63 Empowering Learners through the Standards for Mathematical Practice of the Common Core

Learners through the Standards for Mathematical Practice of the Common Core Juli K Dixon, Ph.D University of Central Florida Solve this… ÷ 1/7 Perspective… When asked to justify the solution to ÷ 1/7 A student said this… Perspective… When asked to justify the solution to ÷ 1/7 A student said this… “Just change the division sign to multiplication and flip the fraction after the sign ÷ 1/7 becomes x 7/1 So I find 3/1 x 7/1 which is 21/1 or 21.” Perspective… When asked to justify the solution to ÷ 1/7 A student said this… “Just change the division sign to multiplication and flip the fraction after the sign ÷ 1/7 becomes x 7/1 So I find 3/1 x 7/1 which is 21/1 or 21.” Is this an acceptable justification? Perspective… When asked to justify the solution to ÷ 1/7 Another student said this… “I know there are groups of 1/7 in one whole Since there are three wholes, I have x or 21 groups of 1/7 in wholes so ÷ 1/7 = 21.” Perspective… When asked to justify the solution to ÷ 1/7 Another student said this… “I know there are groups of 1/7 in one whole Since there are three wholes, I have x or 21 groups of 1/7 in wholes so ÷ 1/7 = 21.” How is this justification different and what does it have to with the Background of the CCSSM • Published by the National Governor’s Association and the Council of Chief State School Officers in June 2010 • Result of collaboration from 48 states • Provides a focused curriculum with an emphasis on teaching for depth Background of the CCSSM 45 States + DC have adopted the Common Core State Stan Minnesota adopted the CCSS in ELA/literacy o Background of the CCSSM “… standards must address the problem of a curriculum that is ‘a mile wide and an inch deep.’ These Standards are a substantial answer to that challenge” (CCSS, 2010, p 3) Engaging Students in Reasoning and Sense Making Consider this… What is important here is that the problem requires diligence to solve and yet with perseverance the solution is within reach Students are reasoning… How we support this empowerment? “… a lack of understanding [of mathematical content] effectively prevents a student from engaging in the mathematical practices” (CCSS, 2010, p 8) How we support this empowerment? “… a lack of understanding [of mathematical content] effectively prevents a student from engaging in the mathematical practices” (CCSS, 2010, p 8) When and how we develop this understanding? Engaging Students in Reasoning and Sense Making    We need to question students when they are wrong and when they are right We need to create an environment where students are expected to share their thinking We need to look for opportunities for students to reason about and make sense of mathematics Consider this 5th grade class What was the misconception? What was the misconception? With which practices were the students engaged? How might you change your practice to address these now? The Standards for Mathematical Practice: 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 Where we start? How we support this empowerment?  What needs to occur at the administrative level?  What needs to occur to support teachers?  What needs to occur to support students? Advice to help parents support their children:  Teach procedures only after they are introduced in school Ask your child to explain his or her thinking to you Discuss this with your teacher  Drill addition/multiplication facts only after your child explores strategies  Help your child become more proficient in using mathematics at home How we support this empowerment?  What we know best might be the most difficult to change How we support this empowerment?  Teachers need content knowledge for teaching mathematics to know the tasks to provide, the questions to ask, and how to assess for understanding  Math Talk needs to be supported in the classroom  Social norms need to be established in classroom and professional development settings to address misconceptions in respectful ways Learners through the Standards for Mathematical Practice of the Common Core Juli K Dixon, Ph.D University of Central Florida ... develop in their students” (CCSS, 2010, p 6) Making Sense of the Mathematical Practices The Standards for Mathematical Practice are based on: • The National Council of Teachers of Mathematics’... developing mathematical practices (CSMC, 2010) Making Sense of the Mathematical Practices The Standards for Mathematical Practice: Make sense of problems and persevere in solving them Reason... the CCSSM The CCSSM consist of Content Standards and Standards for Mathematical Practice ? ?The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all