Reviewed by Cheryl Kopplin
In the last chapter titled, “The Instructional Setting and the Use of
Media” the author suggests other techniques the teacher might implement
to benefit the students. One of the topics he talks about is Computer-Assisted
instruction. He gives examples of how this would benefit the students.
Computers in Elementary Mathematics Education, by Douglas H. Clements copyrighted in 1989.
Reviewed by Cheryl Kopplin
This book is dedicated to using technology with math. The book talks
about the benefits students and teachers would have when the computer is
used in the classroom. He, the author, also gives examples of programs
and projects to use in certain areas of learning, for example computer
programming and problem solving.
Computer Applications in Mathematics
Bibliographies compiled by Elizabeth Coderre
Landesman, E. M. (1999). Visual
Technology in the Teaching and Learning of
Mathematics. Syllabus, 12 (9), 44-46.
Edward Landesman, who was a university teacher
of mathematics for nearly 30 years, found that
by using technology he could address the challenges faced when teaching
basic or fundamental
mathematics courses. Students in these courses had diverse skill levels,
and often required more
individualized attention. Students also sought to link applications
of mathematics to their everyday life
experiences. According to Landesman (1999), "These students needed
to be far more active in their
learning..."(p. 44); and "... technology positions the learner in a
highly active mode, allowing him/her
to continually respond to questions, receive real time feedback, utilize
online manipulatives, and
actively engage in checks for understanding"(p. 45).
Landesman, who is now the Vice-President
of Mathematics Instruction and Professor of
Mathematics in Residence at Academic Systems Corporation, along with
a team of mathematicians,
instructional designers, and engineers produce computer-based, interactive
multimedia materials for
the teaching and learning of mathematics. He gives a few examples that
are taken from the Academic
Systems Interactive Mathematics Series that his company has developed
to show how technology is
being used to maximize student achievement in mathematics. The needs
of students with diverse
levels of math understanding are addressed in this series by introducing
four main characters each
with a particular learning style. Students can receive help from either
one or all of the four characters.
According to Landesman (1999), "Not only are students learning mathematics
in courses taught with
visual technologies, but longitudinal studies conducted by some institutions
are showing that students
who have been exposed to these interactive multimedia learning materials
perform better in
subsequent courses"(p. 46).
Applications: Highline Community
College grants professors added flexibility in
delivering math curricular (1999). T.H.E. Journal, 26
(11), 78-81.
This article ties in nicely with the last article
that I read by Landesman (1999) on interactive
mathematics. It is about how Highline Community College in Washington
is using Academic Systems
Interactive Mathematics software program in their math lab and more
recently on-line. According to
the article, "The instructor-led, computer-based math classes offered
at Highline benefit both
students and professors"(p. 78). The needs of students with multiple
learning styles are addressed
and instructors find more time for one-on-one instruction. Professor
Helen Burn, lead math
coordinator, says the Interactive Mathematics system "…bridges
the gap between instructor
and student. I now have the means to see where students are on an individual
basis and to respond
immediately with assistance. Learning is more effective when the language
of delivery is appropriate
to the individual learner"(p. 80). According to the article, "In addition
to the benefits of one-on-one
interaction with the math instructor, students receive an array of
learning resources from the
software"(p. 80). This allows the needs of students with various learning
styles to be met.
Contact information: www.academicsystems.com
Battista, M. T., & Clements,
D. H. (1991). Using spatial imagery in geometric
reasoning. Arithmetic Teacher, 39, 18-21.
Battista and Clements present a discussion
amongst first, a teacher and two second grade
students, then a teacher and a fifth grade student, and finally of
an episode with a kindergarten
student illustrating student reasoning while using different versions
of LOGO to draw tilted squares
and rectangles. According to Battista and Clements (1991), students
have difficulty recognizing tilted
figures because they use visual imagery to reason in a geometric context.
In light of their findings, two
recommendations for teaching geometry are suggested and three activities
follow.
