Amatyc ignite 2013 first half

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AMATYC 39th Annual Conference Friday night Ignite Event: Twenty slides are automatically advanced every 15 seconds while the speakers have exactly five minutes to share their passion!

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  • Now, when students are given a problem, where do they want to start?In my experience many want to go straight to step 3; they want to start “doing” something,and, for 12 or more years, that’s what most of their mathematics classes have been like.
  • If they have trouble, they often say things like…“Once I know what to do, it’s easy. My trouble is knowing where to start.” or“Don’t make me try to understand this stuff; just tell me what to do and I’ll do it.”
  • For these students I offer the following motivation. In the “real world,” …Whose job is it to “understand the problem?” The company officers and executives.Whose job is it to “devise a plan or strategy?” The managers and engineers.
  • 3. Whose job is it to “carry out the plan?” The assistants, clerks, and laborers.4. Whose job is it to “look back” and see if a satisfactory outcome has been achieved?The officers and executives, again.
  • Now, amongst these groups, who are the least valued, lowest paid employees?The assistants, clerks, and laborers--the ones we might call the step 3 specialists.They are told what to do, and their job is to do it.-----They are not encouraged to think and those who do are often called “trouble-makers.”
  • Also, who is most likely to have their job taken over by automation, outsourcing, or a computer?Again the assistants, clerks, and laborers whose job is just to “carry out the plan.”-----But so far, at least, we don’t have computers which will “understand the problem,” “devise a strategy,” or “look back” and assess the solution.
  • So, if we as instructors focus almost entirely on “carry out the plan,” what are we preparing our students for?...a life at the bottom, both intellectually and financially?I’m afraid so.
  • Now I am not for eliminating the study of how to “carry out the plan.”A thorough knowledge of what can be done is essential to those whose job is to “devise a plan.”But if this is all we teach, we are limiting the future for our students.
  • To prepare our students for a fulfilling, productive, and well-paying career, we must educate our students in all facets of problem solving.And that means we don’t just tell them what to do!
  • An adjunct’s problem: Head explosionKeeping track of different school systems, websites, passwords, proceduresHundreds of Student’s faces, requests, messages: What’s the HW? I can’t make it to class today. I have an emergency. I can’t find my syllabus. Etc. No office hours, No websites, Constantly changing.
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  • Amatyc ignite 2013 first half

    1. 1. Lecture Is Dead! Long Live Lecture! How and why to make class time more exciting and rewarding for your students. Rob Eby Blinn College – Bryan, TX Campus
    2. 2. Lecture is Booooring! ๏ So add commercial breaks ! ๏ First 10 vs. last 40 recall is laughable.
    3. 3. If All You Do Is Lecture 35% 15%
    4. 4. Ten and Two, Hike! ๏ 10 minute lecture 2 minutes to chew on it ๏ Similar to commercial breaks ๏ BUT you engage the students ๏ Think of a TV program
    5. 5. What type of commercials? ๏ Minute papers ๏ Clickers – poll anywhere and such ๏ Turn to classmate ๏ Example in book ๏ “What is wrong here?” ๏ Group quizzes
    6. 6. end of or after class ideas ๏ Minute papers ๏ What do you think was the goal today? ๏ Clearest or muddiest point? ๏ Write your own question ๏ Exit quizzes ๏ Solve and Classmates Grade
    7. 7. Make Them Read! ๏ Readings or videos out of class ๏ GUIDE THE READING! ๏ Follow up with quizzes ๏ Help students learn how to learn
    8. 8. Public Speaking 101 f ( x) 3 x 5 1. Multiply by three 2. Subtract five. 1 f ( x) x ( x5 5) 3by three UNDO Multiply 1 1. 2. UNDO Subtract five.
    9. 9. Pictures! ๏ Not just any pictures Good pictures Why is the sum of the first n odd numbers always a square?
    10. 10. Pictorial Superiority Effect ๏ Our brains are hard wired for pictures Things written in text are not considered a picture
    11. 11. 72 Hours after exposure ๏ ๏ Recall from hearing only Recall from hearing and picture
    12. 12. Pictorial Superiority Effect (x 2 ( x 3)( x 5) 2 3x 13)( x 5 x 42)
    13. 13. (x 2 3x 13)( x 2 (13)( x (3 x)( x 2 ( x )( x 2 2 5 x 42) 2 5 x 42) 5 x 42) 5 x 42)
    14. 14. Brain Rules ๏ The brain seems to rely partly on past experience in deciding how to learn new things ๏ Make sure they understand what is new each time ๏ Our senses evolved to work together ๏ We learn best if we stimulate several senses at once.
