Connections found between social justice and ethnomathematics in culturally responsive mathematics-to be marked

Culturally responsive education can be considered as five focal dimensions; Social Justice, Ethnomathematics, Indigenous education, Equity, and Linguistically Diverse Learners. Each one of the dimensions on its own is has unique place in a classroom, but they are very interconnected. The connections that I developed an understanding from on Monday’s class were the interrelatedness of social justice and ethnomathematics.

Using social justice in mathematics allows students to analyze, interpret, and acknowledge that there are injustices in the world. Some of these injustices directly impact your students, and others will have a limited idea or understanding what injustices are. Educating students on the injustices, and working together to arrive at possible solutions is how social justice is part of culturally responsive mathematics.

Social justice links to ethnomathematics by specifying your teaching towards a group of people, for example if you have a class of all Indigenous students, it would be best to design your lesson to the needs of your students, this can also be said for a group of students who are involved in farming with their families. This allows students to relate to mathematics in the themes and questions that relate to their lives, whether that is specifically dealing with personal struggles, ideals, and difficulties or dealing with injustices that are imposed on them by society.  Seeing the connections between social justice mathematics and ethnomathematics widens the understanding of what culturally responsive mathematics means.

In class we often discuss the overlap between the dimensions of culturally responsive mathematics,  but developing the understanding of each dimension will allow for a full understanding of the concept of culturally responsive mathematics. This can be the pedagogies with use, the lessons we teach, the examples that are used, the themes of our discussions, everything we do can be connected designed with ethnomathematics and social justice in mind.

How has looking at math differently helped me? -To be marked

In our Skype conversation this morning, Swapna stated that culturally responsive education is about “reclaiming the knowledge that has been suppressed, negated, and/or ignored”. Discuss this statement in relation to something you have learned/read so far in this class.

The first chapter of the textbook “Culturally Responsive Mathematics” gave me insight into so many different cultural and historical understanding of mathematics. On page 22, Swetz (2009) discussed different cultures explaining directions. North America Indigenous people use four dimensions of direction, North, South, West, East; these descriptions are recognized everywhere. China however has a fifth additional description which is here.

During grade 7 I hated, like to the point I would cry whenever translations were mentioned. I could never do them, they were always a mess, lucky they disappear in grade 10 and are never mentioned again. During internship I got the happy news that I would be teaching them to a group of students. Panic set in, anxiety attack happened, and I seriously thought about running out the door and never coming back. I then did the only sensible thing someone on internship could do, I started Googling tricks. After about three hours of stress, I had a unit planned out. The only thing I understood was that if I knew the starting coordinates, I should be able to mathematically solve me ending coordinates. This also meant that I should be able to visually know where my translation was going as long as I knew where it started. Not once when I was learning it did I understand to determine my starting point, I was always focused on my ending. In order to teach the math, I needed to relearn it in a way that I understood it. The knowledge was always there, but it was not given to me.

The class as a whole has given me a new meaning to what is “math”. Concepts from the textbook chapter readings, our class discussions, and additional readings have made me think about what math is, and what it can be. CRP is not about news math, but about redefining math in different contexts that relate to the students.

Swetz, F.J.,  (2009). In B. Greer et al., Culturally responsive mathematics education. (pp. 22) New York: Routledge.

The Culture of Mathematics- To be marked

How do we share with others (colleagues and students) that mathematics is actually not value- and culture-free? What are your thoughts on (and response to) this question?

When asked why I loved my in grade 12, I responded with “because no matter who you are, where you live, or the differences in your life, math is always the same, 1+1 will always equal 2”. Looking back I cannot believe how wrong I was, but I looking forward I can also not believe how much I have learned and how much learning I have left in my future.

Quinn gave us names and faces to the objections that come from colleagues and in some cases students. We will have people who say numbers are just numbers, that math has no culture, that nothing changes from country to country; all of these arguments can be heard across Canada and worldwide.

Part of advocating for social justice and ethnomathematics is understanding that there are people who will never agree with you. There are people who without hesitation will have the same teaching beliefs, and than there are people who can be convinced with evidence, readings, and logic. These people are the ones that you start with, these are the ones that you can influence to becoming culturally responsive in their pedagogy.

In order to convince people starting with the student who does not understand math, the student who will say “when am I going to use this”, “why does this matter”, “how is this going to help me in the real world”; using ethnomathematics and social justice gives meaning to the math.

