Inquiry and Dividing by Zero

I had a wonderfully insightful conversation with Susan today regarding my inquiry topic. I was able to share how I sort of changed my topic after doing some research because I don't think students should be disengaged. Among the many insightful things Susan offered, the idea of different kinds of flow was especially intriguing. We discussed how there are times when we can be busy with our hands and find it easier to pay attention and learn something. Susan brought up how Jasmine is able to crochet seamlessly in class while being fully engaged in classroom discussions. This realization was eye-opening. I and I am sure many others have mastered the art of giving someone your full attention and not listening to a single word they say. How to make teachers think that you are listening and paying attention. Susan discussed flow in terms of driving and this is true too! At some point you just get into the flow of three pedals and the shifter and you're no longer thinking about the road in front of you.

Everyone is able to tap into this, everyone can free up other parts of their brain while they engage in some activity that doesn't require thinking - it's almost muscle memory. How can we incorporate this into our classrooms? I was telling Susan it doesn't take long to learn how to crochet; you can get the gist of simple patterns in a few days. If we put in an initial investment for a week in our classrooms, I think it would be of immense help to have students crochet while I have to teach arbitrary concepts. It doesn't have to be crocheting, students preferences can definitely be catered to. Sometimes our fidgetiness contributes to our inability to pay attention. Mitigating this by something like crocheting can be especially helpful during technical, "boring" math classes. We also discussed how it was important to ensure there was some purpose to the physical activity. Just using a fidget spinner can draw all of the students attention because then it becomes a game. Crocheting however fulfills some purpose and tangible result of the student's effort. 

This completely reframes the idea that "Flow" has to be challenging - you can be in this state of flow while doing something that it completely routine and mundane for lack of better words. 

I still don't think I have a good way to explain dividing and multiplying by zero. Showing the asymptotic graph of 1/x certainly visualizes it but for me personally I need to understand it in my head before confirming it through visuals - not the other way around. I only know the rules when it comes to multiplication and division of numbers less than or equal to zero. I think I'm having difficulty because zero is both a number and something that doesn't exist which is a little contradictory. I'm going to have to ask my colleagues again because I think they explained it in a good way but now I can't recall what they said.

Annotated Bibliography Template

                                                                          When I began researching my topic of student (dis)engagement I was noticing a trend in the short abstracts I was reading. There is a common, important connection between student engagement and student success. This led me to revise my inquiry question into ensuring our classrooms are fully engaged. The stance I took prior was about when to allow students to be disengaged and if it could be beneficial. With the concrete evidence that student engagement has many positive effects on students I think it is imperative that we all strive for student engagement as educators. 

Student engagement is an especially passionate topic for me. I think it encapsulates so much of what goes on in a classroom. It captures the teacher-student relationship, the student-curriculum relationship, the student-classroom relationship and the student-student relationship. When I'm observing a classroom, I find that my attention always drifts to those not engaged and I spend considerable amounts of time trying to figure out why this student, in this class, in this classroom, with this teacher is not currently engaged. 

Annotated Bibliography

Skilling, Karen, et al. “What secondary teachers think and do about student engagement in 

    Mathematics.” Mathematics Education Research Journal, vol. 28, no. 4, 5 Nov. 2016, pp. 545–

    566, https://doi.org/10.1007/s13394-016-0179-x. 

    This article offers insight onto teacher’s perceptions regarding student disengagement. If we as teachers     cannot accurately pinpoint where or why our students are disengaged, we won’t be able to help them be     engaged in our classrooms. 

Brantlinger, Andrew. “Critical mathematics discourse in a high school classroom: Examining patterns of 

    student engagement and resistance.” Educational Studies in Mathematics, vol. 85, no. 2, 18 Aug. 

    2013, pp. 201–220, https://doi.org/10.1007/s10649-013-9506-2. 

    

    Often there are reasons outside the classroom contributing to why students are not engaged inside the        classroom. This article offers an alternative method of teaching mathematics that can potentially reach       students who are the least engaged. 

Nielsen, L., Skovsmose, O. “Critical Mathematics Education.” International Handbook of Mathematics

    Education, vol. 4, 1996, pp. 1257-1288, https://doi.org/10.1007/978-94-009-1465-0.

    Based on the last article I needed to find more information on the origins of Critical Mathematics               Education. Chapter 35 in this book offers an overview of Critical Mathematics education as well as a        detailed analysis of the concept.

