2. The evolving math classroom
EMPIRICISM – The traditional classroom
PRAGMATISM – Recognizing the ever-
changing world we live in
PROGRESSIVISM – Teach to the whole child
CONSTRUCTIVISM – Students involved in
their learning
3. EMPIRICISM – teacher role
Teacher transmits
knowledge to student
Learning is a one-way
experience from teacher
to student
Teacher holds
authoritarian role
Teacher does the
majority of the talking
Lecture format
Textbook based
4. EMPIRICISM – student role
Child born as blank slate
Learning happens to the
student – mind is
imprinted with new
knowledge
Learning is based on
correct answers
Students take notes
Don’t ask questions
Information is
memorized
5. EMPIRICISM – My experience
This was the way my math
classes were carried out
Lecture style
Little teacher – student
interaction
Notes then individual
class work
No group work or projects
This was the way I ran my
math classes!
We do what we know…
6. EMPIRICISM – Why not?
A skill base is achieved
through practice and
repetition
Students may know how to
do something without
knowing why it works or why
it is important
Passive acquisition of
knowledge does not lead to
being able to know when or
how to apply the knowledge
Problem solving and
reasoning skills are not
developed
7. PRAGMATISM – change happens
We live in an ever-
changing world and so our
approaches should evolve
and change as well
Goal of education is
student growth
Education is not merely a
technical venture
Education should be
humanized
Students should learn why
in addition to how
Biesta & Burbules (2003)
8. PRAGMATISM – change happens
Offered a new way to think
about how students
acquire knowledge
students are not passive
This is a philosophy of
action and interaction
the student is inherently
involved with their
environment
Students learn by
interacting with what they
are learning and with each
other
Biesta & Burbules (2003)
9. PRAGMATISM – My experience
This year has been a year of
significant change and
growth for me:
New high school building
New curriculum
New math delivery
program
Complex Instruction
New math department
chairs
I have had to embrace the
change and learn how to
meet the needs of my
students in a new way
10. PRAGMATISM – My experience
I needed to move out of my comfort zone and embrace a new way of
teaching
Move beyond the traditional methods I had adopted from my teachers
Our math department realized and accepted that what we were doing
was not working and that we were not being the most effective teachers
we could be
We wanted to find a new teaching method that was:
Interactive
Pushed students to learn math deeply
Had students work together in groups
Encourage creative thinking and problem solving
Embraced all ways of thinking
We discovered Complex Instruction!
We applied and received a grant to support this endeavor
All teachers did a week long training last summer
We have coaches that observe us monthly
Each content area meets weekly to plan tasks and share experiences
11. COMPLEX INSTRUCTION
The 7 practices of
Complex Instruction:
Multidimensionality
Roles
Assigning Competence
Teaching Responsibility
High Expectations
Effort over Ability
Learning Practices
Boaler (2006)
12. PROGRESSIVISM - child focused
Student’s understanding is the
most important thing
Students must be able to assess
their own learning as well as that
of their peers
Encourage
Responsibility for self and
others
Problem solving
Critical thinking
Learning should have value for
the student
Students should be able to
interact with their environment
Olson (2003)
13. PROGRESSIVISM – in the classroom
Cross-curricular integration
Teacher is facilitator
Many types of materials are employed
Including manipulatives
Individual as well as group work
Students can move around the room and interact with
other students
Time is more flexible – pacing is determined by
student understanding
Assessment is done more at the individual level rather
than group comparisons
Labaree (2004)
14. PROGRESSIVISM – My experience
THINGS I HAVE EMBRACED THINGS I STRUGGLE WITH
Student’s understanding is very
important
Move beyond rote learning
Teacher as facilitator
I am not the only expert in the
room!
Encourage responsibility for self
and others
Don’t encourage dependence
Individual as well as group work
I feel like I’m finding the balance
Assessment at group and individual
levels
Time is more flexible
We have already paused and
revisited concepts not fully
understood
Cross-curricular integration
Collaborate with other depts.
Students assess their own
learning
How to do this?
Use many types of materials
(including manipulatives)
Lack of resources, creativity?
Student can move around the
room and interact with
others
Chaos??
