Blog Post #6 - Week 11

Hey everyone! Thank you so much for following along with my math blog all these weeks! It has been a blast sharing my thoughts about math and what I have learned in my math course with all of you! This blog has allowed me to reflect deeply on teaching math and increase my understanding and confidence in my abilities as a teacher candidate. Unfortunately, this is my final blog post, so I hope you enjoy it and thanks for coming along for the ride with me!

This week in-class we shared math games that we had been playing and analyzing in smaller groups by presenting the ones we liked the best to our entire class. I really liked this activity because math can be a subject that is difficult to make relatable or engaging to students if you are always teaching it to them with a pen and paper. By implementing technology and math video games, you can not only show them how math can be engaging and fun, but you are also showing them how math can be fun and practical in their everyday life. I would like to now share some of my thoughts on some of the video games we shared as a class and share my thoughts on how I could incorporate them into classrooms.

Arcademics. Screenshot from Canoe Penguins. arcademics.com. Accessed November 19, 2019. https://www.arcademics.com/games/canoe-penguins

Quite a few of the games shared were from websites like Arcademics or mathplayground. While these games are fun and engaging for a short while, I feel like they lose their lustre quickly and they are not very strong at motivating students to continue playing and completing math work. The main reason I think this is because they are mostly very simple games mechanics-wise they all follow the same pattern of answer a math question and then your character moves forward a little bit in some form of race. While these simple games might work well at motivating younger students in the primary grades, I believe they fall short of being truly effective with junior and intermediate students. In today’s world where the games students play at home for fun have expansive worlds, multiple characters, problems to solve, and agency for the player; these simple design math games are not engaging enough. That is why I believe that games like mPower, Dreambox and Prodigy are the ones that I would try and implement with students.

TVO. mPower. orion.on.ca. Retrieved November 19, 2019. https://www.orion.on.ca/news-events/blog/free-digital-tools-from-tvo-to-improve-learning-at-your-school/attachment/tvo-mpower-900px/

mPower, Dreambox and Prodigy are effective because they are engaging enough to rival the video games that children play at home. This is because they have large worlds with multiple minigames, and they include some form of player agency. On top of that, they each come with a teacher portal where you as the teacher can track student performance and even send students specific lessons that you want them to work on! I could see myself implementing any of these three games into my teaching practice as a way for students to review concepts taught in class and for a way for them to continue having fun while learning math!

Check out this video about Prodigy below! Retrieved from https://www.youtube.com/watch?time_continue=8&v=A0CtplncQnU&feature=emb_logo

Thank you so much for following me on this journey! I hope you enjoyed my blog posts and I wish the best in all of your endeavours! Goodbye!

Blog Post #5 - Week 9

Hi everyone!! Thank you so much for returning to my math blog once again this week!! I learned lots of math in these past two weeks through our textbook and our lectures! I am very excited to share what I have learned while adding my own thoughts and opinions to them as well! So, let’s get started!

I am really intrigued by the van Hiele taxonomy of geometric thinking that we read about and then had a good discussion about in class. The van Hiele taxonomy breaks geometric thinking into 5 distinct levels: Level 0: Visualization, Level 1: Analysis, Level 2: Informal Deduction, Level 3: Deduction, and Level 4: Rigour. Click here for a brief article that provides even more detail about the van Hiele levels to deepen your understanding! These levels interest me quite a lot because they provide a framework from which a teacher can work. By identifying what level of the van Hiele taxonomy a student is in, a teacher then has a reference to determine what that student knows and what thinking rationale they use; without the taxonomy, a teacher would be forced to guess their students’ level of thinking for each geometric subsection. As a teacher candidate, I am glad that I have learned about this taxonomy because I believe it will be of great use when I am teaching because it will make it so much easier for me to identify the level of my students so that I can better serve them. It is important for educators to remember that a student’s spatial experiences, not age, determine their position in the taxonomy which reinforces our importance as teachers to guide them through the levels to be where they need to be. I also had some fun thinking back to when I was a student and what levels of the taxonomy I would have been at when I was a student. I wonder now that I have not been in intensive math courses for a few years if I have lost some of my touch and would now only be at level 3 😊!

