Math fac notes_s1_mtf slides_092809


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  • Slide 1 Slides 1-8, 10 min WG We will explain goals for our work together and the rationale for using what is referred to as practiced-based approach to professional development and for why we are making tasks the primary focus of our work.We will also describe the research from national and international endeavors that informs our work (Quasar & TIMMS).
  • Slide 2 Slides 1-8, 10 min WG Read or have participants read the goals.
  • Slide 3 Slides 1-8, 10 min WG This quote from the NCTM Principles and Standards captures the core challenge teachers in mathematics face on a day-to-day basis - the selection and facilitation of mathematics tasks, particularly those that require students to think deeply, reason, and draw on their conceptual understandings of mathematics concepts. Our work will support your developing the skills and the knowledge for selecting and facilitating worthwhile mathematical tasks in your classrooms.
  • Slide 4 Slides 1-8, 10 min WG We have identified three goals we will pursue in our efforts to support you around this challenge…We expect that these goals will branch and morph, and additional goals may emerge as we grapple with our understanding of this core problem.It is evident that the mathematical knowledge teachers have at their disposal influences their ability to manage challenging tasks in their classrooms; therefore we will collectively work on deepening our own mathematical knowledge. It is important that we all have a sense of what we mean by meaningful interactions among teachers, students, and task; therefore we will spend a lot of time examining those interactions through resources we have selected and reflection on our classroom instruction.Finally, one of our main goals is to help you improve your skills and knowledge to provide opportunities for students to learn mathematics with understanding.
  • Slide 5 Slides 1-8, 10 min WG We will use two main resources, tasks and cases.Because not all tasks are equal - we seek to work with tasks that are called “high-level” and study episodes of teachers implementing such a task and analyzing the maintenance of the demand of the task or how the the level of the task may change.
  • Slide 6 Slides 1-8, 10 min WG 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 (six of which out performed US on TIMSS) although the percentage of high level tasks used US classrooms 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.
  • Slide 7 Slides 1-8, 10 min WG We chose to use cases because we wanted to use resources that emerge from the activity of your classrooms. The work we will be engaged in is often termed “practice-based PD.”
  • Slide 8 Slides 1-8, 10 min WG We would all agree that...
  • Slide 9 20 min Here is an example of 2 different problems that appear to have similar mathematical goals. How would you compare these tasks? How are they similar and how are they different? [We are looking for recognition that they differ in the level of cognitive demand so we can then ask teachers to think about what characterizes a high-level task.] Whole group discussion of similarities and differences. This whole discussion should be brief, just enough to acknowledge that one task is more challenging than the other (5 min.)Small group (5 min.) Give time for participants to talk with each other about their perception of the level of difficulty of tasks and how they might describe high-level tasks.Whole group (10 min.) Question: Thinking about how these and other tasks differ in level of demand, how would you describe high-level tasks? How might you characterize low-level tasks? Record participants’ ideas: Flip chart heading: Characteristics of Tasks and 2 columns: low level & high level. The point to make is that there is a very different level of demand. One can be done using memorized facts, the other requires connecting to underlying meanings or concepts. The key idea is that the tasks plays a critical role in providing opportunities for learning.
  • Slide 10 Slides 10-11; 5 min Researchers have described 2 levels of cognitively less demanding tasks. Go through these briefly noting how the they (the above categories) match with the list participants generated and note what did not emerge from the discussion.
  • Slide 11 Slides 10-11; 5 min Researchers have described 2 levels of cognitively demanding tasks. Focus on these briefly, seeing how the they (the above categories) match with the list participants generated and note what did not emerge from the discussion.
  • Slide 12 Slides 12-17; 5 min The research that INFORMED AND SUPPORTED our work.As noted before, the TIMSS video study involved seven countries, including the US (the other six countries outperformed the US on TIMSS). Although the percentage of high level tasks used was within range of other countries (17%) NONE of the tasks were enacted at a high level The Quasar project studied the relationship between instruction and student achievement in mathematics in high needs middle schools. Findings from research—highest gains were related to the extent to which tasks were set up and implemented in ways that engaged students in high levels of cognitive thinking and reasoning. This supported findings from the TIMMS video study of the factors related to high achievement. Again, high achievement was highly related to student engagement in high-level tasks. This was the ONLY variable associated with high achievement in high needs schools. 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.
