When it comes to math education there is no shortage of opinions on what approach to teaching we as teachers should take and what material should be taught. Perhaps that is what makes the question, ‘how best to teach mathematics’ truly wicked - it can never be FULLY answered because there are too many variables (while my mathematical mind wants an answer, even I understand that in math there are unanswerable questions). In my CEP 812 class we were asked to come up with a wicked question and make a survey to help guide us towards potential solutions. And while I LOVE asking my students truly interesting questions about math, it was difficult to think of questions to ask a wide range of people about how they best understand math. After doing a question quickfire, a first, second, and third draft of a survey I landed on the wicked question, by allowing students to guide the learning process can you make learning math feel more authentic? In my first draft I quickly noticed that I wanted to have teacher and student input, which would mean that I needed a survey with branching paths. After doing some research on survey design I wanted to have as many multiple choice questions as possible, and put any open-ended questions towards the end. This hopefully would encourage people to at least answer the multiple choice questions and not get 'survey exhaustion' from answering too many open-ended questions. And finally, after my professor and classmates gave me some invaluable feedback I was able to revise my questions to be even more precise to get back information that could help me answer this impossible question. Feel free to take my survey here and if you have any additional feedback don’t hesitate to comment below! Resources:
Math Lady/Confused Lady [Image]. (2016). Retrieved from https://knowyourmeme.com/memes/math-lady-confused-lady .
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During my K through 12 education the reason I loved school so much was because of all the different stories I learned. Each class I went to, each teacher I had, each subject we were learning, I always felt like I was learning a new story. Maybe it was a story about math, maybe it was a story about my teacher, or maybe it was a story about some old Greek mathematician - but I was always ready to learn these stories. This is exactly what led me to becoming a teacher - the overwhelming amount of stories that exist in our world, we can never know, but I felt teaching was a way I could connect with a lot of them.
During my undergrad one of my professors rightly stated that if you don’t like children, this is not the job for you. Learning from my students and helping them to learn as well is what brings me so much passion for this job. Understanding that they all come from unique and different backgrounds is a challenge but makes education so much more worthwhile. Another major aspect of my job that I love is collaborating with other teachers. I am so fortunate that I married one who is just as passionate about learning from students as I am. This week in our graduate course we learned a lot about Universal Design for Learning (UDL) and Intersectionality and we (my husband who is also in the course and myself) couldn’t help but share our thoughts through one of our favorite mediums - podcasting. Listen to our thoughts, ramblings, and wishes for the future in our podcast below.
Resources:
McGregor, D & McGregor, M (Hosts). (2021, November 25). Universal Design for Learning & Intersectionality [Audio Podcast episode]. In Two Teachers Talkin' https://www.buzzsprout.com/1893797/episodes/9613782 After mulling over my questions from my quickfire task last week (as well as adding a few more questions to the stack) I was challenged to sort my questions in different ways and make a sketchnote style video documenting my process. To say that I was excited to create a sketchnote style video is an UNDERSTATEMENT. Sketchnoting is simply combining visuals or pictures to note-taking tasks. It took a lot of planning to set up my mini studio (and even then my camera wasn’t as high up as I would have liked), planning out what I would draw and how I would sort my questions, and finally editing the video footage and audio together I knew would be a challenge but my end result below is pretty good first attempt at sketchnoting! I love watching these types of videos, I am a very visual learner, and I feel in a math classroom visual cues go a long way for students too. This is one of the main reasons I decided to move to an Interactive Student Notebook style of taking notes in class. Because it is interactive, creative, and visual for students I feel they tend to use their notes more effectively because they don’t always think of just looking at examples in a textbook. A math blog I follow, mathgiraffe.com has ‘doodle’ notes and I have been super intrigued to try them in class as well because I do feel that math is so creative and students don’t always see this. Adding this style of videos to the videos I currently make for my students would certainly break up the monotony for them and perhaps get them more interested in what we are learning. Resources:
Misura, M. (2021, November 19). Sketchnote Questions [Video]. It is impossible to avoid the current state of things and a big part of this moment is how much of a bubble we are all living in. Not only are we living through a pandemic (so stay in your bubble so as to not spread disease) but the world we can interact with online is and has been created to be our own perfect bubble as well. After watching the TedTalk video below, the realization that even my google searches had been tailored to me set in and nowhere on the internet felt safe. I am not of the TikTok age, but I hear the algorithm is spooky, a few cooking videos and they have you dialed in. I am more of the Facebook age, which has been of late, potentially more damaging than ever. Media is shared and re-shared without knowing the origin or intent, posts and claims are made wildly after simply reading a headline, and if you don’t have the same opinion as someone you are immediately wrong and defriended or reported. I know this is happening all around me and knowing is only half the battle, then we need to act and be critical about everything that comes across our feed. It’s not all negative though, I have found so many wonderful ‘affinity spaces’, as Gee calls them, or learning communities, where I can find other teachers to help me grow by challenging my thinking or giving me new ideas (2004). One in particular that I followed on Instagram was @iteachalgebra and while I take a lot of inspiration from her interactive notebooks, she gives exclusively digital homework and tests, which I just don’t know if I’m there yet or if it aligns with how I feel about math education. Resources:
TED. (2011, February). Beware online "filter bubbles" | Eli Pariser. [Video]. Youtube. https://www.ted.com/talks/eli_pariser_beware_online_filter_bubbles/transcript Gee, J. P. (2004). Situated language and learning: A critique of traditional schooling. Proquest. https://ebookcentral-proquest-com.proxy2.cl.msu.edu/lib/michstate-ebooks/reader.action?docID=200413&query= For a while now I have been really interested in learning how to edit videos and make them more interesting looking. When I make videos for my students I typically use screencastify and do one take and call it good, but I’ve always wanted to make them a bit more interesting. In addition to that I am always trying to add more connections to my activities that my students will be engaged with. An example of this is a google form escape room style review activity for solving simple linear equations that I made and you can use here! This week I decided to dive head first into learning how to use Camtasia when we were tasked to make a remix video over fair use and copyright laws. After reading through portions of Renee Hobbs book, Copyright Clarity: How Fair Use Supports Digital Learning (2010), I summarized my thoughts on fair use in my remixed video below, while incorporating fair use at the same time! I have to admit when it comes to copyright, fair use, transformation, etc. I tend to struggle with all the bits and pieces and I think that is because in some ways it is a bit vague. I also do not interact or deal with copyright issues so much in a math classroom. However, if I plan to produce more content to share with my students or colleagues it is extremely important that I am following fair use guidelines and copyright laws. (Perhaps I'll pay for Camtasia too, that watermark!) Resources:
Hobbs, R. (2010). Copyright Clarity : How Fair Use Supports Digital Learning. Corwin. Misura, M. (2020). Solving Equations Escape Room - Among Us! [Form]. Misura, M. (2021, November 13). Fair Use [Video]. This week in my graduate course CEP 812, we were asked to engage in another quickfire! In a previous quickfire we were asked to ‘cook’ with 3 mystery utensils and relate that to how technology can be not suited for a particular task. This time around after reading the first few chapters of the book, A More Beautiful Question by Warren Berger, we were asked to set a timer and write questions related to our professional role for 5 minutes. After reading, thinking about teaching through a pandemic, and considering how students are still wrestling with ‘getting back to normal’ I had a lot of questions. However - the moment the timer started I felt like they all slipped away from me! Truly reflecting on this experience it makes me think even more of my students who fear math and when that timer to math class starts, or worse yet a math assessment makes its way to their desk I’m sure they freeze right up and all thoughts leave their brain. After graduating high school and interacting with other soon-to-be math teachers, I realized I learned math a bit differently than most of my peers. My school had adopted an ‘integrated’ approach so all math skills were mixed together and then broken up over four courses. During class, we were presented with a problem to solve and then if we needed skills to help us our teacher would lead us to those skills. Every piece of math homework I had was 3-5 story problems. I had never seen a worksheet with 10, 20, 30 math problems on it. We always worked in groups to discuss the problem and come up with solutions, to me this was the natural way to begin teaching math. When I was hired and given our school's textbook I felt really lost as it was not like anything I had experienced before. I tried it out for two years but it just didn’t fit and that’s when it sparked one of my first big questions - Why do I even need this textbook? Am I not the expert here to help guide and assist my students? Another big question that has been on my mind for awhile was the first one I penned to the paper during my quickfire - ‘Why do we have to teach so much?’ I want my students to have a deep understanding of what I am teaching them and it is an impossible task to get through the entire curriculum and have all students feel successful. I had two other really big take-aways while reading and thinking about the first few chapters of Berger’s (2014) book, “would students who are battling against stereotypes be less inclined to interrupt lesson by asking questions, revealing to the rest of the class that they don’t know something?” (pg. 58) He answers that yes, they would likely stay quiet as it is safer. I have seen this a lot with my students, and as a woman in the STEM field I have felt this stereotype but my reaction was quite the opposite, I was so ready to prove everyone that the stereotype is wrong! Why are our reactions to adversity so different? Why will some kids hide and others fight their way out of the stereotype? The other takeaway was how I can incorporate the RQI model into my classroom. The RQI or Right Question Institute came up with a questioning technique designed to help students and adults formulate questions (Berger pg. 65). I wonder if I could use the steps they use in a math classroom and what that would look like? Would I put a function in front of my students and have them ask only questions for five minutes (like our quickfire!), improve their questions, prioritize them, reflect and then move forward to act on their questions? It feels like this would work, but some students, like myself at times, struggle to know how to write a question or even what to ask. This is why questioning needs to be taught and encouraged! If I don’t try it out I’ll never know, and really what is the worst that could happen? Resources:
Berger, W. (2014). A More Beautiful Question. Bloomsbury. Misura, M. (2021, November 10). Question Quickfire [Image].
