Course Reflection by Fae Ung
Mathematics Identity One's own perceived ability to perform mathematics is the general idea of what mathematics identity is, and like most identities people have, mathematics identities develops early on. This development can be observed, with one common phenomenon almost defining a math student's identity being whether or not they are labeled as "'smart' or 'gifted' or 'slow' or 'proficient' or 'atrisk,'[these] students will come to see themselves in particular ways relative to other members of their mathematical communities. Instead of becoming more valued members of their classroom communities, they may come to see themselves as outsiders" (Aguirre et al., 2013). Thus, instead of dealing with absolute labels, or labels pertaining to skill level or ability, it is more effective to give each student the opportunity to have space in the classroom to learn and have that learning be highlighted instead of achievement. A simple example could be giving praise for a student's hard work rather than them getting the correct answer.
Culturally Relevant Pedagogy Learning is not a one-size-fits-all model, as each and every student that enters a classroom comes in with a unique perspective and are an amalgamation of rich, cultural experiences. To address this, instruction should take in consideration of students' cultural experiences, and ideally should be integrated into the curriculum. One phenomenal example was a teacher who took their students' claim that the school was punishing Mexican students more than the other races in the school's diverse student body (Aguirre et al., 2013). The teacher utilized this, rather unfortunate, situation and designed lessons that required students' knowledge about the school and culture to determine whether or not there is a racial disparity in the school's disciplinary system. The most important attribute of the teacher's lesson is the potential importance of these analyses that the students learn how to do and perform as the teacher would report the class's findings to the administration. Although this high stakes/importance is rare, the concept of an engaging, culturally relevant curriculum is not impossible to impose on students. This process may not be easy, however, as this requires deep knowledge about the school culture and the students as a whole. Though if the effort is made, mathematics will come to the students more effectively than if math were taught the traditional way through lectures.
Growth Mindset There seems to exist a dichotomy in the minds of students: the fixed mindset versus the growth mindset. The fixed mindset is the self-perceived inability to learn/improve at a task or subject. Whereas the growth
mindset is the exact opposite, where it's the selfperceived ability to learn/improve at a task or subject. With this phenomenon, there comes differences in student behavior with these two mindsets. "Students with a fixed mindset are more likely to give up easily, whereas students with a growth mindset keep going even when work is hard and are persistent" (Boaler, 2015). Thus, there is an importance to instill a growth mindset in students as we would want our students to go through the academic struggle to form synapses in the brain. Even making mistakes has the brain physically make connections through synapse creation.
Equitable Groupwork Groupwork has traditionally been a strategy that most teachers just tack onto an assignment for students to actually do the assignment, hoping that having an extra person responsible for their grade would be enough reason to bring forth their best work. Though that may be the case sometimes, the majority of the time results in work that both students aren't really engaged and would have preferred to do the work alone. Equitable groupwork introduces the idea of groupworthy tasks where the assignments actually require multiple students in a group for the assignment to be done effectively. These groupworthy tasks benefit students in a multitude of ways, such as bringing up students of low status/engagement in the class, providing students multiple entry points in the activity, and developing teamwork skills. In Teacher Press Video's Heterogenius Classroom, it provides an interesting view of a classroom that uses complex instruction and shows the teacher randomizing groups and having them present, which provides everyone a chance to provide their perspective in the assignment.
5 Practices Despite the name being 5 practices, the practices start at "Practice 0: Setting goals and selecting tasks", then "Practice 1: Anticipating student responses", "Practice 2: Monitoring student work", "Practice 3: Selecting student solutions", "Practice 4: Sequencing student solutions", "Practice 5: Connecting student solutions" (Smith & Sherin, 2019). These practices all help with engaging students with the lesson, and provide students the opportunity to share their perspective on the mathematical concepts. Anticipating student responses is perhaps the most important practice in the 5 Practices, as planning allows you to effectively identify what works to look for in the classroom from students. And requiring students to present their works to the class allows others to learn different perspectives on how to approach the work.
Social Justice Mathematics
In recent years, mathematics has been far removed from other subjects and even farther away from social justice. In Conway et al.'s book, Middle school mathematics lessons to explore, understand, and respond to social injustice, it provides lesson plans on food apartheid and injustice of the US government for not aiding its territories after disasters adequately, all the while being cognitively demanding and requires students to perform real mathematics. Especially in this societal climate where it seems like the majority of the population are unaware of the more unsavory aspects of society. Teachers have the responsibility to teach their students about the happenings of the world, and what they can do to change society for the better.
Equitable Assessment Assessment can come in all shapes and sizes, and as long as it properly assess the student's mastery of the targeted concept, the medium should not matter. Additionally, every student has their own unique set of abilities, and some may be more privvy to certain displays of mastery, and giving students that choice allows them to express their creativity while still showing mastery. This also solves equity issues where some students may not be at their best when doing tests. So an alternative assignment for a culmulative assessment like a project or presentation, or even a podcast could show mastery of the mathematics being learned in the class.
How do they all connect?
