focus for professional development;
bring coherence to PD across sessions; provide a shared language for talking about teaching and learning; and bridge the professional development and K-12 classroom environments. Transition: There are a number of different ways one could organize a series of task-focused activities in a coherent professional development experience. This is the story of ours - a professional development project called Enhancing Secondary Mathematics Teacher Preparation, or ESP. [Say a little about ESP - should we have a dedicated slide that does that?] In designing each session, and the professional development program as a whole, we found it essential to have a framework and tools to:…. Tools help work TRAVEL According to the National Academy of Education (1999), “tools—including student assessments, curriculum and professional-development materials, software programs, questionnaires for probing community attitudes, and protocols for observing classrooms or professional meetings—are powerful carriers of theory and knowledge. Carefully designed tools that educators find useful in their practice can, then, become a powerful means of changing educational practice.”

Frameworks and Tools Framework Tools for:
Analyzing Cognitive Demands (purple) Identifying Classroom Influences (gold) Planning Lessons (salmon) Conferencing after a Lesson Talking about and Sharing Teaching Experiences In our work, we used the Mathematical Tasks Framework, designed by our colleagues Stein, Grover and Henningsen. This framework provides a basis for the activities in which we engage teachers during the project and brings coherency to the sessions over the course of the project. We have also created or adapted TOOLS for: Analyzing Cognitive Demands (purple) Identifying Classroom Influences (gold) Planning Lessons (salmon) Conferencing after a Lesson Talking about and Sharing Teaching Experiences In our view, the power is not in these particular tools, but rather in having a set of tools that provide a focus for the work of teaching and a common language for talking about teaching and learning. These tools serve to organize the task-focused activities and allows the experiences in the sessions to travel into teacher classroom practice.

The Mathematics Task Framework
TASKS as they appear in curricular/ instructional materials TASKS as set up by the teachers TASKS as implemented by students Student Learning Stein, Smith, Henningsen, & Silver, 2000, p. 4

The Mathematics Task Framework
TASKS as they appear in curricular/ instructional materials TASKS as set up by the teachers TASKS as implemented by students [button goes to slide Frameworks and Tools] Student Learning Stein, Smith, Henningsen, & Silver, 2000, p. 4

Summary Task-Based Activities in which Teachers Engage
Characterize mathematical tasks based on their cognitive demands Solve, analyze,and discuss cognitively challenging mathematical tasks Analyze narrative cases w/r/t the MTF and identify the factors that appear to support/inhibit students’ learning Use narrative cases to generate issues which teachers can explore in their own practice Plan, teach, and reflect on lessons based on cognitively challenging tasks

Summary A task-based approach to professional development provides a focus for work with teachers By influencing the tasks that teachers use during instruction and the ways in which they enact them, there is an opportunity to impact student learning Tools help the ideas that emerge in professional development “travel” to the classroom and back Tools help support enactment of tasks in teachers’ own classrooms and foster conservations about teaching between teachers See next slide for a less text-heavy alternative

Pulling it All Together

Is there any evidence that suggests that a task-focused approach to professional development has an impact on teachers’ classroom practices? So we can argue that the specific activity we just looked at engaged Rick Carson in thinking about his practice. Can we do any better than that? YES

ESP: Setting the Context
Workshop focused on selecting and enacting high level tasks Intended for practicing mathematics teachers 7-12 with 3 or more years experience Use practice-based materials with the Purple book (Implementing Standards-Based Reform) as the centerpiece Assignments link to teachers’ practices in very specific ways and use tools (e.g., TTLP) to generalize ideas

ESP: Data Collected Pre- and post task sorts Pre- and post interviews
Videotapes of all workshop sessions Teachers notebooks and all assignments All artifacts generated during the course Task packets Student work packets Classroom observations

ESP: What Teachers Learned
Significant increase in teachers’ ability to distinguish between high and low level tasks following their participation in the workshops Significant increase from fall to spring the number of high-level tasks used per teacher over the 5-day data collection Significant increase in the percent of high-level tasks that were maintained during implementation from fall to spring The PD in which teachers engaged appeared to have an influence on teachers' practice, particularly with respect to their ability to use and maintain high-level tasks in their own classrooms. Teachers who showed the most growth over time were those who consistently made connections between the PD and their own classroom practice. Boston, 2006

