CFN 204 · Diane Foley · Network Leader Engaging Students in Productive Challenge December 9, 2013 Presenter: Simi Minhas Math Achievement Coach CFN204 1

CFN 204 · Diane Foley · Network Leader Research shows… Teachers spend a lot of your time helping students that do not understand a concept. This unfortunately takes time away from the bright students, who would benefit from an additional challenge. By providing students with rigorous word problems that are challenging, teachers can take their learning to the next level. The high performing students in the class can exercise their minds and learn in a collaborative learning group, while teachers continue to bring the rest of the class up to speed. 2

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CFN 204 · Diane Foley · Network Leader According to the National Council of Teachers of Mathematics Cooperative learning activities can be used to supplement textbook instruction by providing students with opportunities to practice newly introduced or to review skills and concepts. Teachers can use cooperative learning activities to help students make connections between the concrete and abstract level of instruction through peer interactions and carefully designed activities. 4

CFN 204 · Diane Foley · Network Leader The concrete level of understanding is the most basic level of mathematical understanding. It is also the most crucial level for developing conceptual understanding of math concepts/skills. Concrete learning occurs when students have ample opportunities to manipulate concrete objects to problem-solve. For students who have math learning problems, explicit teacher modeling of the use of specific concrete objects to solve specific math problems is needed. For higher level students, procedures and computations are not a problem, but they’re not able to explain and justify their thinking. Talking about the process in collaborative groups helps the students articulate their mathematical thinking, and critique the thinking of others. 5

CFN 204 · Diane Foley · Network Leader Collaborative Groups Establish groups based on Data Select the problem aligned to the unit of study Determine the collaborative objectives to target Identify ways to promote the elements of cooperative learning Identify roles Provide protocols Clarify expectations 6

CFN 204 · Diane Foley · Network Leader Five Basic Elements of Cooperative Learning Positive interdependence Face-to-face interaction Individual accountability Group behaviors Group processing 7

CFN 204 · Diane Foley · Network Leader Positive interdependence means that students see the importance of working as a team and realize that they are responsible for contributing to the group's effort. Face-to-face interaction involves students working in environmental situations that promote eye contact and social space so that students can engage in discussions. Individual accountability suggests that each person is responsible to the group and must be a contributing member- not someone who lets others do all of the work. Group behaviors refer to those interpersonal, social, collaborative skills needed to work with others successfully. Group processing is a time after the cooperative learning task is finished when team members analyze their own and their group's abilities to work collaboratively. 8

CFN 204 · Diane Foley · Network Leader Promote Team Work and Collaborative skills Assign Roles (e.g., record keeper, spokesperson, encourager) Provide limited materials thus necessitating sharing Reward collaborative behaviors Ask students to self-evaluate after-task completion Assign a group grade to the math activity Arrange the environment so students interact in small groups 9

CFN 204 · Diane Foley · Network Leader When planning collaborative groups, think about… - Have students learned the strategies and algorithms? - Can students explain the strategies and algorithms to each other? - Do students require visual models for remembering the strategies an algorithms? - Can students apply strategies and algorithms to a variety of problems? - Do students require teacher prompting and questions to help remember the strategies and algorithms? 10

CFN 204 · Diane Foley · Network Leader Major Emphasis Standards Students should be provided with the opportunity to engage in problem solving aligned to the major emphasis standards for the grade. These problems should be multi-step problems. (DOK 3) 11

CFN 204 · Diane Foley · Network Leader Discussion Are we providing students with meaningful experiences that will help them feel confident for the NYS assessment? Are we exposing students to the level of rigor and complexity that they see on the NYS assessment? Are the students engaging in complex problems that require them to persevere? 12

CFN 204 · Diane Foley · Network Leader Major Emphasis Standards What are the major emphasis standards for grades 3- 6? How do these standards build on each other from one grade to the next? 13

CFN 204 · Diane Foley · Network Leader Grade 3 Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. Understand the properties of multiplication and the relationship between multiplication and division. Multiply and divide within 100. Solve problems involving the four operations and identify and explain patterns in arithmetic. Number and Operations – Fractions Develop understanding of fractions as numbers. Measurement and Data Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 14

CFN 204 · Diane Foley · Network Leader Grade 4 Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations – Fractions Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. 15

CFN 204 · Diane Foley · Network Leader Grade 5 Number and Operations in Base Ten Understand the place value system. Perform operations with multi-digit whole numbers and with decimals to hundredths. Number and Operations – Fractions >Use equivalent fractions as a strategy to add and subtract fractions. >Apply and extend previous understandings of multiplication and division to multiply and divide fractions. >Measurement and Data Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 16

CFN 204 · Diane Foley · Network Leader Grade 6 Ratios and Proportional Relationships  Understand ratio concepts and use ratio reasoning to solve problems. The Number System  Apply and extend previous understandings of multiplication and division to divide fractions by fractions.  Apply and extend previous understandings of numbers to the system of rational numbers. Expressions and Equations  Apply and extend previous understandings of arithmetic to algebraic expressions.  Reason about and solve one-variable equations and inequalities.  Represent and analyze quantitative relationships between dependent and independent variables. 17

CFN 204 · Diane Foley · Network Leader Example of Math Word Problem DOK 3 18

CFN 204 · Diane Foley · Network Leader Purposeful Instructional Practices Suspend your own approach to solving the problem Understand the solver’s reasoning Pose questions to prompts justification of the process Keep the space safe, so the students are comfortable taking risks Train students’ to challenge each-other’s thinking in a respectful way ***Related handouts are in your packets*** 19

CFN 204 · Diane Foley · Network Leader Three Questions for Purposeful Work 1.What are the desired outcomes? 2.How can teachers assess if their work is moving towards the desired outcomes? 3.How do teachers get there? 20

CFN 204 · Diane Foley · Network Leader Criteria for Selecting the Math Problems Allow for sense making of the mathematical idea Have multiple entry points Allow for varied solution paths The problem allows for students to make thinking visible 21

CFN 204 · Diane Foley · Network Leader Accountable Talk Prompts 22

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CFN 204 · Diane Foley · Network Leader Reflections Which strategies in this workshop are you most likely to use? How would you adapt the strategies in this workshop to suit your needs? What are the two most important ideas that you would share with your colleagues? 26

CFN 204 · Diane Foley · Network Leader Questions and Feedback 27 Please fill out the feedback form.