Transcript Assessing students` understanding of parallel lines and related

Assessing students’
understanding of
parallel lines and related angle
properties in a dynamic
geometry environment
CHENG, Lo Carol
True Light Middle School of Hong Kong
Assessment in mathematics education
 should not just focus on rote memorization
of number facts or ability for computational
procedures but students’ thinking and
learning potential in mathematics
 mathematics education should help
students to think mathematically and train
up their mathematical thinking.
Ginsburg, H. P., Jacobs S. F. & Lopez L. S. (1993). Assessing mathematical
thinking and learning potential in primary grade children In M. Niss (Ed.),
Investigations into assessment in mathematics education: An ICMI study (pp.
157–167). Dordrecht: Kluwer Academic Publishers.
Technologies shifts assessment format
 For example: use of calculator
Dynamic Geometry as Assessment Tools
 DG software:
 Sketchpad
 GeoGebra
 C.a.R.
 Use of DG:
 Exploration
 Construction
Can we use DG as
assessment tool?
DG Task example
What can we tell from
the assessment?
Learning and Teaching of Geometry
 Perceptual Apprehension
 It is about physical recognition (shape,
representation, size, brightness, etc.) of a
perceived figure.
Duval, R. (1995). Geometrical pictures: Kinds of representation and specific
processings. In R. Sutherland & J. Mason (Eds.), Exploiting Mental Imagery
with Computers in Mathematics Education (pp. 143–157), Springer published
in cooperation with NATO Scientific Affairs Division.
Learning and Teaching of Geometry
 Sequential Apprehension
 It is about construction of a figure or
description of its construction.
Duval, R. (1995). Geometrical pictures: Kinds of representation and specific
processings. In R. Sutherland & J. Mason (Eds.), Exploiting Mental Imagery
with Computers in Mathematics Education (pp. 143–157), Springer published
in cooperation with NATO Scientific Affairs Division.
Learning and Teaching of Geometry
 Discursive Apprehension
 Mathematical properties represented in a
drawing can only be clearly defined with
speech determination.
Duval, R. (1995). Geometrical pictures: Kinds of representation and specific
processings. In R. Sutherland & J. Mason (Eds.), Exploiting Mental Imagery
with Computers in Mathematics Education (pp. 143–157), Springer published
in cooperation with NATO Scientific Affairs Division.
Learning and Teaching of Geometry
 Operative Apprehension
 It is about making modification of a given
figure in various ways:
 the mereological way: dividing the whole given
figure into parts of various shapes and combine
these parts in another figure or sub-figures;
 the optic way: varying the size of the figures;
 the place way: varying the position or its
orientation.
Duval, R. (1995). Geometrical pictures: Kinds of representation and specific
processings. In R. Sutherland & J. Mason (Eds.), Exploiting Mental Imagery
with Computers in Mathematics Education (pp. 143–157), Springer published
in cooperation with NATO Scientific Affairs Division.
Dynamic Geometry Tasks
related to parallel lines
Tasks for orientation preference
 Task 2a
 Students’ answers
More than 70 students
considered just the
horizontal pair.
About 50 students
considered both
pairs
About 20 students
considered just the
vertical pair.
Tasks for orientation preference
 Task 2b
 Students’ answers
About 50 students
considered just the
horizontal (interior angles)
pair.
About 40 students
considered just the
vertical (corr. angles) pair.
About 40 students
considered both pairs.
Task for angle position
 Task 3a
 Students’ answers
More than 100 students got the correct answers 69 but still
there are more than 30 made the angle 62
Task for angle position
 Task 3b
 Students’ answers
More than 80 students the angle as 116 (i.e. 94 + 116 = 180).
About 60 students got the values ranged form 111 to 113
Tasks for making equal areas
 Task 5a
 Students’ answers
More than 50 students
made all the angles
equal 26.
About 50 students
tried to make a
parallelogram.
Tasks for making equal areas
 Task 5b
 Students’ answers
More than 70 students gave correct answers
but many of them tried to make a rhombuslike figure.
More than 100 students
made a rhombus-like
figure.