I agree with Battista and Clements. Many students
do use visual imagery to reason when studying
geometry. Good suggestions are offered. Battista and Clements (1991)
say, "…in teaching
geometry, we should not focus solely on properties of figures and relationships
among them. We
should also help students develop vivid images and coordinate these
images with their conceptual
knowledge"(p. 20). Beneficial examples are given in the listed activities
using LOGO to help
promote students’ coordination of visual imagery and conceptual
knowledge. I particularly
like the special note at the end of the article, which explains how
you can still use LOGO-like
commands if you do not have access to a computer.
Fitch, D. (1993). Quilting by computer. Learning, 21, 37.
Dorothy Fitch illustrates how to create quilts
by using the computer and LOGO. According to
Fitch (1993) by doing this computer quilting project, students of all
ages can apply what they have
learned about symmetry when studying geometry. Quilt making with computers
also uses patterns.
Creating quilts by using the computer is a
great idea. Not only can this project be used with
students of all ages but it can also incorporate various disciplines
such as mathematics, computer
science, history, social science, and art. This project is a fun learning
activity that involves the entire
class. It teaches creativity as well as teamwork.
Bibliographies by Glenn Blaisdell
1. Bamberger, H., & Hughes, P. (1996), Super Graphs,
Venns, and Glyphs: Hundreds of Great Data Collecting
Activities to Build Real-Life Math Skills. :
Scholastic, Inc.
Graphs, Venns, and Glyphs is meant to inspire teachers
to collect data from online sources with their
students every day. The book suggest doing data
collection a morning activity and gives many activity
ideas.
2. Kellough, R. D. (1995), Integrating Mathematics
and Science for Intermediate and
Middle School Students. : Prentice Hall
This book describes ways to teach mathematics in the
most effective way to children in grades 4-9. Chapter
7 discusses integrating mathematics into an effective
curriculum. Graphing, statistics, and probability is
covered in chapter 12. Computers and Electronic
Technology for activities for integrated mathematics
and science is covered in chapters 17 and 18
Bibliography developed by Dameon Kellogg
1. Adams, Kathleen. "The Incredible Shrinking Personal Computer". Time
.
Vol. 150 issue 18 p.39 03 September
97.
This article argues about calculators in the classroom and the defense
of them staying there. The counter in the article argues that students
learn more when they do the math themselves.
2. Davis, Jeanne. "How Mastering Technology can Transform a Math
Class". Educational
Leadership. Vol. 55 n3, p.49-51, Nov.
1997.
This article tells of Maryland middle-school teacher who has made use
of
many technologies in her classroom. From computers to calculators and
even colored printers, this teacher is working hard to meet the
21-century technology goals set by the Dept. of Ed. in 1995.
3. Hunsaker, Diane. "Ditch the Calculators". Newsweek. Vol. 130,
iss.
18,
p. 20, 03 November 1997.
This article discusses one teachers frustrations as she forbids use
of
the calculators because the lack of simple multiplication skills in
her
classes.
4. Sheppard, Robert. "March of the Laptop". Maclean's. Vol. 111 iss.
44,
p. 86, 02 November 1998.
Discusses the use of laptop computers in the classroom and questions
whether computer technology accelerates academic achievement.
Citations developed by Bruce Provencher
Bosch, William & Sizoo, Jennifer (1997), Fishy Formulas. Mathematics
Teacher, v 90
#8 (pgs 666-668).
This article uses graphing calculators to determine
the weight of game fish based
on its given length.
Peterson, Blake (1997), A New Angle On Stars. Mathematics Teacher,
v 90 #8 (pgs
634-639).
This article uses "Geometer's Sketchpad" to explore
different angles used when
making stars with a different number of sides or points.
Vonder Embse, Charles (1997), Visualizing Least-Square Lines of Best
Fit.
Mathematics Teacher, v 90 # 5 (pgs 404-407).
This article uses "Geometer's Sketchpad" to teach
students computations associated
with least-squares regression.