    15. 15. Patterns and Connections ๏ We are better at seeing patterns and abstracting the meaning of an event than we are at recording detail. ๏ Emotional arousal helps the brain learn. ๏ So make it emotional.
    16. 16. Memory and Brain Rules ๏ Most memories disappear within minutes ๏ How do we make sure it gets into long-term memory? ๏ Incorporate new information gradually ๏ Repeat it in timed intervals
    17. 17. Brain Rules Babies are the model of how we learn ๏ observation, ๏ hypothesis, ๏ experiment, ๏ conclusion
    18. 18. Darn Kids these days! ๏ This is not just about “kids these days” this research is decades old ๏ Brains more wired for linear bursts than deep thinking (always on etc.)
    19. 19. Most Desired Skills - Forbes ๏ No. 1 Critical Thinking ๏ No. 2 Complex Problem Solving ๏ No. 3 Judgment and Decision-Making ๏ No. 4 Active Listening ๏ No. 5 Computers and Electronics ๏ No. 6 Mathematics Knowledge of arithmetic, algebra, geometry, calculus, statistics and their application.
    20. 20. Find out more! ๏ ๏ ๏ http://tinyurl.com/k3sbgh5 @RobEbymathdude jeby @ blinn.edu Blinn College – Bryan Campus (next door to Texas A&M)
    21. 21. The Dos and Don’ts of Personal Branding Online Jon Oaks Macomb Community College www.jonoaks.com
    22. 22. 12 Good Words… … and 7 Bad Ones Dave Sobecki Miami University Hamilton
    23. 23. Exercise ✔
    24. 24. Hard ✔
    25. 25. Cancel
    26. 26. Input and Output ✔
    27. 27. Explain ✔
    28. 28. Mimic
    29. 29. Context ✔
    30. 30. Backwards ✔
    31. 31. Real-World
    32. 32. Story
    33. 33. Variable ✔
    34. 34. ALEKS ✔
    35. 35. Assume
    36. 36. Discover ✔
    37. 37. Interpret ✔
    38. 38. Rate-of-change ✔
    39. 39. Formal
    40. 40. Roadblocks
    41. 41. And two bonus words that are always appropriate… Thank you. Facebook.com/Teachingbackwards @teachbackwards ✔
    42. 42. Problem Solving: DON’T Just Tell Them What to Do Joe Browne Onondaga Community College Syracuse NY 13215 brownej@sunyocc.edu Exercises vs. Problems
    43. 43. Exercise Practice a rule or procedure. ๏ Factor this polynomial ๏ Solve this equation ๏ Find the distance between these two points ๏ Differentiate these functions The student is told exactly what to do.
    44. 44. Problem A problem usually requires more thinking and analysis. In most cases there is no formula that immediately gives the answer. y Find a point on a given line which is equidistant from two given points. A P x B
    45. 45. Steps in problem solving process 1. Understand the problem. 2. Devise a plan (strategy). 3. Carry out the plan. 4. Look back.
    46. 46. Steps in problem solving process 1. Understand the problem. 2. Devise a plan (strategy). 3. Carry out the plan. 4. Look back.
    47. 47. Steps in problem solving process 1. Understand the problem. 2. Devise a plan (strategy). 3. Carry out the plan. 4. Look back.
    48. 48. Steps in problem solving process 1. Understand the problem. 2. Devise a plan (strategy). 3. Carry out the plan. 4. Look back.
    49. 49. Steps in problem solving process 1. Understand the problem. 2. Devise a plan (strategy). 3. Carry out the plan. 4. Look back.
    50. 50. When given a problem,… ๏ Where do students want to start? 1. Understand the problem. 2. Devise a plan. 3. Carry out the plan. 4. Look back. ๏ Where should they start? 72
    51. 51. Ever Heard This? ๏ “Once I know what to do, it’s easy. My trouble is knowing where to start.” ๏ “Don’t make me try to understand this; just tell me what to do!” 73
    52. 52. In the “real world”… 1. Whose job is it to “understand the problem?” (Usually company officers and executives.) 2. Whose job is it to “devise a plan or strategy? (Usually the managers and engineers.) 74
    53. 53. In the “real world”… 3. Whose job is it to “carry out the plan?” (Usually the assistants, clerks, and laborers.) 4. Whose job is it to “look back” and see if a satisfactory outcome has been achieved? (Usually the officers and executives again.) 75
    54. 54. Who are the lowest paid? 1. Company officers and executives. 2. Managers and engineers. 3. Assistants, clerks, and laborers 4. Company officers and executives.
