First off, if you haven't heard about #MTBoS (or the MathTwitterBlogosphere), it is an 8-week series of missions designed to connect dedicated math teachers who are willing and interested in sharing their tips, tricks, and experiences. Sounds awesome right?! You should definitely head over to their Wordpress site and learn more about it!
Mission #1: The Power of the Blog
What is one of your favorite open-ended/rich problems? How do you use it in your classroom? (If you have a problem you have been wanting to try, but haven’t had the courage or opportunity to try it out yet, write about how you would or will use the problem in your classroom.)
As a first year teacher, who is new to math, I don't have a large resource of open-ended questions that I have been drawing from. I can, however, share a question that I posed to my Grade 8 students last week that got them really excited about math and got them thinking out of the box (including my reluctant learners)!
I came across the following video via one of my YouTube subscriptions, Numberphile. I was immediately engaged because it got me thinking about math in a way that I hadn't been before. As we had been discussing integers and fractions in class, I decided to share the question with my Grade 8 math class.
*Note: I did not show them the video on the first day, I simply presented the question:
"The following series 1-1+1-1+1-1+1-1+1-1... continues forever, using your knowledge of integers, what do you think the answer(s) to this question might be?"
I had some students say that the answer would be 1, some said 0, some said 2, and I had some students that were unsure. The following day, I showed them the video that I had seen online:
This was the first time all year that I can honestly say that ALL of my students were excited about math! The possible solutions to Grandi's Series got them thinking about math differently than they had before and the fact that the video ends with a challenge had them even more engaged. They are planning on completing the Thompson's Lamp experiment on their own at lunch this week to see how it turns out!
I have always been a fan of including video clips in class as a differentiation method to meet different learning needs but I hadn't specifically thought of videos that ended with open questions. This is definitely something that I will want to explore more with my students as we progress throughout the year!
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On a side note, my students decided to feature this video and question on their class blog and Dr. James Grime (the man featured in the video) actually saw it and commented to them! It was so exciting to see their enthusiasm and surprise when they checked their blog comments this morning!So, I have officially completed Mission 1 of the #MTBoS journey! I look forward to connecting and sharing with you!
Wow, that is a very intriguing problem. The problem starts off very simple and proceeds to really involved ideas. To me, that's what makes this a great problem - it's easily accessible but has a lot of scope for extension as well. Great find! I'm a first time visitor here (via MTBoS, of course!), but have you talked before about which YouTube subscriptions you have? I have not thought before about following some, but I can see that might be worthwhile.
ReplyDeleteThanks for visiting and taking the time to comment :) Some of my favourite math YouTube Channels are:
Delete- Numberphile
- Math Class with Terry V
- TenMarksInstructor
- MathDoctorBob
- yaymath
- WOWmath.org
Cool! I mostly teach sciences, so I haven't spent a lot of time with Numberphile, but I do regularly use a lot of other videos during classtime (if you're interested, check out my blog for a list).
ReplyDeleteWhat do you do with this in terms of further exploration? It's so awesome that Dr. Grime found your comments, but where do you go from here? More seemingly-unanswerable questions? Knowing that there's patterns to follow to get sums?
Hi wwndtd! Thank you for commenting :) Depending on the level of my students we took this a few different ways:
Delete1) Some students performed the experiment introduced in the video to see if they could prove if the answer is either 0, 1 or 0.5.
2) Some students looked at the other pattern 1, 1/2, 1/4, 1/16 ... as a way to practice adding their fractions
3) Some students tried to pictorially represent this series
4) Some students tried to create their own series that could elicit the same type of "shock and awe" that they got with this one!
It is important to note that was not a formal activity for marks, it was an optional activity to get students thinking differently.
What a great problem! No wonder your students were so motivated. I remember learning about calculating large sums of numbers when I was in school, and I hated it. It didn't make sense, and I didn't care to think about why anyone would want to add all these numbers together. This video actually made me intrigued, and it made me wonder what my younger self would have thought if my teacher had used a video like this in class. Thanks for sharing!
ReplyDeleteHi bstockus, thank you for visiting and commenting! I'm glad that you found it as interesting as we did. I had a very similar experience to what you mention so I am especially glad to be finding amazing resources like this to engage and motivate my students.
DeleteInteresting thoughts, I really enjoyed your blog
ReplyDelete