The Ties that Bind: Complementary and Contradictory Agendas Peter Liljedahl

I apologize ...

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?

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

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

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

... 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

... 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

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

How many triangles?

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 ...

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

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

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

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

Curriculum goals – math education

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

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

shift gears Teacher education ...

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

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

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

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

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

Mathematicians in mathematics education refocusing Mathematicians in mathematics education

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

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

Thank you!

Educ 212 - From bridges to balloon animals

"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.