District Learning Day August 5, 2015 Utilizing Tasks to Engage Students in the Mathematics Content Standards District Learning Day August 5, 2015

Do Now Task Angel and Jayden were at track practice. The track is 25 kilometers around. Angel ran 1 lap in 2 minutes. Jayden ran 3 laps in 5 minutes. a. How many minutes does it take Angel to run one kilometer? What about Jayden? b. How far does Angel run in one minute? What about Jayden? c. Who is running faster? Explain your reasoning. (https://www.illustrativemathematics.org/content- standards/7/RP/A/1/tasks/82) Solution (see solution handout) We can create a table that shows how far each person runs for a certain number of laps: Number of lapsNumber of km 1 25 2 45 3 65 We can see from the table that 1 km is exactly half way between 2 and 3 laps. So it will take 2.5 laps to run 1 km. Since it takes Angel 2 minutes to run 1 lap, she will take 2.5 laps1 km⋅2 minutes1 lap=5 minutes1 km. So it takes Angel 5 minutes to run 1 km. Since it takes Jayden 5 minutes to runs 3 laps, she runs 1 lap in 53 minutes. Thus, it takes Jayden 2.5 laps1 km⋅5 minutes3 laps=52⋅53 minutes/km=256 minutes/km=416 minutes/km. So it takes Jayden 416 minutes to run 1 km. Angel runs 1 lap in 2 minutes so she runs 12 lap in 1 minute. Since 1 lap is 25 km, 12 lap is 15 km. So she also runs 15 km in one minute. Since Jayden runs 1 lap in 53 minutes, she will run 35 laps in 1 minute. Since Jayden runs 1 km in 256 minutes, she will run 625 km in 1 minute. Jayden runs the same distance in less time than Angel (alternatively, Jayden runs farther in the same time than Angel), so Jayden is running faster than Angel.

Norms Be present and engaged. Be respectful of differences in perspective while challenging each other productively and respectively. Monitor “air time.” Make the most of the time we have. Stay focused on students. Keep this slide – do not alter We will adhere to the following norms.

Objectives Know: how to provide engaging mathematics with rigorous content how to support and encourage critical thinking and problem solving Understand: the importance of developing and using higher-level tasks that build conceptual understanding and mathematical success the importance of using the resources provided in the instructional map Do: integrate literacy strategies in solving mathematical tasks to facilitate communication, problem-solving, and conceptual understanding develop and plan lessons that will engage students in cognitively demanding tasks

What are Standards? Standards define what students should understand and be able to do in their study of mathematics. But asking a student to understand something also means asking a teacher to assess whether the student has understood it. Standards do not tell teachers what to do at the classroom level or how to begin making essential changes to implement them.

Brief History of Mathematics Standards: In 1989 the National Council of Teachers of Mathematics (NCTM) launched the standards-based education movement in North America with the release of Curriculum and Evaluation Standards for School Mathematics, an unprecedented initiative to promote systemic improvement in mathematics education. So, let’s look at what we do know.

Brief History of Mathematics Standards: Now, twenty-five years later, the widespread adoption of college- and career-readiness standards, including adoption in the United States of the Common Core State Standards for Mathematics (CCSSM) in some states, provides an opportunity to reenergize and focus our commitment to significant improvement in mathematics education.

Principles to Actions: Ensuring Mathematical Success for All The primary purpose of PtA is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards. In response to the inception of CCR and CCSS for math, NCTM released a new document titled Principles to Action: Ensuring Mathematical Success for All. Read the slide: The focus…

Principles to Actions: Ensuring Mathematical Success for All “Most important, it describes the actions required to ensure that all students learn to become mathematical thinkers and are prepared for any academic career or professional path they choose.” Principles to Action, NCTM, p.vii Read slide

Principles to Actions discusses and documents these realities: Too much focus is on learning procedures without any connection to meaning, understanding, or the applications that require these procedures. Too many students are limited by the lower expectations and narrower curricula of remedial tracks from which few ever emerge. Too many teachers have limited access to the instructional materials, tools, and technology that they need. The book discusses some realities that exist in math education/classrooms. Read bullets…

Principle on Teaching and Learning The heart of the matter: Teaching and Learning An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically. Based on the work done in Principles to Action, some guiding principles for school math were developed. One of those principles is the Principle of Teaching and Learning. NCTM, 2014, p. 7

Principle on Teaching and Learning Teaching mathematics requires teachers to be skilled at teaching in ways that are effective in developing mathematics learning for all students.

