Science - Page 42

Comfort
If I had a nickel for every time someone said to me , “ I ’ m not a math person ” – then I could fill hundreds of miser ’ s dream buckets with coins . I have come to understand that the statement really means “ math makes me uncomfortable .” This is often the result of negative experiences in classes ( or with teachers ), and unfortunately it is all too common .

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One of my goals as a teacher is to help change this perspective , for this surely makes better math students . I like for the magic ( and the mathematics ) that I do in class to be inviting , welcoming – and comfortable – to the students . I do my best to avoid “ gotcha ” -type effects , especially in introductory classes of hesitant students . If I can make students comfortable by enjoying some magic , then I am one step closer to having them feel more comfortable with the math behind it . Comfortable math students are better math students .
Coolness
When a student tells me that math is not their thing , I like to add the word “ yet ” to their statement . I suggest that perhaps they have not yet encountered a part of mathematics that has caught their attention , and then I like to try and find something that will do just that . If I can help students find something “ cool ” about math , then they are less likely to have the “ not a math person ” perspective – and that makes them better math students .
• Take any number that is not evenly divisible by 7 , get a calculator , and then divide that number by 7 . If the calculator window is large enough , you ’ ll see lots of numbers to the right of the decimal ( they actually go on forever , but no calculator window is that large !). Find the sum of the first six digits to the right of the decimal . You ’ ll always get 27 . Cool math area : cyclic numbers .
• Start with a three-digit number , perform a particular set of easy operations , and always end up with the number 1089 . ( The operations are readily available via an internet search of the number 1089 .) Cool math area : basic algebra is used to show why this works .
• Fold a piece of paper a certain way , make a single , straight scissor cut . Unfold the paper to reveal a swan , a butterfly , a star , or many other things . Cool math area : the Fold and Cut Theorem .
• Modular Arithmetic : I tell my class that I have a very strange hobby – I memorize Universal Product Codes ( UPCs ) that appear on retail items . They can test me by calling out the codes on items in their possession and omitting one of the digits ( and instead saying “ blank ” at that position ). After a series of questions meant only for show ( and a little bit of basic mental calculation ), I am able to announce the missing digit . I ’ m not sure I fool anyone with my “ strange hobby ” claim , but this is a fun introduction to the area of modular arithmetic , which is the thing upon which the patterns of UPCs are based .
Curiosity
A curious mind is one of the best things a math student can possess . Genuine curiosity involves not only a desire to know more about something , but also a willingness to persevere on the journey toward that knowledge . Sometimes ( many times ?) in math classes , impatience wins out over curiosity . Understandably , it may be difficult for a student to generate genuine curiosity about a word problem involving two trains approaching one another on parallel tracks . Nurturing curiosity takes practice , though . If I can encourage curiosity in other settings , maybe that skill and the associated perseverance can be more fully developed .
An example I have used in class in this setting is an effect similar to David Copperfield ’ s Orient Express trick ( not the one where an actual train disappears , but the one involving a grid of cards similar to the one here . A card is randomly chosen , and , after several steps / moves , Copperfield identifies the current location ).
• Start with a standard deck of 52 playing cards , do eight successive faro shuffles to really mix them up ( wink-wink ). The cards are now in their original positions ! Cool math area : several great ( advanced ) mathematical topics related to card shuffling .
Coolness is in the eye of the beholder , of course , and so I try to use an assortment of different ideas to help students see a new side of math .
Concepts
Magic Mondays can work nicely as introductions to class topics . When students have relatable examples in mind , new concepts are less abstract for them from the beginning .
• Angles , Area , Slope : The pieces in the puzzle on the left can be rearranged into the positions on the right – and there is something missing ! These “ geometric vanishes ” have appeared in various forms over the years , but the reason for their weirdness is all based on angles , areas , and slopes of lines . This effect is a nice introduction to some of these topics .
This is nice because it can be repeated at students ’ desks with their own cards , and the effect / method is in the sweet spot between being too easy and too complex . I have found that this puts their curiosity level at just the right place , and they enjoy working toward understanding the reasoning ( which , by the way , is based on the relationship between even and odd numbers ).