Transcript Slide 1

Investigating a Phase Approach to
Using Technology as a Teaching
Tool
Pep Serow
University of New England
Background
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Van Hiele five level framework.
Opportunity to exhibit insight.
Dynamic Geometry Software (DGS) provides the
potential for student-centred problem-solving
tasks that remain in the control of the individual
student (Goldenberg & Cuoco, 1998).
Many teachers are comfortable using technology
as a display tool, but there is a need to focus on
how technology can be used to enhance
conceptual understandings (McGehee & Griffith,
2004).
Teachers often lack confidence in sequencing
technological tasks as an integral component of a
teaching/learning sequence.
Facilitating the Crisis - van Hiele
Teaching Phases
PHASES
AIM
1. Information
For students to become familiar with
the working domain
2. Directed
Orientation
For students to identify the focus of the
topic through a series of teacherguided tasks.
3. Explicitation
For students to become conscious of
new ideas and new language.
4. Free Orientation
Tasks where students find their own
way.
5. Integration
Overview of the material investigated.
Research Questions
The research questions for this study were:
1. Is the van Hiele teaching phases
framework an effective structure for
designing teaching sequences involving
dynamic geometry software?
2. To what extent does the implementation
of student-centred tasks, which utilise
dynamic geometry software, facilitate
student growth in understandings of
relationships among quadrilateral
figures?
Method
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This study uses a pre-experimental
design
One group of 23 students
Pre-test, post-test, and delayed
post-test
Team teaching intervention
Main written tasks
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Int: Draw a diagram to illustrate each quadrilateral.
Make sure your drawings clearly indicate each
quadrilateral. Draw lines to indicate relationships
among the quadrilaterals. Use circles if you would like
to show groups. Write your reasons for the groups you
have identified. Write one paragraph justifying the
manner in which quadrilaterals are related to one
another.
Students were asked to comment (in written form) on
the following two scenarios.
Scenario 1: John states to the class “The square is a
rectangle”. Do you agree or disagree? How could he
justify this statement if he was asked to explain it?
Scenario 2: Megan writes on her paper that “The
rhombus is a parallelogram”.
6. The class of parallelograms acquire further development
within the formal mode.
All parallelograms—two set s of parallel sides.
Four right angles and two
sets of parallel lines.
A squa re is a rectangle.
Two pair of parallel lines and
two pair of equa l sides.
All sides are equal.
Two sets of parallel
lines.
A rhombus is a special square.
A squa re is also a rhombus.
Two sets of
parallel
lines.
Two sets of
different
sides of the
same length.
Does not relate, no st rict criteria, only
one pair of parallel sides.
Teaching Sequence
Activities 1
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Mechanics of software and recall of known
quadrilaterals.
Write your name using sketchpad.
Create a person and reflect the figure.
What do you notice when you drag one of
your people. Check this with
measurement tools.
Create a house design using the the six
quadrilaterals.(Information and Directed
Orientation).
m AB = 1.04 cm
j' = 0.89 cm
m CDE = 106.73 
m F'E'C' = 50.65 
B
j'
A
All corresponding sides
are equal.
F'
D
E
C
C'
E'
Activities 2
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Creating robust templates for each
quadrilateral using properties and
the drag test.
Describe your construction within a
textbox and record the properties of
each figure on a teacher-designed
table
Explicitation Phase.
Activities 3
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Irregular quadrilateral and midpoints
construction (Directed Orientation).
Create any irregular quadrilateral.
Construct the midpoints. Join the
midpoints to construct another
quadrilateral. What do you notice?
Investigate the properties of this shape
and justify what you have found.
we made sure all sides were paralell
We crossed two lines that bisected each
other with right angles
m EF = 0.53 cm
D
diagonals bisects the angle
G
we then put mid points on each line and
then drew up the square
E
I
Made sure it has four sides with angles of
90 degrees
m GE = 0.53 cm
F
m DH = 2.48 cm
m ID = 2.48 cm
H
B
Activities 4
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Exploration of figures and student
designed spreadsheet (involving a
list of all possible properties with
recording of when each property
applied) of figures and properties
(Explicitation).
Activities 5
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Quadrilateral diagonal starters. Game
design (Free Orientation).
Students create the diagonal formation
needed for each of the quadrilaterals. The
aim is for templates to be created so that
younger students could complete the
figure and explore the properties.
H'
H
G'
G
JI
F
All sides are equal, though
diagonals are not! Angles betw een
diagonals are right angles. The
shape has tw o axis of symmetry
at least. Join the dots to reveal a
- you guessed it, ...............
Activity 6
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Students create;
a) a concept map
b) a flow chart,
to summarise their known
relationships among quadrilateral
figures (Free Orientation).
Activity 7 and 8
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Students design an information
booklet with all material that they
have been working on (Integration).
Routine questions involving known
properties and relationships
(Integration).
Discussion
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Two-week intervention did reinforce the
high level of student interest in the
activities.
Students exchanged their ideas verbally.
There is need to assist in the making the
implicit nature of the relationships –
demonstrated through ‘dragging’ explicit.
This is where the combinations of
different technologies and recording
methods was most beneficial.
Relationships Among Figures
Category
A
B
C
D
11
(48)
4
(17)
4
(17)
3
(13)
Post test
5
(22)
4
(17)
7
(30)
2
(9)
1
(4)
4
(17)
23
Delayed
post test
5
(22)
4
(17)
7
(30)
2
(9)
1
(4)
4
(17)
23
Pre-test
E
F
G
H
1
(4)
Total
23
Conclusion
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This study provides base line data which
is worthy of exploration in greater detail.
The findings point to the benefits in
melding of cognitive frameworks, phases
of teaching, and the embedding of
Information and Communication
Technology within a teaching sequence.
Highlights the importance of embedding
technology within a pedagogical
framework.