With the plethora of apps available that gave students access to not only immediate answers but detailed steps to solve any and all math problems, it was important that I understood how to formulate questions or challenges that encouraged deeper thinking while allowing for technology to support learning.
For this blog post, I wanted to step outside of my role as a technology specialist and take you inside my head from the lens of a high school math teacher exploring ideas for a lesson that integrates technology. Below is an example of a process that I would have followed with the resulting lesson directly below it.
Planning a Technology Integrated Math Lesson from the Lens of a Teacher
The other day, I came across a bag of "smarties" candy and naturally, I wanted to find a way to store them so that they could be eaten gradually. Yes, it would have been simple to just toss them in a cabinet but...what's the fun in that?
I immediately looked for containers and noticed that I had quite a few at varying sizes. This is the moment when the math teacher in me intersected with the technology specialist. I happen to have an app on my iphone called, "My Measures & Dimensions". This is an app that allows users to annotate math measurements on top of images. (I use the free version. The skitch app is great for this as well)
I measured my containers and took the following images which I put together using a simple collage app called "Moldiv". (pic collage works just fine as well)
Now, yes...I can stop right here and have students calculate the volumes and even surface areas of each container but, again...what's the fun in that?
Referring back to my "smarties", I measured them and took a few snaps. Again, using the "My Measures & Dimensions" I labeled those as well. (See the image up top!)
I also notated that a roll of "smarties" contains 15 wafers and with this information, I can easily determine the logistics of not only how many smarties could approximately fill each container but how much space is left in the container that isn't a "smartie".
The list of questions goes on.
Revising this for Student Inquiry: Iteration 2 of The "Smartie" Situation
Inquiry based learning happens when questions are generated from interests, curiosities, perspectives and experiences of the learner. Basically, the learner is presented with a scenario and from that experience, questions are generated and continue to build and generate even more questions throughout the process.
Instead of the teacher "pre-labeling" each image with measurements and asking students to solve one problem, the image or objects are presented to students which prompt their investigation.
What Students need: Objects (This can be anything that is measurable like cubes, checkers, packaged crackers, cookies, dice and even candy wafers...depending on district guidelines), ruler, mobile device (or school issued ipad/chromebook), graphing calculator although not completely necessary since mobile and web tools can help students with calculations), container
For this problem, the scenario changed yet again to a rectangular box instead of the original three cylindrical containers.
1. Estimation/Pre-Thinking: Without solving, estimate the number of "objects" (remember this can be anything) that could possibly fill the square container. What's the smallest possible number? What's the largest? Explain your thinking.
2. Decisions, Decisions: You have over 100 individual rolls of "smarties" and must find a way to package as many as possible into the given container. You can either pack them in their current rolls or take them apart and pack wafer by wafer. Using active investigation along with mathematical reasoning, collaboratively determine the most efficient way of storing candies. Document your process with annotated images, video, calculations and descriptive text.
3. Extension: Do you think that this was the best choice of container? If you could redesign it, what shape would your container be? What about measurements? Justify your choice.
Publish your investigative process via a tool like google docs, TACKK, google slides, thinglink, FastFig, or any other tool of your choice including a blog. You must include your images (with annotations), video and mathematical reasoning through some form of media.
Post the link to your published work via our classroom LMS (learning managements system) - Google Classroom, Edmodo or Canvas if you are using it.
In case you missed it, this is meant to be a collaborative effort.
Important teacher note regarding grading: Always provide a rubric where the focus is on the intended conceptual outcome...NOT the technology. There is a great ipad app called WeLearnedIT that actually allows students to do every piece of the publishing portion of this assignment as well as the rubric creation and grading for teachers.
Student Support FAQ (I always include this piece so that they can be more self-directed while I facilitate)
1. Video: You can upload longer video to youtube or share 15 second increments to instagram. If you use TACKK, both video types can be embedded directly.
2. Audio: You can use an app called audioboo or even a web tool called vocaroo. If you have another tool that you like to use, please do share it.
3. If you use Thinglink, all media can be uploaded directly into the app from your device.
4. (I have no idea where to start) - What is the question that you were asked to answer? Think of obvious as well as "outside of the box" ways to figure it out. Make a plan but understand that it's okay if your plan changes depending on your investigation. Check the rubric throughout.
5. Don't just stop when you feel that you might have an answer. So many other questions should arise during this process. Document them, share them and dig deeper as you feel compelled.
Be aware that this was me taking you inside of MY planning process from the lens of my classroom experience. Yours may be very different and that is okay. Yes, this was pretty nerdy and extensive but it can still be done to the scale that is appropriate for you and your learners. Our goals, in ITD, are to support you as you give students more opportunities to exercise their potential as 21st century learners.
It's not an overnight process but one that builds. We'll get there together.
See an example of a process such as this by checking out Eanes ISD Cathy Yenca, "The Big Nickel" below.
Also check out these two amazing math blogs for more mathematical critical thinking based ideas. Estimation180 and Would You Rather Math