1. Teachers You Remember Who made an impact on you? Why do you remember them?

2. Math Engagement Creating a Student-Centered Classroom! Henrico County Public Schools August 2012

3.  What is your name?  Where do you teach? 3 Introductions

4. Our Goals  Learning about different instructional methods to create a student-centered classroom.  Examining practices for maintaining productive mathematics discussions.

5. What is your definition of a “problem”?  A question to be considered, solved, or answered.  A situation, matter, or person that presents perplexity or difficulty.  If students know the answer, it is practice.

6. What is our goal as mathematics teachers?  Teach kids how to use their critical thinking and reasoning skills to adapt and overcome in unfamiliar settings.  What will tomorrow’s jobs look like?

7. Do we over teach to our students?

8. No Pain, No Gain  Pertains to learning mathematics as well  Let kids struggle to make sense of the mathematics

9. Problem/Project Based Learning Simpson Park  Work individually at first.  When told, discuss with elbow partners. What questions arise in your conversation?

10.  Does the problem challenge students to use higher-level critical thinking skills?  Are there multiple ways to solve this problem?  Is it accessible to all students? Is this a practical and worthwhile task?

11.  What might students struggle with?  Does the problem promote mathematical communication?  This would be an appropriate problem if you were studying… or if you have already studied… Is this a practical and worthwhile task?

12.  In what situation would this task be used?  In which grade level would you use this task?  How would you adjust it for another grade level? Is this a practical and worthwhile task?

13. What kind of learning experiences will prepare students for the 21 st century?  Research tells us that complex knowledge and skills are learned through social interaction.  This is difficult to do in the classroom daily due to curricular demands. The key is to maintain the right balance.

14. Productive Classroom Discussions  How do you make student-centered instruction more manageable?  Creating discussion-based opportunities for student learning will require learning on the part of many teachers. 1.Identify cognitively challenging instructional tasks (Setting Goals for Instruction). 2.Support students as they engage and discuss their solutions (Select Appropriate Tasks).

15. Lesson Structure To foster reasoning and communication focused on a rich mathematical task, use a 3-part lesson structure: 1.Individual thinking (preliminary brainstorming) 2.Small group discussion (idea development) 3.Whole class discussion (idea refinement)

16. Organizing High-Level Discussions: 5 Habits Prior to the lesson, 1.Anticipate student strategies and responses to the task Key Instructional Questions (for the teacher)  What might students struggle with?  What are common misconceptions?

17. While students are working, 2.Monitor their progress, 3.Select students to present their work, and 4.Sequence the presentations to maximize discussion goals Organizing High-Level Discussions: 5 Habits

18. Key Instructional Questions (for the teacher) while students are working  If a student is struggling, what are good questions to ask?  Am I soliciting multiple solutions from students?  How is the students’ work informing my lesson planning? Organizing High-Level Discussions: 5 Habits

19. During the discussion, 5.Ask questions that help students connect the presented ideas to one another and to key mathematical ideas More on 5 Habits can be found in: “Orchestrating Discussions” by Smith, Hughes, Engle, & Stein in Mathematics Teaching in the Middle School, May 2009 Organizing High-Level Discussions: 5 Habits

20. Practicing: Anticipate Work on the following geometry task and think about possible student strategies/solutions: Triangle ABC has interior angle C measuring 105°. The segment opposite angle C has a measure of 23 cm. Describe the range of values for the measures of the other sides and angles of triangle ABC. Explain your reasoning. 20

21. Practicing: Select and Sequence Let the provided samples work on the triangle task represent the work your students observed while monitoring their work. 1.Select 4 to 5 students who you would call on to present their work. 2.Sequence these students to optimize the class discussion of this task. 21

22. Practicing: Connecting For the student work you selected and sequenced, 3.Identify connections within that work that you would hope to highlight during the class discussion. See file TriangleProblem.gsp for model of triangle activity in Sketchpad. 22

23. Thinking About Implementation  In order for students to reason about and communicate mathematical ideas, they must be engaged with high cognitive demand tasks that enable practice of these skills.  BUT! … simply selecting and using high- level tasks is not enough.  Teachers need to be vigilant during the lesson to ensure that students’ engagement with the task continues to be at a high level. 23

