Week 1: Mathematics and the body

The Recalibration of My Own Body

On Tuesday, January 11^th, 2022, I got off work, drove home, and immediately ate a Chinese deep-fried savory dumpling, left at my kitchen table by my aunt upstairs. An hour later, my stomach started to gurgle, and I knew what I ate was not sitting well in my stomach. Like I was possessed by the devil, my body reacted, vomiting, peeing, pooping, cold sweats and the feeling of a sharp pain on my left abdomen. Trying hard to go through the motions of intense suffering and pain, I kept thinking “Why me? What have I done wrong recently? I have been on good behavior for 2022.”  That night I ended up calling 911, but ambulance said the wait time is 2 hours, so I decided to take the taxi to Burnaby General Hospital instead. In emergency, I sat for 4 hours before I got to see the doctor. While I was crunching my body in fetal position, comforting the pain from my left abdomen, I noted how other people in emergency were organized, spacing themselves around the perimeter of the emergency room. I was amazed at how effective the use of chairs as a measure to keep social distancing during the pademic. Once I got to see the doctor, he noted my blood and urine tests earlier and said it was good and sent me to get my x-rays to check my left body for the sharp pain. Everything was okay so the emergency doctor prescribed morphine, which eased me to a deep slumber like a baby. After an hour, the emergency doctor woke me up, and gave me the diagnosis that it was food poisoning. He recommended that I should keep track of the sharp pain on my left abdomen with my family doctor. I got home by 2:30am, took 2 days off work, to rest and recalibrate my body. Looking at my own cycle of pattern with sleep, fluids drunk, washroom, amount eaten, and measure of left abdomen pain level, by day 2, all was restored back to normal. I was able to eat and drink normally, pass bowel movement, and best of all the pain on my left abdomen started to fade.  Ironically through the entire situation, I was able to us math to help me assess the situation, to make important decisions, and using it to help me understand my own body system.

Changing My Perspectives

The memories of my math experiences as a high school student are teacher lead lessons, students seated in ordered rows, listening, copying notes, and working on math exercises, practicing the math skills taught that day. I never questioned the process and scored well on tests based on rote memory. Indeed, the understanding aspect with math was not fully develop, until I reached university.

Flash forward 30 years later, students these days are not complacent at just accepting algorithms and rules to math and are more engaged in math if they understood what they are learning. From being a student in the UBC MAED courses, combined with teaching high school students through the pandemic, my perspective in how and why we teach math is changing. Antosen’s (TED talk, 2015) claimed that “the nature of understanding” is “the ability to change perspective”.  This perspective in understanding me as a math teacher, how my students operate, and what math is relevant and important, helps me plan how I should deliver and teach my lessons. To listen more and learn also from each student, catering to their learning needs, helping them enjoy the math, learning these transferrable skills that will help them make good choices in their future work, family, and personal life.

Seeing the Graph Vs Being the Graph (Gerofsky, 2011)

In Gerofsky’s paper, her study involved the analysis of how well math teachers (4 participants) and secondary students (22 participants) in Grade 8 and Grade 11 communicated mathematical graphs using gestures and non-math language. The secondary students ranged in math ability and were recommended by their math teachers for this study.  Note each student’s math ability was not disclosed to the researcher till after the data was collected, analyzed, and categorized. Participant’s sessions were videotaped the first week and were videotaped a second session the week after to posed questions and analyzed on the gestures used to describe the mathematical graphs.  Her findings categorized participants into three groups:

“Arm’s length visual model” (11 of 22 students):  Average hard-working rote memory students

-          Use small movements and gestures to draw or trace air graphs at the upper body level

-          Students who followed rules and algorithms and lack imagination

-          Kept math ideas at arm’s length for control and being correct

“Being the graph/being in the graph” (9 of 22 students; 4 of 4 teachers):  Top math students

-          Use whole body movement to represent graphs (Visceral approach)

-          Placed x-axis on their bodies

-          Students who can use their imagination to exhibit their understanding

-          Multiple metaphors and verbal/kinesthetic/visual representation

“Inaccurate, not aware of what counts as salient” (2 of 22 students): Risk of failing students

-          Had difficulty making the gestures for the graphs

-          Rushed through the task and omitted sections

-          Struggle with perceiving the graphs

Results from categorizing the students based on the Gerofsky student’s graph gestures study were then compared to the teacher’s assessment of the students in math ability it was 95% accurate (21/22 students were correctly categorized).

This study suggests an alternative perspective can be used to assess students with their math. In this case using gestures graphs as a possible method to catch at risk students who struggle with math early and get them the support and help needed.

The Activity

Currently, I have a grade 11 student name Ricky, who failed Workplace Math 10 last year due to his struggle with the pandemic and his own personal mental health with anxiety and depression. In grade 8 and 9, he was a Learning Support Student (LSP) who did not adapt well as he transition to regular classes in grade 10. As a new teacher at this school this year, I decided to dedicate Workplace Math 10 support online hours every Tuesdays and Thursdays from 4:30 to 5pm. Operating it like a virtual math homework club. Ricky was accountable online and as time progress he was even ready to come to school to do the written assessment in person at lunches.  In December, his mother got offered a new job, and his family was prepared to move from Vancouver to Surrey. He promised to commit and finish the Workplace Math so that he will receive the credits for this course.  His last assignment given tied nicely to the Susan’s math activity using the body to estimate measurements. I asked him to draw out the floor plan to his new home in Surrey and to use his feet to measure the dimensions of his place. Once his floor plan was submitted, I asked him to explain his work, and posed any math questions I had with his diagrams. The question he stumped on was the proportions of his drawings, if it made sense or not.  All in all, he loved the fact that this task made sense, it was tangible, game like and fun. He put in time to not only measure but the details in his legends share with me his excitement living in a new place. Although he struggled in Vancouver, I could hear his excitement in living a new life in Surrey. Going to start fresh in a new secondary school in Surrey for him is his recalibration in his life. I informed him that he has shown me enough to get the credit to pass the Workplace Math 10 course and the tone in his voice was happy and thankful.

If I had stayed in the traditional way of teaching, learning, and assessing perspectives of math, for sure the LSP student would have failed the course. But because I have extended my thoughts and ideas to better support, and understand and listen to each student’s needs and what really is important for their own personal growth and success, does it really matter if a student doesn’t understand an algorithm that has no meaning or relevance to them in their future? This week has recalibrated my mind, body, and soul literally.