Affordances of a Technology-Rich
Teaching and Learning Environment
(TRTLE)
Jill Brown & Gloria Stillman
The University of Melbourne
5th November 2004
RITEMATHS Project
Australian Research Council (ARC) Linkage Project
2004-2006
Enhancing Mathematics Achievement and
Engagement
by Using Technology to support Real Problem
Solving and lessons of High Cognitive Demand
Research Team
• Chief Investigators
– Prof Kaye Stacey
– Dr Gloria Stillman
– Dr Robyn Pierce (University of Ballarat)
• Australian Postgraduate Award (Industry)
– Jill Brown
• Ballarat Project Officer
– Sandra Herbert (University of Ballarat)
• Melbourne Project Officer
– Peter Fox
Industry Partners
• Secondary School Partners
– Ballarat SC
– Canterbury Girls SC
– Luther College
– Mt Clear SC
– Santa Maria College
– Westbourne Grammar
• Texas Instruments
Aim of Project
To discover the most effective ways to
use technology to stimulate higher order
thinking in mathematics classrooms,
in the context of using real world problems.
Technologies
Real-world interfaces bring a virtual world into the classroom for
analysis:
image digitisers, software enabling analysis of video,
dynamic control of simulations, and data loggers.
Mathematics analysis tools are tools that do the computational work
(symbolic, graphical, numerical):
graphing
calculators
spreadsheets,
[GC],
Geometer’s
(including APPS on GC)
Computer
SketchPad
Algebra
[GSP],
Systems
specific
[CAS],
applications
Research Themes
Context Theme: Dr Gloria Stillman
Algebra Theme: Dr Robyn Pierce & Sandra Herbert
Affordances Theme:
Prof Kaye Stacey & Jill Brown
Context Theme
Aim: To discover how teachers can engineer the
learning environment to manage the added cognitive
complexity of applying mathematics to model and
resolve real world problems.
Algebra Theme: Research questions
How can technology be used to:
• help students gain symbol sense, algebraic insight,
algebra expectation?
• increase students’ ability to work with symbols to solve
problems?
• help students tackle ‘bigger’ and ‘harder’ problems?
• change the way students think about using algebra to
solve problems?
• Dr Caroline Bardini and Dr Robyn Pierce presented preliminary
findings for the Algebra theme in a previous DSME seminar .
Affordances Theme
Aim:
To explore the ways in which the
affordances of a Technology-Rich Teaching
and
Learning
Environment
can
assist
students to use their insights from real world
situations to support abstract thinking.
(TRTLE)
The Learning Sciences
A fundamental assumption of many learning scientists is
that cognition is not a thing located within the individual
thinker but is a process that is distributed across
the knower,
(TRTLE)
the environment in which knowing occurs,
and the activity in which the learner participates.
In other words, learning, cognition, knowing, and context
are irreducibly co-constituted and cannot be treated as
isolated entities or processes.
(Barab & Squire, 2004, p. 1)
Design Study:
What is happening?
Purpose of preliminary data collection
• to gain greater insight into the thinking of the
students in project classrooms
•
what it is the teachers of these classes want their
students to learn when introducing linear functions
•
to provide a substrate for theorising and testing
conceptual frameworks.
Data Collection to Date
Project Teacher interviews
Classroom observation
Teacher and researcher reflections
Hidden Function Task (5 classes) & Barbie Bungee (2 classes)
•
Student Record Sheets
•
Post-task Interviews (Students and Teachers)
•
Video & audio recording of focus pairs solving the task in the
classroom
•
Recording of graphing calculator screens during task solution
(HF only)
Research Questions
RQ1: What is it about the TRTLE that allows teachers to
perceive particular affordances for teaching and learning and
act on these to improve student understanding of functions
and the development of higher order thinking?
RQ2: What is it about the TRTLE that allows students to
perceive particular affordances for learning and act on these to
maximise their understandings of functions and engage in
higher order thinking?
What are Affordances?
“When the constant properties of constant objects are perceived …
the observer can go on to detect their affordances. I have coined this
word as a substitute for values … . I mean simply what things furnish
for good or ill” (Gibson, J. J., 1966, p. 285).
