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Active Learning with Desmos

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A few semesters ago, I shifted completely away from graphing calculators and to the free Desmos app as the graphing and calculation technology for math classes. The students are far more comfortable and happier with Desmos but it does require shifts in classroom management, learning activities, and assessment. With technology that feels more natural to students, we can do much more exploration, focus on reasonability, and creation of real-world models (search for GraphsInTheWorld for a few examples). This focus of this workshop is on active learning, relevant learning, and assessment strategies. We’ll simply use Desmos as the common base technology for the activities. If you’ve only dabbled with Desmos or have never opened it, you’ll be fine – we start from scratch.

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Active Learning with Desmos

  1. 1. Maria H. Andersen CEO, Coursetune Math Faculty, Westminster College Active Learning and Assessment (with Desmos)
  2. 2. Get Desmos Web Browser URL: https://desmos.com/calculator
  3. 3. A few tips to get started in Desmos Entering an equation (+ Expression) Pinch to zoom Tap to find graph features
  4. 4. Write down 12 properties of this function.
  5. 5. Let’s see what you’ve got… It’s quadratic (or a parabola) It opens down (because a<0) Vertex is (0.765, 11.988) Axis of symmetry: x=0.765 y-intercept is (0,10) x-intercepts are (2.642,0) and (-1.113,0) Zeros are 2.642 and -1.113 Domain is (-inf,inf) Range is (-inf,11.988] Increasing on (-inf,0.765) Decreasing on (0.765,inf) Vertex form: y=-3.4(x-0.765)2+11.988 Factored form: y=-3.4(x-2.642)(x+1.113) Positive on (-1.113, 2.642) Negative on (-inf,-1.113)U(2.642,inf)
  6. 6. A few more tips for Desmos Wrench Icon to manually scale graphs or use Projector Mode Shift Click for scaling one axis Gear Icon Copy a function
  7. 7. Write the formula for a function that looks like this.
  8. 8. Tips for multiple graphs in Desmos Turning graphs on and off Changing colors or styles on graphs Function notation works
  9. 9. Find a formula for g(x).
  10. 10. Data in Desmos Add a table with + Table Regressions use ~ Zoom Fit to Data
  11. 11. Find a mathematical model for this data
  12. 12. Statistics in Desmos http://bit.ly/Desmos-Stats Lists in Brackets Functions with parentheses
  13. 13. List five properties of the data set Exam Scores: 68, 78, 85, 92, 98, 56, 72, 78, 27, 80
  14. 14. Share a set of Desmos data from a URL Make a Login (Free) Save view / Share view Share URL with Students Use Bitly to shorten links or put in LMS
  15. 15. Find a model for this data for the REXUS-7 Rocket Launch URL from Desmos: https://www.desmos. com/calculator/9khub xejc6 Easy-to-Share URL from Bitly: http://bit.ly/REXUS17
  16. 16. Make classrooms more like online rooms Please go to the chat room for this talk. bit.ly/MichMATYC2019 To do multi-line chat, use Shift-Enter between lines. When I write --- wait --- in the chat, you have to wait to press enter on your answer until I say go.
  17. 17. Declare the meaning of the two variables.
  18. 18. Student Responses
  19. 19. Find and interpret the meaning of S(2.5) in a complete sentence.
  20. 20. Student Responses
  21. 21. Find a linear regression model for the data.
  22. 22. Student Responses
  23. 23. Use the linear regression equation to predict the number of subscribers in the year 2022. Write your answer in a complete sentence.
  24. 24. Student Responses
  25. 25. Where am I finding all the data?
  26. 26. Graphs In The World (GITW) Facebook Search GraphsInTheWorld https://facebook.com/gra phsintheworld Instagram Search@GraphsInTheWorld https://www.instagram.com /graphsintheworld/
  27. 27. Contemporary Algebra Worksheet Collection https://busynessgirl.c om/resources/conte mporary-algebra- collection/ http://bit.ly/Contemp Algebra
  28. 28. Find a partner who teaches something similar Write Write an activity of at least three questions Choose Choose a graph that you can use in class next week Go Go to Graphs in the World Open Open a Word Doc or Google Doc (my preference because we can share)
  29. 29. Desmos Classroom Activity: Finding the Domain and Range
  30. 30. Desmos Classroom Activity: Marbleslides on Lines
  31. 31. Teacher Side of Desmos Activities URL https://teacher. desmos.com Must have login
  32. 32. Desmos Activities Tips Anonymize Option You can display the code or get a URL for the LMS Must be accessed through the BROWSER You can use these in online courses* New Code / URL required for unique class data
  33. 33. Create a Login and Find an Activity You Like URL https://teacher. desmos.com
  34. 34. Now Pair Up – One Teacher / One Student Teacher Create the Assignment Get it to your Student Monitor Their Progress Play with Display Options Student Start the Activity Get some panels right and some wrong
  35. 35. Can you make your own Desmos Activities? Desmos Classroom Activity: Match Up on Population Models
  36. 36. Copy an activity and play with it to get the hang of construction Make a brand new activity from scratch if you want to show as the author.
  37. 37. Assessments Way more data-driven Real-world examples with modern context Way more concept oriented Much higher focus on checking work with technology
  38. 38. Make them make models of what they see
  39. 39. The time scales are often messy
  40. 40. Interpreting real-world graphs is normal
  41. 41. If they can’t do it with real graphs, what’s the point?
  42. 42. Concepts, not algebraic nightmares
  43. 43. Requiring the graph forces reasonability
  44. 44. Data is often messy
  45. 45. Can be done both ways to check in Desmos
  46. 46. The real world is often piecewise
  47. 47. One throwback to old times, but only substitution for systems of equations
  48. 48. List properties…
  49. 49. Checking some little details
  50. 50. Requires knowledge of Quadratic Formula
  51. 51. What about Proctoring Tests? http://bit.ly/Desmos- Proctoring
  52. 52. Questions?

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