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 Task # 2You 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.
Solve each of the following systems.
4x + y =2x – y = 3
x + 7y = 02x – 8y = 22
-6x + 5y = 16x + 4y = -10
Adapted from Illustrative Mathematics Illustrations & Kutasoftware.com
LET’S TRY IT!
(6x2 + 3x) - (2x2 + 8x)
This problem was simplified to
4x2 + 11x 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
LET’S REVIEW
To build a meaningful task you should consider these two things:
Meaningful Task
Standard Mathematical Practices
Cognitive Complexity
THINGS YOU COULD TRY!
Class discussion
Game
Group task
Individual task
Rotating partners
Create your own problems
Fix someone’s homework
Tutor another
Peer to peer tutoring
Puzzle
Cynthia Bell
Numeracy Specialist
Literacy Assistance Center
Phone: 212-803-3306
Email: [email protected]
CONTACT INFORMATION