Ignite AMATYC 2012 Second Half


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Presentations 12-21 of Ignite AMATYC, Jacksonville, FL, November 9, 2012

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  • And everything they need to know is in the book… but that’s not enough.
  • So, I don’t have to take the 3 face to face classes and instead just need one Redesign math class to be able to take college algebra
  • Yes, the 27 doctorates and 51 masters degrees will be outsmarted by the developmental math student because preparation doesn’t prepare you for everything!
  • Don’t forget to let people know about the change!
  • Ignite AMATYC 2012 Second Half

    1. 1. Reducing Remediation Through PartnershipsTed KoukounasAcademic Chair, Mathematics and ScienceAssociate Professor of Mathematics
    2. 2. Remedial Mathematics atSCCC๏ Two Remedial Mathematics Levels๏ Pre-Algebra๏ Algebra I๏ High percentage of High School students place in at least one of these courses.๏ Increase the time needed to complete their program๏ Increase likelihood of attrition
    3. 3. Developmental Course FactsPre-Algebra Algebra IEquivalent to 7th - 8th Grade Math in NY Equivalent to 9th - 10th Grade Math in NYNo Calculators Same concerns as Pre-Algebra +Students frustrated More abstractionFaculty frustrated More formulasResources are depleted More understanding Full time teaching load More critical thinking Coordination More linear and quadratic equation Release time More graphing Assessment More of “solve for x”
    4. 4. College Placement Tests๏ Inconsistent๏ Only a few major exams for such a big decision - CPT, ACT, etc.๏ Non -Standard definition of Remedial Mathematics and Non-Standard Placement Policies๏ “Instantaneous” placement that does not necessarily reflect TRUE knowledge
    5. 5. CPT/ SAT/ Regents๏ Piecewise function to Placing Students๏ Placement is “Okay” at Best๏ Local IE office for current data๏ More discussion๏ Another presentation
    6. 6. CPT Placement at SCCCCombined CPT Developmental Course Mathematics Course LevelArithmetic/Algebra Score<99 Pre-Algebra Developmental100-134 Algebra I Developmental>134 Varied as per program College Credit-Bearing requirements* Students with an 80 or greater on any Regents should not be placed into Pre-Algebra
    7. 7. Developmental MathPlacement at SCCC Semester N PercentFall 2006 5280 41.9%Fall 2007 5394 44.2%Fall 2008 5864 47.2%Fall 2009 6548 52.6%Fall 2010 6908 50.9%Fall 2011 6721 53.1%
    8. 8. Why so much remediation?๏ Lack of Knowledge๏ Lack of Preparedness๏ Time Lapse๏ Testing and Advising๏ Lack of student emphasis - Testing unreliable๏ Poor Coordination between HS and College regarding shared expectations
    9. 9. What can we do to helpstudents?๏ Students, teachers, and high school administrators need to know what happens to their students upon HS graduation๏ Inform the discussion๏ Work collectively๏ Better Alignment๏ SUNY- State University of New York Taskforce for Remediation
    10. 10. HS/ College Partnerships๏ Encourage the discussion๏ No Finger Pointing๏ Mutual Benefits๏ Curriculum Based๏ Guidance Counseling๏ Local Support Necessary๏ Everyone Wins!
