Blog #71 – BEING CREATIVE WHEN TEACHING

Since I started teaching in 1973, I have always worked toward being creative in everything I did in the classroom and with online tutoring. I think that is why I love teaching so much. My creativity focused on integrating my work with the three competitive math events (Number Sense, Calculator Applications and Mathematics).

My experience working with Number Sense has allowed me to be the most creative, since I have been searching for shortcuts to solve mathematics problems for more than 50 years. My search for shortcuts has included problems from basic mathematics to calculus. Although most shortcuts required the use of mathematical concepts, there were other shortcuts that I discovered by studying patterns. I have been fascinated in using mathematics concepts in unconventional ways. Let me provide a simple example. When converting the common fraction 33/80 to a decimal fraction, I disregard the zero and convert the resulting improper fraction, 33/8, to a mixed number. The mixed number, 4 1/8, is then converted into a decimal fraction. The decimal fraction is 4.125. Finally, I move the decimal point 1 place to the left. Thus, 33/80 = .4125.

Since I began coaching Calculator Applications in 1981, I have found numerous ways to use a calculator to teach mathematical concepts. Using students’ love of technology, I have motivated their interest in mathematics. Let me illustrate an example from Algebra 1. Students have a difficult time transitioning from stating that a vertical line has no slope to a vertical line having infinite slope. When finding the slope of a line, students accept that a slope of 3/0 is said to be no slope since division by 0 is undefined. Later, I illustrate a series of examples that show several lines that gradually get closer to being vertical. For example, I select 6 lines whose slopes are 5/2, 5/.2, 5/.02, 5/.002, 5/.0002, 5/.00002. Notice that the denominators are getting closer and closer to 0. When converting all slopes to decimals, the results are 2.5, 25, 250, 2500, 25000, 250000. Students are now able to see that as lines become closer to being vertical, the slope is going towards infinity. Thus, the slope of a vertical line is infinite.

While studying problems on Mathematics tests, I have learned how to obtain solutions in non-traditional ways. When people think of finding the least common denominator (LCD), the first thing that they think of is the addition or subtraction of common fractions. I have used an LCD when dividing common fractions. When solving 35/4 divided by 7/6, I first find the LCD of 4 and 6. The LCD of 4 and 6 is 12. When converting to equivalent fractions, the problem is now 105/12 divided by 14/12. Since the denominators are the same, disregard them to get the final answer which is 105/14.

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