Vojkuvkova. van Hiele Level 0. Proceedings of Contributed Papers. Accessed November 9, 2019. https://www.mff.cuni.cz/veda/konference/wds/proc/pdf12/WDS12_112_m8_Vojkuvkova.pdf

Vojkuvkova. van Hiele Level 2. Proceedings of Contributed Papers. Accessed November 9, 2019. https://www.mff.cuni.cz/veda/konference/wds/proc/pdf12/WDS12_112_m8_Vojkuvkova.pdf

Over the last two weeks in class, we have begun discussing lesson planning in math and how it should look. I am looking forward to working through and completing our lesson plan assignment because I feel like it is the next step that I need to take in order to become an effective math teacher. I think it is crucially important for a math teacher to practice and implement universal design. This way all the learners in a class’ needs can be addressed and everyone can be on the same path of learning. The needs for every math problem and lesson that we discussed align very well with the universal framework. We discussed how a lesson needs variable entry points for learners of all abilities, a low floor and high ceiling so it meets students where they are and offers room for growth, and a lesson much be engaging for all students. I am excited to implement each of these into my own lesson plans!

Margaret Flood. Universal Design for Learning. wtc.ie. Accessed November 9, 2019. https://www.wtc.ie/cpd-courses/post-primary-courses/1109-post-primary-universal-design-for-learning-udl.html

Thanks for reading! See you next week!

Blog Post #4 - Week 7

Hi everyone!! It is such a pleasure to have you all back and visiting my math blog again this week! This blog post is a little later than the typical ones because I had reading week fall in the middle of this blog duration, but it is so great to be back at it!

There were a few very interesting things that we covered in class the last few weeks that I am very excited to discuss and share with you now. The first of which is an interesting discussion that forced me to reflect further about dispelling mathematical myths or misconceptions that our students believe. A math myth might be a belief like “two negatives make a positive” that a student holds which is in fact not always true. For more examples of misconceptions in math check out this article that describes common misconceptions that students have about fractions! Now when I first thought about myths in math, the first thought that came to my mind is that it is important to prevent students from getting in the habit of believing them in the first place. While this is certainly an effective strategy, our class discussion forced me to think more critically because it was mentioned that you do not get to control what knowledge students bring with them when they enter your class and so they might already believe some math misconceptions. When this is the case it becomes much harder to dispel something that a student has already learned and believes to be true. When this is the case, I believe that it is best to show your students comprehensive examples that dispel the mathematical misconception that they hold.

I really loved having the opportunity in class to practice demonstrating to students that the math myth “two negatives make a positive” is not always true. My group was responsible for disproving the math myth for multiplication and division operations using a number line. At first, I found this activity very challenging, but with discussions with my fellow teacher candidates and professor, we were able to successfully represent both examples on a number line and I can say that I am confident in my ability to explain them to a student in the future! Using a number line in this situation really forced me to think things through and reflect on how I could explain and represent them clearly rather than just making a statement like “if you divide two negative numbers, the quotient is always a positive number”. A statement like that would most likely be met with resistance from a student who believes two negatives always make a positive no matter what, but now I can actually prove why to them. This activity has made me more confident in my ability to teach math and dispel math misconceptions.

Math is Fun. Multiplying Negatives. mathisfun.com. Accessed October 27, 2019. https://www.mathsisfun.com/multiplying-negatives.html

Khan Academy. Dividing Negative Numbers Review. khanacademy.org. Accessed October 27, 2019.https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-mult-divide-negatives/a/dividing-negative-numbers-review 

Lastly, I just wanted to add that the activity above and other course content over the past weeks has really let me see the importance of being able to answer student questions in a way that makes sense with an appropriate explanation. If you simply say “you have to do it this way because that’s how it works” or “that’s just how it’s done”, I now understand that you will be met with resistance from students and you will not be doing them a good service. A math teacher needs to be able to prove and explain the reasoning to student questions to be successful and this is something that I am looking forward to learning much more about in the future!