Yerushalmy, Michal & Gilead, Shoshana (1997), Solving Equations
in a Technological
Environment. Mathematics Teacher, v 90 # 2 (pgs 156-162).
This article asks if solving equations with technology
any more meaningful than
solving by rote manipulations. It also determines whether efficient
guessing can be
achieved using technology.
Citations developed by Dana Cooke
McGehee, Jean J. (1998), Interactive
Technology and Classic
Geometry Problems. Mathematics Teacher, v 91 #3 (pg 204-208).
This article discusses the
benefits of having geometry
software. "Interactive geometry software connects visual justification
and empirical thinking with justification in formal proof." Also
they
warn of the lost understanding of overuse, and draw comparison to the
engaging concepts that are embedded in the classic works of the Greek
geometers.
Yerushalmy, Michal and Gilead,
Shoshana (1997), Solving
Equations in a Technological Environment. Mathematics Teacher,
v 90 #2
(pg 156-162).
The article discusses the
use of technology to separate the
process of algebra into two parts--manipulating equations and seeing
solutions. This article is based on a study conducted in Israel
in
which students were given instruction prior to using the technology
and
given quizzes. They were then shown the use of the software and
came
forth with better test results and seemingly a better understanding
of
the material.
Olmstead, Eugene A. (1998),
Exploring the Locus of Definitions
of the Conic Sections. Mathematics Teacher, v91 #5 (pg 428-434).
An interesting article consisting
of tips for uses of
technological software. Specifically, the article discusses the use
of
dynamic-geometry-system (DGS) software to create an environment in
which
all students can explore and extend the locus definitions of conics.
Iovinelli, Robert (1998),
Using Spreadsheets to Analyze the
Historical Perspectives of Apportionment. Mathematics Teacher,
v91 #2
(pg 176-182).
This article demonstrates
the use of spreadshets in the
mathematics classroom. This approach to education through technology
integrates English and social studies along with mathematics in the
use
of spreadsheets. The spreadsheets take away what, even with a
calculator, appear to be mundane arithmetic calculations.
Citations developed by Angela Da Cunha
Burke, William & Kick, Richard. (1998). Technology.
Mathematics Teacher, v91 #1
(Pgs. 84-86).
This article gives examples of different kinds of
mathematical software and then
gives the readers the pro's, con's, and whether the magazine recommends
it or not.
An example of a software package is Calculus Connections: A Multimedia
Adventure. It tells what computers it is compatible with and
it says the pros are that
it shows real world application of calculus concepts. The cons
are that it is limited
interactive capabilities with video, and the recommendations are that
it is useful as a
supplement to good teaching.
Mc Clintock, Edwin & Jiang, Zhonghong. (1997). Spreadsheets:
Powerful Tools for
Probability Simulations. Mathematics Teacher, v 90
#7 (Pgs. 572-579).
This article discusses high school students
to learn more about probability to
improve their intuition and build more formal concepts on theoretical
probability
based on their experiences. This is done by using
spreadsheets which are very
powerful tools for simulating probabilistic situations, such as flipping
a coin and
other complex problem situations.
Thompson, Denisse & Davis, Suzanne. (1998). To Encourage
"Algebra for All," Start
an Algebra Network. Mathematics Teachers, v91 #4. (Pgs.
282-286).
This article discusses an algebra network which has
been created to provide
opportunities for articulation among elementary, middle, and high school
mathematics teachers. It is also to increase awareness of the
algebra curriculum and
d of appropriate teaching strategies at the k-12 levels. The
algebra network focuses
on creating opportunities for more African American and female students
to
participate and succeed in higher level mathematics.
Vonder Embse, Charles & Yoder, Vernon. (1998). Multiple
Representations and
Connections Using Technology. Mathematics Teacher, v 91
#1 (Pgs. 62-67).
This article talkes about how to graph a problem
on a graphing calculator, which
allows the problem to be solved. The article goes in to much
detail and shows
pictures and gives example problems on how to use your graphing calculator
to
solve a problem.