Principle on Teaching and Learning Mathematics Teaching Practices Establish mathematics goals to focus learning. Implement tasks that promote reasoning and problem solving. Use and connect mathematical representations. Facilitate meaningful mathematical discourse. Pose purposeful questions. Build procedural fluency from conceptual understanding. Support productive struggle in learning mathematics. Elicit and use evidence of student thinking. Principles to Actions, NCTM, 2014 There are eight research-informed teaching practices that support the mathematics learning of all students. The 1st Guiding Principle, Teaching & Learning, has 8 Essential Mathematics Teaching Practices

Implementing tasks that promote reasoning and problem solving Research indicates that student learning is increased when teachers regularly engage students in cognitively demanding tasks. (Boaler and Staples 2008; Hiebert and Wearne 1993; Stein and Lane 1996) The one that we are going to focus on is Implementing tasks that promote reasoning and problem solving.

Implement Tasks that Promote Reasoning and Problem Solving Mathematical tasks should: Provide opportunities for students to engage in exploration or encourage students to use procedures in ways that are connected to concepts and understanding; Build on students’ current understanding; and Have multiple entry points. There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. (Lappan & Briars, 1995, NCTM)  

Math Tasks Modeling Activity Pass out task handout Facilitator will use the State’s Structure and Routines of a Lesson Set up problem Explore/private work time Small Group problem solving Share, Discuss and analyze

***Embedded in SCS Math Instructional Maps*** Tasks PtA (NCTM) MARS Illustrative Math Tncore (tneducation fastestimproving) NYC Dan Myer ***Embedded in SCS Math Instructional Maps*** Here are some additional resources for locating meaningful tasks.

Instructional Map -7th Grade Review the components of the curriculum maps When reviewing the components make note of the following: *CLIP Connections Resources provided Major work of the grade Stress the importance of following the maps in order to prepare students for part 1 of the test.

Resource Toolbox – 7th Grade Note Resource Toolbox at the end of each quarter

Instructional Map –Algebra I Review the components of the curriculum maps When reviewing the components make note of the following: *CLIP Connections Resources provided Major work of the grade Stress the importance of following the maps in order to prepare students for part 1 of the test.

Resource Toolbox –Algebra I

Revisit Objectives Know: how to provide engaging mathematics with rigorous content how to support and encourage critical thinking and problem solving Understand: the importance of developing and using higher-level tasks that build conceptual understanding and mathematical success the importance of using the resources provided in the instructional map Do: integrate literacy strategies in solving mathematical tasks to facilitate communication, problem-solving, and conceptual understanding develop and plan lessons that will engage students in cognitively demanding tasks Revisit Objective in closing section. How will you measure successful implementation of the topics covered in your presentation?

Next steps and activities for follow up Collaborate with teachers in your grade-level or subject and examine task resources embedded in your instructional maps. Plan and implement lessons that include the use of tasks to facilitate student conceptual understanding. Throughout the school year plan to attend mathematics PD offerings that will continue to expand on the work that we’ve done today. In alignment with the Effective PD Design Principles, all PD should provide next steps for follow up to ensure the learning will take root in instructional practice.

Reflection: One minute paper on post-it What resonated with you? What are you going to change as a result of attending today’s session? Jot down your “Take-Aways” Consider what you need to know and be able to do to successfully implement what you have learned in this session. What is still unclear? What professional development or additional resources do you need? Presenters please collect post-it notes at the end of each session. Prepare an analysis of the responses and be prepared to share out in DLD debrief.

Camilla S. Horton, Ed.D. Emily B. Barbee, Ed.D. Middle School Math High School Math hortoncs@scsk12.org barbeeeb@scsk12.org 416-7988 416-7985