SHIFTING FROM MATHEMATICAL
WORKSHEETS TO MEANINGFUL TASKS
FACILITATED BY: CYNTHIA BELL
NUMERACY SPECIALIST
LITERACY ASSISTANCE CENTER
SPONSORED BY:
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
OBSTACLES
 “Dominant cultural beliefs about the teaching and learning of mathematics
continue to be obstacles to consistent implementation of effective teaching
and learning in mathematics classrooms” Leiwnad, American Institutes for
Research 2014
Beliefs about teaching and learning mathematics
Unproductive beliefs
Productive beliefs
Mathematics learning should focus on practicing procedures and memorizing
basic number combinations.
Mathematics learning should focus on developing understanding of concepts and procedures through
problem solving, reasoning and discourse.
Students need only to learn and use the same standard computational algorithms
and the same prescribed methods to solve algebraic problems
All students need to have a range of strategies and approaches from which to choose in solving problems,
including, but not limited to general methods, standard algorithms, and procedures
Students can learn to apply mathematics only after they have mastered the basic
skills.
Students can learn mathematics through exploring and solving contextual and mathematical problems.
The role of the teacher is to tell students exactly what definitions, formulas, and
rules they should know and demonstrate how to use this information to solve
mathematics problems.
The role of the teacher is to engage students in tasks that promote reasoning and problem solving and
facilitate discourse that moves students toward shared understanding of mathematics.
The role of the student is to memorize information that is presented and then use
it to solve routine problems on homework, quizzes and tests.
The role of the student is to be actively involved in making sense of mathematics tasks by using varied
strategies and representations, justifying solutions, making connections to prior knowledge of familiar
contexts and experiences, and considering the reasoning of others.
An effective teacher makes the mathematics easy for students by guiding them
step by step through problem solving to ensure that they are not frustrated or
confused.
An effective teacher provides students with appropriate challenge, encourages perseverance in solving
problems, and supports productive struggle in learning mathematics.
WHAT RESONATES WITH YOU?
 After having read through the productive and unproductive beliefs about teaching and learning
mathematics, which ones resonate with you?
 Are there any unproductive beliefs that you may have or have had?
 Which productive beliefs do you firmly hold onto in spite of your environment?
 Share your answers in the chat box with us!
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.
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 = 5p + 3p – 8
Always, Sometimes or Never True
EXAMPLE TASK USING SMP #3
Is the statement
4m – 4 = 4m
Always, Sometimes or Never True
EXAMPLE WORKSHEET
EXAMPLE TASK SMP #2 & 7
1. Create a proportion T-table that includes the given points (3,2) & (5,8).
2. Identify the rate of change on your T-table.
3. Use the slope formula and the given points (3,2) and (5,8) to calculate the slope of the line on
which the points lie. What is the slope of the line?
4. Is the rate of change on your T-table the same as the calculated slope? Why or why not?
5. Develop a real life scenario that demonstrates the relationship between the points on your Ttable.
OTHER TOOLS FOR SHIFTING
To build a meaningful task you should consider these three things:
Instructional
Shifts
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