The Role of Technology in Teaching and Learning Mathematics
Tuba Gökçek
KTÜ Fatih Eğitim Fakültesi-Trabzon
ÖZET
Bu çalışmada Matematik eğitim öğretiminde teknolojinin rolü üzerinde durulmuştur. İlk bölümde,
matematik öğretirken hangi teknolojik araçlardan faydalanıldığına değinilmiş, daha sonra teknolojinin neden
önemli olduğu National Council of the Teachers of Mathematics (NCTM, 2000) teknoloji ilkelerine parelel
olarak örneklerle açıklanmaya çalışılmıştır. Son olarak, teknolojinin hızla ilerlediği günümüzde eğitimci,
öğretmen ve ebeveyn olarak eğitimde teknolojinin yeri ve önemi konusunda sorumluluklarımızı bilmemiz
gerektiği vurgulanmıştır.
Anahtar Kelimeler: Teknoloji, Matematik Eğitimi, NCTM, Dinamik Yazılımlar, Bilgisayar
Introduction:
The general guidelines of the role of technology in teaching and learning mathematics stated
in the Principles and Standards in School Mathematics (NCTM, 2000) under the Technology
Principle as:
 Technology enhances mathematics learning.
 Technology supports effective mathematics teaching
 Technology influences what mathematics is taught (p.25-26).
These ideas suggest that technology is essential in teaching and learning mathematics.
With the development of technology, students begin to use technological tools such as
calculators and computers in the classroom learning environments for constructing and
applying mathematical ideas. First they used scientific calculator, which is later replaced with
graphing calculators, TI, 82, TI-89, TI-92. By using graphic calculators in their activities and
problems, students can furnish visual images of mathematical ideas, facilitate organizing and
analyzing data, and compute efficiently and accurately. Along with calculators, spreadsheets
became commonly used particularly in early stages of algebra in primary grades. In the
middle and high school, students are introduced by Dynamic geometry software (known as
Geometer’s Sketchpad and Capri Geometry). Geometry software helps students to develop an
understanding of geometric concepts and learn their features. Moreover, in higher grades,
based on their knowledge of geometry, students can formulate relevant definitions and
theorems.
With computers, “technology has become a significant tool for promoting
mathematical problem solving, reasoning, and exploration” (Pugalee, 2001, p. 171).
Computers help students develop algebraic thinking. They allow students to explore variables
and relationships among variables. Furthermore, students are motivated to learn to generalize
and formalize so that they can devise their own ways to command the computer to draw
pictures or to solve numerical problems (Clements & Sarama, 1997). Besides, students can
build on their own understanding by using computers as resource tools, or as communication
tool to share their ideas with other learners. They can also share and compare their individual
understanding and experiences.
On the other hand, communication tools like e-mail, listservs, bulletin boards, and chat
groups allow teachers to exchange lesson plans and teaching strategies. In addition, computers
increase the students’ motivation on subject and lessening anxiety among low ability students.
1
Why the use of technology is important in mathematics and how do we use them?
First, and perhaps the most important, technological tools have the power to transform
abstract mathematical concepts into concrete, visual representations. Especially in earlier
grades, students may not be developmentally ready to work with abstractions. If they are
provided tools that support their mathematical development, they can feel confident starting to
learn advanced level concepts. Author of NCTM explicated that “students’ engagement with
abstract mathematical ideas can be fostered through technology” (NCTM, 2000, p.25).
Second, technology allows students to actively participate in mathematical problem solving.
Brown, Galloway and Orrill (2002) stated that “using spreadsheets, graphing calculators, and
dynamic geometry software provides the students with an opportunity to manipulate
mathematical situations in order to observe patterns, relationships, and generalizations”(p.25).
Current reforms in mathematics education recommend extending the study of patterns
to include pattern finding (Thomas, 2002). For instance, Principles and Standards for School
Mathematics (NCTM, 2000) says students should create and use symbolic, graphical, and
verbal representations to analyze and understand patterns.
Technological tools also motivate students. When students allow becoming active in
learning, they can develop their own strategies and understandings. With the help of
technology, students can discover mathematical relationships and connections. In Technology
Principle it is stated “Technology enriches the range and quality of investigations by
providing a means of viewing mathematical ideas from multiple perspectives” (NCTM, 2000,
p.25). Finally, technological tools help prepare students to be future problem solvers and
technology users. As McMullin (2001) states “mathematics in the real words is done with
technology. In today’s world, not introducing students on the use of technology is doing them
disservice” (p.85).
As noted in the Curriculum and Evaluation Standards for School Mathematics
(NCTM, 1989), more attention must be given to (1) developing and understanding of
variables, expressions, and equations; (2) using a variety of methods to solve equations and
informally investigate inequalities. In Algebra classes, students often have problems with
understanding of variables, and equations. At this point, spreadsheets allow them to include
variables in formulas, and thus to test relationships in a way that are not possible to do with
paper-and-pencil work. The most benefits of this are the fact that in spreadsheets, variables do
not have names. Cells play the role of variables. The cell itself corresponds to the variable
whereas the contents of the cell correspond to the current value of variable.
To understand the difference better, we can consider problem of helping students solve
for x, unknown, in the equation 6x + 2 = 3x – 4. By tradition, we focus on solving this
algorithmically. First, we try to have students understand the concept, and then give them a
set of rules to find solution; I believe that makes their thinking limited. However, computer
spreadsheet’s graphing capabilities help them see equations and their solutions in new ways.
With spreadsheets, students can also look for patterns, and investigate sequences and
series. In this manner, I found the activity of Friedlander (1998) focused on the investigation
of sequences presented in a numerical or visual manner in a beginning algebra course. The
results showed that “most students get quite involved in sequence activities if the problems
are not presented in numbers that reduce them to routine exercises”(p.382).