Math is culture-free, this is will be true every time you ask the question, until you remove the box that surrounds the concept of math. Math shows progress, it shows growth, and it shows different concepts that are beneficial to students lives. Lindsay gave many examples to how many can be used for social justice, such as analyzing neighborhoods, using it to determine budgets, and understand injustices. Math can push the boundaries, but only if you are willing to think about the culture that guides, influences, and connects the math to life situations.

Math is a link between cultures, it is the link to inspiring those who is put down by societal norms and standards. Teachers who embrace the culture of math, are able to push learning in way beyond students meeting expectations.

Lesson Analysis Tool: Helping to create culturally responsive lessons-To be marked

I found that the lesson analysis tool to be quite insightful about what it means to have a culturally responsive lesson plan. There are aspect of a lesson plan I would not think to consider, simply because during my three years of creating lesson plans it was never suggested. The first one is asking the question “How does my lesson help students connect mathematics with relevant/authentic situations in their lives?” (Aguirre & Zavala, 2009). I may think about what outcome I am teaching, I usually do an activity showing real-life connection to introduce the topic to the class, but never think about how the topic connects to the students’ lives and communities. Even asking myself that question about some of the lessons that I have taught, I can see where I have gaps and what is needed for meeting the goal of having a culturally responsive classroom.

I think that before I start planning future units, I will first look at who my students are, then look at what resources/knowledge I have in my community. Finally, I will look at the outcomes/indicators of the unit to ensure I have met the requirements of the curriculum as well as the needs of my students.

One of the questions brought up in the class discussion today was how often the table and rubric would be used to evaluate lessons. I would love to say that I will use these strategies on all of my future lessons, but it took us almost an hour to get through one lesson, no teacher has time to spend an hour per lesson going over a rubric. I did like the suggestion as using the rubric to work on a Professional Growth Plan that includes culturally responsive pedagogy. This would allow cooperation with administration, colleagues, and in some cases students. While it may be difficult to use the rubric in full for every lesson I plan, I think it is fully possible to refer to the questions when planning lessons, every answering “Yes” or “No” for a sense of accomplishing the culturally responsive aspects of a lesson. Using the rubric and guiding questions will allow for teachers to become more fluent in creating culturally responsive lesson plans.

Aguirre, J. M., & Zavala, M. D. (2013). Making culturally responsive mathematics teaching explicit: a lesson analysis tool. Pedagogies: An International Journal, 8(2), 163-190. doi:10.1080/1554480x.2013.768518

Why do we teach Mathematics? -To be marked

The foreword of the book provides the readers with a focus of “analysis of the political dimension of the call for a cultural perspective on mathematics education” (D’Ambrosio, 2009, vii)). Right from the start, the writers indicate that a problem with mathematics education is to politics behind it. Curriculum is designed by a group of politicians and teachers, textbooks are supported by government, tests are designed by government, the way a classroom is operated has a lot to do with the expectations of the government. Capitalism is when a private group profits from a country’s trade and industry. I do not know what is more valuable than the development of a country’s youth. The companies who design the textbooks, the teaching materials and the resources available to the teachers are able to have a monopoly on students who have developed exactly as required for the businesses that need workers. There is a mindset that one must add one to one in order to get two, but no one thinks about what needs to be done in order to add one to one and get three. Math is viewed as essential, but people only need to be literate enough to make a society work (D’ Ambrosio, 2009, ix), how literate is “enough” has been determined by corporations who want workers not visionaries.  Mathematics is essential to society, however ensuring that students are getting teachings and knowledge that further their understanding and allow for creative thinking about the problems presented may result in essential members of society rather than followers of corporations. Teachers have two responsibilities, the first is teaching the mandated curriculum, and the second is providing students with a chance to become critical thinkers about the importance of the curriculum. This can only be done by educators who are willing to challenge what they believe as well as what the students believe.

 

D’Ambrosio, U., (2009). In B. Greer et al., Culturally responsive mathematics education. (pp.vii-xii) New York: Routledge.

My Starting Place

My journey in Mathematics started in Kindergarten, when I made a conscious decision to skip over all words that contained a R, because I couldn’t make the R sound. So when I counted I had 1,2,5,6,7,8,9,10…I couldn’t get past 14, but I would only say up to 12. Since I missed 3 and 4, teachers figured I could not understand how to count. Struggling in math continued until I was in Grade 11, when something clicked. I then found math so enjoyable that I decided to start with it as a minor in my secondary education degree. I eventually decided to switch into middle years education, but have always found math one of my favorite subjects to teach.

