1. Engaging Students in High Level Cognitive Tasks Marjorie Graeff April 21, 2010 Division of Teaching & Learning

2. 1.Introduction 2.The Case of Ron Castleman 3.High-level Tasks 4.Marzano and SAS 5.Reflection Agenda

3. Objectives –Understand the importance of selecting high-level cognitive tasks. –Recognize factors associated with maintaining or reducing cognitive demands of mathematics tasks. –Plan to employ these high-level practices and procedures in your classroom.

4. Opening Activity –One way I select tasks for my classroom is… –What is the purpose of asking students to solve problems ? –A type of problem-solving task that I use with my students is……

5. Comparing Two Mathematical Tasks “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” Stein, Smith, Henningsen, & Silver, 2000 http://www.youtube.com/watch?v=2lXh2n 0aPyw

6. Do the Math Shade six of the small squares in the rectangle shown below. Using the diagram, explain how to determine: a) the percent of area that is shaded b) the decimal part of area that is shaded c) the fractional part of the area that is shaded

7. The Case of Ron Castleman Read the case from page 37 through 42 where it is clearly marked “STOP.”

8. Following the second period class: 1.What are some mathematical issues Ron was concerned with during the lesson? Why are these important issues? What non-mathematical issues did Ron seem to be concerned about? 2.How would you describe the thinking Ron was asking students to engage in when he set up the task? Did Ron’s goals change after the students began working on the task? Were Ron’s goals accomplished?

10. Linking to Literature/ Research: The QUASAR Project The Math Task Framework TASKS as they appear in curricular/ instructional materials TASKS as set up by the teachers TASKS as implemented by students Student Learning

11. Cognitive Demands at Set Up Stein, Grover, & Henningsen, 1996

12. Patterns of Implementation In a 3-year study of classroom instruction at four QUASAR middle schools, a handful of patterns emerged that captured characteristic ways in which high level tasks unfolded during instruction.

13. Patterns of Implementation The success of students in the high- achieving school was due in part to the high cognitive demand of the curriculum and the teachers’ ability to maintain the level of demand during enactment through questioning. Boaler & Staples (2008)

14. Factors Associated with the Decline of High-Level Cognitive Demands Routinizing problematic aspects of the task Shifting the emphasis from meaning, concepts, or understanding to the correctness or completeness of the answer Providing insufficient time to wrestle with the demanding aspects of the task or so much time that students drift into off-task behavior Engaging in high-level cognitive activities is prevented due to classroom management problems Selecting a task that is inappropriate for a given group of students Failing to hold students accountable for high-level products or processes Stein, Grover & Henningsen, 1996

15. Factors Associated with the Maintenance of High-Level Cognitive Demands Scaffolding of student thinking and reasoning Providing a means by which students can monitor their own progress Modeling of high-level performance by teacher or capable students Pressing for justifications, explanations, and/or meaning through questioning, comments, and/or feedback Selecting tasks that build on students’ prior knowledge Drawing frequent conceptual connections Providing sufficient time to explore

16. Math Terms 14/16 1/3 3/4 6/12 1 6 5 3 2 7 4

17. I shot an arrow into the air, it fell to the earth I know not where... Obviously this person did not study ALGEBRA ! !

18. Cycle of Effective Instruction--SAS

19. Marzano’s Problem Solving Model Provide students a direction for learning and link their learning goal to the Keystone Anchors and the SAS framework. Provide students with an opportunity to personalize their goals. –I already know –I want to know

20. Essential Questions --SAS How do quadratic equations and their graphs and tables help us interpret events that occur in the world? How do you explain the benefits of multiple methods of representing polynomial functions (tables, graphs, equations, and contextual situations)?

21. Competencies--SAS Represent a quadratic function in multiple ways, including tables, graphs, equations, and contextual situations, and make connections among representations; Relate the solutions of the associated equation to each representation.

22. Task Selection Selecting tasks that build on students’ prior knowledge. Knowledge Connectors –Warm ups –Graphic organizers –Notes

23. Real Math and Real Numbers A Classic Math Problem

24. The Path of a Baseball—Do the Math

25. Maintenance of High-Level Cognitive Demands Modeling of high-level performance by teacher or capable students. Pressing for justifications, explanations, and/or meaning through questioning, comments, and/or feedback

26. Monitoring Progress Providing a means by which students can monitor their own progress Monitoring examples –Self/Peers –Exit tickets –Rubrics –Homework/Notes

27. Aligned Instruction -- SAS Teaching topics that are aligned with the standards. Ensuring the right level of challenge. Focusing teaching based on the learning needs of each student. Implementing instructional strategies to increase student achievement.

28. Keystone Anchors

29. Conclusion Not all tasks are created equal -- they provided different opportunities for students to learn mathematics. High level tasks are the most difficult to carry out in a consistent manner. Engagement in cognitively challenging mathematical tasks leads to the greatest learning gains for students. http://www.youtube.com/watch?v=lulUvYfRl_c&fe ature=relatedhttp://www.youtube.com/watch?v=lulUvYfRl_c&fe ature=related

30. Reflection