Uekawa, Kazuaki, et al. “Student Engagement in U.S. Urban High School Mathematics and Science Class- 

    rooms: Findings on Social Organization, Race, and Ethnicity.” The Urban Review, vol. 39, no. 1, 

    March 2007, pp. 1-43, https://doi.org/10.1007/s11256-006-0039-1.

    This formalized study gives factual evidence based on statistical research on student perceptions of            classroom activities. The authors describe how various factors affect student engagement and how            different students respond to different kinds of activities. 

Shernoff, David, et al. “Student Engagement in High School Classrooms from the Perspective of Flow 

    Theory.” School Psychology Quarterly, vol. 18, no. 2, 2003, pp. 158-176.

    Mihaly Csikszentmihalyi, who is also an author on this paper conceptualized an important phenomenon     by the name of “flow theory”. “Flow” is an important factor in the journey of student engagement and        this paper presents research-based evidence on what helps students get into “flow”.

Kohn, Alfie. “Is It Enough for Learners to Be “Engaged?” https://www.alfiekohn.org/blogs/engagement/. 

    Accessed 16 Nov. 2024

    Kohn challenges our understanding of engagement in this insightful article he wrote and posted on his        website. He highlights the important role of student motivation and objectives and compares it to the        shallow idea of mental focus. 

Walther, Erika. “A Fresh Approach to Supporting Students Who Are Disengaged and Task-Avoidant.”        

    Truth For Teachers, 16 Feb. 2023, truthforteachers.com/supporting-disengaged-task-avoidant-

    students/. 

    This concise and easy-to-read guide on how to help students that are disengaged provides both reasons     for disengagement as well as how to approach them as teachers. 

Lei, Hao, et al. “Relationships Between Student Engagement and Academic Achievement: A Meta-

    Analysis.” Social Behavior and Personality, vol. 46, no. 3, 2018, pp. 517-528

    This article analyzes aggregate research on the correlation between student engagement and academic        success. Since there are arguments on both the positive and negative, this extensive study is important        in showing how there is a positive correlation between the two. 

Gunjuc, Selim. “The Relationships Between Student Engagement and Their Academic Achievement.” 

    International Journal on New Trends in Education and Their Implications, vol. 5, no. 4, 2014, pp. 

    199-214.

    This article studied 304 students to test the correlation between student engagement and student                achievement. Importantly, it examined the factors of cognitive engagement, behavioural engagement        and sense of belonging. 

    

Inquiry Discussion Exit Slip

When we were in the garden and we chose - I have to interject with a sudden thought. That time in the garden when we first said our inquiry topic I realized Susan also had us standing in an oval (a round not circle shape). Why is she doing that for this specific topic? She made us stand in an oval when we first said our topics out loud and then again yesterday we were standing in the same orientation. I wonder why, something to ponder on I guess because if I've noticed anything in Susan's class there seems to be a reason behind everything - it's intentional. 

As I was saying, when we were in the garden and we said aloud our inquiry project I had to make mine up on the spot because I wasn't aware we had such a project in the first place (this seems to be a common theme for me in school). I blurted out student engagement in a haste but also because it is something that really interests me. The first thing I thought about when I imagined a classroom is reaching students that are disengaged. 

During my practicum, I wasn't thinking about my inquiry project when I talked to both of my SA's about student engagement. I'm going to take this as a good thing, because it means I'm genuinely interested in it (like Leon and cheating). 

I think that's it for my exit slip but I do want to discuss one more thing. 

a picture of us following Tak and Kody's talk

I have had the best time engaging with my cohort and listening to their thoughts, ideas and feelings. Going around the circle and listening to everyone's inquiry project was astounding; literally every topic had depth, significance and relevance. It was honestly a joy to hear so many different, wonderful ideas. This brings me to the point of how much I really value listening to my colleagues. I don't think I've ever been in this kind of situation where I spend so much time with a variety of individuals where every single person has something insightful to offer. In the picture we're missing a few including Andy, Mark, Taha and Teij. I could go on but I'll end it there. 

Marking, Grading and Ranking

There are not enough hours in the day or days in the semester to comprehensively and concisely answer the plethora of questions regarding grades in school. 

Assessments, grading and student learning were prominent themes in the many conversations I had with my school advisors over my two week practicum and I sit here still with many more questions than answers. 

