Engaging Math Students in Meaningful Dialogue

1. Engaging Math Students in Meaningful Dialogue Amy Coltharp Program Specialist for Title I, Part D Bureau of Federal Educational Programs Florida Department of Education

2. Common Core State Standards • Adopted by 45 states and 3 territories • Individual states chose whether or not to adopt the Common Core State Standards - not the federal government • Ensures that students are receiving a high quality education consistent from school to school and from state to state. • Designed to ensure that all students across the nation are prepared for success in postsecondary education and the workforce.

3. Florida’s Common Core State Standards(CCSS) Implementation Plan for Math

4. Preparing for the Implementation of the Common Core State Standards in Florida • Statewide Common Core Summer Institutes held in West Palm Beach, Orlando, Ft. Lauderdale, and Panama City Beach • Content-specific regional training will be held in the Fall • Embedded in the teacher preparation program curriculum in colleges across Florida

5. Strategies Used to Engage Meaningful Dialogue Among Students Engaging ELL Learners Mathematical Practices Supporting Meaning Dialogue Engagement of Students

6. “Learning is not a spectator sport. Students do not learn just sitting in classes listening to teachers, memorizing prepackaged assignments, and spitting out answers. They have to talk about what they are learning, write reflectively about it, relate it to past experiences, and apply it to their daily lives. They must make what they learn part of themselves.” Chickering &Gamson, 1987

7. MAKING A CONNECTION • Student Interests • Consider the group of students you are teaching (e.g., students in DJJ programs, 12th graders opposed to 7th graders, etc.) • Probability problems involving race car drivers may not be of interest to a class of all females • Real Life Situations • Demonstrate how concepts can be applied to situations outside of the classroom EXAMPLES: • Using probability to make decisions • Finding percent increases/decrease using proportional relationships • Recognize situations in which a quantity grows or decays • MACC.S-MD.2.7 MACC.7.RP.1.3 MACC.F-LE.1.1.c

8. THINKING IT THROUGH Create a culture of ‘explanation’ instead of a culture of the ‘right answer’ • Collect problems and tasks that have multiple paths to a solution There are at least three different strategies for doing the following problem. • Which strategy did you use? • What is another strategy that you could have used to solve the problem? 5 + 13 + 24 – 8 + 47 – 12 + 59 – 31 – 5 + 9 – 46 – 23 + 32 - 60

9. ENCOURAGE ACTIVE LEARNING Active Learning is defined as any strategy thatinvolves students in doing things and thinking about the things they are doing. Chickering & Gamson, 1987

10. Apply questioning strategies that require students to think and answer

11. ENCOURAGE ACTIVE LEARNING Starter questions These take the form of open-ended questions which focus the student's thinking in a general direction and give them a starting point. Examples:  • How could you sort these.......?  • How many ways can you find to…...? • What happens when we……? • What can be made from……? • How many different……can be found?

12. ENCOURAGE ACTIVE LEARNING Stimulate mathematical thinking These questions assist students to focus on particular strategies and help them to see patterns and relationships. Examples: • What is the same? • What is different? • How can you group these? • How can this pattern help you find an answer? • What would happen if.....?

13. ENCOURAGE ACTIVE LEARNING Assessment questions Questions such as these ask students to explain what they are doing or how they arrived at a solution. Examples: • What have you discovered? • How did you find that out? • Why do you think that? • What made you decide to do it that way? Questions to stimulate mathematical thinking

14. ENCOURAGE ACTIVE LEARNING Final discussion questions These questions draw together the efforts of the class and prompt sharing and comparison of strategies and solutions. Examples: • Why is your solution different than your neighbors? • Why/why not? • Have we found all the possibilities? • How do we know?

15. ENCOURAGE ACTIVE LEARNING Implement pairing activities such as “think, pair, and share” This strategy allows the student to: • Reflect on subject content • Deepen understanding of an issue or topic through clarification and rehearsal with a partner • Develop skills for small group discussion, such as listening actively, disagreeing respectfully • Rephrase ideas for clarity Addresses the Speaking and Listening Standards K-12 for English Language Arts

16. ENCOURAGE ACTIVE LEARNING Assign specific tasks for team members during group assignments Example: T1will be responsible for determining the formula that will apply to problem; T2 will be responsible providing a list of the unknowns; T3 will provide the steps that were taken to reach the solution, and so on.

