Improving Math Achievement Through Engagement, Exploration, and Response

1. Improving Math Achievement Through Engagement, Exploration, and Response Presented by: Ms. Kimberly Strand & Ms. Timberly Walton

2. Objectives/Outcomes • Participants will deepen their understanding of mathematics discourse, including some background and rationale. • Participants will experience Number Talks and consider how they might be used as part of a daily routine. • Participants will deepen their understanding of how mental math, computation strategies and justification of their thinking will impact their student’s achievement. • Participants will experience NIM games and consider how strategy games might be added as part of a daily routine. • Gain tools and strategies for incorporating mathematical writing in class.

3. Agenda Background and rationale Experience a variety of Number Talks Consider implications for implementation of mathematics discourse. NIM games and use of manipulatives. Writing in Math Menu Items Closing

4. Entrance Ticket What effective teaching strategies in mathematics have you implemented in your classroom that have had a positive impact on your students achievement? How do you as an educator currently incorporate writing in mathematics to bridge the gap between the math standards and their achievement?

5. Ice Breaker – Digit Place Guess my number! It’s a 3 digit number! There are no repeated digits! Explain your reasoning behind choosing your 3 digit number.

6. Looking at Mathematics! Our goal as educators is to help students to become confident and competent in mathematics. We strive to create a classroom environment that encourages students to think critically about math in a variety of situations. As students explain their thinking to others, they self-correct and clarify their ideas leading to a deeper understanding of underlying mathematical concepts. Accuracy and the development of efficient problem-solving strategies are essential to student’s learning. The ability to solve problems many different ways and to understand the connections between mathematical ideas is equally important. As children learn to question, reconsider and justify solutions they become more confident in their own abilities as mathematicians.

7. Why Talk About Math? “ Our classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules.” Articles: “How to Get Students Talking! Generating Math Talk That Supports Math Learning” by: Lisa Ann de Garcia http://www.mathsolutions.com/documents/how_to_get_students_talking.pdf “Number Talks Build Numerical Reasoning” by: Sherry Parrish(nctm.org) https://www.youtube.com/watch?v=twGipANcIqg

8. What are Number Talks? Classroom conversations and discussions around purposefully crafted computation problems are at the very core of number talks. Number Talks incorporate: Accuracy: The ability to produce an accurate answer. Efficiency: The ability to choose an appropriate, expedient strategy for a specific computation problem. Flexibility: The ability to use number relationships with ease in computation.

9. Number Talks Number talks were developed for classroom teachers to engage students in “mental math” through grappling with interesting mathematics problems. Number talks is a pivotal vehicle for developing efficient, flexible and accurate computation strategies that build upon the key foundational ideas of mathematics such as composition and decomposition of numbers, our system of tens, and the application of properties. Accuracy denotes the ability to produce an accurate answer; efficiency refers to the ability to choose an appropriate, expedient strategy for a specific computation problem; and flexibility means the ability to use number relationships with ease in computation.

10. Key Components of Number Talks • Classroom Environment and Community • Building a cohesive classroom community is essential for creating a safe risk free environment for effective number talks. • Classroom Discussions • Students are given the opportunity to share their strategies and justifications with their peers. • The Teacher’s Role • Facilitator, questioner, listener, learner, and scriber. • The Role of Mental Math • Encourages students to build on number relationships to solve problems instead of relying on memorized procedures. • Purposeful Computation Problems • Guides students to focus on mathematical relationships to build mathematical understanding and knowledge.

11. Classroom Environment and Community Safe, risk-free environment Students comfortable and offer responses for discussion Classroom exhibits a culture of acceptance based on the common goal of learning and understanding Community of learners based on mutual respect

12. Benefits of Sharing and Discussing Computation Strategies • Students have the opportunity to: • Clarify their own thinking • Consider and test other strategies to see if they are mathematically logical. • Investigate and apply mathematical relationships. • Build a repertoire of efficient strategies. • Make decisions about choosing efficient strategies for specific problems.

13. The Teacher’s Role “Since the heart of number talks is classroom conversations, it is appropriate for the teacher to move into the role of facilitator.” Teachers must change their thinking from concentrating on the final correct answer, to listening and learning about students’ natural thinking through asking open ended questions. “What answer did you get?” “How did you get your answer?”