24. Factors Associated with Lowering High-level Demands  Shifting emphasis from meaning, concepts, or understanding to the correctness or completeness of the answer  Providing insufficient or too much time to wrestle with the mathematical task  Letting classroom management problems interfere with engagement in mathematical tasks  Providing inappropriate tasks to a given group of students  Failing to hold students accountable for high- level products or processes

25. Factors Associated with Promoting High-level Demands  Scaffolding of student thinking and reasoning  Providing ways/means by which students can monitor/guide their own progress  Modeling high-level performance  Requiring justification and explanation through questioning and feedback  Selecting tasks that build on students’ prior knowledge and provide multiple access points  Providing sufficient time to explore tasks

27. Revisiting Simpson Park SOL 8.10 – The student will a) verify the Pythagorean theorem b) apply the Pythagorean theorem From a planning perspective, is this sufficient? Teachers need to examine the Curriculum Framework! Solve practical problems involving right triangles by using the Pythagorean theorem.

28. Is this a high level task? A 12-foot ladder is leaning against a brick wall. The top of the ladder meets the wall 10 feet off of the ground. How far is the bottom of the ladder away from the base of the wall? Think about the Task Analysis Guide from the Math Assessment session.

29. Blended Learning  Refers to mixing different learning environments.  Combines traditional face-to-face classroom methods with computer-mediated activities.  The flipped classroom is a form of blended learning.

30. Project Based Learning article Getting Started with Project-Based Learning (Hint: Don't Go Crazy)  http://www.edutopia.org/blog/project-based- learning-getting-started-basics-andrew-miller http://www.edutopia.org/blog/project-based- learning-getting-started-basics-andrew-miller

31. Flipped Classroom Pete Anderson’s website:  http://geometryonline.pbworks.com/w/page/5 4592258/Purdue%20University http://geometryonline.pbworks.com/w/page/5 4592258/Purdue%20University

32. Performance Task Ideas (some aligned to Common Core Standards)  Project Based Learning - http://www.bie.org/http://www.bie.org/  Math Capstone Course - https://sites.google.com/site/mathematicscapstonecourseunits/ home/ https://sites.google.com/site/mathematicscapstonecourseunits/ home/  Smarter Balanced Assessment Consortium - http://www.smarterbalanced.org/ http://www.smarterbalanced.org/  Illustrative Math Project - http://illustrativemathematics.org/http://illustrativemathematics.org/  Calculation Nation - http://calculationnation.nctm.org/http://calculationnation.nctm.org/  Minnesota STEM - http://www.scimathmn.org/stemtc/http://www.scimathmn.org/stemtc/  Learn Zillion - http://learnzillion.com/http://learnzillion.com/

34. PBL Creation  Pete’s examples – 4 D’s

35. Tiling a Patio  See handout.

36. Math Rigor, Assessments & Engagement  Five goals – for students to become mathematical problem solvers that communicate mathematically; reason mathematically; make mathematical connections; and use mathematical representations to model and interpret practical situations 36

37. Narrowing Achievement Gaps  Ask high-level questions of all students  Consistently provide multiple representations  Facilitate connections  Solicit multiple student solutions  Engage students in the learning process

38. Narrowing Achievement Gaps  Promote mathematical communication  Listen carefully to your students’ words and learn from them  Provide “immediate” feedback on all work  Give students challenging but accessible tasks

39. Real-World Problems + Group Learning = A.P. Calculus Success  Bridging the Achievement Gap  http://www.nytimes.com/schoolbook/2012/07 /30/real-world-problems-group-learning-a-p- calculus-success/ http://www.nytimes.com/schoolbook/2012/07 /30/real-world-problems-group-learning-a-p- calculus-success/

40. No Pain, No Gain  If you are more tired than the kids, it’s not because you are old  Make kids estimate/predict and think before calculating  Don’t ask questions that solicit one word answers  Let kids struggle to make sense of the mathematics 40

41. Key Messages  We must not solely focus on multiple-choice assessments  We must provide students with rich, relevant, and rigorous tasks that focus on more than one specific skill and require application and synthesis of mathematical knowledge  We must connect mathematics content within and among grade levels and subject areas to facilitate long term retention and application  We must reflect on our own teaching and resist the urge to blame students

42. 42 Be the teacher that makes students remember you. Closing Thought