| Admittedly fractions are trouble for most | | | | are manhole covers round?", which I presented in |
| students. In my previous article I talked about | | | | my article Why Study Math - The Circle |
| why this is so. Percents and decimals too present | | | | For those educators reading this, they know that |
| their share of problems to young students-adults | | | | a common rebuttal of the math student is "When |
| as well. There is an interesting connection | | | | am I ever going to use this?" In fact, a common |
| between these three mathematical entities and | | | | gripe I would hear is "This is totally useless stuff." |
| here it is: fractions, percents, and decimals are | | | | In preparation for these questions, I worked |
| variations of one and the same thing. | | | | diligently so that I could show students that there |
| That is correct! These three curious mathematical | | | | actually was a connection-a reason-why they |
| objects, which go parading around as though they | | | | were studying the particular lesson at hand. |
| had independent identities, are really one and the | | | | For the topic in question-fractions, percents, and |
| same. It's like Clark Kent and Superman: you take | | | | decimals-students must be made aware that a |
| off the glasses and suit, and you get Superman. | | | | fraction is a percent and that a percent is a |
| Learn about the personality of one, and you've | | | | decimal. Once students know that they are |
| mastered the intricacies of the other. | | | | dealing with one and the same thing, and not |
| When I pointed this relationship out during one of | | | | three separate ones, they feel less overwhelmed |
| my lessons, one student looked at me in | | | | from having to know all about percents, all about |
| amazement and said that he never realized that. | | | | fractions, and all about decimals. When students |
| This boy had gone through school for twelve | | | | now see 1/8, they know that this is a |
| years-he was a senior in high school-and never | | | | mathematical synonym for 12.5% or 0.125. |
| saw that connection. When I would stress this | | | | Similarly 1/4 is 0.25 which is 25%; 3/8 is 37.5% or |
| relationship throughout my different classes, I | | | | 0.375; ½ is 50% or 0.5; 5/8 is 62.5% or |
| would get similar reactions from many students: | | | | 0.625 and 3/4 is 75% or 0.75. |
| they just never made the connection that linked | | | | As obvious as the previous mathematical |
| these three seemingly different ways of | | | | synonyms are to those who understand them, |
| expressing a mathematical idea. | | | | these relationships elude many students, and they |
| Now this is a problem with mathematics education | | | | end up in ignorance, much like the senior of mine |
| in this country. Connections are not made | | | | mentioned earlier-and this can be a life-long |
| between topics in this difficult discipline. For this | | | | ignorance, unfortunately. Yet once connections like |
| reason, students are left scratching their heads | | | | that among fractions, percents, and decimals are |
| wondering when in the world they will ever use | | | | made, connections and cross links are made in |
| something like a decimal, a fraction, or a percent, | | | | other areas as well. When this is done, |
| even though these basic things are literally | | | | mathematics is no longer the formidable bugbear |
| encountered everyday. This failure to connect | | | | that many take it to be. |
| math to reality harks back to questions like "Why | | | | |