All instructional tools connect with each other in some way, and almost all of them have the potential to advance the other. Having a social justice math lesson is inherently culturally relevant as it most likely affects some student's experience in living in America. Equitable groupwork goes hand-in-hand with Equitable assessment and potentially the 5 Practices depending on the lesson goals. Mathematics identity and growth mindset can both be fostered simultaneously through classroom routines and culture. By using them all in tandem with each other, students will have an enriching learning experience of not just math, but also about themselves and how they should be interacting with society. Whether it be engaging in social movements or just learning how to effectively interact with their peers in groups or just casually.
Application In my teaching, I always try to make the classroom be more student centered, where the teacher plays a more passive role where I just sit back and have students work out the problems themselves. I enjoy having students explain their thinking in front of the class I get a little tired of talking after giving them some notes. This is a direct application of the 5 Practices, as I sort of select and sequence student work to present. I haven't gotten the change to implement social justice math lessons yet, but I do plan on using one or more of their lessons in my classroom. Especially with some of the school cultures I read and hear about from friends, I believe that it would be beneficial for students to understand what's going on with the world by engaging in real mathematics that deals with social issues.
Reflections One of the most important things that I actually learned from this class was the existence of social justice learning. For some time now, I've always wanted to integrate social justice lessons in my class, but I didn't know how to do that in a meaningful way. With the knowledge of Conway el al.'s Middle school mathematics lessons to explore, understand, and respond to social injustice, I have a foundation to build off of as these lessons make good templates for other social issues that I can easily adapt to something the students are facing in my class. The most noteworthy thing about this semester was the wonderful community that this class has built. I really do feel like I can talk about what ever comes to mind when I'm in the class and I can offer my assistance to those that need it as I'm more further along the track than others. More education classes should cultivate the inviting classroom culture we had in this class. It made we want to come to class despite how tired I was after practicum and the fact that it was from 4 to 6:45 pm. I used to think that other per-service math teachers weren't interested in doing things other than lecturing in their class. Now I think math teachers just are not aware of the new techniques and lessons that are out there now to use to make their class more engaging and have more purpose. In my past experience with math education, the majority of teachers and professors never really made the class engaging or meaningful to learn the math. From this, I thought I was the only preservice math teacher that wanted to make the class connect to something that's affecting the students today. Whether it be unreliable shelter or lack of resources, I wanted to connect math to solve or identify that there is indeed a problem in those areas of society. From this class, I've met and now know that there are others like me and from discussions and observations made by peers and classmates, teachers just need to be made aware of these lessons and how to facilitate them and teach their students the social issues and the math goal of the lesson. My favorite reading of the course was the AsianAmerican teacher that discussed their struggle with the stereotypes of being the model minority and at first going into a field that they did not want to go in, as I felt their situation could have been me if I did not advocate for myself to become a teacher. I just found relatability in their story of their math identity and how they became a math teacher. My first year of teaching is going to go extremely well as I feel like I've been well prepared to go into teaching from this class specifically with learning specific teaching techniques and lessons to run. Engaging and talking with students is going to be the most fun, and the most challenging would most definitely be planning for the whole year, but I will have my peers by my side so I'm not stressin' too much.
Self-Assessment Truthfully, I believe I deserve at least an Ain this class as I've participated in class discussion and really engaged with the class in a way that I find meaningful and helped move the class along. I also turned in some pretty solid works, with a few assignments I sorta kinda dropped the ball on (like this one) but I'm proud of what I've done so far and learned from my mistakes and really enjoyed myself in doing the assignments even if it's not my best best work. Additionally, I may have gotten off-task and out of hand in terms of my behavior through silly silly antics and giggles, but I feel like it was all in good fun and made the classroom environment more laid-back and casual rather than the traditional super-serious professional vibes that some may typically expect from a class full of future math teachers. With this, I believe I've fully met the course objects as I have proved that I understand individual differences and diverse cultures and communities to ensure equitable, inclusive, and justice-oriented learning environments, demonstrated application of the materials, resources, and planning for implementing a standards-based approach to the teaching and learning of middle school mathematics through the social justice lesson I've facilitated with a group, and it should be evident through previous works and my interactions with the class.
Thank you Dr. Kari Kokka for making EDMS 453 one of the best classes I've ever taken!
References Aguirre, J. M., Mayfield-Ingram, K., & Martin, D. B. (2013). The Impact of Identity in K–8 Mathematics Learning and Teaching: Rethinking Equity-Based Practices. The National Council of Teachers of Mathematics, Inc. Conway, B. M. I., Id-Deen, L., Raygoza, M. C., Ruiz, A., Staley, J. W., & Thanheiser, E. (2022). Middle school mathematics lessons to explore, understand, and respond to social injustice. Corwin Press. Boaler, J. (2015). Chapter 1: The Brain and Mathematics Learning. In Mathematical Mindsets : Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching (pp. 1– 9). essay, John Wiley & Sons, Incorporated. Smith, M. S., & Sherin, M. G. (2019). The Five Practices in Practice: Successfully Orchestrating Mathematics Discussions in Your Middle School Classroom. SAGE Publications. Teachers College Press. (2022). Heterogenius Classrooms. Retrieved May 8, 2023, from https://drive.google.com/file/d/1fQ83PBL0Rs9OhHcrxsOC4EJvtBR6 GbGd/view.