1. Olive Chapman University of Calgary Canada
Curiosity-Based Knowing in Developing an Inquiry Stance in Teaching Mathematics
Olive Chapman
University of Calgary
Canada

2. Goal
Investigation of the features of a self-directed PD initiative that supported Curiosity-Based Knowing in the mathematics teachers’ development of an inquiry stance in their learning and teaching

3. Background
The Elementary Mathematics Teacher Study Group Professional Development Growth Plan Initial Study Group Activities New direction of Study Group

4. A self-directed professional development approach [PD] aimed at transforming their teaching to an inquiry-oriented perspective.
The PD was completely open-ended in that the teachers controlled and made the decisions for each component of the inquiry process as needed.
They decided on what to do and how to do it.

5. Earlier phase of project
Analyzed the PD regarding the nature of the inquiry process that evolved as a basis of the teachers’ learning and development of an inquiry stance in their thinking and teaching
Key constructs

6. Inquiry as Stance in learning (Cochran-Smith & Lytle, 1999)
“Inquiry as stance is distinct from the more common notion of inquiry as time-bounded project or discrete activity within a teacher education course or professional development workshop” (p. 289).
It is about teachers
“working together in communities … [to] pose problems, identify discrepancies between theories and practices, challenge common routines, draw on the work of others for generative frameworks, and attempt to make visible much of that which is taken for granted about teaching and learning. From an inquiry stance, teachers search for significant questions as much as they engage in problem solving. They count on other teachers for alternative viewpoints on their work.” (pp )

7. Inquiry stance
A disposition to question in order to understand and take “intelligent action” (Dewey, 1933)

8. Curiosity and learning
Research has established that curiosity is important to learning and human development.
Berlyne (1954) first demonstrated that when people are curious about something, they learn more and better.
Recent studies in psychology continue to show that intellectual curiosity influences learning
Curiosity triggers interest and cognitive engagement, i.e., the individual or group is fully and intrinsically committed to learning more about a phenomenon

9. Perspective of curiosity-based knowing
Based on notions of inquiry and literature on curiosity.
e.g.,
Puzzlement/perplexity: Dewey’s inquiry process begins with “a state of ... doubt, hesitation, perplexity, ...” to be resolved by “reflective thinking”
Wonderment: Wells’ (1999) dialogical inquiry is defined as “A willingness to wonder, to ask questions, and to seek to understand by collaborating with others in the attempt to make answers to them” (p.122).
a state of confusion because you do not understand something.
Wonder = to be curious to know something

10. Curiosity: Piaget defined as "the urge to explain the unexpected
Curiosity: Piaget defined as "the urge to explain the unexpected.” Other sources: an urge to know more; a desire to know; interest leading to inquiry.
Curiosity-based knowing [CBK]:
Way of knowing involving a state of curiosity/ wonderment/puzzlement that results in action through questioning/inquiry/exploration to resolve this state in order to learn/know and grow/change.

11. Research questions for current stage of project
What aspects of the PD supported CBK in the teachers’ learning?
How did CBK shape their thinking and teaching?

12. The participants were 14 grades 1 to 6 teachers from the same elementary school
They ranged from 3 to 20 years of teaching experience, with most being over 10 years.

13. Data collection for the larger project focused on two aspects of PD: the way it evolved for the teachers and the way it impacted their learning and practice. This included:
(1) field notes and audio recording of PD sessions of their discussions of, for example, what to do and how, when and why to do it; their plans, observations and evaluation of their research lessons; and their students’ work.
(2) Samples of teaching artefacts (e.g., research lesson plans) and participants’ notes (e.g., observations of video lessons) during the sessions.

14. (3) Several classroom observations of each teacher.

15. Data analysis included: Development of Codes based on the theoretical perspective of CBK and used to identify the features of the PD that supported the teachers’ CBK and aspects of their thinking/actions during the PD and their teaching that were characteristic of CBK. Themes emerging from these categories were used to draw conclusions regarding their learning of CBK and use of CBK in their learning and teaching

16. Findings – Fostering CBK
2 key aspects of the PD emerged as central to the teachers’ engagement in CBK:
(1) Unpacking personal thinking and experience involving teaching mathematics
(2) Developing pedagogical models for teaching mathematics

17. (1) Unpacking thinking/experience
2 key aspects of the PD in which they engaged in CBK:
To understand teaching “self”
(ii) To understand pedagogical “problems”

18. (i) To understand teaching “self”
Initially, this meant sharing of thinking and experience of what they did. [instrumental process
They applied this to the first video of a video study.
They had to be prompted to be curious, e.g., about what was behind their observations in relation to their teaching.
This eventually led them to generate curiosity-based questioning of self to understanding each other’s and own thinking or experience.

19. This type of questioning supported engagement in CBK through dialogic inquiry, where they shared and examined their thinking or actions.
This enabled them to understand themselves and each other regarding how they made sense of aspects of their teaching and the changes they should pursue based on the video-lessons study.

20. Unpacking thinking/experiences (ii) To understand pedagogical problems
Involved trying to make sense of problematic situations of common interest and how to resolve it in the PD.
Naturally led to wondering/puzzlement, resulting in curiosity-based questions of meaning of key ideas that were central to the self-directed PD in defining how it evolved.

21. This type of questioning supported engagement in CBK through Dewey-oriented or scientific-oriented inquiry, where they created and tested “hypotheses” to understand how to resolve the problematic situation

22. Creating pedagogical models
General approaches to guide their teaching
An inquiry-based teaching model
(ii) Problem-solving inquiry model
They engaged in CBK by being puzzled with, posing questions of, and inquiring into the structure of the models they were interested in.

23. (i) Inquiry-based teaching model
They engaged in CBK to understand how to integrate the model in their thinking and teaching.
CBK helped them to frame the model in relation to the students (i.e., learners/learning) and not themselves (i.e., teacher/teaching ).

24. (ii) Problem-solving inquiry model
To guide their teaching of problem solving. They engaged in CBK to understand what they should do before, during, and after a student is engaged in solving a mathematics problem for which the solution method is not known in advance.

25. Impact of CBK on teaching
They developed understanding of CBK through the PD that impacted their teaching in meaningful ways.
In general, there were significant shifts in their teaching that embodied their knowledge and use of CBK.
Their questioning included curiosity-based questions and they encouraged curiosity-based by their students.
They engaged in CBK and engaged their students CBK.

26. Conclusions
Mathematics teachers need to learn to think in different ways that support mathematical thinking and meaningful mathematics pedagogy in their own learning and their teaching.
This study offers CBK as one of those ways of thinking.
It suggests that there is an important relationship between CBK and teacher learning and CBK and teaching.