Curiosity-Based Knowing in Developing an
Inquiry Stance in Teaching Mathematics
Olive Chapman
University of Calgary
Canada
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
Background
The Elementary Mathematics Teacher Study Group
Professional Development Growth Plan
Initial Study Group Activities
New direction of Study Group
• 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.
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
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. 292-293)
Inquiry stance
A disposition to question in order to understand
and take “intelligent action” (Dewey, 1933)
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
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).
• 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.
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?
• 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.
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.
(3) Several classroom observations of each
teacher.
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
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
(1) Unpacking thinking/experience
2 key aspects of the PD in which they engaged in CBK:
(i) To understand teaching “self”
(ii) To understand pedagogical “problems”
(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 curiositybased questioning of self to understanding each
other’s and own thinking or experience.
• 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.
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.
• 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
Creating pedagogical models
General approaches to guide their teaching
(i) 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.
(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 ).
(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.
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.
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.