1. The Ties that Bind: Complementary and Contradictory Agendas
Peter Liljedahl

2. I apologize ...

3. What are my interests? mathematics teacher education
elementary & secondary
pre-service & in-service
teacher beliefs about mathematics, teaching mathematics, and learning mathematics ... and their interplay
instructional design
problem solving
tasks
assessment
What are my interests?

4. What are my interests? creativity in mathematics Mathematicians
undergraduate students
pre-service teachers
mathematicians
Mathematicians
on Creativity
What are my interests?

5. Mathematics education ... at SFU
BEd – major in mathematics specialization
BEd – minor in secondary mathematics education
BSc – major in mathematics education (in progress)
MSc/MEd – secondary mathematics education
MEd – elementary mathematics education
PhD – mathematics education
PDP – Math 190, Educ 475, Educ 415
Q’s – Educ 211, Educ 212, Educ 313, Educ 411
Mathematics education ... at SFU

6. Mathematics education ... at SFU
BEd – major in mathematics specialization
BEd – minor in secondary mathematics education
BSc – major in mathematics education (in progress)
MSc/MEd – secondary mathematics education
MEd – elementary mathematics education
PhD – mathematics education
PDP – Math 190, Educ 475, Educ 415
Q’s – Educ 211, Educ 212, Educ 313, Educ 411
Mathematics education ... at SFU

7. ... graduate work at SFU combinatorics probability inequalities proof
linear algebra
infinity
modeling
functions
indigenous numeracy
creativity
dynamic geometry
neuroscience
teacher education
problem solving
perseverance
attitudes/beliefs
... graduate work at SFU

8. ... graduate work at SFU combinatorics probability inequalities proof
linear algebra
infinity
modeling
functions
indigenous numeracy
creativity
dynamic geometry
neuroscience
teacher education
problem solving
perseverance
attitudes/beliefs
... graduate work at SFU

9. Conclusion #1 ‘We’ are different! this that the other way
what constitutes
pre-requisite knowledge
curriculum
Conclusion #1

10. How many triangles?

11. Homework
Find a 10 digit number (with the digits 0, 1, ..., 9 used once each) such that the number formed by the first N digits is divisible by N.
Possible Project
Consider X (X is a natural number). How many ways can X be written as the sum of consecutive natural numbers?
and then ...

12. Pre-requisite knowledge
I assumed that they had no prior knowledge of triangular numbers, tetrahedral numbers, pyramidal numbers, or how to sum these!
I did not allow the lesson to be built upon a reliance on prior knowledge!
Knowledge gained in the lesson might be relevant for future activities/assignments!
However, I did build the lesson on the assumption of capacities acquired in prior lessons!
Pre-requisite knowledge

13. Curriculum as capacities
group work
communication
reason
inquiry
endurance
perseverance
courage
curiosity
wonder
patience
certainty
argument
visualization
thinking
Curriculum as capacities

14. Curriculum goals - mathematics
a priori
capacities
relationship with mathematics
creative, intuitive, inductive, connected, messy
feel like a doer (verb) vs. a knower (noun)
emerging
certainty and the ... syndrome
articulation
chronological vs. logical
Curriculum goals - mathematics

15. Curriculum goals – math education
3, 6, 9, 15, 24 ?, ?, _, _, 100
Curriculum goals – math education

16. Curriculum goals – math education

17. Curriculum goals – math education
a priori
promoting student doing
understanding student thinking
instructional design
teaching
emerging
traditions of mathematics (ToM)
traditions of teaching mathematics (ToTM)
Curriculum goals – math education

18. Conclusion #2 I am bound to mathematics!
Mathematics content comprises between 50% and 95% of what I teach.
It is the context of all my activities.
It is engages my students.
It is my goal.
Conclusion #2

19. shift gears
Teacher education ...

20. Mathematics for teaching
this is where the two fields collide
tension between content and context
knowledge for teaching mathematics (PCK) is fundamentally different than knowledge of mathematics (CK)
this is my interest
knowledge vs. beliefs
necessary vs. sufficient
means to an end vs. an end unto itself (ToM, ToTM)
recent research
Susan Oesterle
Mathematics for teaching

21. Teaching Mathematics for Teachers
do you do anything different?
do you plan differently?
do you teach differently?
do you assess differently?
do you have different expectations?
do you have different goals?
Teaching Mathematics for Teachers

22. You do! mitigate anxiety increase comfort increase confidence
improve attitudes
increase competency
create clarity
increase ways of understanding
increase ways of explaining
You do!

23. Conclusion #3 We are very similar! improve teachers
use/foster capacities
curiosities about student mis/understandings
interest in student learning of ...
benefits of knowledge about teaching
student/teacher beliefs/efficacy
Conclusion #3

24. Conclusion #4 You are bound to mathematics education!
you teach so that students learn
when they don’t ... you wonder about it
when you wonder a lot you seek answers
when answers can’t be found you create your own means of researching it
when you get find something interesting you seek an outlet (CMESG)
Conclusion #4

25. Mathematicians in mathematics education
refocusing
Mathematicians in mathematics education

26. Mathematicians in mathematics education
"I want to dispel two common myths. First, it is a common belief among mathematicians that attention to education is a kind of pasturage for mathematicians in scientific decline" (Bass, 2005).
"Mathematics education is not mathematics. It is a domain of professional work" (Bass, 2005).
it has its own history
it has its own canon of knowledge
it has its own theories, traditions, and practices
Mathematicians in mathematics education

27. Mathematicians in mathematics education
mathematics for teachers
advanced/specialized mathematics
preparation of instructors (Natasha Speer)
co-supervision of graduate students
provide venue for research
voices in the media
Mathematicians in mathematics education

28. Thank you!

29. Educ 212 - From bridges to balloon animals

30. "Teaching Assistants’ Knowledge and Beliefs Related to Student Learning of Calculus" 
... This study examined mathematics graduate student teaching assistants’ knowledge of student thinking for important concepts from calculus. Findings indicate that participating teachers did not possess rich knowledge of student thinking and that, in general, they were unable to generate solution paths other than the one they had used to solve the problem. In addition, teachers asserted a variety of (sometimes contradictory) relationships between students’ correct solutions and their understanding of the problems’ central concepts.