    11. 11. College Commitment๏ Resources๏ Honesty and Transparency๏ Follow Through๏ Support - Time - Fiscal - Programmatic
    12. 12. HS Responsibilities๏ Receptive to discussions๏ Respond to action๏ Inform parents๏ Programmatic requirements๏ Fiscal support
    13. 13. Remediation Pilot๏ Substantive meetings - Make contact with the right personnel๏ Share mutual information - Honest comparisons - Shared expectations - State goals๏ Identify student deficiencies๏ Develop a remediation plan for students prior to college application
    14. 14. College Responsibilities๏ Up to date Institutional Data๏ FERPA Compliance๏ Confidentiality๏ Resources
    15. 15. Process Begins๏ Students requiring remediation identified in their junior year by an SCCC developed and HS administered Diagnostic Exam๏ If needed, students remediate at HS with the SCCC recommended curriculum during their senior year๏ CPT testing occurs after the remediation process๏ Review Pilot Results and make adjustments as necessary
    16. 16. Three-year studySemester RemedialFall 2010 66.7%Fall 2011 45.6%Fall 2012 31.1%
    17. 17. Who Benefits๏ Students๏ High School๏ College๏ Math Chairs and Deans๏ Faculty
    18. 18. Constraints๏ Not much is being done๏ Everyone is interested๏ Too much testing๏ Bottlenecking of resources๏ Faculty feel stretched - PARCC - Math Regents - Performance expectations
    19. 19. SUNY Remediation TaskForce๏ Reduce Remediation SUNY-wide๏ Inform Discussion๏ Make Recommendations - A Stronger Education Pipeline that Reduces the Need for Developmental Education - Stronger Remediation Practices - More Effective State Funding Policy
    20. 20. Thank You!๏ Continue the Discussion๏ Discuss options for helping local school districts deal with remediation at HS๏ Familiarize yourself with the data from your constituents๏ Contact me for more details๏ Ted Koukounas, koukout@sunysuffolk.edu 631-548-2670
    21. 21. Flipping aDevelopmental MathClass with OER(Open Educational Resources)David LippmanPierce College, Lakewood, WA
    22. 22. Semi-flippedhttp://www.flickr.com/photos/briandewitt/553384683CC-BY-NC-ND http://www.flickr.com/photos/en321/5120100 CC-BY-NC-ND
    23. 23. It began with OERBeginning &Intermediate AlgebraTyler Wallace$25 print, free online
    24. 24. Freedomhttp://www.flickr.com/photos/timypenburg/5605056611/sizes/z/in/photostream/
    25. 25. Traditional 0 Answer HW 10 Lecture ConceptIn Class 20 30 Lecture Examples 40 50 Practice in class Review / Study 60 70 Practice at homeOut of Class 80 90 100 110 120
    26. 26. Traditional Semi-flipped 0 Answer HW Answer HW 10 Lecture ConceptIn Class 20 Practice in class 30 Lecture Examples & Activities 40 Practice in class Lecture Concept 50 Review / Study 60 Practice at home Video Examples 70Out of Class 80 Practice at home 90 100 110 120 Review / Study
    27. 27. Semi-flippedDevelop core concepts Answer HW Practice in classDiscovery activities & ActivitiesContextual activities Lecture Concept Video ExamplesIndividual practice & assistance Practice at home Review / Study
    28. 28. Semi-flipped Answer HW Practice in class & ActivitiesSemi Individualized: Lecture ConceptSkip if they know it Video ExamplesRewatch if they need to Practice at home Review / Study
    29. 29. Planting a garden Cost for aBushes: $3 per foot 5 ft by 5 ft garden? 8 ft by 8 ft garden? n ft by n ft garden? Flowers: Soil: $4 per $2 per foot square foot
    30. 30. Planting a garden
    31. 31. Q: Bob has $10,000 invested in twoaccounts, one paying 4% interest andthe other paying 6% interest. He earned$520 interest last year. How much doeshe have invested in each account?A: Read your statements, Bob!
    32. 32. Q: Bob is retiring with $1 million. Hecan invest in a safe CD earning 1%, or ariskier bond account earning 4%. Hewants to live on interest, and needs$30,000 a year to live on. What’s theminimum he needs to invest in the bondaccount?
    33. 33. OER makes it easier!
    34. 34. Tracker
    35. 35. How many toy cars are there? http://www.flickr.com/photos/53380495@N02/4993931189/in/photostream/
    36. 36. How many toy cars are there? Seriously, that’s all you give them at firsthttp://www.flickr.com/photos/53380495@N02/4993931189/in/photostream/
    37. 37. In 2007, the carbon dioxide concentration in the air wasabout 382 ppm (parts per million). By 2011, theconcentration had increased to 390 ppm. If theconcentration continue to grow linearly, a) Write an equation of a line that describes the concentration, C, of carbon dioxide t years after 2007. b) If this trend continues, when will the carbon dioxide concentration reach 410 ppm?The function s(t) = 3(t – 8)2 + 297 gives the approximatespending (in billions of dollars) by the US Dept of Defense tyears after 1990. a) Find the approximate spending in 2004 b) Find the year(s) in which spending was $309 billion.
    38. 38. One class = $5,000 savings
    39. 39. What Not to do in aDevelopmentalMath RedesignErin CookeGwinnett Technical College, GA
    40. 40. “Redesign is self-paced…”๏ Students hear “Nothing has to be done today!”๏ Students make everything with a due date (and some without) a higher priority
    41. 41. Results๏ Students save most of the work until the last few weeks of the semester๏ Some miracles will happen - students will do 12 weeks of work in 3 weeks๏ Many students do not complete the course
    42. 42. Instead…๏ Have a pacing guide with due dates๏ Give students due date sheets they fill in๏ Give a penalty for missing due dates๏ Remind students that they can work ahead and cheer them on!