2
As another technological tool, calculators are indispensable to use in the mathematics
classrooms. It has been shown that calculator use in the classroom increases test scores for
low and average students (Hembree & Desart, 1992). In my opinion, todays’ calculators mean
more than just computation for students. NCTM (1989) states that every mathematics student
in middle and high school should have a graphing calculator. Students can insert variables,
functions and relations, make value-table for given parameters, and the graph data or function
by using calculator. With a graphing calculator, they are able to see multiple steps as they
solve the problem. Further, complex problem situations can be solved by applying appropriate
features’ of them.
In algebra classes, students are being asked to show their work and justify their
simplifications, often without formal proof process. The exploratory and visual natures of
graphing calculators allow students to investigate algebraic properties, to test, and refine
conjectures; and to find counterexamples (Hirschhorn & Thompson, 1996). I think, the
example the authors explained in their article is useful to mention. They consider the
following sentence as conjecture, and ask students if its valid or not: (x+3)2 = x2+9
They found that when using either the 2nd(TEST), or table generating features, the proposed
conjecture can be tested easily. Even a more general conjecture, f(x)=g(x) can be tested for all
values of the variable on the same coordinate graph.
Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) states
that the reasoning skills that all students should know include making and testing conjectures,
formulating counterexamples, judging the validity of arguments, and constructing simple
valid arguments. Based upon these suggestions, we can say that Dynamic geometry software
is an important technological tool. In the Technology Principle, NCTM stated that “with
technology at hand, young children can investigate characteristics of shapes using dynamic
geometry software”(NCTM, 2000, p. 26).
Especially, Geometers’ Sketchpad (Jackiw, 1995) allows students to create and
manipulate geometric constructions to test conjectures. In the middle school, by drawing
variety of geometric figures, students can understand their definitions, their properties, the
relations among them, and the methods of measurement and construction. According to the
NCTM Standards (2000), technology-based investigations can help students visualize, solve
problems, explore and test conjectures, access data, and verify solutions. However, the
validity of conjectures should not lead students to accept these verifications as proofs. In high
school, using Sketchpad can motivate students to generate proofs of the properties of
geometric shapes. Geometers’ Sketchpad also affords opportunities to experiment
transformational geometry (Manouchehri & Enderson, 1998). For example, the “Transform”
option in the menu allow us to reflect, dilate, and rotate geometric figures already drawn in
the workspace.
In addition to the Dynamic software environment, the Logo-based environments can
facilitate transition from visualization level to the analysis level (Glass & Deckert, 2001).
With Logo, students can create geometric objects and apply constructions and transformations
of those objects (translation, rotation, and reflection). NCTM Technology Principle also
supports the use of Logo in young children by saying that “ work with Logo can allow young
children to extend physical experience and to develop an initial understanding of sophisticated
ideas like the use of algorithms” (NCTM, 2000, p.27).
3
Conclusion:
So far, I tried to examine the role and the importance of technology in teaching and
learning mathematics considering Technology Principle in NCTM 2000 Standards.
I believe that, as people living in the 21st century, we must be aware of the importance
of the technology in our children’s life by giving them every possibility to make them critical
thinkers, and good decision makers. We, as teachers, must have much responsibility to imply
technology in our teaching that needs professional education. By doing this, we should realize
that how can technology be used and applied into the curriculum? What changes are
necessary to make? How are students interacting with the tool? Besides, we should always
remember that technology could only be a way to support our teaching, to help our students
understand mathematical concepts deeply.
I always think that today’s children are lucky than our generations since they have so
many opportunities than we had at school. Our possibilities of using computers were too
limited. So, I think it is a great opportunity to have those entire technologies around if they are
properly used in learning mathematics. What is better is technology supplies real entertaining
stuff that can be very helpful in teaching.
4
References:
Brown, S., Galloway, C., & Orrill, C. (2002). Lead you students in mathematical discovery.
Learning and Leading with Technology, 29 (5), 22-27.
Clements, D. H., & Sarama, J. M. (1997). Computers support algebraic thinking. Teaching
Children Mathematics, v.3, p.320-325.
Friedlander, A. (1998). An excellent bridge to algebra. Mathematics Teacher, 91 (5), p.382-3.
Glass, B., & Deckert, W. (2001). Making better use of computer tools in geometry.
Mathematics Teacher, 94 (3), p.224-9.
Hembre, R., & Dessart, D. (1992). Research on calculators in mathematics education.
Calculators in Mathematics Education: 1992 Yearbook (p.23-32). Reston, VA:
National Council of Teachers of Mathematics.
Hirschhorn, D. B., & Thompson, D. R. (1996) Technology and reasoning in algebra and
geometry. Mathematics Teacher, 89, p. 138-42.
Jackiw, N. (1995). The Geometer’s Sketchpad. Berkeley, California: Key Curriculum Press,
Software.
Manouchehri, A., Enderson, M. C., & Lyle, A. (1998). Exploring geometry with technology.
Mathematics Teaching in the Middle School, 3, p.436-42.
McMullin, L. (2001). Soundoff! Algemetic. Mathematics Teacher, 94 (1), 84-85.
National Council of the Teachers of Mathematics (NCTM). (1989). Curriculum and
evaluation standards for school mathematics. Reston, VA: Author.
National Council of the Teachers of Mathematics (NCTM). (2000). Principles and Standards
for School Mathematics. Reston, VA: Author.
Pugalee, D. K. (2001). Algebra for all: the role of technology and constructivism in an algebra
course for at-risk students. Preventing School Failure, 45 (4), 171-176.
Thomas, C. S., & Thomas, D. A., Wallace, M. L. (2002). Finding infinity in a snowflake.
Learning and Leading with Technology, 29 (7), p.28-31.
5