Week 2: Multisensory Mathematics

Multimodality and mathematical meaning-making: Blind students’ interactions with Symmetry (The Reading)

              In this article, Healy et al. (2013) investigates the relationship between the body and the brain using multimodal resources.  Interviews on Geometry (Symmetry and Reflection) were conducted on two blind male high school students separately, to analyze what means they use to conceptualize the geometric ideas mentally. Geometry questions were posed using geoboards with elastics.  The ideas and terms involved with geometric transformation were new concepts for both participants but both participants were familiar with basic shapes and relations. 

              Participant #1: Edson lost his sight on the left side at the age of four and his sight on the right side at the age of fifteen.  Edson used memories from his experience with shapes combined with current enhanced sense of touch, he was able to simulate the ideas.  He used the “action of folding” to understand the term “axis of symmetry”. With the concept of reflection, the interview guided questions and ideas involving mirrors.  This triggered Edson’s memory, simulating the ideas of mirroring with the shapes on the geoboard to imagine reflection in his mind.  He was able to use measures of equidistance with the senses on his hands, to mirror the image of the shape over the reflection line.

              Participant #2: Lucas lost his sight completely at the age of two due to congenital disease.  He used the symmetrical cardboard figures to define how the “axis has the property of changing a figure into two figures of equal dimensions.” With the symmetry task, he was able to use his sense of touch to feel the axis of symmetry to reflect the vertices of the triangle across the line.  When Lucas made a mistake with the reflection of a horizontal line segment, intervention from the interviewer to guide Lucas to recognize not only the image but the angles must be considered when reflecting across an axis of symmetry.  Through the mistakes and experiences with the geoboard activity and guidance from the questioning of the interviewer, Lucas was able to conceptualize the ideas of symmetry and reflection of geometric shapes.

                Healy et al. (2013) drew on the three phases of Piaget and Garcia’s epistemological categorization of geometry the intrafigural, interfigural and tansfigural to explain how the blind participants were able to embody the math through their experiences. Edson through memories of his past with his sense of touch verses Lucas through his prior learnt math knowledge and intervention with the interviewer to guide him to understand the concepts. 

              This article made me reflect on how it is important for us teacher to find strategies to build on students’ strengths. Instead of focusing on the disability, how can we teachers use what a student must make them responsible and accountable for their own abled learning?  The ideas of using multi-sensory math activities as an option to embody the math, gives students the opportunity to learn through the action of doing with their senses.

              My mother lost her sight in her sixties because of diabetes. Because of this disease, she can now only see shadows and is deemed partially blind.  She tries her best to be independent, using her memories and her other senses.  Instead of treating her as a person who is disabled, I realized I had to find mechanisms to help her still be independent, to reduce my worries when I go to work. Examples of modifications made around the house to help her independence: her using a walker around the house to help her mobility, a button machine that tells her the date and the time, and tons of GAIN pods for her to have the correct amount of detergent to do laundry. If I had caved in and did everything for my mom and treated her as someone disabled, then she would have lived her life as a dependent on me. But by finding multi-sensory methods to accommodate my mothers’ daily needs, like our students, then they will be able and capable of functioning on their own.  This paper made me realize the parallels between my mom and my students.

   

The Activities

a)       Hexaflexagon

While my Foundations and Pre-Calculus students were writing their Trigonometry test on Friday, I took that time to make the hexaflexagon. I have watched the video the night prior, and still have the “how to make a hexaflexagon” ideas presented by Jen W. and Jen B. from the Math Fair. I also made my community service student (grade 11) watch the Vi Hart video and ask her to make the hexaflexagon to compare who was able to construct the hexaflexagon best. She has never seen the videos, nor has she heard of hexaflexagon prior.  In the end, my community service student constructed the better hexaflexagon. Her clean, crisp, structure made it easier to fold and maneuver. I think because I thought I knew how to make it from watching people prior, I was missed the finer details that would have made the hexaflexagon better to flip.

Photos: Hexaflexagons made my Ms.A.Jung

Community service student's hexaflexagon

                                      

b)      Rockets Candies

Inspired by the Vi Hart’s Smarties video, students can use it to see how much volume the candies occupy within each roll. The students can also calculate the surface area of the roll of rockets, and to measure how much plastic wrap does it require for each roll?  Is there a way to wrap the candies with less plastic?

I thought about how the Rocket candies can be used in the Pythagorean Theorem unit as well.  I have made geometric shapes this year using straws and tape but now with the Rocket candies that may be more fun, and the students gets to keep it after as a treat.  Use the rockets to make an application 3D problems. What is the measure of the diagonal of this cube?  Prove it with calculations and measurements.

 

Tin Bot Projects

              My workplace math 10 has recently finished the Geometry Unit. Students developed skills with measuring, estimating, calculation perimeter, area, surface area, and volume of basic and composite shapes. For their summative assessment, I decided instead of a writing a test, to try an activity I found on the internet in having the students plan and create a robot, build their bots, calculate how much paper was used to make the bots, and calculate how much air was in the bots.  Based on their surface area calculations, they would request an amount of aluminum foil, which I would supply them with, and use it to wrap their bots. Students recognized instantly if they did not have enough foil paper to wrap their bots, then they must have had a miscalculation and will write on this in their reflection.  Students have a choice to work individually or in pairs but had clear directions that each person is responsible to build and calculate their component of the bot to be assessed. Students were engaged and communicated with their partners using their measurement and geometry diagrammatically and verbally to ensure the ideas of the bot were in sync. The multimodality of this project was evident where students reflected on how they used their tools to measure, hands to build, tackling problems that may arise as they progress in this project.

              When I read through the Workplace Math 10 students’ reflections on which form of assessment do, they like better for the geometry unit? The tin bot project or a standard written quest (bigger than a quiz smaller than a test)? Half the students enjoyed working on the project because it was more fun and creative, but the other half said that a written quest assessment is better because it was more direct and easier.  Conversations with each pair of students will be held next week as I give them their grade and feedback on their tin bots. I wonder if their perspectives would change from our conversation?

Final Thoughts:

              There is indeed a huge difference when math is shifted from 2D printed images to real 3D living things.  For students to be able to relate math in a tangible manner engages them with the activity.  Reflecting on my students’ responses how half the workplace students would rather do a 2D quests instead of making a 3D object, I believe is because they can replicate the answers by using an algorithm to get to an answer.  Verses when they had to move to problem solving and making a 3D tin bot, where they had to work with the objects they created, and really think for themselves because no one else in the class has the same bot body parts to compare answers with.  I found it interesting to read that some of my students were concerned with their creative portion of the bot project and how it may affect their overall marks.  But I think this may have come into play when they saw how creative some of their peers were with the project and was comparing.  Note that when assessments are project base, it does take more class time, than a simple written quest.  And keeping the students on task also can be difficult dependent on how the students’ mood is that day.  Is there a way to do math projects in a timely fashion?  Is there a better way to manage the range of student paces when working through a math activity?  Would blending the two ways, traditional with multisensory mathematics be the best method to enhance and engage student learning with math? I wonder………