    43. 43. “The instructors are on thesame page - I sent the email.”๏ No, really, they are not๏ Just because an email has “everything” the instructors needed does not mean they are trained๏ Only the person who wrote the syllabus finds the syllabus interesting
    44. 44. Results๏ Faculty feel lost, uninformed๏ Students get misinformation and inherit the lost feeling๏ Redesign satisfaction may decline because it feels “undirected”๏ Faculty acquire more pigment-challenged follicles
    45. 45. Instead๏ Let the faculty experience a module!๏ Put the course materials in a course - Syllabus - First day of class PowerPoint - Student handouts - Summary sheet of Redesign๏ Put a quiz at the end of the materials and require 100% from all math faculty
    46. 46. “Everything the students needis in the syllabus”๏ Syllabi can be confusing๏ If instructors do not like reading the syllabus, most students will not either
    47. 47. Result๏ Students are unsure about what is expected of them๏ There may be many “Well, can I…? What about…?” questions from students๏ Worse than many questions is no questions!
    48. 48. Instead๏ Give the key points in as many ways as possible - PowerPoints - Handouts (think colorful and hole punched) - Email - Signs in the room๏ Flow charts are great!
    49. 49. “Students are fine - I haven’tgotten any questions.”๏ Students know there was a lot of information on the first day - Students feel they should already know everything๏ Mimicking classmates does not necessarily mean they are doing the right things.
    50. 50. Result๏ Students work on the wrong assignments๏ Do not know proper protocol for the class – attendance, notes, testing, etc.๏ Students quit attending class or withdraw
    51. 51. Instead๏ Keep an eye on students via the gradebook๏ Send supportive emails and encourage them to ask questions๏ Tell students in class to check their email๏ Remind the class this is new and is it perfectly normal to feel uncertain.
    52. 52. “Redesign is on - so advisorsand students know about it.”๏ Knowing of Redesign is much different than knowing about Redesign๏ There will be many students who do not know why they are attending lecture in a computer lab๏ Advisors may have incorrect information
    53. 53. Result๏ Students and advisors are hesitant about Redesign and will search for F2F alternatives๏ Students may be told they have a faster path than they do
    54. 54. Instead๏ Change the name of the course to include Redesign๏ Have a link to a video explaining (briefly) about Redesign๏ Inform administration about Redesign
    55. 55. “We’re set! All our bases arecovered!”๏ Welcome to education! (you must be new)๏ Students are creative and will work hard to think of something that the entire department did not think about or plan for
    56. 56. Result๏ There will be periods of chaos for instructors and students๏ The program looks unorganized or unplanned๏ Happy hour sales at local pubs and restaurants go up
    57. 57. Instead๏ Know that new situations are possible๏ Decide who needs to be involved in “immediate” policy decisions๏ Have those people on speed dial and in one email contact
    58. 58. The most important parts?๏ Keep a positive attitude, roll with the punches and do not utter the words “self- paced”๏ No time for questions, but feel free to applaud, whistle and cheer wildly! (or sit and smile quietly) Thank you!!
    59. 59. Students HelpingStudents:Passing the Batonof SuccessThrough FilmBy Martha Whitty, Washington, DC
    60. 60. ๏ Math 090: Introductory Algebra
    61. 61. What you’ll Need:-1 digital movie camera-1 tripod-1 microphone-1 Computer with editing software-1 DVD burner- Some blank DVDs
    62. 62. “If you do the homework, you won’t have to study. Doing the homework IS my studying.”
    63. 63. “Even if it makes the tutor mad, just keep telling them to go over and over it because you HAVE to get it.”
    64. 64. “Though this does take a lot of time, I have made myself sample tests. I make sure to put problems I struggle with on the sample test.”๏ the sample test.”
    65. 65. “If you miss class, it’s your job to find out what you missed. The teacher’s not going to want to re-teach the work and your friends may not want to help you either.”
    66. 66. “I paid attention a lot in class. I think that’s the key.”
    67. 67. “If you miss a day, you miss a lot. Messing up one time will mess you up throughout because everything’s connected in Math.”
