MATH MISERY? Manan Shah, PhD. September 20, 2014 NJPAECET2. Math mathmisery.com
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1 @shahlock mathmisery.com MATH MISERY? Manan Shah, PhD NJPAECET2 September 20, 2014 c 2014 Think. Plan. Do. LLC All Rights Reserved 1 Manan Shah (@shahlock)
2 @shahlock mathmisery.com SOME BACKGROUND BS ELECTRICAL ENGINEERING MS, PHD MATHEMATICS EDUCATION STRUCTURED FINANCE GAMING / GAMBLING c 2014 Think. Plan. Do. LLC All Rights Reserved 2 Manan Shah (@shahlock)
3 Logical Logical Linguistic Mechanical c 2014 Think. Plan. Do. LLC All Rights Reserved 3 Manan Shah (@shahlock)
4 Logical Logic logic = legalism of mathematics c 2014 Think. Plan. Do. LLC All Rights Reserved 4 Manan Shah (@shahlock)
5 Logical Mathematics Mathematical theorems are non-negotiable c 2014 Think. Plan. Do. LLC All Rights Reserved 5 Manan Shah (@shahlock)
6 Logical Mathematics If f is differentiable at x Then f is continuous at x c 2014 Think. Plan. Do. LLC All Rights Reserved 6 Manan Shah (@shahlock)
7 Logical Mathematics What happens if f isn t differentiable at x? c 2014 Think. Plan. Do. LLC All Rights Reserved 7 Manan Shah (@shahlock)
8 Logical Social Social theorems are negotiable c 2014 Think. Plan. Do. LLC All Rights Reserved 8 Manan Shah (@shahlock)
9 Logical Social Clean your room Get pizza c 2014 Think. Plan. Do. LLC All Rights Reserved 9 Manan Shah (@shahlock)
10 Logical Social What happens if the room isn t cleaned? c 2014 Think. Plan. Do. LLC All Rights Reserved 10 Manan Shah (@shahlock)
11 Logical Social Pizza is still possible! c 2014 Think. Plan. Do. LLC All Rights Reserved 11 Manan Shah (@shahlock)
12 Logical C-C-C Conditional: X Y Converse: Y X Contrapositive: Y X c 2014 Think. Plan. Do. LLC All Rights Reserved 12 Manan Shah (@shahlock)
13 Logical Mixed Worlds Social Logic Math Logic c 2014 Think. Plan. Do. LLC All Rights Reserved 13 Manan Shah (@shahlock)
14 Logical Math & Pizza Clean room Get pizza c 2014 Think. Plan. Do. LLC All Rights Reserved 14 Manan Shah (@shahlock)
15 Logical Contracts Logic is contractual c 2014 Think. Plan. Do. LLC All Rights Reserved 15 Manan Shah (@shahlock)
16 Logical Truth Table p q p q F F F T T T T F F (broken contract!) T T T c 2014 Think. Plan. Do. LLC All Rights Reserved 16 Manan Shah (@shahlock)
17 Logical Missing In Math Ed We need to teach more logic and fewer rules c 2014 Think. Plan. Do. LLC All Rights Reserved 17 Manan Shah (@shahlock)
18 Logical Assumptions I ll see you in the middle of the week c 2014 Think. Plan. Do. LLC All Rights Reserved 18 Manan Shah (@shahlock)
19 Logical Assumptions How many numbers are between one and ten? c 2014 Think. Plan. Do. LLC All Rights Reserved 19 Manan Shah (@shahlock)
20 Logical Assumptions Overassume, Underassume c 2014 Think. Plan. Do. LLC All Rights Reserved 20 Manan Shah (@shahlock)
21 Logical Assumptions 3 x+2 > 1 = 3 > x + 2? c 2014 Think. Plan. Do. LLC All Rights Reserved 21 Manan Shah (@shahlock)
22 Logical Missing in Math Ed We don t stress context enough c 2014 Think. Plan. Do. LLC All Rights Reserved 22 Manan Shah (@shahlock)
23 Linguistic Logical Linguistic Mechanical c 2014 Think. Plan. Do. LLC All Rights Reserved 23 Manan Shah (@shahlock)
24 Linguistic English Is A Disaster! food good pear hear hear rear rear bear dough rough read read c 2014 Think. Plan. Do. LLC All Rights Reserved 24 Manan Shah (@shahlock)
25 Linguistic Definitions Definitions! Definitions! Definitions! c 2014 Think. Plan. Do. LLC All Rights Reserved 25 Manan Shah (@shahlock)
26 Linguistic Colloquial Students define: continuous never-ending it goes on forever always on repeating (periodicially) c 2014 Think. Plan. Do. LLC All Rights Reserved 26 Manan Shah (@shahlock)
27 Linguistic Colloquial Students define: infinity never-ending it goes on forever it contains everything it s the biggest number c 2014 Think. Plan. Do. LLC All Rights Reserved 27 Manan Shah (@shahlock)
28 Linguistic Overused Vocabulary as in English, context dependent χ 2 test χ 2 distribution χ 2 statistic c 2014 Think. Plan. Do. LLC All Rights Reserved 28 Manan Shah (@shahlock)
29 Linguistic Overused Symbolism σ (standard deviation) σ (permutation map) σ-field σ-algebra σ vs Σ c 2014 Think. Plan. Do. LLC All Rights Reserved 29 Manan Shah (@shahlock)
30 Linguistic Mathematics Abuse of notation Wrong if student does it Abuse of notation if done by mathematician c 2014 Think. Plan. Do. LLC All Rights Reserved 30 Manan Shah (@shahlock)
31 Linguistic Symbolic Overload a n x n + a n 1 x n a 0 c 2014 Think. Plan. Do. LLC All Rights Reserved 31 Manan Shah (@shahlock)
