SHIFTING FROM MATHEMATICAL WORKSHEETS TO MEANINGFUL TASKS FACILITATED

SHIFTING FROM MATHEMATICAL WORKSHEETS TO MEANINGFUL TASKS FACILITATED BY: CYNTHIA BELL NUMERACY SPECIALIST LITERACY ASSISTANCE CENTER

OBJECTIVES Build understanding of the effects of meaningful tasks Understand the levels of cognitive demand as they relate to depth of knowledge and be able to identify the levels in a task Discuss how the 8 Standard Mathematical Practices can be the focus when developing tasks

WHAT IS A MEANINGFUL TASK? A mathematical task is a problem or set of problems that focuses students’ attention on a particular mathematical idea and/or provides an opportunity to develop or use a particular mathematical habit of mind Is engaging, relatable, and can maintain student interest

WHY ARE TASKS/ACTIVITIES IMPORTANT? Tasks and activities lead to prolonged retention Tasks help educators shift their instruction from how to get the answer to understanding mathematics

IMPLEMENT TASKS THAT PROMOTE REASONING AND PROBLEM SOLVING “Student learning is greatest in classrooms where the tasks consistently encourage high-level thinking and reasoning and least in classrooms where the tasks are routinely procedural in nature” (Boaler and Staples 2008; Hibert and Wearne 1993; stein and Lane 1996) Tasks need to have a range of cognitive demand both low and high. They should range from complex challenges to a routine exercise

ADDRESSING COGNITIVE COMPLEXITY Lower Level • Memorization • Procedures without connections Higher level • Procedures with connections • Doing Mathematics

COMPARE THE TWO TASKS Task # 1 You are trying to decide which of two smartphone plans would be better. Plan A charges a basic fee of $30 per month and 10 cents per text message. Plan B charges a basic fee of $50 per month and 5 cents per text message. How many text messages would you need to send per month for plan B to be the better option? Explain your decision. Task # 2 Solve each of the following systems. 4 x + y =2 x–y=3 x + 7 y = 0 2 x – 8 y = 22 -6 x + 5 y = 1 6 x + 4 y = -10 Adapted from Illustrative Mathematics Illustrations & Kutasoftware. com

WORKSHEET FOR TASK #2

LET’S TRY IT!

LET’S TRY IT! (6 x 2 + 3 x) - (2 x 2 + 8 x) This problem was simplified to 4 x 2 + 11 x which is incorrect. Explain why this is incorrect by citing any mathematical property or connecting the concept to another mathematical skill.

CONNECTING THE PRACTICES Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problems solving and allow multiple entry points and varied solution strategies. Source: Principles to Actions – Ensuring mathematical success for all by the NCTM 2014

EXPERIENCES OF THE PRACTICES Habits of Mind Reasoning & Explaining Modeling & Using Tools Seeing Structure & Generalizing

EXAMPLE WORKSHEET

EXAMPLE TASK SMP #3 Is the statement p – 1 = 5 p + 3 p – 8 Always, Sometimes or Never True

LET’S REVIEW To build a meaningful task you should consider these two things: Standard Mathematical Practices Cognitive Complexity Meaningful Task

THINGS YOU COULD TRY! Class discussion Create your own problems Game Fix someone’s homework Group task Tutor another Individual task Peer to peer tutoring Rotating partners Puzzle

CONTACT INFORMATION Cynthia Bell Numeracy Specialist Literacy Assistance Center Phone: 212 -803 -3306 Email: cynthiab@lacnyc. org