Final Review Math

My Takeaway from this course!

There were a number of things that stuck for me in this course. The first of these was the discovery that the ability to do fractions in grade 4 would usually be the difference between excelling in math and having a tough time. The idea of arithmetic vs algebra also played a big role as the difference always occurred to me but I never thought of it to much. making sure students know the difference between the two and can use them interchangeably is important for the creation of their mathematical mind. Visual aids, different approaches and expanding their idea of math from a set of ordered equations to problem solving, critical evaluation and creativity is paramount in having students succeed with their mathematics. I learnt that there is no such thing as being either good or bad at math, and saying that I am not good at math on the basis of hereditary genes is more of a self fulfilling prophecy rather than a fact. Students who challenge themselves and make mistakes are expanding their mind and allowing themselves to know knew concepts and rewire their brains to take in the new information. Without mistakes there is no learning. I enjoyed the course very much as it showed me a different side to mathematics as well as demonstrated that as a teacher there are always things I can learn about how to help students succeed academically. 

Math Weekly Reflection 5

youcubed (2018). Illustrated graphs outside of a book. [image] Available at: https://www.youcubed.org/resources/visual-math-improves-math-performance/ [Accessed 22 Oct. 2018].

Great week this week in exploring mathematics. Multiple solutions, graphing and illustrating different types of mathematical ideas in a number of way has always been a focus and this week was no different. Overall the concepts of all the weeks have begun to blend together. Illustration, demonstrating solutions in different way allow math to be more accessible and also differentiated for different types of learners.

Introducing leadership roles for students who excel in math is a way to engage them but that doesn't mean that they should not look at their own peers work just because they got the answer right the way the teacher taught them to get it. Have your students always take a look at what others are doing. This allows them to see the creativity in mathematics and possibly simpler and more to the point solutions then otherwise they might have thought of.

Math Weekly Reflection 4

RenjiAbaraiGR (2018). Espada Numbers Brushes. [image] Available at:        
                https://www.deviantart.com/renjiabaraigr/art/Espada-Numbers-Brushes-192776736 

The Focus this week in our mathematics course was to take a look at how students solve problems differently and how there are many different ways to represent math problems. By having students explore their peers’ solutions to problems they can start becoming more flexible in their mathematics. With this in mind we had gallery walks this week and solved a number of problems. This showed each of the teacher candidates that there are many ways to solve the problem and that creativity is important in math. This is especially compounded by the videos we watched in our Math Minds Module this week.

                The Math Minds Module this week looks at how students who are successful at math tend to be the ones that can be flexible with numbers. Creativity, being open to multiple solutions, as well demonstrating an ability of connect different math concepts together is the marker for success in mathematics. To Further this concept, it is known that “individuals persist in using one general but not always optimal strategy for solving a group of mathematics problems, even when they have knowledge of more efficient alternatives.” (Liu, Wang, Star, Zhen, Jiang, Fu, 2018) With this in mind most students might get trapped by the idea that there is only one way to go about solving a problem. I at times have struggled with this and not knowing the process impeded my way of solving the problem because I was not seeing the problem as something solvable with a number of solutions but rather something that had to have a formula or a set of steps to solving. With this in mind having students think about problems would be very beneficial in making it something solvable with creativity and not something that a robot could solve with the right set of prompts.

Ru-De Liu, Jia Wang, Jon R. Star, Rui Zhen, Rong-Huan Jiang, & Xin-Chen Fu. (2018). Turning    

                  Potential Flexibility Into Flexible Performance: Moderating Effect of Self-Efficacy                        and Use of Flexible Cognition. Frontiers in Psychology, Vol 9 (2018).  

                  https://doi.org/10.3389/fpsyg.2018.00646/full

Math Weekly Reflection 3

S. (n.d.). Ferb math [Digital image]. Retrieved September 23, 2018, from https://www.deviantart.com/shoyzzfanart/art/Ferb-math-255364862

   