    55. 55. Who are most likely to be replaced by automation, outsourcing, or a computer? 1. Company officers or executives. 2. Managers or engineers. 3. Assistants, clerks, or laborers 4. Company officers or executives. 77
    56. 56. So, if we focus almost entirely on step 3, “carry out the plan,” what are we preparing our students for? 78
    57. 57. A thorough knowledge of what skills, techniques, and procedures are possible is necessary, especially to those who “devise a plan.” But this is not sufficient. 79
    58. 58. To fully prepare our students for a productive (and well paying) career, we must emphasize all facets of problem solving. 80
    59. 59. Math + Facebook = Success Nancy Che Mahan Santa Ana College NancyCheMahan@gmail.com
    60. 60. Ack! Problems… No office Hours No website Keeping track of different campus’ systems, passwords, websites.  Keeping track of Students’ requests, names, faces, Needing a place to upload documents
    61. 61. My Experimentation
    62. 62. WHAT can you use this Facebook class group for? 1. Repository
    63. 63. WHAT can you use this Facebook class group for? 1. Repository 2. Announcements
    64. 64. WHAT can you use this Facebook class group for? 1. Repository 2. Announcements 3. Class Discussions
    65. 65. WHAT can you this Facebook class group for? 1. Repository 2. Announcements 3. Class Discussions 4. Etc.
    66. 66. WHY Facebook? 1. Math is always in front of them
    67. 67. WHY Facebook? 2. Efficient
    68. 68. WHY Facebook? 3. Social Environment Face it Facebook is FUN! And Math can sure use some fun!
    69. 69. HOW to get started
    70. 70. HOW to get started
    71. 71. HOW to get started…
    72. 72. OTHER Important Tidbits  Policy: I have a very clear written policy on the use of this forum stated on the "About" section of the class FB page. I warn them that any inappropriate use of the forum results in immediate removal from the group (although this has never been an issue).
    73. 73. OTHER Important Tidbits  Optional: The use of FB is optional, but I always strongly recommend it. For those who are FB-haters, I tell them that they can create an account with their school email and only use it for this purpose. Once in a blue moon, I have someone who is adamantly against FB, so I just tell them that it's their responsibility to get info from a classmate or myself.
    74. 74. OTHER Important Tidbits  Privacy
    75. 75. What STUDENTS think!
    76. 76. What STUDENTS think!
    77. 77. What STUDENTS think!
    78. 78. http://nancychemahan.blogspot.com/2013/07 /math-facebook.html
    79. 79. How Math is Like Golf Laurie K. McManus, Ph.D. Professor of Mathematics St. Louis CC – Meramec lmcmanus@stlcc.edu www.mcmathprof.com
    80. 80. There are rules that must be followed.
    81. 81. You must use the proper equipment.
    82. 82. Your skills improve with regular practice.
    83. 83. Sometimes it’s necessary to consult an expert.
    84. 84. Your skills do not improve by watching someone else play the game.
    85. 85. Patience …
    86. 86. Persistence may be rewarded.
    87. 87. Sometimes you have to calculate.
    88. 88. You must be prepared to interpret the result of your calculations.
    89. 89. A good score can be very satisfying.
    90. 90. It can be a social activity.
    91. 91. Sometimes it’s fun.
    92. 92. And now for something completely different … Mary Beth Orrange orrange@ecc.edu AMATYC Board Secretary
    93. 93. 3.14% of sailors are Pi Rates
    94. 94. Q: Why can't you say 288 in public? A: Its two gross!
    95. 95. Very Bad Math Jokes: Q: What did the zero say to the eight? A: Nice belt! ***************** Q: How does a cow add? A: It adds one udder to an udder. ****************** Q: Why is the snake so good at math? A: Because he’s an adder.
    96. 96. Even Worse Math Jokes: Q: Why is the math book so upset? A: Because it has lots of problems. ***************** Q: What did the math plan grow? A: Square roots. ****************** Q: How do you make seven even? A: Take away the “s.” **************** Q: What did the dollar say to the 4 quarters? A: You’ve changed.
    97. 97. There are 10 kinds of mathematicians. Those who can think binarily and those who can't...
    98. 98. "What's your favorite thing about mathematics?" "Knot theory." "Yeah, me neither." In Alaska, where it gets very cold, pi is only 3.00. As you know, everything shrinks in the cold. They call it Eskimo pi.
    99. 99. Q: What does the little mermaid wear? A: An Alge-bra Q: What's a polar bear? A: A rectangular bear after a coordinate transformation. Q: What is a dilemma? A: A lemma that proves two results.
