Math Reflection Week 3: Learning Styles and Mistakes

Class began this week with a small math game. We played a version of I Have/Who Has? which involves everyone getting a card with a math problem, the sum of that number is the number you have. The card also gives you a number that someone else has to have who goes next. It's a really simple game but I think it would work really well in a math classroom. There are just a few modifications I would do to it to help better scaffold math learning. For example I would make sure every card had to do with the same type of math problems (multiplication, division, exponents, etc.). I would then make sure that this activity functions like a math string, having each question build on the skills, patterns, and knowledges of the previous questions. As a teacher I would also try and write down the moth problems on the board for every student to see and work out. I think with these small modifications the game can be more accessible and enjoyable for more students.

After that we had a long talk about learning styles in math. Learning styles meaning people being auditory, visual, or kinesthetic learners. I know I was definitely not the only one in class who was kind of rolling their eyes at the idea of taking another learning styles quiz or just hearing about learning styles again. As many of you may or may not know learning styles has (at least in academic pedagogical circles) fallen out of favour. Why? Well for starters the study that argued for learning styles had weak evidence to begin with and made very large claims about how catering to them could affect learning. There are a lot of studies critiquing learning styles so I won't belabor the point. A quick look online will give you some places to start for further reading. 

The last thing that I looked into this week was the idea of mistakes helping us grow in math. Scientifically you experience more neural growth in the brain when you get a math question wrong than when you get it right. This seems to make sense, as there really isn't any new information received in getting a question right, but there certainly is in getting one wrong. I think a lot of people, particularly young students, are afraid of failure. I think as educators we have a responsibility to create an environment where mistakes are good and seen as stepping stones to success. There's a phrase that I really like called "failing forward". I've heard this phrase a lot in the context of table-top games, where a failed dice roll usually means nothing happens, in a fail forward game it means that something interesting still happens. The idea is that the game still goes forward even if a dice roll is failed. I like the idea of applying this to learning. Just because you failed to give a correct answer should not mean you failed to progress, to learn, or to enjoy yourself.

Michael Feagan. (Sept.21 2017). Math Quote [photo].

Math Reflection Week 2: Math Mindsets

Our class this week largely focused on how we as students and teachers conceptualize math. The way we started this conversation was with another card trick. The card trick involved us picking a number from 10 to 20 and then adding the two place values together (for example 15 would be 1+5=6). Our instructor would draw 15 cards and then subtract 6 from the pile and draw a queen. The trick was basically one involving particular placement of the cards based on a mathematical rule that if you choose a double digit number and subtract the total of the two place value you will get the same number within certain ranges as shown in the photo below (i.e. 10-19, 20-29. 30-39 etc.).

Michael Feagan. (Sept. 15 2017). Card Trick Math [photo].

For the online portion of our class I watched a video about growth mindsets in math. The idea of growth mindsets originated from Carol Dweck and argues for students and educators to have a mindset that anything can be learned by anyone with enough effort put into it. Dweck's ideas have become very popular in the world of education, with the term growth mindset becoming entrenched in educators' vernacular. Overall I agree with the fundamental concept of a growth mindset, as opposed to a fixed mindset which Dweck asserts is the belief that an individual can only learn so much and is incapable of learning more advanced concepts. I still have some issues with Dweck's concept of the growth mindset. A cursory glance at criticisms involving Dweck's theories should leave any educator questioning how they integrate this approach in their classroom. One of the things I always thought of when hearing about growth mindsets is "what if the student is already trying their hardest?" As someone who has struggled with math I would not feel more motivated if I was told to try harder if I had already tried my hardest. Likewise if a student is already trying their hardest and can't get it, and is told that anyone can do it if they try hard, I as a student would be left wondering what's wrong with me. I feel like a growth mindset might be encouraging students to unfairly push students who are trying and still struggling with any academic concept. I therefore think that teachers need to be reflective about how they're integrating the ideas of a growth mindset into their classes and make sure that they are applying it fairly to all students.

Math Reflection Week1: Assumptions About Math

Beginning this week of our math class we were asked a lot of questions to help us think about our own experiences and thoughts about learning math. For this week I watched two videos about public perceptions on mathematics. The first one was a Discovery Education video where children and adults were asked their honest feeling about math, you can watch it here. I felt like this video did a good job of highlighting the very mixed feelings both children and adults have about doing math. From my own personal experiences I never really like math a lot. As I got older I got better at doing math, but I wouldn't say I enjoyed doing it. This might have something to do with how math in schools was presented, I never felt like it was something that felt relevant to me. I still think that not everyone has to love math, but that people need to be comfortable with it and know that there are certain problem solving skills that can be developed by doing math.

The other video that I watched this week for class was titled Hollywood Hates Math. I found this video to be really interesting though I came out of it with more questions than answers. One of those questions was this; are movie's and television's attitudes towards math reflective of larger societal opinions, or are people's opinions about math influenced by how the media presents math? I posted this question in our class forum and the responses I got were very well thought out. One response I got was wondering what the historical trends were like about mathematics to try and find when the dislike for math as a subject of study began. As someone whose field of study was history this interested me greatly. I did a little bit of research into this and found a few interesting ideas. One of which is that the feelings of nervousness or inadequacy about math is such a common thing that it is called Mathematical Anxiety. The historical roots of this anxiety might date all the way back to 19th century schools. According to teachers such as John Taylor Gatto who argues that Western industrialized schooling beginning in the 19th century was designed to create an environment of confusion and intellectual dependence on an expert. I think it's possible that a lot of people's mathematical anxieties can come from the culture of memorization in math classes.

I really enjoyed looking into this topic and hope to challenge my ideas of what teaching mathematics is about .

wecometolearn. (Sept. 11 2017) Overcoming Math Anxiety [image]