Ed Kobelski's Citations:
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Battista, Michael T. "Calculators and Computers: Tools
for
Mathematical Exploration and Empowerment." Arithmetic
Teacher.
March, 1994. (p. 412-417)
This article explains various methods for incorporating calculators
and computers into mathematics lessons, with an emphasis on
student exploration. Included are calculator games and
Logo
applications.
------------------------------------------------------------------------------
National Council of Teachers of Mathematics, Curriculum and
Evaluation Standards for School Mathematics. Reston, Va.:
NCTM,
1989.
This detailed report provides an ideal framework for school
mathematics, which American school should strive to achieve.
A
large portion of the NCTM Standards is devoted to convincing
school
personnel that the use of technology is critical in teaching
mathematics at all levels. This report reveals how computer
software "transforms the mathematics classroom into a laboratory
much like the environment in many science classes, where students
use technology to investigate, conjecture, and verify their
findings."
Included are some specific examples on calculator uses in actual
problem solving situations.
----------------------------------------------------------------------
Cuevas, Gilbert J. Empowering All Students to Learn Mathematics.
Reston, Va.: The Council, 1995.
This article talks about the need to involve all students in
the
mathematics reform movement, and addresses approaches
educators can use to empower students in mathematics.
One of
these methods is through the use of technology in the classroom.
The role of technology is discussed, and issues of equity in
the
distribution of technology are studied.
------------------------------------------------------------------------
Connecticut State Department of Education, Division of Teaching
and Learning. Mathematics Curriculum Framework.
March, 1998.
This document is an outline of content goals and standards for
K-12
mathematics in the state of Connecticut. Included everywhere
throughout the report is a reference to the "use of real-life
experiences, physical materials and technology to construct
meanings" for various mathematical concepts. This shows
how
technology is necessary to bring mathematics instruction and
learning to its fullest potential, even here in Connecticut.
TITLE: How K-12 Teachers are Using Computer Networks [Internet Use in
Schools: Observations and Issues]
AUTHOR: Peha, Jon M.
JOURNAL: Educational Leadership, October 1995, pp. 18 - 25.
SUMMARY: The article discusses ways in which the internet can be integrated
into the classroom curriculum and how this would affect school systems.
Several ways in which students may use computers are presented, including;
sending work to another party for evaluation or response, group projects
in which students look at different locations and collaborate on activities,
and students can take advantage of the data sources and processing capabilities
o the network. The internet was successful at giving students an awareness
that they are part of a global community. The internet gives students a
wide variety of resources, stimulates thinking, and improves computer literacy.
The teachers surveyed, offered several suggestions for avoiding difficulties
when introducing the internet in the classroom. Additionally, the article
presents some ideas for teacher preparation and support.
Overall I found this article to be quite useful. It is slightly outdated
and therefore some of the resources mentioned (reference guides for "cruising"
the net) have been replaced by newer versions. This article provides some
"food" for thought.
Hembree, Ray and Dessart, Donald J. "Research on Calculators in
Mathematics Education." Reston, Va. 1992.
Focuses on ways that calculators are used in the classroom, and
strategies that work the best.
LCSI. Logowriter. Montreal: Logo Computer Systems. 1986. Software.
Ways to incorporate logo in the classroom.
Wheatley, Grayson H. and Shumway, Richard. "The Potential for
Calculators to Transform Elementary School Mathematics."
Updates new ways to use technology in the classroom to transformc
the traditional ways of teaching mathematics in elementary school.
2) Teaching Children Mathematics, An Exploration of Fifty Nifty
States, NCTM,
Sheryl Ormen and Debra Schneider, Feb. '96, Volume 2, Number 6, p.
330-334.
The Fifty Nifty States is a unit that integrates math, social studies,
and technology. Students learn about the U.S. using computers as a
resource.
Not only do students have access to graphs, charts, maps, tables, etc.
of facts
on the country and states, but they also have access to people through
the
Internet.
3) Teaching Children Mathematics, Using Data to Make Decisions
About Chance,
NCTM, Graham Jones, Cynthia Langrall, and Carol Thornton, Feb '96,
Volume 2,
Number 6, p. 346-350.