One of the most important concepts I promote in my classroom is that mistakes are good. Mistakes in math are powerful learning tools and during the first few days of school I show my students the following video made and promoted by Youcubed.com, a website started by teaching math innovator Jo Boaler. In addition, after reading her book, Limitless Mind, I knew how important it was for my students to struggle, make mistakes, and have the right mindset (a growth mindset) when it comes to learning math (Boaler, 2019).
I remember my own journey learning math and how important and big it felt when I found my mistake and learned why it was wrong and what was actually correct. I also remember early into my teaching career I really wanted to make a big change in how I was presenting material to my students. I would give them notes and follow a pretty standard ‘I try, we try, you try” model, but recently I had heard about interactive student notebooks (ISN) and was really intrigued by it.
Using a notebook a new topic is introduced by the teacher through creative note taking methods on one side of the page and then students create and practice the skill on the other side of the page. These notes are meant to be fast so that more time can be spent practicing, creating, and discovering a topic. I took a big risk and ditched the school provided textbook and decided my students and I were going to create our own math textbook by way of the ISN. There were absolutely failures along the way, but what I was making was so rewarding. This was seven years ago and after years of iteration to fine tune the product I still add, adjust, and recreate some parts of it each year. Even that said I know I will never be done thinking of new ways to create and make my students' learning journey better. One of the biggest things I have been thinking about this year is having the note taking portion come after a discovery activity or some sort of problem based solving. I have been doing this more in my Algebra 2 course and I need to start bringing it more into my Algebra 1 section. The challenge always being the making part - how do I make an activity to guide my students through the topic we are meant to be learning.
Experts tell us that collaborative learning and taking into account student context is essential for deep understanding (Bransford et al. 2000). Through the creation of our ISN’s each year my hope is that students will have more time doing problem based discovery or hands-on activities because note-taking is not the focus and when it must be done it should be done quickly.
Two theories of education that play off of each other, constructivism and constructionism, seem to fit in well within my classroom setting also. While constructivism encourages students to take ideas and come to their own conclusions, it is better to take it a step further and that is where constructionism takes over. Constructionism has students rather than thinking about ideas, begin creating something, making something to show their ideas about what they are learning (Ackermann, 2011). Dive right into the deep end because that is where the good type of struggle and failure really occurs. In my infographic below I think about my own journey in my classroom with making, innovating, failing, and how I can still improve.
It is a task that I put to myself each year to come up with more discovery and problem based activities, but even more so now I think I want to have my students come up with more creative outputs. Adding more labs and real life context into my classroom where students can produce and create their own meaning is so powerful.
Resources:
Boaler, J. (2019). Limitless Mind. HarperOne. Bransford, J.D., Brown, A.L., & Cocking, R.R. (2000). How people learn: Brain, mind, experience and school. National Academies Press. http://www.nap.edu/openbook.php?isbn=0309070368. Ackermann, E. (2001). Piaget's constructivism, Papert's constructionism: What's the difference. Future of Learning Group Publication, 5(3), 1-11, doi:10.1.1.132.4253 Misura, M. (2019, March). ISN Graphing Rational Functions [Image]. Misura, M. (2021, November 6). Make, Create, Innovate!. [Image]. A major disruption to learning more recently is the anxiety that students come to class with. Anxiety can manifest itself in many different ways and for many different reasons, but it can be particularly unique and intense in a math classroom. “For students there is often a perception that the expectations about mathematics skills are unrealistic, for example, in the requirement to answer questions quickly.” (Chinn, 2008) Not only is it unrealistic to expect students to answer math quickly but also there is often a disconnect between how this actually applies to anything they care to learn about. Another big issue Chinn states in the article, Mathematics Anxiety in Secondary Students in England, is an over reliance on rote learning that can lead to anxiety and unrealistic goals of knowing the one correct answer quickly (Chinn 2008). Both of these things can attempt to be solved by using the amazing web based calculator, Desmos.com. In my video below I go over just a few of the many features desmos has to offer (as well as it’s minor drawbacks). Jo Boaler, in her book Limitless Mind, talks about how it is important for students to understand math deeply and that this takes time (Boaler 2018). She also encourages all students to share their ideas and that patterns can be seen in different ways, speaking to the anxiety that there is only one correct answer (Boaler 2018). Students should be encouraged to play with math, search for patterns, ask interesting questions and desmos is a platform that allows students to play with math (while following all appropriate mathematical rules), ask non-threatening questions (because no one else is watching or judging), and because they are able to see a lot of correct examples quickly can become better pattern seekers! Resources:
Chinn, S. (2008, December 18). Mathematics Anxiety in Secondary Students in England. Dyslexia, 15:61-68. https://doi.org/10.1002/dys.381 Boaler, J. (2019). Limitless Mind. HarperOne. Misura, M. (2021, November 4). Desmos and Anxiety [Video]. YouTube. https://youtu.be/0nU0yYNZJ2I |
AuthorMarissa McGregor, high school math teacher extraordinaire. I love my husband, daughter, and family dearly. Archives
August 2022
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