1. Mathematical
Processes in Senior
Math
Cindy Smith
Math 7-12
1
2. 2
Research-Based Practice
“Human thinking is inherently social in its
origins…”
There is a “fundamental link between
instructional practice and student
outcomes”
-Marilyn Goos, Journal of Research in Mathematical
Education, 2004
4. 4 November 21, 2012
Mathematical Processes
The outcomes in K-12 mathematics should
be addressed through the appropriate
mathematical process as indicated by the
bracketed letters following each outcome.
Teachers should consider carefully in their
planning those processes indicated as
being important to supporting student
achievement of the respective outcomes.
-Saskatchewan Renewed Math 9 Curriculum
5. November 21, 2012
Problem Solving
Build new mathematical knowledge
through problem solving
Solve problems that arise in mathematics
and in other contexts
Apply and adapt a variety of appropriate
strategies to solve problems
Monitor and reflect on the process of
mathematical problem solving
NCTM
6. 6
Reasoning and Proof
Recognize reasoning and proof as
fundamental aspects of mathematics
Make and investigate mathematical
conjectures
Develop and evaluate mathematical
arguments and proofs
Select and use various types of reasoning
and methods of proof
NCTM
7. 7
Representation
Create and use representations to organize,
record, and communicate mathematical
ideas
Select, apply, and translate among
mathematical representations to solve
problems
Use representations to model and interpret
physical, social, and mathematical
phenomena
-NCTM
8. Visualization
Being able to create, interpret, and
describe a visual representation …Spatial
visualization and reasoning enable
students to describe the relationships
among and between 3-D objects and 2-D
shapes including aspects such as
dimensions and measurements.
Saskatchewan Math 9 Curriculum
9. 9
Connections
Recognize and use connections among
mathematical ideas
Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole
Recognize and apply mathematics in
contexts outside of mathematics
NCTM
10. 10
Communication
Organize and consolidate their mathematical
thinking through communication
Communicate their mathematical thinking
coherently and clearly to peers, teachers,
and others
Analyze and evaluate the mathematical
thinking and strategies of others;
Use the language of mathematics to express
mathematical ideas precisely.
11. 11 November 21, 2012
Through communication, ideas become
objects of reflection, refinement, discussion,
and amendment. The communication
process also helps build meaning and
permanence for ideas and makes them
public (NCTM, 2000). When students are
challenged to think and reason about
mathematics and to communicate the results
of their thinking to others orally or in writing,
they learn to be clear and convincing.
Listening to others’ thoughts and explanation
about their reasoning gives students the
opportunity to develop their own
understandings.
-Huang
13. 13
Partner Discussions
Allow ALL students an opportunity to
express their thinking, where calling on
students allows only few to participate
Allows debate, original ideas,
conceptualizing
Teaches to female modes of learning:
Boys speak up in class more often, and
we often direct our richest questions to
boys.
14. 14 November 21, 2012
Boys will argue longer for an answer they
are not sure of than girls will argue for an
answer they KNOW is right (Guzzetti &
Williams, 1996).
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Connections and Communication
are inextricably linked
16. 16
Piaget
knowledge is constructed as
the learner strives to organize
his or her experiences in terms
of pre-existing mental
structures or schemes
17. 17
Communication works together with
reflection to produce new relationships
and connections. Students who reflect on
what they do and communicate with
others about it are in the best position to
build useful connections in mathematics.
(Hiebert et al., 1997, p. 6)
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Math to Math
Solving single degree equations
Arithmetic sequences
Linear functions
Slope
Related rates
Science
End behaviours of polynomial functions
Zero behaviour of polynomial functions
Asymptotes
26. 26 November 21, 2012
Math to Math
Factoring Quadratics
Solving Quadratics
Graphing Quadratics
Completing the Square
Quadratic Problems
End Behaviour Models
Zero Behaviours
Asymptotes
Curve behaviours
Local min/max
30. 30
How does our summative
assessment reflect deeper
learning?
3 -2
31. 31 November 21, 2012
How does it all fit together
DI
RTI
Formative Assessment
Small Group Instruction
Outcomes, Indicators
Instructional Practices
Pre/Post Assessment
UbD
Inquiry
Editor's Notes
We need to recognize that the way we are being asked to teach has a firm base in research. So does the renewed curriculum
Show of hands: Who understands content standards? Process Standards? Goals of Math Ed? Broad areas of learning?
STOP here: Do concept attainment activity
Stop to brainstorm formative assessments. Offer Frayer model