14. The Role of Mental Math Students need to approach problems without paper and pencil, and are encouraged to rely on what they know and understand about numbers and how they are related. Mental computation helps students strengthen their understanding of place value.

15. Mathematical Thinking • Counting All • Counting On • Known Facts • Derived Facts • Decomposing • Recomposing Duality, Ambiguity, and Flexibility in Successful Mathematical Thinking Research by Eddie Gray and David Tall, 1994

16. Purposeful Computation Problems Careful planning BEFORE the number talk is necessary to design “just right” problems for students. This planning is important because we want to have a purposeful number talk with a common focus/specific skill in mind.

17. Establishing Procedures and Setting Expectations: The Four Essentials The number talk is designed to be only five to fifteen minutes of focused discussion. Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions. Provide appropriate wait time for the majority of the students to access the problem. Accept, reject, and consider all answers. Encourage student communication throughout the number talk.

18. Number Talks and Time Number Talks (about 10 minutes) Mini-Lesson (10 to 20 minutes) Lesson (more than 20 minutes)

19. Understanding Math Discourse • Talk Formats • Whole-Class Discussion • Small-Group Discussions • Partner Talks Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

20. Number Talk Examples • Dot Patterns • Mental Math • Number Strings • True/False Statements • Dilemmas • Spatial Reasoning • What’s My Rule? • Error Analysis and Coaching

21. Holding Students Accountable for their Learning Ask students to use finger signals to indicate the most efficient strategy. Keep records of problems posed in the corresponding student strategies. Hold small-group number talks every day. Create and post class strategy charts. (living document) Require students to solve an exit problem using the discussed strategies. (use an index card) Give a weekly computation assessment.

22. Four Goals for K-2 Number Talks Developing Number Sense Developing fluency with small numbers Subitizing Making Fives and Tens Number Conservation Number Talks -Sherry Parrish

23. Five Goals for Number Talks 3-5 Number sense Place value Fluency Properties Connecting mathematical ideas

24. Hand Signals • Solution • Strategy • Question • Comment • I agree • Integers • Fractions

25. Number Talks in Action Video http://www.insidemathematics.org/classroom-videos/number-talks/5th-6th-grade-math-guess-my-rule/number-talk-part-1

26. Experience a Number Talk Now you will be participating in a number talk.

27. NIM Games NIM is a mathematical game of logic and strategy. There is a winning strategy and all the moves can be analyzed mathematically. Current NIM Games: Dominoes, Connect4, and Solitaire. Can you find the winning strategies?

28. Other NIM Games • Game of 21 • The game "21" is played with two players who take turns saying a number. The first player says "1" and each player in turn increases the number by 1, 2, or 3, but may not exceed 21; the player forced to say "21" loses. This can be modeled as a subtraction game with a heap of 21–n objects. • Game of 100 • A similar version is the "100 game": two players start from 0 and alternatively add a number from 1 to 10 to the sum. The player who reaches 100 wins. • Balloon Ride • The goal of the NIM is to be the player who removes the last of the ten objects from the table. A player must remove one or two objects during their turn. The player who removes the last object wines. • Oddly • This game always starts with an odd number of counters and they can be arranged in any number of piles. The players in turn take any number of counters from a single pile. The winner is the player who ends up with an odd number of counters.

29. NIM Games – Let’s Play NIM 21 SNAP Balloon Ride

30. Use of Manipulativesfor Problem Solving Building on the learning theory work of Piaget and Bruner, a solid history of research supports the regular use of manipulatives in classroom mathematics instruction. While children can remember, for short periods of time, information taught through books and lectures, deep understanding and the ability to apply learning to new situations requires conceptual understanding that is grounded in direct experience with concrete objects. It is also important to note the critical role of the teacher in helping students connect their manipulative experiences, through a variety of representations, to essential abstract mathematics. National Council of Supervisors of Mathematics (2013). Improving student achievement in mathematics by using manipulatives with classroom instruction. Denver, CO: Author.