    100. 100. Motto of the society: Mathematicians Against Drunk Deriving : Math and Alcohol don't mix, so... PLEASE DON'T DRINK AND DERIVE
    101. 101. “The trouble with Mobius is that he thinks there is only one side to every question.”
    102. 102. “Uh, yeah, Homework Help Line? I need you to explain the quadratic equation in roughly the amount of time it takes to get a cup of coffee.”
    103. 103. Cat Theorem: A cat has nine tails. Proof: No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.
    104. 104. Life is complex. It has real and imaginary components.
    105. 105. Q: What is the first derivative of a cow? A: Prime Rib! Q: What is purple and commutative? A: An abelian grape...
    106. 106. Math problems? Call 1-800-[(10x)(13i)2] sin(xy)/2.362x] "The number you have dialed is imaginary. Please, rotate your phone by 90 degrees and try again..."
    107. 107. Math Is Hard Luke Walsh Catawba Valley Community College Hickory, North Carolina lwalsh@cvcc.edu @lukeselfwalker
    108. 108. “Young man, in mathematics you don’t understand things…
    109. 109. …You just get used to them.” ~John Von Neuman
    110. 110. I am a math instructor.
    111. 111. NOR
    112. 112. I TEACH MATH WHAT’S YOUR SUPERPOWER? OPERATORS STANDING BY
    113. 113. A. Morgan B. Russell C. Gauss
    114. 114. D. Hilbert E. Bell F. Viete
    115. 115. G. H. Hardy
    116. 116. {1, 2, 3,…n}
    117. 117.
    118. 118.
    119. 119. “I have never been good at math!”
    120. 120. “Letters are not math!”
    121. 121. “When I was in school…”
    122. 122. “…we didn’t do this type of math!”
    123. 123. “In all of my classes I have A’s…”
    124. 124. “…except for math!”
    125. 125. “I have been here for two years…”
    126. 126. “…trying to avoid math!”
    127. 127.
    128. 128.
    129. 129. 2 Yes,math is hard!
    130. 130. Fair Price Why play?
    131. 131.
    132. 132.
    133. 133. T T F F T F T F T F T T
    134. 134.
    135. 135. Soap Box Net
    136. 136.
    137. 137.
    138. 138. Yes, math is hard. And so is life. “You just get used to them.”
    139. 139.
    140. 140.
    141. 141. Creating an Aha! Moment with Function Models Dennis C. Ebersole Northampton Community College
    142. 142. Linear Models Slope-Intercept Form Form if the y-intercept is (0,0) 8 8 6 6 4 y = 2x + 3 4 2 2 -5 5 -5 y = 2x 5 -2 -2 -4 -4 -6 -6
    143. 143. Numeric Representations y = 2x x –2 –1 0 1 2 3 y –4 –2 0 2 4 6 y = –3x x –2 –1 0 1 2 3 y 6 3 0 –3 –6 –9
    144. 144. Numeric Representations Table with Initial Value Not 0 x 5 6 7 8 9 y –1 2 5 8 11 Table After Translation of Axes and the Associated Equation x–5 0 1 2 3 4 y+1 0 3 6 9 12 y + 1 = 3(x – 5)
    145. 145. Graphic Representations Convert Graph to a Table Now Translate the Table and Find the Equation of the Line 12 10 8 6 4 2 5 -2 10 15 x 4 6 8 10 12 y x-4y-8 8 0 0 7 2 –1 6 4 –2 5 6 –3 4 8 –4 y – 8 = –1/2(x – 4)
    146. 146. Verbal Representations The Problem Statement Jan has had a plumber do work twice in the last month. The first time she was charged $140 for a 1-hour job. The second time she was charged $320 for a 3hour job. Find a linear model showing the charge as a function of the number of hours on the job. Associated Table, Translated Table, and Symbolic Representation x y x - 1 y - 140 1 140 0 0 3 320 2 180 y – 140 = 90(x – 1)
    147. 147. Quadratic Models Vertex Not at Origin; General Form Vertex of Parabola at Origin; One Parameter! 6 4 4 2 2 6 2 y = 2x - 4x + 3 -5 5 -5 5 -2 -2 -4 -4 -6 -6 y = -2x 2
    148. 148. Numeric Representations Vertex at Origin y x –2 –1 0 1 2 y 12 3 0 3 12 x –2 –1 0 1 2 2x 2 y –8 –2 0 –2 –8
    149. 149. Numeric Representations Vertex at (h, k) Vertex is max or min function value x 0 1 2 3 4 5 6 y 0 25 40 45 40 25 0 Translated Table Yields Equation in Vertex Form x–3 –3 –2 –1 0 1 2 3 y – 45 –45 –20 –5 0 –5 –20 –45 y - 45 = –5(x – 3)2
