Hamilton Hardison
Reaction to
“The Role of Computers in Mathematics Teaching and Learning”
The beginning of Wiest’s article overviews three
ways technology is changing mathematics education. The first of
which is that “some mathematics skills have decreased in
importance.” I am not sure that I agree with this statement
completely. Computations and constructions are not important
alone; however, the concepts and processes associated with these skills
are critical for future application to advanced mathematical
topics. If students do not understand addition of numbers, how
are they to understand more abstract addition as what is involved in
algebra? I am not sure where the line is regarding when students
should be allowed to use technology to skip steps, but I do think it is
important for students to be able to reason through basic arithmetic if
technology is unavailable. Wiest acknowledges this concern toward
the end of the article; yet, the issue is sidestepped by emphasizing
the importance of technology.
The third way mentioned by Weist regarding the
reshaping of mathematics education is one of great importance.
The ability to view the work of others, display ideas, and collaborate
is essential to the development of good mathematics.
I agree that the focus of technology should be on
“higher order thinking with an emphasis on inquiry, reasoning, and
engagement”. Students will not benefit from using technology to
spit out the answers to mathematical situations. For example,
providing a student with a program that calculates the area of a
rectangle does not better the student intellectually. Technology
should “foster rather than replace” mathematical ideas; replacing
mathematical understanding with technology looks good, but results in
students becoming familiar with a procedure rather than ideas.
Of the common uses of computers in mathematics
education, I found the instructional software to be the least useful
for school adaptation. Concept instruction and tutorial software
seek to replace teachers with computer programs. After observing
a novanet classroom, I feel that these types of programs result in
students learning the software rather than the mathematics.
Students learn how to get through the instruction and get to the answer
portion of the program. On multiple choice type questions,
students are able to guess rather than reason. There are other
problems associated with formats involving students keying in
solutions. Computers can only be programmed to do so much and
frequently students can enter correct answers in unrecognized forms; as
a result the computer will recognize the students’ responses as
incorrect and the student will be discouraged. These types of
programs are also limited in terms of explaining mathematics. One
explanation is seldom enough and it would be difficult for a piece of
software to incorporate adequate multiple solutions for all topics
involved.
The portion of the article associated with
programming was very interesting to me, as I have never thought of
incorporating it into a mathematics classroom before. A nice
wrap-up to a unit on logic would be to have students create a simple
program, perhaps like the one outlined in the article. I agree
that programming allows students to “exercise logical, sequential
thinking, … and learn the importance of language precision”. By
allowing students the opportunity to experiment with literal logic,
students may be able to observe logical fallacies that are important
for a reasonable person to be aware of.
The teacher preparation section of the article is
the most unrealistic to me. I agree that teachers need constant
education in order to keep up with the ever-changing technologies
available to them; however, is it financially and physically possible
for teachers to get the training they need? I do not know much
about educational spending but the amount suggested in the article for
teacher preparation seems a bit unreasonable. Even if one-third
of the technology budget were reserved for teacher preparation, as
suggested by ETS, would educators have the time to participate in the
amount of preparation necessary?