Of course, I won't do "A Day in the Life" today, but I will say a few things about today. First of all, the bell schedule today is different -- tutorial is replaced with a winter sports pep rally. The theme of the rally is Hogwarts Holiday -- indeed, the seating in the gym is decorated so that the freshmen sit in Hufflepuff colors (gray/gold), the sophomores in Ravenclaw (gray/blue), the juniors in Slytherin (black/green), and the seniors in Gryffindor (red/gold). Our special ed students participate in a P.E. program where they compete against other students with special needs in the district. Because of this, they are introduced as one of the winter sports teams at the pep rally.
Later on, a game of Jeopardy is played to review a short article that they've read. For "math," the students cut out pictures of food to create a meal. I assume that they're supposed to add up the prices to find the total cost of the meal, but there's no time for any such calculations today.
Today is the second day of finals week. It has been my tradition on the blog on the second finals day to explore the Math Twitter Blogosphere, or MTBoS.
Well, since I played Jeopardy in class today, let's start with links to some members of the MTBoS who also use Jeopardy games. A Google search returns the following link:
https://mathisajourney.wordpress.com/2018/10/14/pimp-those-practice-review-activities/
The author of this blog is Sarah -- Martin, not Carter or VanDerWerf (even though many of the activities posted here are similar to Carter's or VanDerWerf's). Her Jeopardy is for groups of four -- the Jeopardy we played today was more individual (but then again, this is a small special ed class).
Let me post some of the other activities that Martin includes here:
Scavenger Hunts:
- So far I have gotten these from Teachers Pay Teachers
- I love that these get students up and moving
- I use the hallways around the 7th-grade math room
- Students work in pairs and can’t move on to finding their next question until they have a correct answer
- My goal is to start creating my own (when I can find the time)
Quiz Quiz Trade
- Create questions on index cards. (Answers on the back)
- Each student gets a card. Ask students to review both the front and back of the card.
- Students then stand up and find a partner. They stand shoulder to shoulder. One student starts asking their question. The other student works it out and says the answer. If the student is wrong the other student gives a hint, hint, hint then answer.
- Students then switch and repeat the process. When finished students trade cards and find a new partner.
Notice that Sarah Martin is a seventh grade teacher -- and I do see posts dating all the back to the year I taught at the old charter school. Of course, it would have been difficult for me to play any of her activities that year due to the Illinois State curriculum. But some of her posts from back then (on Twitter, posters, and the seating chart) could have helped me out that year.
Meanwhile, here's a link to an AP Calculus teacher who also uses Jeopardy:
https://techiemusings.com/2015/03/30/ap-jeopardy-review-lets-eportfolio-that-using-peardeck-wacom-tablets-and-msonenote-edchat/
https://techiemusings.com/2015/04/07/ap-calculus-jeopardy-using-peardeck-wacom-tablets-msonenote-edchat-mathchat/
This teacher suggests using technology to enhance the Jeopardy game:
That takes me to this year. I decided to use PearDeck to push out the Jeopardy questions to each student’s computer screen. Briefly, the way PearDeck works is that the teacher creates an interactive presentation within the platform and then students’ log into that presentation from their own computers. The teacher controls the pace of the presentation and students engage with the interactive slides. The teacher receives student responses in real-time.
Well, I can't have an MTBoS post without Dan Meyer. Here's a Meyer post from last month:
https://blog.mrmeyer.com/2019/estimation-isnt-just-calculating-badly-on-purpose/
I think it’s possible we should cut the student some slack here.
If the student has all the tools, information, and resources necessary to calculate an answer, we should be excited to see the student calculate it. Asking students to do anything less than calculate in that situation is to ask them to switch off parts of their brain, to use less than their full capacity as a thinker.
If we treated skills in other disciplines the way we often treat estimation in math …
This addresses a traditionalist concern as well -- why estimate instead of give the exact answer. (I once recall a Common Core horror story where the student answered 9 * 9 = 81 and was marked wrong, because the student was supposed to estimate the answer as 10 * 10 = 100.)
Actually, I wish I could find the "9 * 9 = 100" horror story now. It was something that I read several years ago, well before I found the blog. The teacher had told the students to round each 9 to 10 before multiplying, the student just multiplied 9 * 9 straight, and then the parent complained that the child was marked wrong.
This is what Meyer is trying to point out here. He writes:
Estimation shouldn’t ask students to switch off parts of their brains or use less than their full capacity as thinkers. It should ask them to switch on new parts of their brains and expand their capacities as thinkers.
In other words, we shouldn't ask students to estimate 9 * 9 = 100 -- and thus that parent was right to criticize the student's grade. Meyer tells us what should be estimated instead:
Estimation and calculation should also be mutually supportive in the same way that …
… knowing roughly the balance of yeast and sugar in bread supports you when you pour those ingredients exactly.
… knowing the general direction of your destination supports you when you drive with turn-by-turn directions.
… knowing the general order of your weekend schedule supports you when you carry out your precise itinerary.
Meyer lists two types of activities that teachers can use here. One type is where estimation is the most efficient method. His example is a worksheet where we order the sums from least to greatest before adding them. For example, it's obvious that #1 (145 + 325) is less than #4 (608 + 3210 without needing to use the standard algorithm -- in #1 the first addend is less than 200 and the second less than 400, making the sum less than 600, while in #4, the first addend exceeds 600 by itself (with all addends positive).
The other type is where estimation is the only method to use. He presents these examples in his favorite "3-Act Task" format -- his worksheet directs students to estimate the number of coins in a fairly large pyramid.
I'll include Meyer's "featured comments" here:
Featured Comment
One thing I love about calculus is is proceeds from estimation to exact calculation, and there’s no way to justify the exact calculations without working through the estimation first. We often think of mathematics as a discipline that proceeds deductively from perfect truth to perfect truth, but there are whole swaths of mathematics where the best way forward is to work from an answer whose incorrectness we understand towards an answer whose correctness we don’t yet understand.
I agree with you, but I think it’s interesting to turn your non-math examples into better activities that reflect what we’re trying to do with “good” math estimation tasks.
Mr. K references Fermi problems, which fall really nicely in the category of “tasks where estimation is the only possible method.”
And so estimation is a handy tool. The traditionalists fear that the Common Core encourages the use of estimation to replace finding exact answers -- and with that 9 * 9 = 100 worksheet, can anyone blame them? To me, this is a tough one -- was 9 * 9 = 100 based on a misinterpretation of the Common Core standards, or was it the actual intention of the standards writers?At the beginning of the year, I fill four jars around the room. One with M&M’s, one with eraser caps, one with cotton balls, and one with paper clips. They are all allowed a guess for how many in each jar. They enter their answer and their name on a slip of paper and place it in a collection jar. Whenever we come to a question where I want them to estimate first, I remind them of what they did when they first looked at the jar. I don’t tell them how many in each until the winter break – the suspense is awesome. Then in January I start with four new jars.
Speaking of estimation, let's conclude this post with a Square One TV song on estimation. This song mentions examples similar to Meyer's -- estimation is the best way to determine, say, whether there is too much weight on an elevator.
No comments:
Post a Comment