  • Slide 13 Slides 12-17; 5 min This framework “specifies several points at which a teacher mediates students’ engagement with the tasks found in curriculum materials and highlights the ways that task demands may change as a teacher uses them with students. A teacher decides which tasks to assign and which to omit, and he or she may transform tasks substantially when reading and interpreting the curriculum materials, when setting up the tasks during instruction, and while interacting with students during enactment of these tasks.” (Silver, Ghousseini, Charalambous, & Mills, 2009, p. 248)
  • Slide 14 Slides 12-17; 5 min QUASAR Findings: Teachers’ decisions and actions influence the nature and extent of student engagement with challenging tasks, and ultimately affect students’ opportunities to learn from their work on such tasks.
  • Slide 15 Slides 12-17; 5 min These are some of the challenges teachers face when they are using high-level tasks.
  • Slide 16 Slides 12-17; 5 min Research findings identified these factors that undermine the cognitive demand of a task.
  • Slide 17 Slides 12-17; 5 min Using this framework (MTF) to analyze cases, positive teacher actions were identified as….
  • Slide 18 5 min WG or IW Use 5 minutes to summarize the key ideas from the session or allow time for individual refection.
  • Math fac notes_s1_mtf slides_092809

    1. 1. Overview of Session <ul><li>Challenge and Goals </li></ul><ul><li>Resources: Tasks and Cases </li></ul><ul><li>Task Analysis </li></ul><ul><li>Research That Informs Our Work </li></ul><ul><li>Mathematical Task Framework (MTF) </li></ul>
    2. 2. Goals of the Session <ul><li>To understand what characterizes a cognitively demanding task </li></ul><ul><li>To become familiar with findings from research on the critical role tasks play in instruction </li></ul>
    3. 3. Core Challenge <ul><li>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.” </li></ul><ul><li>NCTM, 2000, p.19 </li></ul>
    4. 4. Goals for Professional Development <ul><li>To provide opportunities for teachers to deepen the mathematical knowledge used in teaching mathematics in the middle grades </li></ul><ul><li>To build a collective vision of meaningful interactions among teachers, students, and mathematical tasks that positively influence student learning </li></ul><ul><li>To develop teachers who will have the skills and knowledge to create more effective mathematics learning environments for their students </li></ul>
    5. 5. Central Resources <ul><li>Tasks - complex mathematical tasks that provoke examination of underlying mathematical concepts </li></ul><ul><li>Cases - accounts of mathematics instructional episodes that depict interactions that occur when a teacher uses a complex mathematical task in the classroom </li></ul>
    6. 6. Why Focus on Tasks? <ul><li>Classroom instruction is generally organized and orchestrated around mathematical tasks. </li></ul><ul><li>The tasks with which students engage determine the mathematics they learn. </li></ul><ul><li>Teachers’ facilitation of tasks determine how students learn the mathematics within the tasks. </li></ul><ul><li>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. </li></ul>
    7. 7. Tasks & Cases <ul><li>Emerge from the activity of classrooms </li></ul><ul><li>Provide opportunities for teachers to become involved in critical discussions of actual teaching situations (Loucks-Horsley, 1998) </li></ul><ul><li>Promote reexamining our assumptions about what “understanding mathematics” really means (Schifter, Russell, & Bastable, in press) </li></ul>
    8. 8. Mathematical Tasks <ul><li>“ Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” </li></ul><ul><li>(Stein, Smith, Henningsen, & Silver, 2000) </li></ul>
    9. 9. Comparing Tasks <ul><li>Task 1 - Shade 6 small squares in a 4 x 10 grid. Using the grid, explain how to determine each of the following: a) the percent area that is shaded, b) the decimal part that is shaded, and c) the fractional part that is shaded. </li></ul><ul><li>Task 2 - Convert the fraction 3/8 to a decimal and percent. </li></ul><ul><li>What similarities and differences do you notice about the two tasks? </li></ul>