17. “Getting students involved in their education programs is more than having them participate; it is connecting students with their education, enabling them to influence and affect the program and, indeed, enabling them to become enwrapped and engrossed in their educational experiences.” Wehmeyer & Sands,1998

18. ENCOURAGE ACTIVE LEARNING • Provide surveys or questionnaires to students to collect feedback on collaboration among group members • Surveys can be valuable tools in figuring out what engages your math students. • Share feedback with students if suggestions will be used

19. Making the Content Comprehensible for English Language Learners • Use the standards vocabulary as a teaching tool. “Generalize, develop, describe, analyze, apply, measure,” etc. are all words ELLs will hear in the classroom and need to understand. • ELLs may know how to perform the skill using their language, they just don’t yet have the English vocabulary. • Use pictures, graphs, and charts whenever possible. • Make use of root words and cognates.

20. Classroom Strategies for English Language Learners • Group ELLs with non-ELLs to work together • Allow more wait time for ELLs to respond. Silence does not necessarily mean the student does not know the answer, the ELL may be translating the answer and need more time. • Remember that ELLs from different countries may display mathematical functions in different ways.

21. Standards for Mathematical Practice • Describes the varieties of expertise that mathematics educators at all levels should seek to develop in their students. • They rest on important “processes and proficiencies”. • Although the practices are presented individually, it's important to keep in mind that the practices can, and should, be evident together in a lesson.

22. Common Core State StandardsMathematical Practices Mathematical practices develop dispositions and habits of mind characteristic of an education person. • Precision in thought • Precision in the use of language and terms • Precision in argument • Sense making happens through conversations • http://www.youtube.com/watch?v=9pKcO9E4Flw&feature=relmfu

23. Mathematical Practices Supporting Meaningful Dialogue • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning

24. STANDARD 1Make sense of problems and persevere in solving them Examples: • A middle childhood teacher might post a set of different approaches to a solution and has students evaluate the success of a strategy. • An early adolescence teacher might have students articulate a specific way of laying out the terrain of a program and evaluating different starting points for solving. • A teacher of adolescents and young adults might frame the task as a real-world design conundrum, inviting students to engage in a “tinkering” process of working toward mathematical proof, changing course as necessary as they develop their thinking.

25. STANDARD 3Construct viable arguments and critique the reasoning of others Examples: • A middle childhood teacher might post multiple approaches to a problem and ask students to identify plausible rationales for each approach as well as any mistakes made by the mathematician. • An early adolescence teacher might post a chart showing a cost-analysis comparison of multiple DVD rental plans and ask his students to formulate and defend a way of showing when each plan becomes most economical. • A teacher of adolescents and young adults might actively engage her students in extended conjecture about conditions for proof in the construction of quadrilaterals, testing their assumptions and questioning their approaches

26. STANDARD 6Attend to Precision Examples: • A middle childhood teacher might engage his students in a "number talk" in which students use an in/out table and a plotted graph to "guess [the teacher’s] number." • An early adolescence teacher might distribute cards with different symbol strings to his students, asking them to mingle to group and categorize their symbol strings, explaining and defending their groupings. • A teacher of adolescents and young adults might continually probe her students to defend whether their requirements for a particular quadrilateral will always be the case, or whether there are some flaws in their group’s thinking that they need to refine and correct.

27. Online Resources • http://www.corestandards.org/ • http://www.insidemathematics.org/index.php/common-core-standards • http://www/teachingchannel.org

28. http://www.insidemathematics.org/index.php/mathematical-practice-standardshttp://www.insidemathematics.org/index.php/mathematical-practice-standards

29. Amy ColtharpProgram Specialist IV for Title I, Part DFlorida Department of Education Amy.Coltharp@fldoe.org Office #: 850.245.7892