Data and chance is a program that explores probability. Students were
involved in activites pertaining to chance. Theyn had to collect their
data,
record, and make conclusions. However, the class had trouble imagining
1000
tosses, for example. They then used the computer to generate and graph
a large
number of trials.
4) Teaching Children Mathematics, Adding Taste to Mathematics,
NCTM, Champee
Kemp, Dec. '95, Volume 2, Number 4, p. 224-225.
This article discusses a unit on measurement and fractions using
computers and going on a field trip. The students learned fractions
and
different types of measurements in recipes through mind-play software.
Prichard, Mary Kim. "Mathematical Iteration through Computer Programming." Mathematics Teacher. 2 (Feb, 1993 ): Vol 85 p150-156.
This article is about math iteration. Iteration is a process for
generating a
sequence in which one or more intitial terms are given and each subsequent
term is determined from its predecessors in the same way. The article covers
why to teach iteration, teaching iteration,and the problems related to
mathematical
iteration.
Allinger, Glenn D. "Reviewing and Viewing Computer Materials,
Logo
Geometry." Arthmetic Teacher. 1 ( Sept 199: Vol 40 p 56.
The aticle is about the software, Logo Geometry by Silver Burdett
and
Ginn. The article briefly discusses the program and its weaknesses.
This program is ideal for grades k-6. This is a new way to learn geometry
by being able to actively construct geometric concepts.
Clements, Douglas H,. Shielack, Jane. "Reviewing and Viewing Computer
Materials." Arithmetic Teacher. 6(Feb 1993): Vol 40 p 366-369.
This article is reviews the program on Ten Base Blocks. Ten Base
Blocks
centers on exercises involving place value, patterning and counting,
primarily using simulations of Dienes blocks.
Lehman, Jeffrey. "Technology Use in the Teaching of Mathematics and Science in Elementary Schools." School-Science-and- Mathematics. Vol. 94, No. 4, p. 194-202, April 1994.
This article presents surveys of elementary school principals assessing the nature and extent of technology use in elementary mathematics and science. They found out that teachers used microcomputers more in mathematics than in science, and microcomputer and caculator use was more common in intermediate grades than in primary grades.
Moreira, Candida, and Richard Noss. "Understanding Teachers' Attitudes to Change in a LogoMathematics Environment." Educational-Studies-in-Mathematics. Vol. 28, No. 2, p. 155-76, March 1995.
This article describes and analyzes attitudes of two Portuguese elementary teachers toward mathematics, mathematics teaching, and use of computers in instruction. Semistructured interviews and questionnaires, before and after an inservice LOGO computer course, showed that both teachers changed their attitude, but only one implemented her ideas in teaching.
Perry, Mike, and Gary Kader. "Using Simulation to Study Estimation." Mathematics-and-Computer-Education. Vol. 29, No. 1, p. 53-64. Winter 1995.
This article illustrates how to use computer simulation models in statistics to study the quality of an estimation procedure and concurrently the subtle concepts of randomness and convergence. Special emphasis is given to the use of graphical representations.
Wagner-Pine, Linda, and Donna-Graham Keith. "Investigating Various Volcanic Eruptions and Volcano Heights." School- Science-and-Mathematics. Vol. 94, No. 8, p. 432-38, Dec. 1994.
This article presents an integrated math/science activity that shows students the differences among the three types of volcanoes using observation, classification, graphing, sorting, problem solving, measurement, averages, pattern relationships, calculators, computers, and research skills.
Young, Michael. "Assessment of Situated Learning Using Computer Environments." Journal-of-Science-Education-and-Technology. Vol. 4, No. 1, p. 89-96, March 1995.
This article suggests that, based on a theory of situated learning, assessment must emphasize process as much as product. Several assessment examples are given, including a computer-based planning assistant for a mathematics and science video, suggestions for computer-based portfolio assessment, and speculations about embedded assessment of virtual situations.
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