32 Linguistic Missing In Math Ed Not enough emphasis on reading mathematics Hyperfocus on right and wrong c 2014 Think. Plan. Do. LLC All Rights Reserved 32 Manan Shah (@shahlock)
33 Linguistic What We Should Do Parsing symbolism is hard 1 t e x2 2 dx is a dense 2π statement Pretend it is a page of text c 2014 Think. Plan. Do. LLC All Rights Reserved 33 Manan Shah (@shahlock)
34 Linguistic A/An vs The Give me a fork for my steak. Give me the fork for my steak. c 2014 Think. Plan. Do. LLC All Rights Reserved 34 Manan Shah (@shahlock)
35 Linguistic A/An vs The Find a solution for x 2 1 = 0 Find the solution set for x 2 1 = 0 c 2014 Think. Plan. Do. LLC All Rights Reserved 35 Manan Shah (@shahlock)
36 Linguistic 0,, Non-existence Solve for x in x + 3 = 3 x = 0 It s nothing! There s no solution! c 2014 Think. Plan. Do. LLC All Rights Reserved 36 Manan Shah (@shahlock)
37 Linguistic The Dodo Bird (sometimes) zero = non-existence The dodo bird is extinct There are zero dodo birds in existence c 2014 Think. Plan. Do. LLC All Rights Reserved 37 Manan Shah (@shahlock)
38 Linguistic Degrees Celsius (sometimes) zero non-existence Water freezes at zero degrees Celsius. Water freezes at a temperature that does not exist??? c 2014 Think. Plan. Do. LLC All Rights Reserved 38 Manan Shah (@shahlock)
39 Linguistic The Bankers Zero is a number Banker 1: We have a number of bidders. Banker 2: Really? How many? Banker 1: Zero. c 2014 Think. Plan. Do. LLC All Rights Reserved 39 Manan Shah (@shahlock)
40 Linguistic Missing In (Math) Ed Collaboration with Language Arts Emphasis on language and math reading comprehension c 2014 Think. Plan. Do. LLC All Rights Reserved 40 Manan Shah (@shahlock)
41 Mechanical Logical Linguistic Mechanical c 2014 Think. Plan. Do. LLC All Rights Reserved 41 Manan Shah (@shahlock)
42 Mechanical Rules! Is 0 1 = 0? or is it 1 0 = 0? or is it 0 1 = 1? or is it 1 0 = 1? c 2014 Think. Plan. Do. LLC All Rights Reserved 42 Manan Shah (@shahlock)
43 Mechanical Path To Math Misery Point-getting memorization Memorization done at expense of understanding Lack of understanding math misery c 2014 Think. Plan. Do. LLC All Rights Reserved 43 Manan Shah (@shahlock)
44 Mechanical Penmanship! 50Mɛ Eχ mρles 6, σ, δ O, o, 0, θ, Θ, z, Z, 2 l, I, 1, 7 c 2014 Think. Plan. Do. LLC All Rights Reserved 44 Manan Shah (@shahlock)
45 Mechanical Penmanship! Hard to do math, if one is confused by one s own handwriting Emphasize numbers along with ABCs c 2014 Think. Plan. Do. LLC All Rights Reserved 45 Manan Shah (@shahlock)
46 Mechanical Fractions! Too many types, too many rules Mixed fractions Improper fractions 3 2 Proper fractions 2 3 c 2014 Think. Plan. Do. LLC All Rights Reserved 46 Manan Shah (@shahlock)
47 Mechanical Fractions! Confusion for students when there are no numbers a b + c d c 2014 Think. Plan. Do. LLC All Rights Reserved 47 Manan Shah (@shahlock)
48 Mechanical Fractions! Convert improper fractions to mixed fractions when adding or subtracting, but don t when multiplying or dividing c 2014 Think. Plan. Do. LLC All Rights Reserved 48 Manan Shah (@shahlock)
49 Mechanical Fractions! Change and flip for division c 2014 Think. Plan. Do. LLC All Rights Reserved 49 Manan Shah (@shahlock)
50 Mechanical Fractions! Always reduce. Always convert improper fractions to mixed fractions for the final answer. c 2014 Think. Plan. Do. LLC All Rights Reserved 50 Manan Shah (@shahlock)
51 Mechanical Fractions! Cross multiply. c 2014 Think. Plan. Do. LLC All Rights Reserved 51 Manan Shah (@shahlock)
52 Mechanical Fractions! You must find the lowest common denominator. c 2014 Think. Plan. Do. LLC All Rights Reserved 52 Manan Shah (@shahlock)
53 Mechanical Fractions! This is craziness! c 2014 Think. Plan. Do. LLC All Rights Reserved 53 Manan Shah (@shahlock)
54 Mechanical All Jumbled Too many rules = Zero rules Cross multiply to add / subtract? What do I change and flip? Greatest least common multiple of the dividend? c 2014 Think. Plan. Do. LLC All Rights Reserved 54 Manan Shah (@shahlock)
55 Mechanical The Coup De Grâce x is the independent variable because it has two legs. y is the dependent variable because it has one leg and needs x s support to stand. c 2014 Think. Plan. Do. LLC All Rights Reserved 55 Manan Shah (@shahlock)
56 QED: THE CASE IS SOLVED Thank you! KEEP IN Catch the blog at mathmisery.com c 2014 Think. Plan. Do. LLC All Rights Reserved 56 Manan Shah (@shahlock)
Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together
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