Saw this tweet from Christopher Danielson today:
[post publication addition – Danielson has written a blog post about the activity. It is here:
A New Calculus Activity Builder activity by Christopher Danielson ]
I was looking for short activity to try with my older son this afternoon and this looked like it would fit the bill pretty well.
He’s not a calculus student – obviously – but I was interested to hear what he thought of the activity and also what he thought of the definitions of a few of the terms.
We jumped into the activity after he got home from school – I had to help him a bit with the definition of “continuous” but other than that getting going was pretty easy. It was fun to hear his reason behind the first set of questions:
I accidentally stopped the video before we’d finished the first activity in the exercise, so we finished that part quickly and moved on to the second activity.
The function here looks like a horizontal line, so he initially assumes that it is a line. The ability to see other student answers shows him that there’s some possible shapes of the function that he has not considered.
The 3rd part of the activity looks at a function continuous on an interval while showing a larger interval. He seems to be catching on to the idea of this activity and doesn’t have too much trouble here.
The last part of the activity looks at non-continuous function. One suggestion for the activity is to make the non-continuity more clear at the beginning, which is what I chose to do. I also had to give an alternate definition of continuity from what I gave in the first part because I’d not make the idea of continuity clear enough.
At the end of the activity the student is asked to explain how we can tell if a function definitely has a root. He answer isn’t quite right, but he did still have a pretty good idea here. My one other suggestion for the activity is to come up with some way to ask this question at the beginning of the activity, too. That’ll allow you to compare some ideas which will have probably changed a bit over the course of the activity.
So, a nice little computer activity for students. I liked seeing how other student answers led to my son thinking about the problem differently. It seemed like that feature would provide a few good discussion points in class.
Mike's Math Page 
The way that these questions and answers are set up is something that I haven’t seen before, and I find it to be incredibly friendly. The way that the circles move to reveal the curves at the end of each section make it an activity of discovery rather than a right/wrong activity. I like how we can see how other students answered the question as that provides an opportunity and motivation to rethink one’s own response, and to give opportunities, at times, to defy the majority.
Thought I’d commented, so apologies if this is a duplicate.
The last example isn’t a non-continuous function. It is a function (stated in the activity) that isn’t defined on an interval, but rather two intervals forming a disconnected domain. Where it is defined, it does appear continuous. I wonder what folks would have made of it if continuity was also stated?
Interestingly, I’ve looked at about 15 answer to the last question (updating the page at different times) and haven’t seen anyone give the full conditions for IVT. Maybe because it is a focus topic and seems more complicated, continuity has drawn everyone’s attention, while connectedness of the domain doesn’t register.
That’s a great catch – wasn’t even on my mind going through this with the kids.