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"Identifying characteristics of math inquiry experiences"
Methods course documentation
Identifying characteristics of math inquiry experiences (D5.1)
Facilitator's plan (by Raffaella Borasi)
First reading assignment on inquiry and related literature:
(Assign these readings prior to the first discussion about characteristics
of math inquiry instructional experiences, both to prompt the participants'
own reflection and not having a too heavy reading assignment the next time)
- NCTM (1991). Professional standards for teaching mathematics. (pp.
1-67) -- to provide some criteria and perspective to think about the
stiries read, and to make connections with well-recognized sources in the
literature
Plan for the first discussion on characteristics of math inquiry experiences:
- After the participants have shared their impressions on the various
"stories" of inquiry classroom experiences read for homework
(see Section D4.2), ask them to share what they think are important elements
of these experiences that make them different from "traditional"
math instruction.
- After several items have been generated (no need to try to be exhaustive
at this point), make comments about which of the elements they have identified
are usually considered characteristics of "teaching math through inquiry"
in the math education community, and introduce those elements that have
not yet been mentioned from the list of ten characteristic features listed
below -- distribute the list in a hand-out to participants as a reference.
Key characteristics of
inquiry-based math classes
- Students actively engage in the construction of mathematical
knowledge by trying to make personal sense of the mathematical rules, concepts
and problems they encounter.
- Students develop ownership of their learning by participating
in the generation/choice of the questions and/or problems to be studied.
- Students engage in inquiry not in isolation, but as a
community of inquirers that build on each other's ideas and results, and
continuously negotiate meanings.
- Mathematics is portrayed as the product of human activity
-- i.e., students come to realize that mathematical knowledge (both the
one achieved by mathematicians in the past and their own) is tentative
and dependent on context and purposes.
- Anomalies, ambiguity and controversy are valued as potential
stimuli for inquiry.
- Priority is given to instructional goals such as becoming
mathematical problem solvers/inquirers, understanding the nature of mathematics
and "big ideas" in mathematics, and developing mathematical confidence.
- The above priorities are reflected in appropriate assessment
of student learning.
- The teacher orchestrates opportunities for students'
inquiry and learning by setting up "rich" mathematical situations,
and developing activities around them which are meaningful, complex, and
open-ended.
- The teacher facilitates students' inquiries and learning
in the classroom through the use of appropriate teaching practices and
techniques.
- The teacher listens to students and takes their input
into consideration in all pedagogical decisions.
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- also bring up the "components of an inquiry cycle" that informed
the design at least of our illustrative inquiry units -- present those
since I do not think that they are characteristics of inquiry experiences
that the participants would bring up themselves
- Use the following slide as a reference point (but look back at the
description for each component given in the introduction of the Tessellation/Area
unit Supporting Materials for Teachers for more detail):
INQUIRY CYCLE
- Setting the stage
- Defining the scope of the inquiry
- Modeling the process
- Gathering the necessary mathematical tools
- Carrying out the inquiry
- Culminating experience
- Reflecting on the experience
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- make sure to point out that this is not a linear, step-by-step approach
and to go over (or ask participants to articulate) the function of each
of those components and why they are important; also, point out that not
all math inquiry experiences need to follow this structure
- have some discussion on these lists
- introduce the more theoretical readings on an inquiry approach to mathematics
education as a follow-up of this discussion, that will enable the participants
to get even a better sense of the rationale and theoretical foundations
of the principles identified here.
Second reading assignment on inquiry and related literature:
- Borasi & Fonzi (1998). "Characteristic features of teaching
mathematics through inquiry" (see Instructional materials) --
to synthesize and elaborate on the previous discussion;
- Borasi (1992). "Rethinking mathematics as a humanistic discipline"
(see Instructional materials) -- to elaborate on a key aspect
of teaching mathematics through inquiry that methods course participants
are likely to be least familiar with.
- Borasi (1996). "Rationale for an inquiry approach to teaching
mathematics" -- to examine some of the more theoretical foundations
of an inquiry approach and better understand it nature and rationale.
Follow-up discussion on second set of readings on inquiry and related
literature:
- If there is time, before starting with the new topic, ask participants
to comment on what they have read for homework -- make sure the newsprint
compilation from the previous lesson is displayed, so that people can refer
to it and add if necessary.
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