#### Transcript Mathematical Tasks and Higher Level Mathematics

```Mathematical Tasks, Cognitive
Demand and Higher Level
Mathematics
Essential questions:
1. What do we mean by higher level
mathematics in middle school?
2. How can teachers ensure that middle school
English Language Learners have maximum
opportunities to learn high level
mathematics?
Quasar Project
University of Pittsburgh
• Conducted five years of research in urban middle
schools
implemented appropriately in classrooms is the
key to success for urban students
• Developed a teaching approach to ensure that all
students are engaged in problem solving,
mathematical thinking, mathematical
communication
“… students who performed best … were
in classrooms in which tasks were … set
up and implemented at high levels of
cognitive demand … for these students,
having the opportunity to work on
classroom environment translated into
substantial learning gains on an
instrument designed to measure student
thinking, reasoning, problem solving and
communication.”
Consider two tasks with the same
underlying math content:
Task 1. Find the surface area and volume of a rectangular
prism that measures 2” x 4” x 24”.
Task 2. The EZ-Play Toy Company makes a set of 24 alphabet
blocks. Each block is a 2” cube. EZ-Play plans to ship the
blocks in a box that uses the smallest amount of cardboard.
What are the dimensions of the box that EZ-Play should use?
what you have done.
• Students know how to compute volume and
surface area of a rectangular prism.
• Teacher will help students remember which
formula to use.
• Task provides practice with arithmetic
• Task at low level of cognitive demand:
procedures without connections
• Students decide what is needed to solve the problem and
make their own plans for solving it.
• Students determine volume of 24 blocks and generate
several different rectangular prisms with that volume.
• Students compute and compare surface areas of several
rectangular prisms, finding the prism with the smallest
surface area.
• Students explain their thinking clearly.
• Students have opportunity to practice arithmetic
• Task is at a high level of cognitive demand: procedures
with connections.
Levels of Cognitive demand
Lowest to Highest
•
•
•
•
Procedures without Connections
Procedures with connections
Doing Mathematics
• Memorizing definitions, facts and formulas
• Using memorized definitions, facts and
formulas, exactly as learned
• No connection to underlying concepts
Procedures Without Connection
• Using known algorithms to produce correct
• Following steps in a given order
• Little doubt or confusion about what is to be
done
• No explanations other than describing the
procedure
• No connection to underlying concepts
Procedures with Connections
• Using procedures to help illustrate or understand
underlying concepts
• Making connections among multiple
representations (diagrams manipulatives, symbols,
formulas, problem statements)
• Drawing on conceptual understanding needed to
solve problem
• Following broad procedures rather than narrow
algorithms