    The focus of our discussions this week tended to continue on making mistakes, but also introduced the concept of math speed. There are many ways in which students struggle with their ability to make mistakes and that does not allow them to grow. With this in mind teachers should always strive to frame their student’s mindset around seeking excellence but enjoying the learning that comes from making a mistake. When a student makes a mistake its exciting because that means they have more to learn. They have something new to discover and they should follow that lead. On the premise of speed there needs to be an emphasis on better understanding the problems which are talked about in mathematics. Students need to know that not being quick at doing math does not mean they are necessarily worse at it. It could just mean that they rather take a look at all the angles of a problem before trying to solve. This does not mean that having speed when solving problems is a bad thing, but it does mean that students should not be punished for not being able to do their math problems in time. When I was in high school there was always a teacher in our mathematics class that would make tests very difficult because not a lot of time was given for them. He would say "When you get to university you won't have a lot of time on your exams, so you need to get good at doing math quickly now". This was not the case when I went to university because math turned into mathematical reasoning and solving proofs which meant that the mechanical skill of solving math problems was less important then understanding their logic and the mechanisms that made a math formula true. Every university math exam I had was 3 hours and did not have to many questions. Not finishing the test was never the problem, the ability to reason out and solve a couple of difficult questions was more important in university then it was in High school. 

    When I was researching a little bit about the topic of speed however I found a very interesting article on the topic. The article suggested that the using of an abacus to both demonstrate numbers visual and stimulate mental math were very helpful in having students become more efficient with their mathematics and have less anxiety when performing them (N, V., Perumalla, R., & M, N, 2018). Students, I would venture to guess, who have had more experience with numbers at an earlier age tend to be less anxious with mathematics as well as excel better when manipulating them. I think while it is important to focus on having students develop a deep understanding of mathematics and not be swayed by being slower at doing them, teachers should still hope to give students the tools to become more efficient in their mathematical ability. Yes, this might mean that students might miss some part of their development of mathematics, but for a majority of students the ability to do quick math is important and shouldn't be lost. Calculating your taxes, doing groceries, making a budget for yourself, buying t-shirts for your baseball team and calculating their cost are all regular math activities that do not require extensive math knowledge but rather math familiarity and speed. These are tasks that will help individual students take less time in their daily lives to perform these tasks, so I don't want to forgo mathematical speed altogether but understand the necessity to make it not the 'be all end all' of junior intermediate mathematical thinking.

N, V., Perumalla, R., & M, N. (2018). Effect of abacus training on maths anxiety. 
             National Journal of Physiology, Pharmacy and Pharmacology,8(6), 854.

doi:10.5455/njppp.2018.8.0204508022018

Math Weekly Reflection 2

        Riva, E. (2018). Brain drawing with math equations. [image] Available at:

            https://pixabay.com/en/brain-mind-  psychology-idea-drawing-2062057/ [Accessed 17 Sep. 2018].

    The Second week started to focus on the challenges that we face as math teachers in schools. It seems like more and more math is portrayed as a subject that no one likes and that is difficult. While it is true that the subject is difficult it is important to maintain the idea that anyone can be good at math as long as they are led in the right direction. For this reason, it seems like teachers tend to play a very important role in making students become good at math. 

    You have to praise the students the right way and criticize them the right way or you may get a student that doesn't enjoy mathematics because of you. If someone does well, you can't say that the student is smart at math because that puts pressure on them to maintain a high mark and might dissuade them from taking on difficult challenges. Due to the fact that the students don’t want to fail, the student now might shy away from taking risks making them develop less and turning off their growth mindset. 

    By the same token blaming a student’s mistakes on them simply not being good at math will feed into their fixed mindset making them detest the subject and throw it away altogether. What was learned this week has to do with Teachers being precise in what they say to students as well as knowing that they have a great deal of impact as it relates to the student’s ability to succeed in mathematics. 

Math Weekly Reflection 1

SchoolHouse (2018). Big House Numbers. [image] Available at: https://www.schoolhouse.com/products/big-house-numbers-black-anodized [Accessed 16 Sep. 2018].

    The first week of Math was really informative this week. We took a look at a number of different ways in which math is taught in school now a days and how we as teachers must evolve with the way we teach math. In particular the focus on making sure students establish a growth mindset was important this week. We looked over a number of different ways to do this which mostly come from establishing a classroom environment that doesn’t focus on grade level and individual achievement but instead looks at making sure students know how to learn and develop themselves instead of being stuck thinking they are not simply good at a subject especially when it comes to math. 

    With this in mind many of the things that kept reappearing is that students tend to find math practical or relatable to their daily lives. There might be students who enjoy math for the sake of it but there were rarely any students who loved it as a subject. For this reason, teachers need to bring math our of the abstract and into the literal for students. Students should have to solve problems that involve daily problems and things that they can see themselves needing to use in the future. Such an approach would make math more meaningful and engaging for students.