My deep concern over the discomfort and confusion that my students exhibited around negative integers and using counters has sent me on a search for resources. Yesterday, I had my students use #VNPS (vertical non-permanent surfaces, or "whiteboards") to display their thinking and convey their reasoning to others.
It went off with mixed results. I am determined to use the whiteboards more often and will be incorporating #VNPS into my class on a regular basis.
Today, however, I had access the computer lab and wanted to try something else, which brings me back to Michael.
He is on the teaching faculty at Desmos, the online graphing calculator that is changing the face of mathematical educational technology.
He is also the designer of multiple activities, one of which I used today!
What I LOVE about it is that from the teacher dashboard, I'm able to see what they are doing in real-time. I can tell a student to go back and check a certain problem or add more explanation to their answer.
I'm always interested in how some kids will talk on and on, verbally explaining their answers in novel-length expository monologues, but will only type 2-3 broken words if asked to write it down.
At the same time, there are many students who when asked to verbally explain will simply shrug their shoulders. If, however, you put a keyboard in front of them and ask them to write out what they are thinking, they have no problem going into incredible detail.
If there is any better argument for differentiation of assessments, I don't know what it is.
At the end of the activity, I handed back the quizzes from Wednesday. The mean class scores for the five sections, out of 19 possible points, were 8, 10, 11, 13, and 14.
"I got a 10?? Out of 19?? I failed!!!"
"Not at all. You got 10 correct. That's a very solid foundation on which we can build! Look at the test and figure out which ones gave you difficulty and why so that we can work together to ensure that you understand the material and can demonstrate that understanding."
"Again, it means you have room to grow. If you're so upset by this score, then use this experience as something from which to learn. The studying strategies, or paying-attention-in-class strategies that you've been using may not be the best.
"I'm terrible at math!!"
"I'm sorry you feel that way, but I don't. Let's fix the way you see it!"
And so on and so forth...
It's a process.