1. Coaching Cadre Breathitt/Jackson/Estill April 10, 2013 Jennifer McDaniel Jennifer.mcdaniel@clay.kyschools.us

2. Instruction Guiding Question What factors promote (or discourage) students’ involvement in thinking about and developing an understanding of content?

3. Motivation in the Math Classroom In pairs discuss: ◦ What, ideally, does student involvement in learning mathematics look and feel like from…  your perspective as a teacher?  the perspective of your students?

4. Research on Motivation “Involvement” is more than being physically on-task ◦ Focused concentration and care about things making sense ◦ Intrinsically motivated to persist ◦ Cognitively engaged and challenged Two areas of focus: ◦ Cognitive Demand of Mathematical Tasks ◦ Discourse Strategies References Henningsen & Stein (1997). Mathematical tasks and student cognition. Journal for Research in Mathematics Education, 28(5), 524-549. Turner et al. (1998). Creating contexts for involvement in mathematics. Journal of Educational Psychology, 90(4), 730-745.

5. Mathematical Tasks What is cognitive demand? ◦ Focus is on the sort of student thinking required. Kinds of thinking required: ◦ Memorization ◦ Procedures without Connections  Requires little or no understanding of concepts or relationships. ◦ Procedures with Connections  Requires some understanding of the “how” or “why” of the procedure. ◦ Doing Mathematics Lower level Higher level

6. Examples of Mathematical Tasks (1) Memorization Which of these shows the identity property of multiplication? A) a x b = b x a B) a x 1 = a C) a + 0 = a Procedures without Connections Write and solve a proportion for each of these: A) 17 is what percent of 68? B) 21 is 30% of what number? Too much of a focus on lower level tasks discourages student “involvement” in learning mathematics.

7. Examples of Mathematical Tasks (2) Procedures with Connections Solve by factoring: x 2 – 7x + 12 = 0 Explain how the factors of the equation relate to the roots of the equation. Use this information to draw a sketch of the graph of the function f(x) = x 2 – 7x + 12. Doing Mathematics Describe a situation that could be modeled with the equation y = 2x + 5, then make a graph to represent the model. Explain how the situation, equation, and graph are interrelated. Higher level tasks, when well-implemented, promote “involvement” in learning mathematics.

8. Characteristics of Higher-Level Mathematical Tasks Higher-level tasks require students to …  do more than computation.  extend prior knowledge to explore unfamiliar tasks and situations.  use a variety of means (models, drawings, graphs, concrete materials, etc … ) to represent phenomena.  look for patterns and relationships and check their results against existing knowledge.  make predictions, estimations and/or hypotheses and devise means for testing them.  demonstrate and deepen their understanding of mathematical concepts and relationships.

9. Recall: The Border Problem 1.Without counting 1-by-1 and without writing anything down, calculate the number of shaded squares in the 10 by 10 grid shown. 2.Determine a general rule for finding the number of shaded squares in any similar n by n grid.

10. Talk Partners Discuss with your “talk partner” examples of students “Doing Mathematics” within your classroom, grade level, or school setting. Be prepared to share with the entire group.

11. Discourse Strategies (less involvement): I-R-E Initiation-Response-Evaluation (I-R-E) ◦ Ask a known-answer question ◦ Evaluate a student response as right or wrong ◦ Minimize student interaction through prescribed “turn taking” ◦ Establish the authority of the text and teacher Examples ◦ What is the answer to #5? ◦ What are you supposed to do next? ◦ What is the reciprocal of 3/5? 5/3. Very good! ◦ That is exactly what the book says.

12. Discourse Strategies (less involvement): Procedures Procedures ◦ Give directions ◦ Implement procedures ◦ Tell students how to think and act Examples ◦ Listen to what I say and write it down. ◦ Take out your books and turn to page 45.

13. Discourse Strategies (less involvement): Extrinsic Support Extrinsic Support ◦ Superficial statements of praise (focus is not on the learning goals and objectives) ◦ Threats to gain compliance Examples ◦ You have such neat handwriting. ◦ These scores are terrible. I was really shocked. ◦ If you don’t finish up you will stay after class.

14. Discourse Strategies (more involvement): Intrinsic Support Intrinsic Support ◦ View challenge/risk taking as desirable ◦ Respond to errors constructively ◦ Comment on students’ progress toward the learning goals and objectives ◦ Evoke students’ curiosity and interest Examples ◦ That's great! Do you see what she did for #5? ◦ This may seem difficult, but if you stay with it you'll figure it out. ◦ Good. You figured out the y-intercept. How might we determine the slope here?

