Math Reflection Week 4: Rich Tasks and Number Flexibility

This week in our math class we focused on participating in and assessing rich learning tasks in math. A rich tasks boils down to one that is: essential, authentic, engaging, and active. One such task that we performed in class was a problem involving counting the fingers on a hand. The basic problem was that if you started counting your fingers starting with your thumb, index, middle, ring, pinky, ring, middle, index, thumb, index, etc. what finger will you land on when you count your 10,000 finger? Everyone came up with different ways of solving this question but the one that I found most interesting was the one Mina shared with the class. It was a video of how someone else solved the problem by thinking of it as an eight fingered hand rather than just one five fingered hand.

Michael Feagan. (Sept.29 2017). Hand Problem [photo].

I think that all of the different ways students had to express this problem help support that this is a rich learning activity.

The final thing I did this week was watch the math mindset video on number flexibility. The exercise the video wanted us to do was to do 18x5 in our heads. I did this by knowing that if 10x10 was 100 then 5x10 would be 50 and 5x8 is 40, so 50+40 is 90. Perhaps a longer way of doing it, but I would not be surprised if I had many students in my math classes who would mentally answer this question this way. This exercise is pretty similar to doing math strings, which I think are an excellent way of bettering number flexibility.

Math strings I think are an excellent way to better a student's mental math flexibility. Recently I presented a webinar with my classmate Paula that highlights the benefits of doing math strings, you can see it in the video below.

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]

AER Reflection

1.      Assessment Page During First Teaching Block

  As I am going into my first teaching block I am looking for resources that can help me along the way.  For assessment I will be using my digital portfolio on assessment to help guide me.  The first thing that I would use to help guide me would be the AER Strategy Form.  This form will be a constant reference for how I will use assessment to tackle a variety of challenges such as ELL learners, special needs learners, or report cards.  I have included two resources for every section from the Ministry document Growing Success to help guide me in future uses of assessment.  

  I would also like to use my assessment page from my digital portfolio to continue to blog about my continuing experiences and challenges with assessment.  I believe I have already started off quite well with my first two posts on my past experiences with assessment and my recent experiences with assessment.  I would like to continue this blog by detailing how I am dealing with assessment during my first teaching block and how I am adjusting to assess my placement class.  I believe that this will help with my self-reflection as a teacher and allow me to refine my assessment strategies.  

3. Professional Learning Goal for Job Interview

  If I were to highlight one of my professional learning goals from my AER Strategy Form I would want to highlight my goal to better facilitate support learning for students who are form an Aboriginal, Metis, or Inuit background.  In my AER Strategy Form I have highlighted the need to research the need to study the social and economic conditions these students come from as well as talking to experts and advisors from these communities.  This will be done to help better understand the context that these students learn in and what challenges they might have to learning.  I have highlighted two Ministry of Education documents to help me develop this learning goal.  These resources can be found here and here.  Both of these documents help inform teachers about the learning styles these students might have based on the communities they are from while also providing practical strategies and tools for the successful instruction of Aboriginal, Metis, and Inuit students.  I believe that teachers in Ontario are under-equipped and to help with the effective education of these students.  I therefore believe that highlighting my knowledge and willingness to learn and develop this knowledge would be a desirable asset during a job interview.   

AER Strategy Form

 

 

 

 

Math Reflection Week 11: Formative Assessment

  This was an interesting week for math.  We got the chance to play an "eggcelent" game called, you guessed it, Egg Hunt.  The game requires students to plan out a route through Ontario cities where in each city you get a certain amount of eggs for only one visit.  The catch is that you only have 4,000 kilometers that you can travel.  The objective is to get as many eggs as possible while remaining within the allotted four thousand kilometers.  For this activity we worked in pairs and it was nice to have someone to bounce ideas off of and plan with.  Obviously this activity involved a lot of problem solving to find the optimal solution, but it also involved a lot of number sense keeping track of how many kilometers you have traveled.  For the activity we were provided the distances between cities, but students could perhaps measure it themselves and use a scale to convert it into kilometers.  I also like how this activity does a great job of incorporating Ontario geography into it.   Overall the activity was a lot of fun and I think it really got people thinking and planning which is great.  This activity or something similar to it is certainly something I would like to implement for a math or even geography class.

  Before this game though I class took the time to brainstorm about some ideas for formative assessment for math.  A lot of really good suggestions were given by my colleagues such as math problems of the day, gallery walks, KWL charts, exit cards, self-assessments, and just regular conversations and questions.  I have posted a photo of all the strategies we wrote on the white board below.  I would certainly be interested in implementing some of these forms of assessment in my own classroom or during my placements. 

 

 Michael Feagan. (Nov. 24, 2016). Strategies for Assessment [photo].