Thank you so much for reading! I will see you in two weeks!

Blog Post #3 - Week 5

Hi everyone!!! Thanks so much for returning to my blog this week! I am excited to share my thoughts on several different topics that we discussed in lecture and saw in our course material over the last two weeks! Let’s get started!

This week in class we focused much of our attention on fractions and decimals and I learned a lot from what we covered. A really impactful moment for me was when we discussed the importance and necessity of visualization in these topics of mathematics. Visualization of fractions is needed for students to understand the concept behind them. As educators, our goal is to teach students math concepts so that they can apply them in authentic situations, and I have learned that visualization is a key technique for achieving this with fractions. I now understand the reasoning and value behind all the pizza and pie fraction problems I solved as a student and why we still use them to teach fractions with students today. Fraction problems with a pizza allow students to visualize how fractions are relevant to their lives and give them a representation of the values that fractions represent. This realization encouraged me to think deeper about visualization and decimals. Decimals and fractions are related and intertwined, and yet as a student, I always struggled more with understanding decimals. I now wonder if this is because I did not have the opportunity to visualize the values of decimals as I did with fractions! I will look into techniques and examples I could use to help students visualize with decimal numbers.

The talk of visualization brought my mind to thinking about manipulatives once again. I know I discussed manipulatives and how they can sometimes distract students in my introductory blog post, so I won’t spend too much time on the subject here. However, in this context, I felt it was important to share that manipulatives can be an excellent tool to help students visualize mathematical concepts and thus improve their comprehension. Manipulatives can serve as real, tangible representations that help allow students to see math concepts in practical concepts. For that reason, I do believe that manipulatives can be useful and valuable tools to students, but they must be implemented correctly to remain effective. Below are two examples of manipulative use for fractions!

Alycia Zimmerman. Lego Fractions. Scholastic. Accessed October 4, 2019.  https://www.scholastic.com/teachers/blog-posts/alycia-zimmerman/using-lego-build-math-concepts/

Nasha Bailey. Pizza Manipulative. Pinterest. Accessed October 4, 2019. https://www.pinterest.ca/pin/387520742917896416/?lp=true

The last notion that I wanted to touch on in this blog post was the potential for intersectionality between math and other subjects and the potential that this has to create meaningful, authentic tasks for students. This thought process was sparked by a teacher candidate in my class who did an amazing presentation on how we could teach fractions through music. What I have come to realize after this presentation is that by connecting math to other subjects, we can not only make math more interesting and engaging for students, but it can help students succeed in math by tying in other strength areas. I am curious to look into more connections between math and other subjects!

Thank you so much for reading!! See you next time!

Blog Post #2 - Week 3

Hi everyone! Welcome back to my math blog and my second ever blog post! This post (and each of the ones that follow it!) will contain some of my reflections, thoughts, and reactions to course content be it lectures, readings, videos we’ve watched, and more! I will use this space to really express what I’ve learned so far and how I feel about it! With that being said, let’s get started!!

One of the most important and impactful things we discussed in class this week is that there is no such thing as a “math brain” or “not having a math brain”. This is a discourse that is unfortunately so prevalent in our society and in our schools. I can recall so many of my classmates who refused to put in their full effort in math because “they just weren’t made for it” and worse yet teachers who wouldn’t believe in students or push them to succeed once again because they felt that math just wasn’t their strong suit. The discourse goes the other way too and being a student who succeeded at math, I remember peers discrediting the effort I would put in because they felt I was “just made to do math”. As our conversations in class concluded, these discourses are harmful to students because they truly limit their chances of success and reduces the outcome of possibilities they have in life. Instead of believing in this “math brain” illusion, we as future educators need to approach math with a growth mindset and do our best to instil it in all our students. That is, we need to encourage our students that they CAN do math, they CAN problem solve, and they CAN overcome challenges if they are prepared to embrace them and view them as an opportunity for growth and improvement.  