My friends always hated math, and they would tease me about why I like math so much, I always had what I thought was the perfect answer for this question. Math was always going to be the same, 1+1=2 no matter which country you were in, no matter what race, gender, abilities, or what is happening in your personal life.

The more classes I have taken in math, and the more I have taught math classes, the less I believe this. Math has so many different meanings, contexts, and interpretations. I am learning that math is more than a subject in school but also has valuable connections to worldwide paradigms and has the ability to bring cultures together. I am hoping that EMTH 425 enhances my understanding of the role that culture has on Mathematics, as well as the role that Mathematics has on culture.

PAA-Practical Applied Arts also known as Please Anticipate Accidents

With my first teaching contract, three of the classes I was assigned were Practical Applied Arts. The school I am at is great because it has a large woodworking shop, welding supplies, a full home ec room complete with three stations, and administration who was willing to help as needed. All of this is great…except I know nothing about PAA. I mean I took PAA in middle school, and I am very knowledgeable  about the school, but throughout the whole experience I felt completely out of my comfort zone.

My goal for the classes was that I would never have two classes based out of the same area, this would prevent any arguments about who is responsible for cleaning what, and anyone wrecking someone else’s work. In theory the plan is great…in reality this plan rarely worked. I started with having my PAA 30 class finishing the projects they started with their former teacher in the woodworking shop. PAA 9 was going to start with cooking, while the PAA 10 class did drafting. The biggest problem with this was that PAA 9 could not handle the responsibility of  cooking for more than 2 weeks, and the 10s did not take drafting seriously. Realizing a change of pace was needed I decided to go way out of my comfort zone…and guilt my dad, who is a welding instructor at Moose Jaw Sask Polytech, into teaching welding for a week, followed by three other experienced welders into coming in for two following consecutive weeks to help facilitate the actual welding. This means that I had to get all the supplies for welding, and contact people and actually have a general idea what was going on in the shop. Since I was offering this to one class, I figured that I would offer it to all classes. That was until the grade 10s complained so much two weeks in  that I cut their short, and decided to switch them to baking. I felt throughout the whole semester that I was changing the units every time the students started to get difficult. Part of this was to keep them entertained, part of it was to keep myself sane, and part of it was to keep the rest of the staff happy as I seemed to always be in the way.

During my time teaching PAA I took on the following projects,

PAA 30

  1. individual woodworking projects
  2. welding pencil holders
  3. Group woodworking creation
  4. Cooking
  5. building a shed

PAA 10

  1. drafting
  2. welding pencil holders
  3. baking
  4. CO2 cars
  5. cooking

PAA 9

  1. cooking
  2. welding pencil holders
  3. CO2 cars
  4. wildlife management

During the units, many things happened that I was not prepared for, like having 4 drafting sticks be broken by other students, which halted my drafting unit for a few classes while I found more. I was not prepared for regularly blowing the breakers during my welding unit, or to have a valve leakage which means by oxy-acetylene welding was going to be only stick and mig welding. Every class I got to face an unanticipated situation, some caused by students, some caused by equipment, and some caused from me still figuring things out. Teaching students to respond to accidents that happen while working with tools and dangerous equipment, was one of the lessons I value most, because while you hope that a student will never have to deal with a dangerous situation as a result of human error or faulty equipment.

With every class I learnt something new, with every class I wondered what I was doing, and at the end of every unit I figured out what I liked, what I hated, and how I would do it differently. Even though I started having no idea what I was doing, I actually enjoyed what I was doing. I would be quite happy teaching PAA again, and actually look forward to having the opportunity.

Classroom Management-The Dos, Don’t and Oops.

Classroom Management is a massive focus during university, but no matter how much emphasize professors put on classroom management they cannot predict how our classrooms will be, how the students will act, situations that will come up, school/division policies, or  how I will handle different things. No amount of university, internship or classes could have prepared me for the classes that I started with in February. The students are commonly referred to as damaged, which I get because for the past 5 years, every teacher they have had, had left mid way through the year. Every time a teacher leaves this means that new rules, expectations, instructional practices, and personalities change. It is not the students fault that the teachers left, in many cases it is not even the teachers fault that they left, uncontrollable event occur, decisions have to be made, unfortunately the students are the ones who are affected the most. With this being said the way that they treated me is not excusable. I have learned more about classroom management in the past 6 weeks, than I knew was possible to know, and I also (now) know that I have a WHOLE LOT MORE TO LEARN.