    150. 150. Converting Graphic Representations Convert Graph to Translate Table and Find the Table Equation in Vertex Form 6 4 2 -5 5 -2 -4 -6 x 0 1 2 3 4 y 0 –3 –4 –3 0 x–2 y+4 –2 4 –1 1 0 0 1 1 2 4 y + 4 = 1(x – 2)2
    151. 151. Absolute Value Models One Parameter 6 6 4 4 2 2 -5 5 -5 -2 -2 -4
    152. 152. Absolute Value Models 6 6 4 4 2 2 -5 -5 5 5 -2 -2 -4 -4
    153. 153. Numeric Representations Vertex at (0, 0) x –3 –2 –1 0 1 2 3 y 6 4 2 0 2 4 6 x –3 –2 –1 0 1 2 3 y –9 –6 –3 0 –3 –6 –9
    154. 154. Numeric Representations Vertex at (h, k) Vertex is max or min function value x –1 0 1 2 3 4 5 y 9 7 5 3 5 7 9 Translate vertex to (0, 0) and find equation in y = a|x| form x–2 y–3 –3 6 –2 4 –1 2 0 0 1 2 2 4 3 y – 3 = 2|x – 2| 6
    155. 155. Graphic Representations to Numeric Vertex is max or min Convert Table to One with Vertex at Find points 1 away (0, 0); Find Equation in y = a|x| Form x -5 –1 2 –3 0 0 –1 2 –1 –2 4 y –3 6 x+2 y+3 –1 1 2 0 1 2 4 5 -2 -4 y + 3 = 2|x + 2|
    156. 156. Symbolic to Numeric Representations Find a and Vertex (h, k) Create Table Using Previous Patterns in y – k = a|x – k| x –4 –3 –2 –1 0 y 1 – 3 = –2 4–3=1 4 1 –2
    157. 157. Symbolic to Numeric Representations II Convert Equation to Form Use Patterns to Create Table x y –1 1 0 –1 1 –3 2 –1 3 1
    158. 158. Other Functions Models Exponential Model Same Model After Translation 8 8 6 6 4 4 2 2 -5 5 -5 5 -2 -2 -4 -4 -6 -6
    159. 159. Other Function Models Sine Function Models After Translation of Axes 8 8 6 6 4 4 2 2 -5 5 -5 5 -2 -2 -4 -4 -6 -6
    160. 160. Questions, Comments, Suggestions? Email me: debersole@northampton.edu
    161. 161. Discovering the Art of Mathematics Mathematical Inquiry in the Liberal Arts -- Innovative Materials and Pedagogical Support Julian Fleron, Phil Hotchkiss, Volker Ecke, and Christine von Renesse, Westfield State University www.artofmathematics.org
    162. 162. Discovering the Art of Mathematics Project Julian Fleron, Phil Hotchkiss, Volker Ecke, Christine von Renesse, Westfield State University, Massachusetts This project is based upon work currently supported by the National Science Foundation under NSF1225915 (TUES) and previously supported by NSF0836943 (CCLI) and a gift from Mr. Harry Lucas.
    163. 163. Our Vision: Mathematics for Liberal Arts students will be actively involved in authentic mathematical experiences that ๏ are both challenging and intellectually stimulating, ๏ provide meaningful cognitive and metacognitive gains, and, ๏ nurture healthy and informed perceptions of mathematics, mathematical ways of thinking, and the ongoing impact of mathematics not only on STEM fields but also on the liberal arts and humanities.
    164. 164. Rubik’s Cube:
    165. 165. Perspective Drawings:
    166. 166. Board Work:
    167. 167. Projecting Cubes:
    168. 168. String Art:
    169. 169. Maypole Dancing:
    170. 170. Anamorphic Art:
    171. 171. Slice Forms:
    172. 172. Student Artwork:
    173. 173. Dancing Tessellations:
    174. 174. Math and Music: Palindromes and Tuning
    175. 175. Spirographs:
    176. 176. Tangles and Knots:
    177. 177. Prime number sieves:
    178. 178. Gabriel’s Wedding Cake
    179. 179. More Student Art:
    180. 180. Resources/Opportunities: ๏ 11 free books for MLA: Art & Sculpture, Calculus, Dance, Games & Puzzles, Geometry, Knot Theory, Music, Number Theory, Patterns, The Infinite, Reasoning & Proof ๏ Topic Index (other math classes) ๏ Individual mentoring or collaboration (stipend) ๏ Beta-test/review (stipend) ๏ Traveling workshops www.artofmathematics.org

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