    68. 68. “I sit in front on purpose. I never sit in the back of the room because that’s where all the chitter-chatter is.”
    69. 69. “You have to come to class and that’s as simple as it is. Just get up and come… sleep ain’t that precious.”
    70. 70. “Me personally, I always came to class, but I always came late. You would think 5-10 minutes is nothing but that 5-10 minutes always put me so far behind.”
    71. 71. “Do your homework when you’re supposed to do it and not at 3 o’clock in the morning, the night before it’s due.”
    72. 72. “Ask questions even if you’re the only one asking them. You never know if someone else has that same question.”
    73. 73. “Come in with an open mind and leave your old feelings behind. These teachers really want to help you.”
    74. 74. “You’ve got to DO the problems, not just look at them. Because just seeing it, you won’t remember how to do it. Happened to me a lot… mm, mm, mm.”
    75. 75. “I noticed my friend was getting better grades than me so I would get her to help me.”
    76. 76. “Think about what you want to become in life and use that to press yourself.”
    77. 77. “Make sure you get a professor who explains things well. That helps a lot.”
    78. 78. “To face your challenges would be a nice self-accomplishment. Also you’ll be able to help others in the future.”
    79. 79. Slip-Slidin’ Away!Ann E. CommitoFrederick Community CollegeFrederick, Marylandacommito@frederick.eduJohn A. CommitoGettysburg CollegeGettysburg, Pennsylvaniajcommito@gettysburg.edu
    80. 80. Linear, circular, spiral, cylindricalWood, bamboo, metal, plastic, paper
    81. 81. Basic Slide Rule: Logarithmic Scalesbody cursor slide1 2 3 4 5 6 7 8 90
    82. 82. Log scales make slide rules powerful. Multiply Divide Reciprocate Powers and roots Natural log Sine and tangent Hyperbolic sine/tan Conversions Multiple operations
    83. 83. 0.7 y = log x0. 0 0 1 2 3 4-0.1-0.2 1.5 x 2 = 3 log 1.5 + log 2 = log 3 + =
    84. 84. 1.5 x 2 = 3
    85. 85. 1.728 x 10-6 ? 1.728? 1.728 x 109 ? 0.0120? 1.20? 1200?
    86. 86. You have to be smart to use a slide rule!You need to estimate the answer before you get it!You need to have common sense!
    87. 87. Slides rules were in use for 350 years.They are historically important. They are part of our material and social culture.
    88. 88. 1614 Napier logarithms 1620 Gunterlogarithmic scales 1630 Oughtred slide rule
    89. 89. 1675 Newton hairline (cursor) 1850 Mannheimstandardized scales 1800’s Industrial 250+ different designs Revolution Duplex slide rule
    90. 90. 20th Century Slide rules rule!Engineering Architecture MathematicsIndustry Radio Statistics Space R&D http://sliderulemuseum.com/
    91. 91. Slide rules are cool! http://sliderulemuseum.com/
    92. 92. Icon of industryhttp://sliderulemuseum.com/
    93. 93. Tool for the futurehttp://sliderulemuseum.com/
    94. 94. Manly, too!http://sliderulemuseum.com/
    95. 95. Mind and bodyhttp://sliderulemuseum.com/
    96. 96. Oughtred Society http://www.oughtred.org/International Slide Rule Museum http://sliderulemuseum.com/
    97. 97. ImprovingCommunicationJennifer GreenwoodCarroll Community CollegeWestminster, MD
    98. 98. Teaching Math Online๏ Improve and encourage communication๏ Designed for an online population๏ Consider modifications for classroom students
    99. 99. Help Students To:๏ Ask for help๏ Understand the help they get๏ Build relationships
    100. 100. I have not had success using:๏ Email๏ Phone calls๏ Office hours
    101. 101. The fix:๏ Flexible๏ Accessible๏ See it๏ Hear it๏ Interact with it
    102. 102. I AM NOT A TECHIE!
