The impact of dynamic geometry software on student achievement: Action
research on urban, high school geometry classes
Abstract: The purpose of this work is to quantitatively investigate the impact of interactive
geometry software on student learning. I teach at a comprehensive, urban, inner-city high school
with a population of over 2000 students from grades nine through twelve. The student population
is of low-SES demography and is typically considered “underserved.” Historically, geometry
assessment scores have always ranked the lowest among all math subjects taught at my site. To my
knowledge, student-centered technology is not used in any of the geometry classes. This work will
examine the integration of a specific program, GeoGebra, into my geometry curriculum; the
anticipated outcome is that student learning will increase as indicated by assessment scores.
Introduction
One may believe, or at least expect, that technology and mathematics go hand-in-hand in classrooms, that
technology should naturally fit within mathematics curricula. If this is the case, then exactly how well do they fit
together? The primary motivation for this study stemmed from an observed absence of technology from all
geometry classes found in an urban high school in California. Basic need also drives this work. As stated earlier,
geometry assessment scores have always ranked at the bottom compared against all other math subjects taught at my
site. To this date, nobody has explored why this phenomenon has occurred, and why it has not yet been addressed.
As a geometry teacher, I personally feel the need to explore alternative options that might lead to an increase in
student learning. As the lead geometry teacher at my site, I also (professionally) feel the need to assist my fellow
geometry teachers in finding, exploring, and/or creating new ways to engage our students. It is my hope that this
work will shed some light on just one alternative to traditional teaching.
Literature Review
Baki, Kosa, and Guven (2011) researched the impact of dynamic geometry software on spatial visualization
skills of pre-service mathematics teachers. Lopez (2010) researched the use of interactive technology with
elementary students, specifically targeting English Language learners’ mathematical abilities. Doerr and Zangor
(2000) studied the role, beliefs and knowledge of a high school pre-calculus teacher, and the impact on student
learning, concerning the use of graphing calculators. All three of these studies resulted in positive indications of
increased student learning. This work seeks to combine elements from these studies to examine the effect of
interactive geometry software on student learning in high school geometry.
Research Question and Anticipated Outcome
The question this work hopes to address is: to what extent does the integration of interactive geometry
software like GeoGebra impact student learning in high school geometry? I am hoping that a significant increase in
learning results from the use of GeoGebra.
Definitions
For clarity, the following definitions are provided. GeoGebra is interactive software that emulates compass
constructions at the basic level, and also provides more advanced features like angle and length measures, formulaic
calculations, and graphing capabilities. Formative assessments are meant to test students’ knowledge during the
learning process, and are used to form a teacher’s subsequent instruction as well as provide feedback to the students.
Although formative assessments can be scored for correctness, they are typically ungraded (i.e., they are not a part
of a student’s overall grade); they are used to establish what else students need to learn in order to be successful on a
future summative assessment. Summative assessments are meant to test students’ knowledge after the learning
process, as a “final” demonstration of what the students have learned. These assessments are usually scored and
graded.
Innovation/Intervention
This work will involve two of my high school geometry classes; one will be used as a control group and the
other as the experimental group. The treatment will occur during a two-week time period within which the
geometric concepts of area formula derivation and area calculation for given polygons will be taught. These
geometric concepts were chosen because students have historically performed poorly on the relevant assessment,
which in turn have negatively impacted student performance on subsequent assessments pertaining to the geometric
concepts of surface areas and volumes of three-dimensional solids (which are dependent on knowledge of polygon
area). The control group will receive traditional instruction in a typical classroom setting, in which the teacher will
demonstrate the derivation of the area formulas of given polygons. The experimental group will be placed in a
computer lab and will receive instruction that is paired with GeoGebra, involving exploratory experiences that lead
students to the derivation of the area formulas of given polygons. Pre- and post-tests, assessing area calculations
using the area formulas, will be administered, scored, and analyzed to determine the extent of the impact GeoGebra
had on the experimental group.
Methodology
Four sets of data will be collected: pre-test scores and post-test scores from both the control and
experimental groups. The pre-test scores would be used to establish baseline knowledge at the beginning of the
experiment. The post-test scores would then be analyzed against the pre-test scores to measure the change in
learning. The post-test scores of both groups would also be analyzed against each other to determine if there is a
significant difference in learning. Since I will be conducting action research with my own students, these data sets
are readily accessible.
Assumptions
Two assumptions are made for this work. First, students from both groups will try their best to demonstrate
what they have learned. Second, the assessments are valid and reliable because they are based on state-approved
standardized test questions.
Limitations and Delimitations
The following limitations will be placed on this work. I will be limited to using classes of students that are
already placed and assigned to me. I will not have the opportunity to construct a truly random sample of students
for both groups. I will be limited to using common assessments, meaning that all geometry teachers are required to
administer the same assessments. These assessments are pre-constructed; I will be unable to change, reword, or
adjust the questions in any way. The computer lab may not have enough working computers so that each student
can work their own computer. I may have to pair students together as they work within GeoGebra. This should not
affect their post-test scores (post-tests are completed individually). The control and experimental groups will be
limited to a specific student population; therefore, the results of this action research may not be generalizable to a
wider student population.
The following delimitations will be placed on this work. Both groups will receive identical pre-tests at the
beginning of this study, as well as identical, form-equivalent post-tests at the end. I will use the same setting to
administer these assessments: students sitting at desks, working individually, without the aid of any other technology
aside from a standard scientific calculator.
Preliminary Steps
To execute this work, I will first need to obtain permission from my principal; he needs to be aware of what
I will be researching and how it will be done. Once that is secured, I will then need to reserve time in the computer
lab for my experimental group. Naturally, I will be in control of my classes, and therefore by association, in control
of this study. Since my site’s geometry team uses common assessments, and those assessments are already written,
obtaining the collection tool and collecting data will not be an issue.
Data Analysis
This work is a quasi-experimental design. The data sets will consist of students’ raw scores (number of
questions answered correctly) on the assessments. Descriptive statistics such as central tendencies and variability
will be calculated. Inferential statistics will also be performed; ANOVA will be the primary analysis method.
Validity can be assured through the use of previously-validated assessments (aligned to state-approved content
standards). Reliability will be assured by administering equivalent forms of the assessments.
Special Considerations, Resources and Cost
In order for the study to be successful, requisite permission/consent/assent must first be obtained. Then it is
just a matter of amassing resources. Computer lab time must be reserved and scheduled. Since GeoGebra is
internet-based software, the computers in the lab must be internet-connected. Copies of the assessments must be
ready for distribution. There are no perceived direct costs, and all indirect costs will be paid by my site.
References
Baki, A. , Kosa, T. , & Guven, B. (2011). A comparative study of the effects of using dynamic geometry software
and physical manipulatives on the spatial visualisation skills of pre-service mathematics teachers. British
Journal of Educational Technology, 42(2), 291-310.
Doerr, H. , & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in
Mathematics, 41(2), 143-163.
Lopez, O. (2010). The digital learning classroom: Improving english language learners' academic success in
mathematics and reading using interactive whiteboard technology. Computers & Education, 54(4), 901915.