2. Why Focus on Tasks?
Classroom instruction is generally organized and
orchestrated around mathematical tasks
The tasks with which students engage determine
what they learn about mathematics and how
they learn it
The inability to enact challenging tasks well is
what distinguished teaching in the U. S. from
teaching in other countries that had better
student performance on TIMSS
3. The Importance of Mathematical Tasks
“…a teacher of mathematics has a great
opportunity. If he fills his allotted time
with drilling his students in routine
operations he kills their interest, hampers
their intellectual development, and
misuses his opportunity.
4. The Importance of Mathematical Tasks
But if he challenges the curiosity of his
students by setting them problems
proportionate to their knowledge, and
helps them to solve their problems with
stimulating questions, he may give them a
task for, and some means of, independent
thinking.”
Polya, 1973/1945
5. The Importance of Mathematical Tasks
“Not all tasks are created equal, and different
tasks will provoke different levels and kinds of
student thinking.”
thinking
Stein, Smith, Henningsen, & Silver, 2000
9. Popsicle Sticks
Example
Say, “We have nine ones. Let’s put the nine ones using
the popsicle sticks in the ones place (cup). The problem is
9 + 3. Let’s count three more popsicle sticks and add
them to the nine ones.”
10. Popsicle Sticks
Example
Say, “Oh no! What’s wrong with the ones place?”
Students respond, “There can only be nine ones in the
ones place. We have to regroup by making a group of ten.”
Count the ten popsicle sticks with the class and make a
group of ten.
11. Popsicle Sticks
Example
Say, “How many groups of ten do we have in the tens
place? How many ones do we have in the ones place? We
have 9 + 3 which equals one group of ten and two ones.”
12. Popsicle Sticks
Solve
Summarize: “We learned addition with regrouping one
digit, how we can do regrouping with popsicle sticks, and
how we use regrouping every day.”
13. Jerry made a drawing
using an empty number
line to solve this
problem
Zena also used an empty
number line but her solution
does not look like Jerry’s
solution.
Explain how Jerry solved the problem.
Explain how Zena solved the problem.
Are both solutions correct? How do you know?
16. Sorting Tasks
You will need the complete set of the Task
Sort Card set (File name: Task Cards
(PV)082909).
Before you continue, make sure you have
each task as a separate sheet so you can
move them individually as you sort them.
Also make sure you have the Task Sort
Chart to record your decisions.
17. Sorting Tasks
Make two piles: those tasks that your
group considers to be high cognitive
demand tasks and those tasks that your
group considers to be low cognitive
demand tasks.
As you sort, take notes on your thoughts
about what makes a task high or low in
terms of cognitive demand.
18.
19. Some Features of
High Cognitive Demand Tasks
A high cognitive demand task begins where the students
are (zone of proximal development; scaffolding)
The problematic or engaging aspect of a high cognitive
demand task is due to mathematics that students are to
learn.
A high cognitive demand task requires justifications and
explanations for answers and methods.
20. Task-Focused Activities
High cognitive demand tasks or
activities are the vehicle through
which the curriculum can be
developed. Maintaining the cognitive
demands of high-level tasks during
instruction affects the learning that
occurs.
21. Maintaining
The Mathematical Tasks Framework
Student
Learning
TASKS
as they are
summarized
implemented
set up in
appearby the
by students
teachers
curricular/
teacher
and students
instructional
materials or
are designed
by teachers
Adapted from Stein, Smith, Henningsen, & Silver, 2000, p. 4
22. Maintaining
The Mathematical Tasks Framework
Student
Learning
TASKS
as they are
summarized
implemented
set up in
appearby the
by students
teachers
curricular/
teacher
and students
instructional
materials or
are designed
by teachers
Adapted from Stein, Smith, Henningsen, & Silver, 2000, p. 4
23. Maintaining
The Mathematical Tasks Framework
Student
Learning
TASKS
as they are
summarized
implemented
set up in
appearby the
by students
teachers
curricular/
teacher
and students
instructional
materials or
are designed
by teachers
Adapted from Stein, Smith, Henningsen, & Silver, 2000, p. 4
24. Maintaining
The Mathematical Tasks Framework
Student
Learning
TASKS
as they are
summarized
implemented
set up in
appearby the
by students
teachers
curricular/
teacher
and students
instructional
materials or
are designed
by teachers
Adapted from Stein, Smith, Henningsen, & Silver, 2000, p. 4
25. Maintaining
The Mathematical Tasks Framework
Student
Learning
TASKS
as they are
summarized
implemented
set up in
appearby the
by students
teachers
curricular/
teacher
and students
instructional
materials or
are designed
by teachers
Adapted from Stein, Smith, Henningsen, & Silver, 2000, p. 4
26. Maintaining
The Mathematical Tasks Framework
Student
Learning
TASKS
as they are
summarized
implemented
set up in
appearby the
by students
teachers
curricular/
teacher
and students
instructional
materials or
are designed
by teachers
Adapted from Stein, Smith, Henningsen, & Silver, 2000, p. 4
27. Maintaining
The Mathematical Tasks Framework
Student
Learning
TASKS
as they are
summarized
implemented
set up in
appearby the
by students
teachers
curricular/
teacher
and students
instructional
materials or
are designed
by teachers
Adapted from Stein, Smith, Henningsen, & Silver, 2000, p. 4
Editor's Notes
First, classroom instruction is generally organized and orchestrated around mathematical tasks. That is, students’ day-to-day work in mathematics classrooms consists of working on a tasks, activities, or problems. For example, an analysis of 100 eighth grade lessons revealed that the delivery of content “was accomplished primarily by working through problems” (NCES, 2003, p. 144)
.Second, the tasks with which students engage determines what they learn about mathematics and how they learn it. According to Doyle (1983, p.161), “tasks influence learners by directing their attention to particular aspects of content and by specifying ways of processing information.”
Third, in the TIMSS video study involving seven countries including US (all who out performed US on TIMSS) although the percentage of hl tasks used was within range of other countries (17%) NONE of the tasks were enacted at a high level.
Refer participants to the blue sheet -- which contains these two problems.
Give participants a few minutes to review the problems and to indicate how they are different or how the same.
Get at the fact that content same - processes required to solve are different. We call these high level vs. low level tasks.