It is not unknown that marks, grading and ranking create stressful environments for students and teachers alike. The easy answer would be to say, "get rid of those things!" However, we cannot. If you ponder on it within the schooling system (up to and including high school) from the top down where the top is university admissions, it is certainly impossible to get rid of grading. Even if we hypothetically remove that overbearing aspect of schooling, we need to be able to assess students to measure their learning. In the purest sense, this is what grading should be - an assessment of student learning. 

In my own experience, grades for the most part didn't mean much to me. I did really poorly in university during the first couple years of my undergrad. If I wasn't failing, then I was getting somewhere in the 50s and maybe 60s. I recall in the first semester of my second year I received a test back in my probability class. If I remember correctly I had gotten a 90 (I believe it was a 36 or 37 out of 40). I remember getting it, looking at the mark and then putting it in my bag as I did with all my tests. I had a profound moment after I put it in my bag - I realized I was doomed. I felt the same about that 90 as I did my other tests that I failed. The grade was supposed to be a reflection of my learning or my performance but whichever it was, I realized I didn't care. And if I didn't care, then why was I there? I started improving my grades in the latter half of my third year and all through fourth year when I found out there was a minimum GPA required in my program. Extrinsic motivation right? I do remember something from that year and a half though. I struggled mightily in a certain professors statistics class - in one of them according to my math I should have failed but he gave me a 51 which I was not happy about. In fourth year I had him again for a time series analysis class. I was determined to do well. I remember studying extremely hard and I actually got an A on the first test. I remember feeling so happy with myself. There was something there, it was that hard work and reward relationship. I think that's something that all humans can attest to and find common ground in. It can be about anything, not just grades. 

John Sarte and Sherri Hughes are touching on this but there still lies this underlying question of how can we get students interested in the content to motivate them to get to that place of working hard. If it's not that, then what motivation can exist to push them there? 

I'm sure I'll be asking this question my entire career God willing I become a teacher one day.  

Poetry

 It feels like these grapes are breathing life into me every Thursday...

Poetry is not something foreign to me however I haven't been able to write a poem in many, many years. Not to say I haven't tried. When I used to write poems, they would come to me naturally however at some point that stopped. I think perhaps it's because I switched from writing poems to "just" writing. I guess for me as long as I have the ability to let my thoughts flow through words, I'm happy. I'm also happy that I was actually able to write something resembling a poem for this class (maybe it's because I sat with purpose to write a poem). I've shared it below.

"Oh grapes, bunches of grapes
As I walked to your dwelling
I did not know what to expect
I felt that you would not be there, to make me smile

My fingers are a little numb
And I have seen many leaves succumb to the cold
Oh grapes, as I walked to your dwelling
I felt that you would not be there, to make me smile

Your leaves have lost their green
To a pale yellow
Some have wilted
And some have fallen

But as I sit in your dwelling, I am so happy to see
That you have not changed much
You are still round, and green, and small
And now I know you are also strong

Some of you have changed, but in a good way
Because you have gotten a little dry
And surprised me the same way you did
The first time I saw you

So as I walked to your dwelling
And as I sat in your dwelling
And as I walk back from your dwelling
You have made me smile

Because you are grapes
Sweet, sometimes bitter
But always tasty, and I forgot
That you are also raisins"

Braiding Sweetgrass

 I'm writing this entrance slip quite late and I have accumulated some knowledge during my two week practicum that changes how I would've have written this one month ago. Thinking on it now, there's a trend in mathematics that you define what you need and within the confines of which you need it. For example, a quadrilateral is defined as a four-sided polygon. We take it further by confining it within the boundaries with which we will see, study and use them; usually at least one set of parallel lines and all angles being less than 180 degrees. This type of approach although useful to serve a specific purpose could be considered a disservice to the imagination of people and to the things themselves. 

In Dr. Robin Wall Kimmerer's "Braiding Sweetgrass" she talks about a bay - or more accurately, to be a bay. In English we've used the word "bay". In Ojibwe, the word used to describe the same thing is "wiikwegamaa" which translates to, "to be a bay". Her explanation on a bay being alive and that it is not dead and thus cannot be referred to as a noun but instead a living, moving being as a verb is something that truly captivated me. If you go to a bay you can see the current from the sea/ocean. You can see the tide rhythmically bouncing off the shore. It is being. 

I think the grammar of animacy itself as Dr. Kimmerer calls it is something important that can be shared and discussed in every classroom - especially with younger students. Adding this layer of recognizing plants and animals for something outside what we as humans interpret them as will allow one to show a more wholesome level of respect to their surroundings.