15. Discourse Strategies (more involvement): Negotiation Negotiation ◦ Adjust instruction in response to students ◦ Model strategies students might use ◦ Guide students to deeper understanding Examples ◦ What information is needed to solve this problem? ◦ Try to break the problem into smaller parts. ◦ Here is an example of how I might approach a similar problem.

16. Discourse Strategies (more involvement): Transfer Responsibility Transfer responsibility ◦ Support development of strategic thinking ◦ Encourage autonomous learning ◦ Hold students accountable for understanding Examples ◦ Explain the strategy you used to get that answer. ◦ You need to have a rule to justify your statement. ◦ Why does Norma’s method work?

17. Talk Partners Discuss with your “talk partner” methods of encouraging “math talk” or student discourse in your classroom, grade level, or school setting. Please be prepared to share with the entire group.

18. Effective Questioning

19. How do we expect students to answer questions? http://www.youtube.com/w atch?v=Boxsh_onY5E http://www.youtube.com/w atch?v=Boxsh_onY5E 19

20. How can quality questioning transform Classrooms? Reference for all slides in power point: Quality Questioning: Research-Based Practice to Engage Every Learner (Jackie Acree Walsh & Beth Dankert Sattes)

21. Focus Questions How can effective questioning help transform a traditional, teacher-centered classroom into a student-centered, inquiry- oriented community of learners? What are the connections between quality questions and student learning and achievement? Why are there gaps between what we know about effective questioning and what we do in classrooms?

22. How many questions do- Teachers ask in a 30 minute period? Students ask in a 30 minute period? Teachers estimated they would ask 15 questions and that 15 would be the desired rate. Teachers estimated that their students were asking about 10 questions, which would be below their desired target of 15. Actual observations : Teachers asked an average of 50.6 questions and their students posed only 1.8 questions!

23. Research about Current Practice and Implications for Change 1. Teachers ask many questions. 2. Most teacher questions are at the lowest cognitive level- known as fact, recall, or knowledge. 3. Not all students are accountable to respond to all questions. Teachers frequently call on volunteers, and these volunteers constitute a select group of students. 4. Teachers typically wait less than one second after asking a question before calling on a student to answer(wait time 1). They wait even less time (usually 0 seconds) before speaking after a student has answered (wait time 2). 5. Teachers often accept incorrect answers without probing; they frequently answer their own questions. 6. Students ask very few content-related questions.

24. What does effective questioning look like in the classroom?

25. Students asking Questions Teachers take up to two-thirds of the classroom talk time. Students are “talk-deprived ” (Alvermann et al., 1996) Student discussion increase retention as much as 50%. (Sousa, 2001) 25

26. What does effective questioning look like in the classroom?

27. Questioning Norms Examples of Questioning Norms: We all need time to reflect on past experiences if we are to gain new understandings. We all need time to think before speaking We all need time to think out loud and complete our thoughts. We learn best when we formulate and answer our own questions. We learn from one another when we listen with attention and respect. When we share talk time, we demonstrate respect, and we learn from one another.

28. Take Home Message There is a gap between best practice and current practice when it comes to “questioning”. Teachers seem to know what constitutes “best practice” but we aren’t always good monitors of our own performance.

29. Questions for Reflection

30. “The important thing is to not stop questioning.” -Albert Einstein

31. From CHETL TO TPGES CHETL 1) Learning Climate 2) Classroom Assessment and Student Reflection 3) Instructional Rigor and Student Engagement 4) Instructional Relevance 5) Content Knowledge TPGES 1) Planning and Preparation 2) Classroom Environment 3) Instruction 4) Professional Responsibilities 5) Student Growth (For Consideration)

32. Reflecting on Instructional Practices: 1. How you can strengthen the ways student involvement and motivation are promoted and supported in your classes? 1. Write 3-5 statements about specific strategies you’d like to work to improve. Examples: ◦ “I give students tasks that require them to think about mathematical relationships and concepts.” ◦ “I provide feedback to students that promotes further thinking and improved understanding.” ◦ “I allow opportunities for students to be an authority in mathematics.” 2. Identify where you are now and where you want to be.

33. http://www.jennyray.net/tpges- resources.html www.reneeyates2math.com http://www.jennyray.net/tpges- resources.html www.reneeyates2math.com CHETL & TPGES RESOURCES

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35. Habits Are Hard to Break A teacher with 20 years of experience will have asked something like 1.2 million questions in her career. And when you’ve done something the same way, over a million times, it’s quite difficult to start doing it another way. Wiliam (2003) 35

36. Random thoughts Random thoughts Whether the students are working independently or working in small groups, effective questioning can take the class to new heights. Take time to allow students to “think” and formulate responses. The goal is for students to generate content related questions instead of all questions coming from the teacher. Often, questioning reveals student misconceptions. We want all students to feel comfortable demonstrating their level of understanding and develop the ability to formulate their own questions to guide their learning. We need a classroom climate that fosters the idea that there may be more than one way to solve a problem and we all have something to offer when it comes to the class discussion. Even if a student is “incorrect”, important misconceptions can be uncovered and discussed. It is powerful when these conversations are student driven.

