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Andrew Shauver high school math and science Pennfield High School, Battle Creek, MI thegeometryteacher.wordpress.com @hs_math_phys #MTBoS (Twitter-based international math PLN) Using Photography and Video to Support Math Learning Slide 2 A quick word about #MTBoS (mitt-boss) #MTBoS = MathTwitterBlogosphere International PLC of math teachers who blog, tweet, or simply read blogs and tweets. Diverse, effective, and excellent sharers. Slide 3 Slide 4 How many jars will you need to frost that wedding cake? Slide 5 What information do you need to know to solve this problem? What will you do with the info when you get it? Slide 6 frosts about 200 in 2 5 inches tall 4-inch radius 5 inches tall 5 -inch radius 5 inches tall 7-inch radius r = radius of cylinder h = height of cylinder Slide 7 Slide 8 Solution I got Top frosted surface (only 1 base): ~176 in 2 Middle frosted surface (1 base minus on top base): ~218 in 2 Bottom frosted surface (1 base minus middle base): ~ 279 in 2 For a grand total of :~ 673 in 2 Which means youll need four containers of frosting. Slide 9 What teacher moves did you see? Lesson design loosely modeled after the #3Act Instructional Model (described and introduced by Dan Meyer, embraced by many in #MTBoS) Slide 10 Student Decision-Making How does the math model the task? Cylinder Surface area (bases included?) Once I decide how to model the task, which measurements do I need? Which do I not need? I have an answer. Is it reasonable? Slide 11 The value of modeling with mathematics The tradition of formal mathematics leaves many able students both innumerate and undereducated. However, when the traditional symbol-intensive curriculum is anchored in authentic applications and modeling by students, many will reveal aptitude for mathematics that was previously undeveloped. Burkhardt, H., Muller, E.R. et al (2007) Slide 12 Find the volume and surface area of Taken from Geometry, Holt 2007, Pg 684 Slide 13 What teacher moves did you see? Also, I was snapping pictures the whole time. Part classroom-management (manage-by- walking-around) But, pictures of student work can be used later Slide 14 Four students from a different hour tried to reflect the trapezoid on the right over the line. Rank them in order from closest -to- perfect to most improvement needed. Slide 15 All of them need some improvement Questions for students: 1.What does it mean for a reflection to be better than another? 2.What data can we pull from the pictures to check? Slide 16 Then Using GSP or GeoGebra or paper/pencil/protractor/ruler, have the students pull the measurements Or Slide 17 Slide 18 Slide 19 Slide 20 Slide 21 PROBLEM: Textbooks have to simplify the complicated world, but simplify the wrong part. You dont simplify the thought process. That part needs to stay thick and rich. You simplify by using an accessible context and asking a simple question. Slide 22 How many jars will you need to frost that wedding cake? Slide 23 Slide 24 What Im NOT suggesting I am not suggesting that peppering students with pictures and videos is the magic bullet The key is to allow the pictures and videos to support an authentic experience of the content This isnt about increasing real world problems. Slide 25 Pam and Tommy collect geodes. Pams parents gave her 2 geodes to start her collection and she buys 4 every year. Tommy has two geodes that were given to him for his birthday. He buys 4 every year. If Pam and Tommy continue to buy the same amount of geodes per year, when will Tommy have as many geodes as Pam? Explain your answer. Slide 26 Postage stamps are popular collectors items. Many cultures use them to commemorate famous events or people who are historically significant for any of a number of different reasons! Postage Stamps Pam and Tommy collect postage stamps. Pams parents gave her 2 postage stamps to start her collection and she buys 4 every year. Tommy has two postage stamps that were given to him for his birthday. He buys 4 every year. If Pam and Tommy continue to buy the same amount of postage stamps per year, when will Tommy have as many postage stamps as Pam? Explain your answer. Stamp photo credit courtesy of Flickr user matsuyuki used under Creative Commons Slide 27 Bottle Caps are popular collectors items. People like to drink the drinks that are bottled in the capped bottles. Some of the drinks dont exist anymore making their caps interesting to collect. Pam and Tommy collect bottle caps. Pams parents gave her 2 bottle caps to start her collection and she buys 4 every year. Tommy has two bottle caps that were given to him for his birthday. He buys 4 every year. If Pam and Tommy continue to buy the same amount of bottle caps per year, when will Tommy have as many bottle caps as Pam? Explain your answer. Bottle Caps photo credit courtesy of Ashley McKinnon used under Creative Commons Bottle Caps Slide 28 Pam and Tommy collect Chewbacca Pez dispensers. Pams parents gave her 2 Chewbacca Pez dispensers to start her collection and she buys 4 every year. Tommy has two Chewbacca Pez dispensers that were given to him for his birthday. He buys 4 every year. If Pam and Tommy continue to buy the same amount of Chewbacca Pez dispensers per year, when will Tommy have as many Chewbacca Pez dispensers as Pam? Explain your answer. Chewbacca Pez Dispenser photo credit courtesy of Peter Taylor used under Creative Commons Chewbacca Pez Dispensers are popular collectors items. Chewbacca is a wookie from Star Wars who became the trusted companion of expert bounty hunter Han Solo. Chewbacca Pez Dispensers Slide 29 Effective use should Create an intellectual need for the targeted content Allow intuition to play a role in the problem-solving process Reduce the literacy demand Make the context accessible to all students (Meyer, 2013) Slide 30 Hershey Bar Slide 31 Pencil Sharpener Problem https://www.youtube.com/watch?v=OEbgxRcePF4 https://www.youtube.com/watch?v=gQnHXbWRDVk https://www.youtube.com/watch?v=13QnV9YMYf0 Slide 32 Slide 33 Slide 34 Slide 35 Speedometer https://www.youtube.com/watch?v=5AXYImzuV4c Slide 36 Time A common concern Slide 37 Slide 38 Dont worry if you are intimidated by the process. Dozens of these types of activities are made available right now Research and steal Slide 39 Slide 40 Slide 41 Slide 42 Open Q & A Slide 43 For extended discussion - @hs_math_phys http://thegeometryteacher.wordpress.com Slide 44 For more info or extended discussion Slide 45 Andrew Shauver high school math and science Pennfield High School, Battle Creek, MI thegeometryteacher.wordpress.com @hs_math_phys #MTBoS (Twitter-based international math PLC) Using Photography and Video to support math class Slide 46 The Process Gather photos Make your camera your constant tag-along. Photos and videos are cheap and disposable. I use an iPad and a cell phone. Lots in class. My students shave stopped being bothered by a camera on their work. Slide 47 Transfer photos to workspace I use dropbox to transfer photos onto my laptop. Snipping Tool has become my best friend Also, Windows Movie Maker