Calc
Found another awesome calc website( created by two professors at Hofstra Univeristy)! I used it yesterday to have students practice with continuity and differentiability and then today to practice matching polynomial graphs with their first derivative graphs (this was the table perspective which we did first). I hope that using these intense practice sites really gives the students a better understanding of what they are doing, thereby making it more than just "magic".
We also discussed questions they had on their homework last night and I pointed out that we were doing Algebra (the Calculus version). It's so great to poke at their brains with questions about processes they know and see if they can make the connections. Today's BIG questions were:
How do position and velocity relate to each other? At what time does the object hit the ground? When does the object reach its highest point? What is the velocity when the object is "x" feet off the ground?
Here's where I find it ironic that they are stumped. I have to ask them what the graph of position looks like. It doesn't take much to get them to see it is an upside down parabola. But then I ask them where in the graph is reaches it's highest point and how they can find it without using Calculus. I tell them they have more than one way that they knew when they started the year in the class. It takes awhile for the wheels to churn and spit out things like midpoint value of the x-intercepts, or complete the square, or -b/2a. Much discussion happens over these ideas. Then, and only then, we get to the calculus option of finding the derivative. But getting all the other ideas back in their brain and to a level of it making sense is a challenge. I marvel at how little students remember. When we discuss the -b/2a option, I ask them if they have seen that anywhere else. Someone inevitably says "quadratic formula" and I ask if we should sing. Several do. I say isn't that great, but you aren't even aware that what that formula does is generate the x-intercepts equidistant from the midpoint (and proceed to split the formula apart). They are amazed as though I just performed a magic trick. I re-emphasize the importance of graphs to help them see what is happening.
Wish graphical approach was used a lot more in the earlier classes. Seems like we teach a lot of "just memorize this formula" without the pictures to help it make sense. If we taught reading that way (no pictures), do you suppose kids would come to high school not being able to read all that well? Wonder why kids prefer "the movie" over "the book" when its available? Do you suppose we are more picture driven in our brains? I do. I tell the kids "I love pictures". I know they help. Getting them "back to basics" takes some time. It makes me sad that they have had it "beaten out of them".
I knew that once they started they would want to play it over and over, so I made sure they entered they data for only the first two trials. We'll use this data to test for normality next week. Even one of the students said "that was a great way to end class after our quiz."
I just need to find some more Stats video games!
Here's where I find it ironic that they are stumped. I have to ask them what the graph of position looks like. It doesn't take much to get them to see it is an upside down parabola. But then I ask them where in the graph is reaches it's highest point and how they can find it without using Calculus. I tell them they have more than one way that they knew when they started the year in the class. It takes awhile for the wheels to churn and spit out things like midpoint value of the x-intercepts, or complete the square, or -b/2a. Much discussion happens over these ideas. Then, and only then, we get to the calculus option of finding the derivative. But getting all the other ideas back in their brain and to a level of it making sense is a challenge. I marvel at how little students remember. When we discuss the -b/2a option, I ask them if they have seen that anywhere else. Someone inevitably says "quadratic formula" and I ask if we should sing. Several do. I say isn't that great, but you aren't even aware that what that formula does is generate the x-intercepts equidistant from the midpoint (and proceed to split the formula apart). They are amazed as though I just performed a magic trick. I re-emphasize the importance of graphs to help them see what is happening.
Wish graphical approach was used a lot more in the earlier classes. Seems like we teach a lot of "just memorize this formula" without the pictures to help it make sense. If we taught reading that way (no pictures), do you suppose kids would come to high school not being able to read all that well? Wonder why kids prefer "the movie" over "the book" when its available? Do you suppose we are more picture driven in our brains? I do. I tell the kids "I love pictures". I know they help. Getting them "back to basics" takes some time. It makes me sad that they have had it "beaten out of them".
Stats
What a great day....if you like a lot of quiet followed by A LOT of noise! Sheep bleating, that is! Since the kids are in groups and I didn't want to move the furniture for a quiz, I came up with (if I do say so myself) a clever idea of making 4 versions and putting them on different colors. I also gave them a divider to put up between the side-by-side students (they didn't really need it). It really was easy! Just change the numbers! Sure it meant I had to make 4 keys, but it was totally worth it! Will do that again!
We had just enough time to gather data at the end of class that I plan to use next week. We used a website that tests your reaction time. It has you tranquilizing sheep and it is SO MUCH FUN! Their expressions say it all!
I just need to find some more Stats video games!
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