    10. 10. Levels of Cognitive Demand: Low level <ul><li>Procedures without connections </li></ul><ul><ul><li>Algorithmic and use of procedure is specifically called for </li></ul></ul><ul><ul><li>Have no connection to the concepts or meaning that underlie the procedure being used </li></ul></ul><ul><li>Memorization </li></ul><ul><ul><li>Reproducing previously learned facts </li></ul></ul><ul><ul><li>Committing facts, rules, formulae to memory </li></ul></ul>
    11. 11. Levels of Cognitive Demand: High level <ul><li>‘ Doing’ mathematics </li></ul><ul><ul><li>Requires complex and nonalgorithmic thinking </li></ul></ul><ul><ul><li>Requires students to explore and understand the nature of mathematical concepts, processes, or relationships </li></ul></ul><ul><ul><li>May involve some level of anxiety </li></ul></ul><ul><li>Procedures with connections </li></ul><ul><ul><li>Focuses student’s attention to the use of procedures for the purposes of developing deeper levels of understanding </li></ul></ul><ul><ul><li>Suggest pathways that have close connections to underlying mathematical ideas </li></ul></ul><ul><ul><li>Usually represented in multiple ways (e.g. visual diagrams) </li></ul></ul>
    12. 12. Quantitative Understanding: <ul><li>Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) & Trends in International Mathematics and Science Study (TIMSS) </li></ul>
    13. 13. The Mathematics Task Framework TASKS as presented in curriculum/ materials TASKS as set up by the teachers TASKS as enacted by students and teacher in the classroom Student Learning (Adapted from Stein, Smith, Henningsen, & Silver, 2000)
    14. 14. MTF - The Bottom Line <ul><li>Tasks are important, but teachers also matter! </li></ul><ul><li>Teacher actions and reactions … </li></ul><ul><ul><li>influence the nature and extent of student engagement with challenging tasks, </li></ul></ul><ul><ul><li>and </li></ul></ul><ul><ul><li>affect students’ opportunities to learn from and through task engagement. </li></ul></ul>
    15. 15. Challenges in Using High Level Tasks <ul><li>Resisting the persistent urge to tell and to direct </li></ul><ul><li>Allowing time for student thinking </li></ul><ul><li>Knowing when/how to ask questions and to provide information to support rather than replace student thinking </li></ul><ul><li>Helping students accept the challenge of solving worthwhile problems and sustaining their engagement at a high level </li></ul><ul><li>(Stein, Smith, Henningsen, & Silver, 2000) </li></ul>
    16. 16. Factors that Undermine the Cognitive Demand of a Task <ul><li>Routinizing problematic aspects of the task </li></ul><ul><li>Shifting the emphasis from meaning, concepts, or understanding, to the correctness or the completeness of the answer </li></ul><ul><li>Not providing enough time </li></ul><ul><li>Not holding students accountable for high-level products or processes </li></ul><ul><li>(Stein, Smith, Henningsen, & Silver, 2000) </li></ul>
    17. 17. Factors that Support Maintaining High Cognitive Demand <ul><li>Building on students’ prior knowledge of concepts and meanings </li></ul><ul><li>Scaffolding students’ thinking </li></ul><ul><li>Providing appropriate amount of time </li></ul><ul><li>Modeling high-level performance </li></ul><ul><li>Sustaining pressure for explanation and meaning </li></ul><ul><li>Drawing frequent conceptual conceptions </li></ul><ul><li>(Stein, Smith, Henningsen, & Silver, 2000) </li></ul>
    18. 18. Reflection <ul><li>What were the important mathematical ideas you encountered today? </li></ul><ul><li>Did this experience generate any insights/connections relate to teaching? (What about the day prompted these?) </li></ul>
    19. 19. The MMSTLC Program <ul><li>The MMSTLC program and these materials were developed under a Mathematics and Science Partnership grant awarded by the Michigan Department of Education. </li></ul>