The Dos

  • expectations need to be outlined and agreed upon at the start of class
  • refer to these expectations as needed
  • communicate expectations to admin, they are your support if needed
  • review expectations with the class, make changes if its not working
  • stay calm
  • if you need to walk away from the situation to calm yourself down, than do that
  •  listen to the students side of the story, WITHOUT interrupting (I am still working on this)
  • explain to them why you are not pleased with their actions
  • pick your battles, not everything is worth fighting over
  • treat everyone fairly (I have a problem with only seeing part of the story, I am working on this)
  • respect goes two ways, you have to give it to receive it
  • a little bit of trust goes along way
  • ASK FOR HELP FROM PEOPLE WHO KNOW WHAT THEY ARE DOING, IT IS A SIGN OF STRENGTH NOT WEAKNESS (I am learning this, but it is a hard lesson)

Don’t

  • Yelling does nothing but cause everyone to be upset
  • ones actions cannot result in a punishment for everyone
  • make assumptions
  • place all the blame on the students (no matter how frustrated you are)
  • change your mind without a reason, explanation, or discussion
  • carry resolved situations into the future
  • hesitate to contact parents if the student is creating massive problems in the classroom
  • hesitate about removing a student if they are create an unsafe learning environment
  • place all the blame on yourself (you cannot control everything)

I am sure that there are 100s of more D0s and Don’ts that I could include, but right now these are my main learnings. After the past 5 weeks that I have had, I know a change is needed, my students know a change is needed, my colleagues and parents know that a change is needed. The idea of changing something that does not work is understandable, however, my students and I have a concern that the other side will not live up to their expectations. I can say that I will do my best, but they are skeptical, they do not know me, I have only been with them for a few weeks, none of which have been successful . I wouldn’t trust me either, how do they know that I am only agreeing to the ideas of our open discussion because the principal is there? They have no evidence of it. How do I know that they are not agreeing to terms because the principal is in the room. This agreement takes a lot of trust, on both parts. I have to earn their trust, they have to earn mine. Standing in front of the room does not earn me respect, having an education degree does not earn me respect, but listening to their complaints, hearing them out, and giving a little makes more of a difference than I realized.

Classroom management is a never ending experience, there is no right way, nothing will happen the way you expect, and changes are not instant. Stay positive, find a positive in every day, and see the situations from both sides. No matter how bad it seems, it will get better.

 

 

What does it mean to “level” math–and why was I not taught it in university?

With my new job I now teach grade 9/10. I took over grade 9 at the end of the polynomial unit, and start with the grade 10s Foundations and Pre-calculus class. In grade 9 and 10 I hated math, like cried everyday, would wake up with nightmare about math before tests, would be violently sick before finals. It was bad; however, in grade 11 math suddenly clicked. I understood it so well that I even took it as my minor my first two years of my degree before switching to Middle Years. Math was one of my favorite subjects to teach during my internship, because you can have fun with it, its easy to grade (the right answer is the right answer, regardless of how you do it), there is more than one way of thinking, and you can connect to all types of learners. Teaching this class was not even a concern for me, I am teaching at my old high school, and would have the support of a lot of fantastic teachers. Within three days of taking the job I realized how under prepared I was for math. We are told as graduates of the University of Regina, that an education degree allows you to teach any grade, and any subject. I quickly learned that this does not mean you are prepared by the university to teach any grade or any subject. I took two math curriculum classes during my education degree and four higher math courses, I don’t know how much more I could learn about math. I even sat in on some secondary math curriculum classes, and attended professional development based on secondary math. Yet, I cannot seem to follow any thing that the former teacher did with her students, which are now mine, and I have no idea what I am missing. Even when I ask how she did her math and grading, it still makes no sense. She uses a system where the students do as much as they can, and that determines their grade, but if they only want to do the harder questions, they will get a higher grade because the level of thinking is higher. How does she determine what the levels are, I looked at her notes, and I looked at my math notes, and at a dozen different sites, but I have no idea where she sees the levels. If this is the new way of teaching, why was it not taught in University. It makes sense that higher level of thinking allows for higher marks, but how do you know something is higher, just by how long it takes to solve, how many steps are involved. I’m trying to use the strategies that I learned for teaching math in university, but I quickly realized that those strategies do not work with a group of students who do not want to learn, and who believe math has no use in their lives (regardless of how many real-life problems I give them). What am I missing? What do I need to change? And can someone please explain to be what leveling questions means, and how do it? I love math, and I want my students to love math, but I feel like I’m failing them.