    103. 103. Technology must be practical ๏ Easy to use ๏ Inexpensive ๏ No special equipment
    104. 104. Skype ๏ Internet program ๏ Free account ๏ Live video chat
    105. 105. Skype:You only need a computer and the Internet
    106. 106. Skype:You don’t need a webcam or microphone
    107. 107. Skype – Screen Share
    108. 108. Skype Screen Share๏ Student watches your screen๏ Work a solution while student watches๏ Discuss the process with student
    109. 109. Interactive Solutions
    110. 110. Writing on the Computer๏ Use any program with Drawing Tools๏ Write with the mouse
    111. 111. Record Online Sessions๏ Post video to web for others๏ YouTube
    112. 112. Increase Communication Office hours vs. Online help
    113. 113. Flexibility ๏ Time ๏ Determine Your Limits
    114. 114. Reconsider What ComesHome๏ Grade papers, plan lessons during office hours๏ Communicate with students at home
    115. 115. In Short…๏ Go beyond office hours, phone, and email๏ Use technology to enhance communication๏ Teach all students as you would in class
    116. 116. Want to know more? Jen Greenwood jgreenwood@carrollc.edu
    117. 117. Flipping Back to the FutureEvan EvansProject ACCCESS Cohort 4eevans@frederick.edu
    118. 118. Brief History of Learning
    119. 119. Oral
    120. 120. Recorded Text
    121. 121. Cultural Exchange
    122. 122. Scrolls
    123. 123. Libraries
    124. 124. Greek EraKnowledge isgained through dialogueThe Learner is an active participant
    125. 125. University Era InitiallyStudent-Centered Learning
    126. 126. University EraLecture Based Instruction
    127. 127. Flip Teaching:Form ofBlended Learning
    128. 128. Problem Solving IN-CLASS
    129. 129. Critical Thinking IN-CLASS
    130. 130. Application IN-CLASS
    131. 131. Small Group Work IN-CLASS
    132. 132. Because It Works Evan Evans Project ACCCESS Cohort 4 eevans@frederick.edu
    133. 133. Super Computation AMATYC, 2012 – IGNITE! Jacksonville, FL
    134. 134. J. Sriskandarajahjsriskandara@madisoncollege.edu
    135. 135. Audience,Think of a 3 digit number, Say 270
    136. 136. The final answer is……The sum of five 3 digit numbers is a4 digit number with 2 as lead digit and the remaining three are, original – 2 2268
    137. 137. Audience,Another 3 digit number please!Say 581
    138. 138. Here’s my number or its 9 thcomplement is…. 418
    139. 139. Now you have three 3 digitnumbers….270+581+418
    140. 140. One more 3 digit numberplease….Say 999
    141. 141. And my next number is its 9 thcomplement ….. 000
    142. 142. Now you have a total of 5three digit numbers and thesum of these five numbers….270+581+418+999+000
    143. 143. Same as the final answergiven soon after the firstnumber! 2268Mathemagics
    144. 144. www.wisc-online.online.com/ Objects/ViewObject.aspx?ID= GEM3309
    145. 145. Add a notch…This time, sum ofseven 4 digitnumbers…
    146. 146. Audience, 4 digit numberplease….Say 1776
    147. 147. The final answer is 31773Subtract 3 from youroriginal number andinsert a 3 as theleading digit
    148. 148. Another 4 digit numberplease….Say 2012
    149. 149. My number is its ninthcomplement 7987
    150. 150. Another 4 digitnumber, please…Say 1881By now one shouldknow, my number is its 9thcompliment 8118
    151. 151. One last 4 digit numberplease….Say 9999And my number is 0000
    152. 152. And the sum of1776+2012+7987+1881+8118+9999+0000Is same as what we predicted before! 31773! Thank You!
    153. 153. Numerical FulcrumsA Mathematical Exploration from Prealgebra to Post-Calculus Richard Zucker Irvine Valley College
    154. 154. What is a Numerical Center? 204 is the Numerical Center of the list 1 to 288.
    155. 155. A number is the Numerical Centerof a list of consecutive naturalnumbers starting at 1 if it separatesthe list into two groups that have thesame sum.6 is the Numerical Center of the list 1 to 8.
    156. 156. Is every number a Numerical Center? No, not 5.
    157. 157. 35 is the Numerical Center of the list 1 to 49. 595 = 595
    158. 158. Is 1 a Numerical Center? ? = ? Arguably, yes.
    159. 159. Numerical Centers are likeburied treasure. Students ofall abilities can experience thethrill of discovery!
    160. 160. Can you find other NumericalCenters?1, 6, 35, 204, 1189, 6930, 40391, …Is there a pattern? There is a recursion relation, but I’ll let you find it.