For More Information

Results from Data Analysis The Task Sort
Pre- and Post-Workshop Task Sort: During the first (October) and last (May) session in the workshop, teachers were asked to: classify a set of tasks as High-Level or Low-Level; justify their classification of each task; and provide a set of criteria for High-Level and Low-Level tasks. Middle school task sort from Smith et al (NCTM, Melissa will need to say a word or two about how this was scored to contextualize the results in the next slide) Refer to Pink Handout

Pre- and Post-Workshop Task Sort: Highly significant increase between the pre- and post-workshop task sort scores Teachers in the workshop scored significantly higher on the post-workshop task sort than a contrast group of secondary mathematics teachers who did not participate in the workshop Teachers improved their ability to distinguish between high and low level tasks following their participation in the workshop. These results suggest that ESP teachers’ knowledge of the cognitive demands of mathematical tasks increased following their participation in the ESP workshops.

Pre- and Post-Workshop Task Sort: Improvements in teachers’ justifications and criteria for high and low level tasks No “inconsistent” criteria identified on the post i.e., “Difficult is High-Level” or “Use of a diagram is Low-Level” Criteria and justifications closely connected to our work in solving and distinguishing tasks in the sessions Inconsistent criteria: on the pre-test, 6 teachers (out of 19) listed inconsistent criteria Nature of the improvements: Connections to our work: Used specific labels & language from the Task Analysis Guide (TAG) Used “big ideas” from the TAG & from discussions of task levels during the sessions: Presence of a stated or implied procedure Open-ended; opportunities for multiple strategies Multiple representations Opportunities to make connections

Results from Data Analysis Tasks Used in Teachers’ Classroom
Teachers were asked to submit tasks used over 1-week period in Fall, Winter, and Spring. In each data collection, 5 main instructional tasks scored using IQA Academic Rigor in Mathematics rubric Boston & Wolfe, 2004; Matsumura et al., 2004 Score of 1 or 2 = Low-level cognitive demands as described on Task Analysis Guide Score of 3 or 4 = High-level cognitive demands as described on Task Analysis guide Stein, Smith, Silver & Henningsen, 2000 IQA rubrics - Academic Rigor in Mathematics. Identify quality instruction in mathematics. Rates the task on a scale of 1-4 and the implementation of the task. One set of rubrics for observations and one for student work. Based on MTF (slides ##) and TAG (purple). Under went testing for validity and reliability in large urban schools.

Results from Data Analysis Tasks Used in Teachers’ Classroom
Comparisons of Tasks Used From Fall to Spring: Significant increases in Task Scores Significant increase in overall % of H-L tasks used Significant increase in the number of high-level tasks used per teacher over the 5-day data collection

Results from Data Analysis Student Work Collected from Teachers’ Classroom
Collections of Student work: Teachers submitted 3 class-sets of student work in the Fall, Winter, and Spring. Student-work was scored using the IQA rubric for student work Implementation Scale of 1 to 4 Score levels based on Task Analysis Guide Low-Level < 2 High-Level > 3 Student work tasks subset of main instructional tasks, so analyzed the implementation scores.

Comparisons of Student-Work Implementation Scores from Fall to Spring: Significant increase in mean scores Significant increase in number of high-level student work implementations Significantly less occurrences of decline of high-level cognitive demands

In all data collections, Implementation scores were lower than task scores. The number of high-level implementations per teacher is lower than the number of high-level tasks used per teacher. These findings indicate a persistent trend of decline in the level of cognitive demands. In all data collections, task Implementation means were lower than task Potential means, the number of high-level implementations per teacher is less than the number of high-level tasks per teacher. These findings identify a trend of the decline of cognitive demands during instruction that persisted across data collections. Even when teachers selected high-level instructional tasks for use in their classrooms, these tasks were often enacted during the lesson in ways that did not maintain students’ opportunities to engage with high-level thinking and reasoning.

Was the decline in the level of cognitive demands significant? Fall and Winter: Implementation scores were highly significantly lower than task scores Spring: Implementation scores were not significantly lower than Task scores Increase in # of high-level implementations per teacher Increase in % of high-level tasks that were maintained during implementation Determined whether the decline between student work was significant The student work Implementation means were highly significantly lower than the Potential means in Fall (p <0.001) and Winter (p = 0.002), but only marginally lower in Spring (p = 0.048). Hence, high-level task demands had an extremely high tendency to fall to lower levels of cognitive demand during implementation in Fall and Winter, but not in Spring. This implies that teachers improved their ability to maintain high-level cognitive demands during instruction following their participation in the ESP workshops. This is further evidenced by the increase of high-level implementations from less than 1 (out of 3) per teacher in Fall to 2 (out of 3) per teacher in Spring, or similarly, by the increase from 25% of high-level tasks maintained at a high-level during implementation in Fall compared to 67% in Spring.