37. Observation Plan Yates form Administration Peer-to-Peer Connections to TPGES

38. Reasons for student disengagement from classroom questioning: Teachers do not require engagement. There is no intrinsic pressure to be engaged because of the disconnect between the student’s world and classroom curriculum. Fear; students do not want to take risks in front of peers and the teacher. Goal is to just “get through” school, and the easiest path is to just show up and go through the motions. How can I become a better questioner?

39. Working in groups of 3, prepare one ‘power point slide’/question with answers/suggestions for each of the following: How can we convince all students that their answers matter to us? How can we engage all students in coming up with their own answers to each of our questions? How can we promote equitable participation of all students in classroom questioning? How can I become a better questioner?

40. What one word sums up what you have learned about effective questioning? What are 1 to 3 things with respect to effective questioning that you will do differently/better this school year? Enter a reminder in the calendar on your phone. Set the alarm to remind you! How can I become a better questioner?

41. “The important thing is to not stop questioning.” -Albert Einstein

42. Assessment Formative Assessment Tasks www.mathshell.org www.mathshell.org

43. What are FAL’s? Lessons designed to move students away from simply getting the answers and toward learning the mathematics that they need to solve the problem. Formative Assessment Lessons

44. Clarifying and sharing learning intentions and criteria for success Engineering effective discussion, questions, activities, and tasks that elicit evidence of learning Providing feedback that moves students forward Activating students as instructional resources for one another Activating students as owners of their own learning 5 Strategies of Formative Assessment

45. Completed 2/3 of the way through a unit. Completely scripted (They are not intended to be changed.) Students are grouped according to pretest/misconceptions or by ability Most take 2-3 days Scaffold learning (all students are expected to show growth, but do not all reach the same level of understanding) Key Characteristics of a FAL

46. Problem Solving Concept Development Types of a FAL

47. Begins with a task Encourages students to formulate questions and reason logically Given sample student work showing different approaches with mistakes Critique and improve the work Revise their original approach or change it Communicates and reflects on results Video http://map.mathshell.org/static/draft/pd/modules/3_Problem_Solving/html/video s_d1.htm http://map.mathshell.org/static/draft/pd/modules/3_Problem_Solving/html/video s_d1.htm Problem Solving Characteristics

48. Begins with a task or pre-assessment Students are exposed to feedback questions Involved in a learning activity (small group) Class discussion (whole group) Post-Test to measure growth Video http://map.mathshell.org/static/draft/pd/modules/2_Concept_Lessons/html/videos_e1.ht m Concept Development Characteristics

49. Work through the FAL as a student to make sure it fits Complete the pre-assessment 2-3 days prior to completing the activity Use results to group kids according to misconceptions Meet as a math team to develop feedback questions based on pre-assessments Process of a FAL

50. Frame the lesson Students complete the process according to script -individual -collaborative -whole group Post-assessment/reflection Teacher uses results to guide instruction for the remainder of the unit Process of a FAL cont’d.

51. MAP Assessment Task Types The task types indicate the breadth and depth of CCSS mathematical practices assessed by the task. Novice tasks involve only MP2 and MP6 and do so at a low level. Apprentice tasks add MP3 and MP7 but, because of the guidance within the task, do so at a comparatively modest level. Expert tasks aim to cover the full range of practices.

52. 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning Mathematical Practices

53. Activity Card Sort Mathematical Practices

54. How did we do How did we do SMP-1. D SMP-2. H SMP-3. A SMP-4. E SMP-5. B SMP-6. F SMP-7. C SMP-8. G

55. Curriculum Integrating FAL Lessons and Tasks Where are you now? Where would you like to be? What might be some strategies to close the gap?

56. Reflections IMPACT Goals Observation Plans Goals for upcoming year

57. IMPACT Goals I (Instruction)-Learn about effective strategies and activities for you classroom M (Mathematics)- Strengthen and expand your subject area expertise P (Problem Solving)-Explore and create tasks to help students become better critical and creative thinkers A (Assessment)- Experience and discuss effective uses of formative and summative assessment C (Content)-Identify and align resources designed to satisfy content requirements T (Technology)- Gain hands-on experience using technology as a tool for teaching and learning mathematics.

58. Observation Plan Yates form Administration Peer-to-Peer Connections to TPGES