TECHNOLOGY-INTENSIVE INSTRUCTION
WITH HIGH PERFORMING AND LOW
PERFORMING MIDDLE SCHOOL
MATHEMATICS STUDENTS
Master’s Thesis Research
James P. Dildine, 1999
Introduction
NCTM recommends Utilizing
technology to help all students learn
mathematics.
PCAST- President’s Report on
Technology in Education
– Learn through not the technology
– Equitable Universal Access
Calculators put hand-held technology in
all students’ hands
Background Literature
 Steele-academic disidentification, “process that
occurs when people stop caring about their
performance in an area, or domain that formerly
mattered a great deal.”
 Hill- “many intrinsic qualities of a traditional
mathematics classroom offer motives for student
disidentification from mathematics.”
 Oakes-Low tracked classes require more rote
memorization and less critical thinking than high
tracked classes where teachers pursue
understanding of complex themes.
Background Literature
 Mevarech and Kramarsky (1997) report that
graphing involves interpretation - the ability to read
a graph and gain meaning from it - and
construction - building a graph from data or
points.
 NCTM Emphases include appropriate calculators should be available to all students at all times;
 a computer should be available in every classroom for demonstration
purposes;
 every student should have access to a computer for individual and
group work;
 Students should learn to use a computer as a tool for processing
information and performing calculations to investigate and solve
problems.
Students using graphing technology
Dunham-review of calculator research (1993)
 Students who use graphing calculator technology





can better read and interpret graphical information;
obtain more information from graphs;
have greater overall achievement on graphing items;
are better at finding an algebraic representation for a graph
better understand global features of functions;
better understand connections among graphical, numerical, and
algebraic representations;
 had more flexible approaches to problem solving, were more willing to
engage in problem-solving and stayed with a problem longer; and
 concentrated on math problems and not on algebraic manipulation;
Research Design
Technology Intensive Instruction in
Middle School classrooms
Two weeks of instruction
Two 8th grade Math classes: Basic,
Algebra
Equipment: TI-82 and CBR
Activities reading and interpreting
information from graphs while learning
about rate
Two Classes
Algebra & Basic Math
Demographics
Basic Math
Male
White
Black
Latino/a
Asian
Mid Eastern
Totals
Percent
5
4
1
0
0
10
43
Female Totals Percent
11
16
70
2
6
26
0
1
4
0
0
0
0
0
0
13
23
100
57
100
Algebra
Male
6
1
0
2
1
10
53
Female Totals Percent
8
14
74
1
2
10.5
0
0
0
0
2
10.5
0
1
5
9
19
100
47
100
Equipment
TI - 82 Graphing Calculator
CBR - Calculator Based Ranger Connects to calculator to act as a realtime data collection device
Distance a walker is away from sensor is
plotted as a graph of distance v. time on
calculator
Instructional Activities
Match-the-graph
– Students are presented with a graph and
expected to match the shape of that graph
by directing walker properly
Match-your-graph
– Students create their own graph on paper
and attempt to recreate it on the equipment
Determine speed
– Students measure the change in distance
over an interval vs. change in time.
Data Collection
Survey Items - Attitudes toward
mathematics and technology
Achievement Items - Items about
knowledge of reading graphs and
determining rate
Classroom observations/Videos
 Interview of 4 students (each class) 3
each as case studies
Survey Item Results
Percentages of favorable responses
More favorable responses on the post
survey.
Achievement Results
Statistically Significant Gains for each
class
Basic Math Mean: 3.53 to 4.27
– (p=.02, t=2.32, df=14)
Algebra Mean: 8.32 to 9.11
– (p=.01, t=2.80, df=18)
Observations: Basic Math Class
Students actively participating
Collaborative learning environment
promoted negotiation and exploration
Students presented what they discovered
and explored ideas
Related activities beyond classroom:
Transfer of meters/second to
miles/hour
Difficulty identifying specific points
Observations: Algebra Class
Students worked together in groups but
consistently worked individually on the
activities
Attempted to make graphs that were not
possible (vertical lines)
Also transferred graphing ideas to
situation beyond the classroom
Most were able to use specific end points
to determine average speed over an
interval
Snapshot 1-Big Ideas
Horizontal Line - No movement.
Change in x but no change in y
Dip and Peak-Represent points where
walker stopped and changed direction.
Indicate specific point where no change
in y (distance) but brief change in x
(time).
Vertical line - Not possible - requires
enormous change in y (distance) with
little or no change in x (time).
Snapshot 2-Basic Math Group
"woman backs up for a few feet. pauses,
switches into drive, and pulls forward for
about half the distance. Pauses again and
backs up a few more feet, pauses again and
pulls all the way out and drives off."
Snapshot 3 - Ashley’s Bus Trip
Math: Boring but important to consumers
• "Going to the store, yes. Like seeing if the person gives
you the right amount of change."
Evidence of identifying with ideas
• "It was fun and I think the school should get some of
those calculators.”
• Now: “I think about the bus like a graph”
Snapshot 4 - Michael
View of math: review/useless
• in high school you do lots of algebraic word
problems or something, and some of that you’ll
never use in your life
Chalk-Board Explanation
= moving away from the motion sensor
and
= back toward the sensor
Snapshot 4 - Algebra “Cheats”
Vertical Line - impossible to create
“We can make it”
“We just need to find a way that makes
large distance changes in almost no time”
Example of a “cheat”, student jumping in
and out of the range of the sensor.
Snapshot 5 - Calculate Speed
Algebra students traced specific points to
determine speed over an interval
Distance End  Distance Start
2 .5 m  2 .0
.5m 1m



Time Finish  Time Start
16.5s  10.5s 6.5s 13s
Conclusions - What did this Tell
Me?
Basic Mathematics Students were able to
“handle” the technology and concepts
Lowest tracked students performed very
well within this type of instruction
Most Students were motivated to learn
the material.
Each class attained conceptual
knowledge
Evidence of more positive attitudes
during instruction
Limitations
May not generalize beyond these classes
Achievement tests were limited to ten
items and may not have linked directly
with instruction
Survey items may need better selection
Implications & Recommendations
Pilot included instruction to teachers
and preservice teachers - can they use
this type of instruction in their
classrooms?
When and at What level should graphing
concepts be introduced?
Are lower tracked classes capable of
learning complex concepts in this
environment?
Further Study
More classes
More time necessary with technology
instruction - novelty of research
environment
More concepts
Transfer of concepts - Do the students
use the knowledge they may have gained
later?
Do the students retain the positive
attitudes they may have exhibited?
Fin
James P. Dildine, 1999