Here’s a short video that explains growth mindset by contrasting it with fixed mindset which is where thoughts like “not having a math brain” originate.

Another valuable discussion that we had in class this week was around the idea that we shouldn’t be afraid to make mistakes in front of our students, to admit to them that we don’t always have the answer right away, or to let them know that we are learning alongside them. I think this can go a long way in helping to establish positive relationships with students. Being open and honest with them allows them to see you as human and more likely to trust you, in my opinion. I know personally, I always connected and learned best under teachers who were transparent with me. The other key takeaway for me was that when you make mistakes in front of your students and are honest about it, it models for them that making mistakes is okay and that they are opportunities for growth. By seeing teachers make mistakes and approach them with a growth mindset I think it is more likely that students will experience less anxiety when they make mistakes of their own and even begin to adopt a growth mindset of their own!

I am excited to keep learning in this course and I am confident that my development as a future math educator will continue. Thanks for reading!

Introductory Blog Post

Hi everyone in 8P29! This is my introductory blog post so I figured I would share a little bit about myself and then start discussing the two blogs I read from http://www.learningscientists.org/archive/ and why I chose them! To start with some background, I am 22 years old and am from Aurora, Ontario which is about an hour north of Toronto. I am an only child, so I grew up there with just my parents as immediate family. I was in French Immersion for elementary and high school which led me to choose French as my teachable here at Brock. I am in the concurrent education program in the junior/intermediate stream, so this is my 5^th year at Brock. I live off campus in a house with 5 of my friends and they are all in the teacher education program as well. In addition to teaching, I am most passionate about sports especially tennis, basketball, football, and soccer. I taught at a tennis camp in Aurora for 6 summers and was on Brock’s tennis team for some time during my undergrad. My favourite professional tennis player is Fabio Fognini. I coached basketball for 2 years while I was in high school and I love catching Raptors games on tv. I am a very very very passionate supporter of the LA Rams (NFL) and AS Roma (soccer, Serie A) so my Sunday’s are usually full of me watching their matches. I also referee soccer during the summer which keeps me very involved in the sport. This is my first experience with writing or even reading blogs, so I hope to learn much more about it all as this course goes on!

Marcello Leone. Passion Cloud. WordArt. Accessed September 10, 2019. https://wordart.com/ 

The first blog I chose to read for this week was titled “Manipulatives – Why They Can Hinder Learning and What You Can Do About It” by Sara Fulmer. It can be found at the following link: https://www.learningscientists.org/blog/2017/4/4-1 . This blog post really intrigued me because teachers often turn to manipulatives as a learning tool to help students in math and I also often used manipulatives when I was tutoring students in math at the Brock Learning Lab. In many of my experiences though, I found that the manipulatives did not serve their intended purpose and only helped distract students. These experiences are what influenced me to read this blog and I found the content very interesting. Some of the main points from the post were that manipulatives that are too visually interesting can increase off-task behaviour and that constantly using manipulatives in class can make students too reliant on them. I still believe manipulatives can be useful, but I will try to use them sparingly and give real thought to the type of manipulative I use.

The second blog post I read is “Rethinking Teacher Training – How Mathematics and Education Departments Can Help” by Bryan Penfound at https://www.learningscientists.org/blog/2016/4/19-1 . This blog post caught my eye because we, of course, are in a teacher education program! Bryan suggests that teacher candidates take a course that covers the grade specific curriculum content they will be teaching and another course on the pedagogy of math such as how to sequence mathematical ideas etc. While Bryan’s suggestions seem a little different to how we are learning Math at Brock, I am sure they both have strengths and that they would both produce very strong teacher candidates!

Thanks for reading!