15. CONSTRUCTIVISM –
student involvement
Learning happens when the
student interacts with their
environment
Wrong answers are a vehicle
to deeper understanding
because they trigger deeper
reflection
Students need to be
intentional about their
learning
When students challenge each
other in groups more learning
happens
Complex reasoning is an
indicator of successful
learning
16. CONSTRUCTIVISM –
students’ experiences
Interdisciplinary exploration
Collaboration amongst
students
Reflection
Self-examination
Experiential learning
Abdal-Haqq (1998)
Presented with:
Materials that captures one’s
interest
Conceptual clusters – Big
ideas
Questions are posed
Complex situations or
problems are tackled
Activities are student
centered:
Ask their own questions
Follow through on their own
experiments
Make their own conclusions
Hanley (1994)
17. CONSTRUCTIVISM –
the role of the teacher
Teacher as a resource
Everyone in the room can
contribute
Teacher is not the only expert
Challenge students
Question previously held
beliefs
Let students’ needs help drive
the lesson
Allow think time
Student understanding
should help guide pacing
Encourage questioning
Ask open-ended questions
Support student autonomy
Relinquish classroom control
Use many forms of materials
Manipulatives
Games
Activities
Honor the discover y process
Many vehicles to get to
understanding
Ask for clear communication
If students can explain their
thinking well they have
deeply learned
Hanley (1994)
18. CONSTRUCTIVISM – My experience
THINGS I HAVE EMBRACED THINGS I STRUGGLE WITH
Complex situations and problems
are presented to students
Group work
CI tasks
Teacher as a resource
I am not the one with all of the
answers
Asking open-ended questions
Scaffold learning
Let students’ needs drive the
pacing
Re-teach when necessary
Honor the discovery process
Allow for messiness while
learning
Interdisciplinary exploration
Integrate different content
areas
Student reflection
How do I do this??
Challenge students by
questioning their previously
held beliefs
Ask the right questions
Relinquish classroom control
Still working on this
Many forms of materials
Time, money, creativity
20. References
Abdal-Haqq, I. (1998). Constructivism in Teacher Education: Considerations for Those Who Would
Link Practice to Theory. ERIC Digest. ERIC Identifier: ED426986. Retrieved on December 11,
2009 from http://www.ericdigests.org/1999-3/theory.htm
Biesta, G. J. J. & Burbules, N. C. (2003). Pragmatism and Educational Research. Lanham, MD:
Rowman & Littlefield Publishers Inc. Retrieved on December 8, 2009 from
http://books.google.com/books?hl=en&lr=&id=U5d637yZX9YC&oi=fnd&pg=PP9&dq=pragmatis
m+education&ots=DbtrpGe7dA&sig=JSQEyP3GFqYt3bIZUK7weM16iVE#v=onepage&q=pragmati
sm%20education&f=false
Boaler, J. (2006) “Opening our ideas”: how a detracked mathematics approach promoted respect,
responsibility, and high achievement, Theory into Practice, 45(1), 1-11.
Hanley, S. (1994). On Constructivism. Maryland Collaborative for Teacher Preparation . Retrieved
on December 11, 2009 from http://www.inform.umd.edu/UMS+State/UMD-
Projects/MCTP/Essays/Constructivism.txt
Labaree, D. F. (2004). The Trouble with Ed Schools. USA: Yale University Press. Retrieved on
December 8, 2009 from
http://books.google.com/books?id=aDUDPnKXrqsC&pg=PA129&dq=progressivism+education&lr
=&ei=lcsiS5rqKZqIlQSL9cDNCw&cd=1#v=onepage&q=progressivism%20education&f=false
Olson, D. R. (2003). Psychological theory and educational reform: how school remakes mind and
society. Cambridge, UK: Cambridge University Press. Retrieved on December 8, 2009 from
http://books.google.com/books?id=3LZIq2tpmtEC&pg=PP1&dq=).+++Psychological+theory+and
+educational+reform:+how+school+remakes+mind+and+society.&lr=&ei=5s4iS5DRFZv-
lATX5o3JCw&cd=1#v=onepage&q=&f=false