    161. 161. One of my students was thrilled to discover this recurrence relation that depends only on the one prior number in the sequence: 2 2Cn 1 17 C n 1 6C n 1 1 8 Cn 1
    162. 162. Is there a general formula that predicts the n th Numerical Center?Several of my students derived the generalformula by studying Binet’s formula for Fibonaccinumbers. n n 1 5 1 5 Binet’s Fn 2 n 5 Formula: Numerical Cn ????????? Center Formula:
    163. 163. Do Numerical Centers have anyinteresting properties? Their squares are also triangular numbers. 6 8
    164. 164. This shopping center is in Costa Mesa, CA, not far from Irvine Valley College.
    165. 165. A Numerical Fulcrum is similar to aNumerical Center, but the list ofconsecutive natural numbersdoesn’t have to start with 1. 14 is a Numerical Fulcrum for the list {4, 5, …, 19}.
    166. 166. 9 is a Numerical Fulcrum for two lists!
    167. 167. R.J. Liljestrom (my student in 2002) discovered and proveda significant theorem about Numerical Fulcrums: F is not a Numerical Fulcrum if and only if 4F2 + 1 is prime. For example: • Since 101 = 4(52) + 1 is prime, then 5 is not a Numerical Fulcrum. • Since 9 is a Numerical Fulcrum, then 4(92) + 1 = 325 is composite.
    168. 168. R.J. Liljestrom (my student in 2002) discovered and proveda significant theorem about Numerical Fulcrums: F is not a Numerical Fulcrum if and only if 4F2 + 1 is prime. For example: • Since 101 = 4(52) + 1 is prime, then 5 is not a Numerical Fulcrum. • Since 9 is a Numerical Fulcrum, then 4(92) + 1 = 325 is composite.
    169. 169. Why is R.J.’s theorem significant?In 1912 at the International Congress ofMathematicians, Edmund Landau asked fourquestions about prime numbers. His fourthquestion was, “Are there infinitely many primesof the form n2 + 1?”One hundred years later, the question is stillunresolved.Because of R.J.’s theorem, Landau’s questionis equivalent to asking, “Are there infinitelymany natural numbers that are not NumericalFulcrums?”
    170. 170. Why is R.J.’s theorem significant?In 1912 at the International Congress ofMathematicians, Edmund Landau asked fourquestions about prime numbers. His fourthquestion was, “Are there infinitely many primesof the form n2 + 1?”One hundred years later, the question is stillunresolved.Because of R.J.’s theorem, Landau’s questionis equivalent to asking, “Are there infinitelymany natural numbers that are not NumericalFulcrums?”
    171. 171. Maybe one of yourstudents will find the answer! Thank you Richard Zucker Irvine Valley College rzucker@ivc.edu
    172. 172. Games to Learn Math Presenter: Dan PetrakDes Moines Area Community College Email: dgpetrak@dmacc.edu Twitter handle: dgpetrak
    173. 173. What is a Game?
    174. 174. Is Math like a Game?Goals? Yes Rules? YesFeedback system? Eventually…Voluntary participation? Are you kidding me?
    175. 175. What are we missing? Image from www.bigfishgmes.com blogEngagement and Motivation!
    176. 176. Raph Koster – A Theory of Fun
    177. 177. Flow
    178. 178. Learning within Flow  Optimal Learning comes from Desirable Difficulty  Students should be making errors if we want to optimize learning  Normally very uncomfortableThis is a natural dynamic for games!
    179. 179. Digital Games provide…๏ Instant and non-threatening feedback๏ Mentally Demanding๏ Customized learning through leveling, challenge, and game mechanicsHard Fun!
    180. 180. Fun is the Feeling we getfrom learning in Flow๏ http://www.flickr.com/photos/seandreilinger/2187892869/sizes/o/
    181. 181. Why Digital Games for Math? Image from www.bigfishgmes.com blog
    182. 182. Games can help the diverselearners in our classrooms by  Individualized and targeted instruction  Remediation  Optimized learning with Flow
    183. 183. Much of the skills based portionsof our math fit this model.
    184. 184. Experience
    185. 185. Hypothesize๏ Feedback loop helps students construct understanding of the rules.๏ We crave patterns and we want to fit our experiences into a schema.
    186. 186. Formalize and Practice๏ We can help students formalize what they are experiencing.๏ Games can also be used to practice the skills. Image by Lisa Haney
    187. 187. Ultimately what is our goal?๏ Deep procedural understanding๏ Deep conceptual understanding
    188. 188. Digital games can help studentslearn and practice math in a funand natural way
    189. 189. To learn more consider joining
    190. 190. Let the Games Begin!