Activities
There are a few math activities that I do with candies and one starts similar to the video.
Take a box of Smarties and sort them by colour.
Create a bar graph to represent the frequency of each colour in the box of candy. *Use a fairly large scale for the graph
Calculate the fraction of each colour.
Calculate the percentage of each colour.
Cut out the “bars” of your graph and tape them end to end to make a circle.
Trace the circle and use your bar graph to make a pie chart.
Use the percentages in step 4 and the 360 degrees of a circle to calculate the angle of each piece of the pie.
Use a protractor to measure the angles and compare with your results in step 6.
Calculate the fraction of each piece of the pie and compare with your results in step 3.
Explain any differences in the angles and/or fractions.
Compare your results to the rest of the class.
I do not have a printer so I used a ruler and compass to make my hexaflexagon based on the template provided. The paper was 28cm long so I marked off 5.6cm intervals and used a compass to find the apex of my equilateral triangles. I looked at the fidget spinner template to see where to colour each side, then folded my paper according to the instructions. It took a few tries to get comfortable flipping/folding my hexaflexagon, but it worked as intended.
I did not have the ingredients for a Flex Mex burrito, but I did have tortillas so I rummaged around the kitchen and opted for an homage to a tuna melt instead. The trickiest part was folding the cheese into the middle as it was the opposite of how I had practiced with the paper version. Also, the tortillas were a little on the dry side so they cracked a bit during the folding process. I wasn’t crazy about the tuna leakage, but I do think this would enthrall and astound my nieces and nephews and could alleviate some picky eating!
I did not have any bagels either, so I used modelling clay to make something that was not entirely unlike a bagel. I “drew” the equivalent of the black and red lines with a toothpick then used a small paring knife to cut my “bagel”. By ensuring the blade entered the bagel on the black line and exited on the red line I obtained the two interlocking circles.
Reflecting on this experience, I found that I had to check my attitude throughout the activities despite enjoying the videos. I think it was the amount of time it took that I found frustrating as it didn’t feel like physically doing the activities added to my personal experience significantly. (Time I would have preferred to use folding the heap of laundry that inhabits my living room. C’est la vie.) I could relate to the students in my classes who have said to me, “I get the concept, do I actually have to do this?” I chose to (over)compensate for my lack of enthusiasm by adding a Monty Python soundtrack to my videos.
The introductions discussed some of the difficulties experienced by students with sensory impairments and raised the argument that multisensory experiences not only benefit these students, but they also benefit all students. Stylianodou and Nardi’s article suggests that “multimodal” tasks develop other ways to think about math, reminding me of the video on perspectives from last week. This article specifically examined tactile perception of shape and the mathematical meaning generated by visually impaired and sighted pupils. Students between the ages of 6 and 10 were given the task of exploring a shape “X” made from waxed yarn using touch and sight and comparing the shape to a circle. The shape “X” is described in the article as “a circle minus a circular segment” as if a short chord were drawn and then removed from the circle.
The sighted student did not initially see the shape was not a circle until he perceived a “straight line” using his hands. The visually impaired student noted the circle would roll while shape X would not, a contribution later used by the teacher when describing properties of circles. The tactile activity gave the visually impaired student a chance to make meaningful contributions to the understanding of shape that benefitted the whole class. The authors argue this is just a single example of ways inclusive learning activities broaden the understanding of all students while challenging ableism. The activities this week were a similar opportunity for us to experience and interact with shapes in a different and tactile way.
The introduction and article both challenge the ableism present in our school systems and society. The ideas seem similar to the work of CAST and their Universal Design for Learning (UDL) framework outlining multiple means of engagement, representation, and expression. I fully agree that we should be designing learning activities that are inclusive and accessible to all students. Yet, I wonder about the difference between providing multisensory learning opportunities and requiring them. UDL gives students a fair bit of autonomy and choice, but does that allow them to remain in their comfort zone? It is human nature to follow the path of least resistance. Is it a bad thing to require students to do things they would not ordinarily choose to do so they experience something in a different way and broaden their perspectives? (Like actually making a Flex Melt and not just watching the video?)
I felt the same in my experience with the first 4 attempts at making a hexaflexagon. I even had my EA attempt to make one and he got just as frustrated as me. Now that I have mastered making them my daughter keeps asking for more so she can decorate them. She loved the discovery that when it flips the pattern changes and she wants a bigger one with more sides. I told her to tell her teacher about them...haha!
ReplyDeleteAlso good job on attempting the burrito and the bagel. I didn't have the ingredients for either and the thought of interacting with food after the videos were less than appealing. I am like your students: "okay I get it...now I don't want to actually do it"!
