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College Algebra without the Algebra MichMATYC

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Have you ever dreamed of teaching a pre-calculus level course where the algebraic manipulation is de-emphasized and the emphasis is shifted to conceptual understanding and practical skills that directly apply to transfer classes? For students to learn concepts, students need to have the time to explore and make mistakes around the concepts (not the procedures). You can teach the same curriculum and make time for active learning and concept focus, but you do have to redesign the learning and assessment while looking at the objectives through a new lens.

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College Algebra without the Algebra MichMATYC

  1. 1. Taking the Algebra out of College Algebra Maria Andersen Westminster College CEO, Coursetune busynessgirl@gmail.com Twitter: @busynessgirl Busynessgirl.com
  2. 2. Partial Fraction Expansion Conic Sections Polynomial Long Division Log Product and Sum Rules Integration by Trig Substitution Factoring, Factoring, and more Factoring Rational Expression and Equation Hell
  3. 3. Drowning in problems like this:
  4. 4. 1878 Algebra text problems
  5. 5. Topics of Algebra may actually be the only similarity between 1878 and 2009.
  6. 6. In 2009 we could not yet see what would transform modern life (again).
  7. 7. https://www.statista.com/statistics/201182/forecast-of-smartphone-users-in-the-us/
  8. 8. https://www.statista.com/chart/15561/smartphone-sales-by-os/
  9. 9. Smartphone usage
  10. 10. Partial Fraction Expansion Conic Sections Polynomial Long Division Log Product and Sum Rules Integration by Trig Substitution Factoring, Factoring, and more Factoring Rational Expression and Equation Hell
  11. 11. The word problems don’t even make sense anymore.
  12. 12. Data is at our fingertips, we would never calculate this stuff anymore.
  13. 13. I left behind the classroom I’d worked for 5 years to build.
  14. 14. And traded it for conference rooms and open offices.
  15. 15. There were other reasons we moved to Utah.
  16. 16. Have you been to Utah?
  17. 17. WGU has Unbundled Faculty Roles Curriculum Development (instructional design) Course Mentors (content experts) Program Mentors (counselors and weekly accountability) Evaluators (grade the student work)
  18. 18. On top of that … All the classes are self paced Students can start a class on any day of the year Students have access to 100% of their curriculum on day one of their degree WGU is often running 3+ versions of a course
  19. 19. Why not get another degree?
  20. 20. Into which socket could you place an Intel Core i5? A. Socket LGA 775 B. Socket LGA 1155 C. Socket C D. Socket AM3+
  21. 21. You have 5 minutes and no technology to find the zeros for this polynomial.
  22. 22. You have 5 minutes and no technology to find the zeros for this polynomial.
  23. 23. You have 5 minutes and technology to find the factored form for this polynomial.
  24. 24. You have 5 minutes and no technology to find the factored form for this polynomial.
  25. 25. Find a factored form for this polynomial. Use what you want.
  26. 26. Suppose we needed to find a factored form for this polynomial.
  27. 27. Find the zeros by factoring:
  28. 28. Get Desmos Web Browser URL: https://desmos.com/calculator
  29. 29. Why do we still teach this stuff?
  30. 30. Write Competencies
  31. 31. Competency: Graphs and Relationships Interpret the key features of graphs and relate graphs to the mathematics of their equations to wisely use math in other contexts. Competency: Create Models from Data Create an appropriate mathematical model for a set of data to make interpolations and extrapolations.
  32. 32. A decent competency or course learning objective (CLO) should have several properties:  Relevance - to program, workplace, or daily life  Longevity - Should not change as technologies and learning resources change  Purpose – context is king  Verb choice / verb level - will someone else be able to assess accurately?
  33. 33. Competency: Technology Use a TI graphing calculator. Use technology. Apply technology to enhance mathematical interpretation in the real-world.
  34. 34. Competency: Technology and Reasonability Apply technology to enhance mathematical interpretation and determine reasonability of solutions since real-world models rarely involve integer coefficients.
