Icons vs. Symbols

The students completed their tip to Detroit (without me) and were still excited about the experience the day after when I returned to the classroom. They knew that they were supposed to create a “trip-line” to document their trip but before they could get started on it they had to understand that the “trip-line” is made up of icons, which brings up the question, what is an icon? The curriculum teaches this by explaining the difference between a symbol and an icon. The example given in the book was centered on the number thirteen. Three representations were shown – thirteen small stars, the Arabic Numeral 13, and the Roman Numeral XIII. The thirteen stars were considered an icon because thirteen stars were shown, the Arabic Numeral 13 was a symbol because it was man-made and we have agreed that the numerals 1 and 3 next to each other represent the quantity thirteen, and the Roman Numeral XIII was a mixes symbol because the X is a symbol and the three I’s can be seen as icons. At this point the students are completely lost and the next step is to have them create their own chart of symbols and icons. The teacher, a math Professor from Eastern Michigan University who helps in the class weekly, and I were trying to come up with another example that might hit a little closer to home and I thought of Nike shoes. The icon would be a basketball shoe and the symbol would be the swoosh (the check-mark that appears on everything Nike makes). I went up to the board to explain this new example for my first every impromptu teaching moment. The explanation went pretty well and the students were starting to distinguish between the two representations and by the end of the class each group in the class was able to share a different icon/symbol pair. This lesson about symbols and icons seemed so out of place to me during the class but after some reflection (and some help from others involved in the AP) I realized that the ability to represent an item with a symbol is a fundamental concept in algebra and in math in general. Had I (or the other teachers) made this connection during the class we could have offered a more complete and insightful explanation of the difference between icons and symbols and even encouraged the students to make their own symbols as mathematicians, scientists and engineers do when they create mathematical models.