31. Let’s try it

32. Writing is Essential in Mathematics • Why write in math class?

33. Research says…

34. Quick Glance “Writing is nature’s way of letting us see how sloppy our thinking is” (Wolfe, 2001) Writing is essential in mathematics as it: • Increases and deepens content understanding • Helps Identify misconceptions • Improves lesson planning and delivery of instruction

35. What should math writing look like?

36. Types of Writing • Opinion:Support a choice. The writer must use evidence to clearly argue his/her opinion. • Content: Provide descriptive information about a topic. • K-2 The student uses mathematical (oral) language to express understanding by using words, sentence stems, and full sentences to express and label mathematical content. (progress) • 3-5 The writer must use vivid details to paint a picture for the reader. • Process: Explain the steps or procedures of something. • K-2 The student translates informal language to mathematical language and symbols. By developing summary statements. • 3-5 The writer must provide a clear coherent explanation of problem solving and procedure

37. Make sure your Math writing includes: • Complete response with mathematical notations. • Clear, coherent explanation. • Clear and labeled diagrams when used. • Shows understanding of the question • Identifies the elements of the question. • Includes examples and/or counter examples. • Combines words with symbols. • Uses correct mathematical notation • Provide details. • Submit neat work (AVID 2008, Lee 2010, Crannell 2008) “elegance in the writing is essential to how we see the subject” Dr. Vakil

38. Mathematical Writing Frequency * Provide students opportunities to use their notes during a test to encourage good note taking.

39. Vocabulary and Writing in Math Post the necessary vocabulary for a particular lesson, unit, problem—you decide. Model for the class the kind of writing you expect using precise vocabulary, diagrams, labels, etc. to explain a concept or skill.

40. Write an Explanation Marsha had 120 stamps. First she gave her sister half the stamps and then she used 3 stamps to mail some letters. How many stamps does Marsha have left? 1. What does the problem ask me to find? What do I know about this problem that will help me solve it? 2. What information does the problem give me? Do I need additional information.? 3. What strategy or operation will I use to solve this problem? 4. Does my answer make sense? Why or why not? If not, what will I do?

41. Write an explanation This problem wants to know how many stamps are left. This problem tells me how many stamps Marsha had to start with and it also tells me she gave half to her sister and used another 3 to mail letters. First I will figure out half of 120 which is 60. Then I have to subtract 3 more that Marsha used on letters. That is 60-3=57. This makes sense because 57 is a few less than half of the 120 stamps she started with.

42. R.U.M.O.R.S. At the Tasty Bakery, cupcakes cost fifty-cents each. Bagels cost a dollar twenty-five. How much more do two bagels cost than two cupcakes? Read the problem Underline question Mark information Operation/Strategy Recheck for reasonableness State what you did and why you did it

43. Centers with Math Stories Write a math story as a whole group. Use ideas of putting together, taking away, putting into groups of equal number, dividing equally, etc. Draw pictures to depict what is happening, highlighting vocabulary, number sentences, and ways to show in diagrams what is happening. Have them construct these at centers independently or in pairs.

44. Math Centers to Develop Arithmetic Understanding True or False? Task Open Sentences Task True, False, an Open Sentences Task Cuisenaire Rods - Zig Zag Fence Painting

45. Now for Menu Items - Centers Here is a fresh take-out, pun intended for math centers. Menu items. Create a menu for the students of activities for them to complete while in centers. Asterisks ones are a must do. All the activities support the current content being taught. Students are given a wide variety of activities to choose from which keeps them interested and motivated on the content and promotes mastery.

46. Menu Items – It’s Your Turn! Work with your group to complete the must do on the menu. Poster Station (must do) True False and Open Equations and Expressions Cuisenaire Rods/Zig-Zag Math Stories/Writing

47. Exit Slip: Taking a Look at your Own Practice What changes might you make in your math instruction based on the information you learned in today’s session on Number Talks, NIM Games and Math Centers? Things to think about: • Learning community in your classroom • Your role as the teacher • Questioning techniques • Use of models, tools and mathematical reasoning games to support student thinking • Addressing student wonderings.

48. Please Remember that… “Teachers incorporate writing in math class to help students reflect on their learning, deepen their understanding of important concepts by explaining and providing examples of those concepts, and make important connections to real-life applications of the math they are learning.” (Mathwire.com, 2013)