Mathematics Teachers Kindergarten – Grade 2

1. Mathematics TeachersKindergarten – Grade 2 Joy Donlin & Ryan Dunn October 7, 2013

2. Agenda • Welcome and introductions • Discussion – how do students learn mathematics? • Exploring the paradigm shift • Participating in a lesson that meets the shift • Translating the standards • Designing a lesson • Reflections

3. Outcomes Participants will consider their educational platform. Participants will increase their knowledge and understanding of Operations and Algebraic Thinking and the Standards for Mathematical Practice in the CCSSM . Participants will apply their knowledge and understanding to develop a lesson.

4. Design Methodology

5. College and Career Readiness

6. Common Core Standards Framework Curriculum Assessment Equity Teaching & Learning

7. Content Focus Areas

8. Race to ‘0’ This is a 2 player game. The idea of the game is to be the person that lands on zero. You begin at the number 10 Each turn you can choose to go back by 1 or 2.

9. Race to ‘0’ • What are some questions we could ask to prompt students to think more deeply about this game? • Is this a rigorous activity to undertake with kindergarten students?

10. Race to ‘0’ Some questions to prompt deeper thinking: • Is there a strategy that can help you win the game? • Are there numbers along the way that can help you land on zero? (powerful numbers)

11. What are some variations… How would the game change if we: • Started at 12 or 15 • Raced from 0 to 10 • Could move by 1, 2 or 3

12. 5 Minute Brainstorm… Why do you think it is so common for students (and adults) to talk about mathematics as being hard? • 2 minutes to discuss this with the person next you. • 3 minutes to share thoughts with your table.

13. Make a list of the top 5 things that support elementary students in learning mathematics. Rank them from 1 to 5.

14. Share your #1’s with a neighbor. • Are your #1’s the same?

15. How do children learn mathematics? There are two major theories on how children think and learn: • Behaviorism – has long been associated with mathematics learning. • Constructivism – has been shown to promote meaningful learning.

16. Behaviorism • Has roots in stimulus response and conditioned learning. • Asserts that behavior can be shaped through rewards and punishment. • Focus on low level thinking, not mathematical thinking.

17. Behaviorism… Behaviorism has had a significant impact on mathematics programs: • Students are shown algorithms. • Mathematical relationships are illustrated in textbooks. • Produces mastery of specific objectives but lacks critical connections that make knowledge meaningful and useful

18. Constructivism Constructivism advocates that: • Knowledge is not passively received, but actively constructed by the learner. • The learner uses prior knowledge to construct new meaning (Piaget). • Learning is a social process (Vygotsky)

19. What is your Educational Platform? • Think back to your list of top 5 things that support elementary students to learn mathematics. • Is there evidence of Behaviorism and/or Constructivism on your list?

20. CCSS for Mathematics Paradigm Shift Mathematics learning that goes beyond the demonstration of procedural content by: • providing extensive opportunities to reason and make sense of the mathematics students are learning • emphasizing student understanding, problem solving and sense making • developing deep understanding of content and use of conceptual understanding as a precursor to developing procedural or symbolic fluency.

21. Standards for Mathematical Practice L Legend • Make sense of problems and persevere in solving them • 6. Attend to precision 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others Reasoning & Explaining Modeling & Using Tools • Model with mathematics • Use appropriate tools strategically Seeing Structure & Generalizing Overarching Habits of Mind of a Productive Mathematical Thinker 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

22. SCUSD SMP Emphasis - 2012-2013 SMP 1,4,6 - 2013-2014 SMP 2,3,7

23. Break

24. Choose a playing card from the materials bag. 1 – Student 2 – Observer for SMP 3 – Observer for use of teacher moves/ questioning strategies 4 - Observer for use of formative assessment

25. Lesson Grade 1 OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Grade 2 OA.2 Fluently add and subtract within 20 using mental strategies.By end of Grade 2, know from memory all sums of two one-digit numbers.

26. Number Tiles The Task Using only the numbers 3, 4, 5, 6, 7. Place any 4 numbers into the frame below to make a true equation. Try to find other solutions. ___ + ___ - ___ = ___

27. Deepening the Investigation • How many solutions do you think there are? • How would you know when you have found them all? • What do we notice from the solutions we have already found?

28. Applying the Knowledge • How could students apply the mathematical knowledge from this investigation?

29. Deepening the Learning For the original problem, the tiles are consecutive starting at 3. What happens if you use five consecutive numbers beginning with a different number? (4, 5, 6, 7 and 8) Will there be the same number of solutions?

30. Debrief As a school team discuss the following: • Describe what the student(s) know, understand and are able to do based on your role during the lesson and provide evidence to support your answer. • Describe the implications for instructional design of a mathematics lesson.

31. LUNCH

32. Arithmagons Try these as a warm up after the lunch break. Given the numbers on the edges try to work out the numbers in the vertices. Here is an example:

33. Try these…

34. Honoring the CCSSM 3 Big Ideas: • Read • Translate • Design Units and Learning Activities Wiggins, 2011

35. Unpacking the Standards Domain: Operations and Algebraic Thinking Kindergarten: 1 Cluster Grade 1: 4 Clusters Grade 2: 3 clusters

36. Taking It Back As the grade level/band teacher leader at your school, you will have a role: • As the content expert • As a content pedagogy expert • As the leader of collaborative planning – units of study and lesson design • As the leader of peer observation experiences • As the lead learner and sharer of information

37. “you can’t lead where you won’t go” Barth, 2002

38. Lesson Design In a lesson that you will be teaching in the next week, will my students be experiencing a similar kind of learning? Work with a colleagues to adjust your lesson design as necessary for the following: • How will the problem/task or activity provide students the opportunity to engage in the Standards for Mathematical Practice? • How/when will students make sense of problems and persevere in solving them? • How/when will students be reasoning abstractly and quantitatively? • How/when will students be explaining their thinking to each other? • How/when will students be critiquing the reasoning/thinking of others? • How/when will students be modeling with mathematics? • How/when will students be attending to precision? • How/when will students be looking for and making use of the structure of the lesson content? Be prepared to share the lesson with another grade level team and your school team.

39. Receiving feedback • Share the lesson(s) with another grade level team. • Share the lesson(s) with your school team.

40. Reflection

41. Reflection Questionnaire • Enter the following link and complete the online questionnaire: https://www.surveymonkey.com/s/TYP8ZMG

42. “Professional development works, if it works at all, by influencing what teachers do . . .” Instructional Rounds in Education, pg. 24.