White Like Me

“White Like Me: Reflections on Race from a Privileged Son, The Remix: Revised and Updated Edition” by Tim Wise provided me with a lot of questions. When I first started this book it was during my summer before my third year of university started at the University of Regina in the Faculty of Education, but I did not finish the book until the first few weeks into my internship, starting my fourth year.

I am not a slow reader, but I could not finish this book in one go, like I do with most books. This one had me starting, and after a few chapters needing a change, needing to reflect. This process continued until I finished the book, more than a year later.

I have no idea what made me pick up this book in Chapters, and decide to buy it, maybe it was the conversation with friends earlier that day about White Privilege. Or maybe it was because I was in a faculty that focuses on diversity and eliminating the society norms, yet being from a small town in Saskatchewan I had until that moment put little thought into my own thoughts on white privileged and racism.

This book gives evidence that racism is taught not generic but that it is not always taught intentionally. Simple things like crossing the street when someone of a different race is walking towards you, or clutching your purse tighter, or turning away when someone of a different skin color looks at you. We are not born to notice skin color but we watch how other people behave, we learn from watching, we learn from overhearing, and we learn without ever realizing what we are learning. University was my first real experience getting to know people that had a non-white ethnic background. It was also the first time I ever seen racism happen to someone I knew. I grew up hearing thoughtless comments about Indigenous people, or Africans, or Asians, this list can continue hitting almost any person who is considered a minority in Canada, but I never realized the impact that they had on a person. The more I branched out my group of friends, the more I seen out racist Canadians can be, and the more I seen how I have an unspoken amount of white privilege. “White Like Me”, gave me a chance to think about the experiences that I have faced, and take notice in other issues around me, without even realizing it I had (and in some cases still struggle with) my own racial stereotypes and racist thoughts.

The more I read the book, the angrier and more frustrated I became, because there seems to be such little progress happening in the world, it may be directed towards a different group of people but their is still bigotry, and hatred directed at people who are different than the majority, as if it is acceptable to judge people because their voices are quieter or  lesser in quantity than the majority populations.

Changing the way people think, especially when they are unaware of their own inner thoughts, opinions and struggles, is challenging. It starts  with their education, it starts with the lessons they receive both in and out of the classroom. Having students identify their own values, and prejudices is hard at a university level, it is way harder with middle years students, because not only do you have to take into account the students beliefs but also the parents, grandparents, and all of the people who influence the students. Open discussions, honesty, and personal thoughts play a part in the lessons, but keeping your own emotions in check because the students are still learning and may have conflicting feelings, even more so if no one, or very few people in their communities are of a minority.

Besides using this book to talk about racism in society, it can be linked to the colonialist history of North America, using stereotypes and assimilation to make connections with Treaty education, and struggles that are found in Canada. This book may not be based in Canada, but similar beliefs are found between the United States and Canada, meaning that material in this book still carries wait when used in the right context.

Reading this book gave me a starting place for Social Justice, but it also made me more passionate about teaching students about social justice and they role in society. Teaching students that their voices matter, that they can make a difference is a starting point for students. One of the reasons I got into Middle Years Education is because someone once told me, “if you get middle years students passionate about something they will plan to change the world, and if you encourage and support them, one day they might”, early primary grades are sometimes to young to understand bias and unjust situations, while secondary students have seen too much failure to believe the world can be changed, this only gets stronger with age.

At some point I will likely re-read this  book, because I am still learning, I am still gathering more questions, and I am still wanting answers, ideas, and solutions to work with problems that occur in classrooms, communities, and in society. How can I preach the idea of a diverse society? I am not sure if I have a full understanding of white privilege, racism, and internalized biases. I am not sure if I will ever fully understand, but I am willing to keep learning, to keep researching, and to do my best to be aware of my own biases, the more I understand the more I can work on teaching students to question society norms, and to think about their biases and actions.