Engaging Learners and Realizing the Development of Mathematical Practices ALM Conference July 15, 2015 Trena L. Wilkerson Professor, Mathematics Education Baylor University NCTM Board of Directors

Session Overview What are Mathematical Practices for students and Mathematical Practices for Teaching – Principles to Actions: Ensuring Mathematical Success for All, NCTM 2014 – Focus on problem solving, perseverance, and reasoning Sample problems, activities, and resources Brainstorm & Discuss ways of incorporating MPs and MTPs-connecting to adult learners and adult educators 2

Polya “Mathematics is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean to be doing mathematics? In the first place, it means to be able to solve mathematical problems.” (from a lecture on teaching) 3

CCSS-M Mathematical Practices Represent what students are doing as they learn mathematics 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. 4

Mathematics Teaching Practices (NCTM, PtA 2014, p. 10) 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking. 5

Questions to Consider What are ways that we, as adult leaner educators, can approach or include the development of MPs in our programs? What are mathematical practices for teaching (MTPs) that we can include to support teachers and learners? What is the role of reasoning and perseverance in problem solving as related to the development of MPS and MTPS? What are exemplary tasks, tools, and activities we can include in our programs? What are the available resources to support this work? 6

Candy Jar Problem 7 Principles to Actions: Ensuring Mathematical Success for All, NCTM 201, p minutes to work individually 2.10 minutes to share at table (various approaches) 3.10 minutes to record different strategies to post on wall

Candy Jar Problem-Sample Student Answers I do not know I do not understand R 9 50/50 Less than 78 but more than 65

CCSS-M Mathematical Practices Represent what students are doing as they learn mathematics 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. 9

Mathematics Teaching Practices (NCTM, PtA 2014, p. 10) 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking. 10

Teaching & Learning Principles / Curriculum – include the concepts of number, data, geometry, and algebra at all levels of learning so that students can develop and connect mathematical ideas. – weave together all the elements of mathematical proficiency – not only procedural fluency, but also conceptual understanding, ongoing sense-making, problem solving, and a positive attitude about learning mathematics. – feature worthwhile tasks, such as activities that are drawn from the context of real life experience. Learning Environment – build on what students already know, valuing the various informal and alternative strategies students use to solve problems. – include opportunities for students to question, reason, solve problems, define goals and monitor their own progress by using estimation, mental math, computation, and technology when appropriate. 11

Teaching & Learning Principles Continued Design – begin with teachers as mathematics learners and thinkers. – be a continuing process that is connected to curriculum and assessment standards, program policy and instruction and current research. – be welcoming and accessible to all – to literacy and language teachers as well as to those who primarily teach mathematics. – be evaluated with respect to its impact on teacher behavior in relation to increased student learning. Content – establish a deep understanding of the mathematics of the curriculum and its principles. – understand how adults’ mathematical knowledge develops, how to recognize previous misconceptions, and how to assess and engage prior knowledge. – use a broad range of instructional strategies that utilize a variety of materials to accomplish learning goals. – understand how research can be used to improve their effectiveness as teachers. 12

ANN Adult Numeracy Components NCSALL, 2006 Context: the use and purpose for which an adult takes on a task with mathematical demands Content: the mathematical knowledge that is necessary for the tasks confronted Cognitive & affective: the processes that enable an individual to solve problems, and thereby, link the content and context 13

The Calling Plans Task Actions-Toolkit/The-Case-of-Elizabeth-Brovey-and-the-Calling-Plans-2-Task/ Long-distance company A charges a base rate of $5.00 per month plus 4 cents for each minute that you are on the phone. Long-distance company B charges a base rate of only $2.00 per month but charges you 10 cents for every minute used. Part 1:How much time per month would you have to talk on the phone before subscribing to company A would save you money? Part 2:Create a phone plane, Company C, that costs the same as Companies A and B at 50 minutes, but has a lower monthly fee than either Company A or B. 14

Video Viewing Focus Student Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Mathematical Teaching Practices 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking. 15

Pose Purposeful Questions PtA, 2014 Effective Questions should: Reveal students’ current understandings; Encourage students to explain, elaborate, or clarify their thinking; and Make the mathematics more visible and accessible for student examination and discussion. Teachers’ questions are crucial in helping students make connections and learn important mathematics and science concepts. Teachers need to know how students typically think about particular concepts, how to determine what a particular student or group of students thinks about those ideas, and how to help students deepen their understanding. (Weiss and Pasley, 2004) 16

Development/Professional-Development-Resources/ Development/Professional-Development-Resources/ NCTM New PD Resources-MTPs 17

NCTM Classroom Resources 18

Sample NCTM Resources Implementing the CCSS though Mathematical Problem Solving: For various grade bands Connecting the NCTM Process Standards and the CCSSM Practices 5 Practices for Orchestrating Productive Mathematics Discussions Principles to Action: Ensuring Mathematical Success for All 19

20 NCTM Board of Directors