  35. 35. Streamline the Curriculum
  36. 36. ESIL Lens Strictly deals with the level of information or skill depth, not the ability to perform higher cognitive level activities. Existence Supported Independent Lifetime
  37. 37. How do we use the ESIL lens? We need to untangle the curriculum first. Then put it back together and eliminate the extra stuff.
  38. 38. Learning Objectives are more granular in and feed into competencies. LOs get their purpose from the competency they correspond to.
  39. 39. Old LO: Solve a radical equation. Solve a radical equation with only one algebraic term using algebra. Solve a radical equation with multiple algebraic radical terms using algebra. Solve a radical equation of any kind using technology.
  40. 40. Old LO: Understand quadratic functions. Solve a quadratic equation using technology. Solve a quadratic equation using the quadratic formula. Solve a quadratic equation by factoring. Solve a quadratic equation by completing the square. Write the factored form for a quadratic equation if it exists (this can be done with technology assist). Determine the vertex and axis of symmetry of a quadratic function using technology. Write the vertex form of a quadratic function. Write the vertex form of a quadratic function by completing the square. Write a quadratic function given a selection of its properties. Describe the properties of a quadratic function (intercepts, vertex, opening up or down, axis of symmetry, domain, range).
  41. 41. 5 7 7 L I or L S
  42. 42. X 2 X I
  43. 43. Use Friendlier Technology
  44. 44. Get Desmos Web Browser URL: https://desmos.com/calculator
  45. 45. What if they don’t have a SmartPhone? Required Technology: You must have either a laptop, smartphone, or tablet in class every day to use the Desmos Graphing app. If using a laptop, you’ll need to download the Chrome Desmos Testing app.
  46. 46. Just sayin…
  47. 47. Tips for allowing SmartPhone Use in Class Phone and WiFi must be off during class. (airplane mode with WiFi off) If a 2-hr class, provide a 5-min break where you tell them this is time they can check their phones. Provide a robust formula sheet for tests.
  48. 48. Embrace Modern Examples
  49. 49. Graphs In The World (GITW) Facebook Search GraphsInTheWorld https://facebook.com/graph sintheworld Instagram Search@GraphsInTheWorld https://www.instagram.com/ graphsintheworld/
  50. 50. Contemporary Algebra Collection http://bit.ly/ContempAlgebra
  51. 51. http://www.pewinternet.org/fact-sheet/mobile/
  52. 52. Transform the Assessments
  53. 53. Not all assessment must be tests. Assess supported skills another way. Projects Problem Sets Essays Videos Take Home Exams
  54. 54. When you DO test, you’ll just have to be more creative.
  55. 55. Tell me eight mathematical properties about f.
  56. 56. Write the factored form and the vertex form of this equation.
  57. 57. Use relevant scenarios
  58. 58. Remove “the answer” as the goal.
  59. 59. Show me two ways to find when the population is 2,000.
  60. 60. Explain how to find when the population is 150. When does the population peak?
  61. 61. Which procedure would you say is more important?
  62. 62. Contemporary Algebra Curriculum (2020) 1. Functions and Graphs 2. Graphs of a Line 3. Equations of a Line 4. Regression Models 5. Linear Inequalities and Systems 6. Domain and Range 7. Piecewise Functions 8. Quadratic Functions 9. Square-Root Functions 10. Translations 11. Quadratic Models
  63. 63. Contemporary Algebra Curriculum (2020) 12. Transformations 13. Exponential Functions 14. Applications with Exponential Functions 15. Logs and Exponentials 16. Properties of Log and Exponential Functions 17. Applications of Log and Exponential Functions 18. Circles and Trigonometry 19. Periodic Functions 20. The Unit Circle 21. Transformations of Periodic Functions 22. Periodic Models 23. Right Triangle Trigonometry
  64. 64. A “simple” 5-step plan Write Competencies 1 Eliminate Curriculum Bloat 2 Use Friendlier Technology 3 Embrace Modern Examples 4 Transform the Assessments 5
  65. 65. If a student successfully takes a full semester’s worth of classes at your college, and then drops out, will they be better off for it?
  66. 66. We must ensure value to the student.
  67. 67. Contact Info e: busynessgirl@gmail.com w: busynessgirl.com t: @busynessgirl e: maria@coursetune.com w: coursetune.com

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