Delete"okay I get it. . . now I don't want to actually do it" when I asked my grade 12 students to help me build polyhedrons, about half jumped right in. The other half couldn't be bothered. "Do a good job, teacher needs a good mark" cracked them up. Those that were making them were snapping photos and posting them on social media and one sent the photo to Dad who called his son a genius. They didn't stop at one shape, most went on to do more. Because we were having fun, some of the others decided to join in. I guess the point I'm trying to make is, success after struggle is fun!!! It's the same satisfaction I see after students are able to solve complicated Trig identities or logarithmic equations.
DeleteYou make a fair point, Maria. I guess I just wasn't in the mood for productive struggle this week.
DeleteI think for us it is that so many things are at play. We have numerous responsibilities including keeping small humans alive. So it feels like just another chore. For students, they are being provided the time to explore and they should cherish it before they too have responsibilities weighing them down. Don't be too hard on yourself Mama!
DeleteDitto! To be honest, the reason I roped in my students in to do the polyhedrons with me was that I didn't think I could do more than one. I too wasn't in the mood for productive struggle. Marks were due and the stress and pressure the students had to get the impossibly high marks needed for university was so heavy and almost tangible. But because they were having fun I ended up doing all!
DeleteI found that this week's reading and its focus on students with vision impairments was a struggle for me to find specific multisensory learning opportunities for all. I simply have never had a student in class with vision loss. Hearing loss yes and accommodations were made for that. I think that your questions in the last paragraph are profound and ones that all educators struggle with. I am often placed between trying to challenge my students and being told by their special education case manager that they cannot do what I am asking. It becomes clear that the student is often no longer an active participant in the learning and more that they are just passively engaging simply to get done and through the activity, day, course...There is significant pressure to just move them along by their support team. And I can see that by the time they are in grade 9 they have learned that they can do the bare minimum and still get through with no actual learning, or to as you said, have their perspectives broadened. Educators can make an activity hands-on or with the engagement of the senses but if students do not wish to participate then what can we do?
ReplyDeleteYou are describing what goes on in my classroom for students with IEPs! I am told by both parents and the SpEd caseload teacher to give more accommodations like take home quizzes (that the tutors or parents can do for them). Just move them along is what I hear all the time. How do I pass students who decide against all recommendations, to go to FOM11 from Workplace 10, and haven't passed a single quiz or test? The parents are livid at each "I" report sent home. They hired tutors, that's the solution I'm told, so now just pass them! I hold firm that some evidence of mathematical understanding is necessary for passing but they seem to think that attending classes and tutor session is sufficient. Entitlement and learned helplessness are bad words not to be spoken or even thought of. It must be the unreasonable, difficult teacher who is at fault.
DeleteI definitely find some people treat an IEP as if it is a golden ticket that allows you to float through courses unchallenged. The line between supporting and enabling (in the negative sense of the word) can be rather blurry sometimes.
Delete"Learned helplessness" describes what I was implying perfectly without me wanting to actually say it. I have a nephew with an IEP (autism spectrum) that told me to flat out that he will just find anyone to do it for him. He is now in grade 10, does not go to school, and they have him on an Evergreen track. I am so upset and cannot do anything about it (another district). Had there been more checks and balances through the years would he be more successful? I would think so. He is bright and articulate and while his struggles are with reading, the fact that he has no desire overpowers everything. I am so sad about his path...
DeleteMy daughter has a lot of learning challenges and is in an adapted program at her school (now in Grade 13). She has this practiced "blank" look that works on most people that enables her to get away with doing nothing. When she was in grade 8 her elder sister (grade 12 then) came to visit her in class. The teacher proudly showed the older sister that Clara was reading a graphic novel of the assigned book. The sister looked at the teacher and exclaimed "You have been had! Clara can read a three-inch thick novel in a few days." For which Clara responded with a guilty look "Busted!". I wish I could have supported her more, taught her to be more independent, more capable but I have to work long hours at this job to support us. I worry about her future but have chosen to worry about the heres and nows rather than the ifs and whens. <3
DeleteI was thinking about how I would adapt the activity I listed for a visually impaired person. I think it would still work if the person had some vision because I use poster paper and a very large scale. For students with severely impaired vision I wonder if you could also use scented markers and candies with corresponding flavours. Or a small bag of mixed candies that have distinct shapes like rockets, jelly beans, smarties, gobstoppers, and jolly ranchers?
ReplyDeleteI was thinking you last suggestion is the best. Instead of different colours, different sizes.
DeleteThanks Danielle for a fantastic post! Great job attempting the burrito and the bagel. I like how you immediately recognize the same "do I actually have to do this" feeling our students sometimes show. And thanks to the group for a great discussion. I share very similar experiences working with students with IEPs in my classroom. On many occasions, I disagreed with the special ed teachers. I sympathize with colleagues in special ed for their overwhelming caseload, but like all of you said, our system, unfortunately, is just getting them through school without really learning. It's doing these students a disservice.
ReplyDeleteDanielle, I also really like your idea of adapting the activity using distinct sizes and shapes for visually impaired students!