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I. Introduction
The product to be evaluated was a self-instructional unit on base 2. The
purpose of the one-to-one formative evaluation was to examine the changes
necessary in the instructional materials in order to maximize their
effectiveness for homeschooled students to teach themselves how to create a base
2 table and recognize the base in which a number is written, convert numbers
from base 10 to base 2, and convert numbers from base 2 to base 10.
II. Methods
After I had completed a rough draft of the materials, I had the unit
simultaneously checked by the following experts who are also homeschoolers, or
have had experience with homeschooling:
- An editor checked that everything made sense, and I had used the correct
words and punctuation to convey my intended meaning;
- An elementary school teacher checked that the materials were appropriate,
i.e., likely to work;
- A high school math teacher checked that I included the necessary facts, and
made no mathematical errors;
- An artist evaluated the graphics and layout.
As a control that I had estimated the range of abilities correctly, I also
asked a sixth grader with an average B-grade in math to evaluate the materials.
Obviously, I have not included her tryout in the evaluation because she is not
from my target audience of homeschoolers.
The instruction was then ready to be tried out by three homeschoolers. The
students assessed that the instruction was easily understood, interesting enough
to sustain their attention throughout the project so that they completed it, and
met the performance objectives and instructional goal.
The homeschoolers were 11 to 14 years old. The first one has a high math
ability. He has high standardized test scores and takes advanced math courses
for his age. The second student is an average math student, with average math
(but high verbal) scores, and takes math at the grade level associated with her
age. The third student is a math phobic who has always done the minimum of math
she could get away with. All the evaluations were done at my dining room table,
a setting not entirely unfamiliar to the homeschoolers. I know all the students
well.
III. Results and discussion
The first student had no problem with any of the math concepts. He quickly
completed the math problems, noticed a transposed number in a solution, and
filled in all the answers correctly. He pointed out that he found one of the
graphics distracting. He then wanted to know how I had drawn up the magic cards.
I showed him and he made more complicated ones. He also wanted to know why there
was more than one way of converting numbers from base 10 to base 2. I explained
that the first method was to make sure he understood the concept of place value,
and the checking method was the method most often used in converting other
bases, such as, base 8 to base 16. He then demanded examples of those.
The second student did not understand what a subscript was, nor what was
meant by the ten digits that we use to write a base 10 number. She had a problem
with the explanation of where to start writing in the base 2 numbers when
converting a number from base 10 to base 2. Once she was shown where to start
she had no further problems with the unit and quickly completed the questions,
using her own (correct) method. I made the necessary changes to the instruction
(see revisions), and the third student had no problems.
All the students thought that the unit was interesting and challenging but
not too difficult. They experienced no problems following the directions and
thought the number of examples and questions "just right". None of
them had studied base 2 prior to the instruction and, not surprisingly, none
wanted to take a pretest. They all completed the unit and could answer the
assessment questions correctly. They liked the way the questions were written.
They made use of the solutions to check their work and commented that they
appreciated the immediate feedback. They all took between 30 and 35 minutes to
complete the instructional unit. I was unsure whether to include the paragraph
on the use of binary numbers by a computer, but they all said that it made the
subject much more relevant to them.
After they had completed the unit they all:
- Drew a base 2 table and identified a base 2 number,
- Converted three numbers from base 10 to base 2 (and checked their answers
using a different method of calculation), without referring back to examples or
solutions,
- Converted three numbers from base 10 to base 2 without referring back to
examples or solutions.
Thus the performance objectives were met.
The unit was not as successful with the school student I had asked to
evaluate the instruction. I may have misjudged the generalizability of the unit
to other students accustomed to different methods of instruction.
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