Results from Data Analysis Observation of Teachers’ Classroom
Eleven teachers participated in 1 classroom observation per data collection Marginally significant increase in lesson implementation from Fall to Spring Teachers significantly more likely to maintain high-level cognitive demands during implementation in Spring than in Fall or Winter. In Spring, teachers implemented tasks at a significantly higher level than teachers in a contrast group who did not participate in the workshop

Connecting Professional Development to Teacher’s Practice
Focusing on a particular factor (light gold sheet) they wanted to work on and use the factor as a lens for reflecting on classroom instruction Expectations Teachers would teach a lesson based on a high-level mathematical task of their choice Teachers would select several pieces of work produced by students during the lesson that they felt accurately reflect the lesson Teachers would bring blinded copies of the student work to share

Rick Carson’s Case Story
Teacher: 9 years of experience First time student work has been shared in this format School Setting: 10th grade Integrated curriculum in a probability unit

Case Stories: Storytelling through Student Work
Storyteller will distribute a complete set of student work to each team member without comment. The team members will individually review the work in silence. 5 minutes allowed Please review the student work provided.

The team should share what they saw in their review of the student work. Only factual statements can be made. Do not share your evaluation of the work, or statements of personal preference. Start comments with, “I noticed that…” The storyteller is quietly listening and making note of statements. 5 minutes is allowed Facilitator should engage participants in whole group discussion, charting responses. Anticipated responses are: Switching Sherry/Gary on axes All work looks similar Teacher made comments Students didn’t follow directions on rounding No requirement was made for an explanation Didn’t ask why they were drawing lines certain ways All students used the whole grid Labeled the same way

The team should share questions they have about the student work. Responses should be in the form, “I’m wondering…” The storyteller should make note of the wonderings, and should continue to remain quiet. 5 minutes is allowed. Facilitator should engage participants in whole group discussion, charting responses. Anticipated responses are: Was this a group or individual assignment What prior knowledge did the students have Was this a summary activity or an investigation Where other methods allowed Why students did show that they checked their answer with a point on the grid. Did students see a value to this type of mathematics Was it tied to their world Did this lead to a discussion of gender stereotypes (girls are always late) How much time did the students have to complete this task What followed this task

Rick Carson Shares His Perspective

Case Stories - What Emerged
The Facilitator started: …I’d like to talk about the extent to which the student work facilitated your discussions about teaching. If you recall, last month when we did this, we told stories, but we didn’t have any artifacts, we didn’t have any student work or anything else that came directly from the lesson. So I’m wondering to what extent, and in what ways, the student work actually might have facilitated the discussion? To what extent did the student work facilitate your discussions about teaching? Peg: …I’d like to … talk about to what extent did the student work facilitated your discussions about teaching. If you recall, last month when we did this, we told stories, but we didn’t have any artifacts, we didn’t have any student work or anything else that came directly from the lesson. So I’m wondering to what extent, and in what ways, the student work actually might have facilitated the discussion? HM: Looking at the student work, we were able to see the teachers’ expectations, and whether that was one of our constant goals, instead of just a goal for that particular lesson, …it showed more of what we do throughout the year instead of just with the one lesson we talked about last time. Peg: …So the student work brought out questions about the frequency with which students do things, sort of insights into more general goals and teaching practices. Anything else you want to say about that? Pete? Pete: When we saw so many papers, you could see a lot of uniformity between what the kids were doing and that led us into a discussion about how much did the teacher lead the discussion, how many hints did you give them, and whether that’s a good thing or a bad thing. Peg: So this may have happened in more than one group, that when you see uniformity across work, it starts raising questions about what was the nature of instruction How leading was it, how directive, was everyone told to do it a particular way, if they weren’t but did it anyway, how do you account for such things, so that it may cause questions about the relationship between what students were doing and the nature of the instructional experience. Anything else?

Rick Carson’s Response
“When we saw so many papers, you could see a lot of uniformity between what the kids were doing and that led us into a discussion about how much did the teacher lead the discussion, how many hints did you give them, and whether that’s a good thing or a bad thing.” When we later looked at the tape from his small group we noted that he was talking specifically about HIS OWN WORK. And that the student work he shared was very procedural in nature.

Peg Smith University of Pittsburgh February 15, 2007

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