“The verb to afford is found in the dictionary, but the noun affordance
is not. I made it up.
It implies the complementarity of the animal and the environment”
(1979, p. 127)
Gibson’s Affordances
Relationships between objects and actors involved in interactive
activity.
– Offerings or action possibilities in the environment in relation to
the action capabilities of an actor
– Independent of actor’s experience, knowledge, culture or ability
to perceive
– An affordance exists or it does not
– Affordances don’t change as an observer’s needs change
– They can be promises or threats
Gibson’s Motivation
•To understand what motivates human behaviour
•Before one can act, action must be perceived as
possible
•The perception of an affordance motivates the doing of
an action
•Affordances define allowable actions
Need for Research into Affordances
“Research
examining
the
concept
of
affordances is crucial if we are to build … a
more flexible design orientation to the
practices of education” (Pea, 1993, p. 52).
“Affordances describe how the interaction
between perceiver and perceived works - and
that is exactly what we need to understand in
educational research”
(Laurillard, Stratfold, Luckin, Plowman, & Taylor, 2000, p. 3).
Affordances of a TRTLE
Affordances of a TRTLE
- are the offerings of such an environment for both facilitating
and impeding learning
-
are potential relationships between the teacher and/ or
student and the environment
-
involve interactive activity between the human and the
environment
Affordances of a
TRTLE
To take advantage of the opportunities arising,
affordances need to be perceived and acted on by
both teachers and students.
This action may well include the rejection of a
particular affordance in favour of another affordance.
What Specifies an Affordance
To perceive an affordance a person has to become attuned to the
invariant or disturbance specifying it.
An invariant is a property of something in the environment relative
to some source of change (eg, a moving point of observation)
which leaves it unchanged in a way that is typical of the thing
specified.
Invariants are what remains despite a transformation.
A disturbance is a property of something in the environment
relative to some source of change (eg, an approaching predator)
such that a pattern of change is presented that is typical of the
thing specified.
Learning in a
TRTLE
Learning in a TRTLE happens through becoming attuned to the
invariants and disturbances which specify the affordances.
Example 1: Invariants and Cubic Functions - what specifies a
cubic function?
Example 2: Disturbances and Cubic Functions
A person becomes attuned to affordances through greater
noticing of critical differences and less noticing of irrelevancies.
Affordances as Disturbances
Affordances and Affordance Bearers
It is essential to distinguish between affordances and
affordance-bearers.
The manifestation of an affordance involves, an event in
which both the affordance bearer and the organism are
involved. (Scarantino, 2003)
In a
TRTLE
the affordance bearer is, broadly speaking,
the technology, more specifically some feature of the
technology. The affordance is the interactivity between the
user and the technology for some specific purpose.
Salient and Enacted Affordances
Drijvers points out that for affordances present in a
TRTLE
to be realised in the classroom depends not only on the existence of
the affordances “but [also] on the exploitation of these affordances
embedded in the educational context and managed by the teacher”
(p. 78).
Doerr & Zangor, (2000), also note the importance of teachers being
aware of the affordances of a technological environment.
Affordances need to be both perceived and enacted or thoughtfully
rejected in favour of another affordance.
Affordances, NUD*IST, and
Inspiration
My Emergent Framework
NUD*IST and Inspiration!
• Analysis tools
– Non-numerical
Unstructured
Data*Indexing Searching and Theorising
(NUD*IST)
– Inspiration
The Affordance Framework
• What I have done allows me to characterise
what I am seeing.
• I also need to find some explanation for
non-perception
– May emerge from the data
– May be able to apply some theory of
mispercerption
– May use Scarantino’s constructs of doing versus
happening affordances (The former involve
intention while the latter do not).
Truly and Falsely Ascribed Affordances
• A falsely ascribed affordance is what Gibson refers
to as the misperceiving of an affordance.
• Two examples both using the Scale Marks as the
affordance bearer
– Two students carefully edit the scale marks to facilitate
their by-hand sketch of a function
– Two students when confronted with an unexpected view of
a function on several consecutive occasions edit the scale
marks in the apparent belief that this will change their view
of the function. It does not.
Thanks
jillb@unimelb.edu.au