Math / Mistakes &Success

      This week, we looked at making mistakes in math! Mathematics is one of the subjects that people often find it very difficult to allow for freedom in. Everyone believes that math has one right answer- and that is not necessarily true. Math work has multiple ways people can express the same numbers in different sequences or formats, and oftentimes the answer can be found in a variety of ways. It is important to recognize that creativity is available in math work, and if honed in on, can encourage students to make mistakes and thrive in an environment of imperfection.
       I also took the time to read the Math and Speed Forum because I feel like this is something I personally struggle with in math and was reminded of this week. During class, we did a Minds On activity that had us doing very quick math work on the fly, without calculators! This was something I had not done in a very long time. I was shocked at how long it was taking me to do more simple math without a calculator.
      Upon reading Charlene's post on the Forums on the Math and Speed section, I was enlightened by what she was saying. She stated, "speed does not equal intelligence" (Charlene Day). This is a super important thing to teach students when learning fundamental math skills. When teaching younger grades basic math such as multiplication and division, its important to repetitively practice at the students own pace to ensure that they have the skills before pushing them to do it faster.

This week was also the first week of Webinars! This took up a lot of my math-brain this week, because Charlene and I had to prepare our 30 minute interactive lesson. We had quite a challenge on our hands, but we pushed through and managed to come up with a Webinar based on creating a safe environment for math inquiry.
This is a topic I am pretty passionate about as a future educator, because I feel allowing for inquiry is super important. Inquiry allows students to freely explore what they find the most interesting in a subject. For mathematics, allowing for this to happen in an emotionally safe environment is extremely essential. Math somehow, and for some reason, often brings out the sensitive side in people, maybe because there is that fear of judgment in relation to a persons intelligence. This means that creating a positive learning environment for students is absolutely necessary to encourage a safe learning environment that allows for students to make mistakes! Charlene and I detailed a variety of ways to allow for safe exploration of inquiry. I am very proud of the work we did, and loved using the tools Charlene had explored during her first teaching block. I really learned a lot from the Webinar process, and loved facilitating it!
I also had the task of watching Ally and Nicole's webinar, focused on problem solving. I super enjoyed the way they played out their webinar! I loved learning about problem solving in a very realistic way. I really feel like I learned a lot of new math strategies this week.

Math-ittudes

This week was another challenging one in the world of math! During our online tutorial, I watched a really inspiring video about math mindsets and maintaining a positive attitude. This is something that I think is super important as a future educator. I want to be the kind of teacher that encourages that little voice in my students head that says, "I can do it if I work hard!" I want my students to maintain that growth mindset, and feel like they can take on the challenging work of mathematics.

I also read an article about spatial reasoning. I chose this article because I do not have a lot of information on the topic, and wanted to learn more. The document states, "Spatial thinking, or reasoning, involves the location and movement of objects and ourselves, either mentally or physically, in space. It is not a single ability or process but actually refers to a considerable number of concepts, tools and processes" (3).  The benefits of studying spatial reasoning are clear in all aspects of mathematics, as the concepts often intertwine with one another and all of them work together. As stated in the article, "By exploring the spatial aspects of mathematics, we make it more accessible, more engaging and more relevant" (4). Below is a picture I took from the article that I found very helpful. 

Support Document for Paying Attention to Mathematics Education (4). 

Further, I found that this week, I am really starting to notice the way that math works together to assist students everyday life. Creating connections to real life allows students to find meaning in mathematics in an easier way. Also, using creative ways to present information will allow students to subconsciously learn math, like through the card games we have been doing as a Minds On portion of our classes. Metacognitive thinking allowed me to acknowledge the way I am learning in math lecture, and apply it to how I want to teach in the future. I plan on being the kind of teacher that uses positive words, that acknowledges the negative but tries their hardest to make it into a positive.

Back @ it !

Almost a year later, and here we are again, bloggin', teachin' and doing some learnin'.

I am excited at the opportunity to really work on my blog this year and make it look pretty, as well as flush out some math content on it! I am hoping to employ Charlene to help me! (Fingers crossed!) 

This week , we began our math class again, and I'm not going to lie, the first class was a little stressful! We had a lot of stuff to organize, groups to get together, and math to learn. I am once again scared at the thought of being in a math class again, but excited and feel more prepared this time around. 

At the start of the week, we were assigned an online module in place of our Monday class. This is excellent for me, as a commuter and person who loves online learning! We got to watch a variety of math videos, all of which I loved and each which had its own excellent and thought-provoking message. My personal favourite is this one: 

     I personally like this one because while I was watching it, I was thinking of all the ways students eyes could be opened up to the way they see math, and why they see it that way. I was also thinking of the cross curricular intersections I could do with math and language based on a video like this! How awesome would it be to be able to write about math perceptions from a social media/ TV and movie perspective. I think the students would have some very interesting opinions on a video like this.

Attitudes Towards Math. 2017. Retrieved from Pinterest. 

         In class this week, we really discussed dispelling myths about math. I loved having an in-depth conversation with my fellow teacher candidates about why a large majority of us feel uncomfortable with the idea of teaching math, especially to higher grades! Really getting into why we still hold onto these math myths that we have been taught at a young age was enlightening.

       As we move into the semester full force, and I prepare to teach math in my second teaching block, I am really hoping to remember not to fall into these math stereotypes. There is no such thing as a "math person". And one of the biggest things I learned this week was that there is still a very deep need to dispel gender stereotypes in math. The fact that students as young as grade 2 are identifying and associating "boy" names with math, and "girl" names with reading is astonishing. As a teacher and a feminist, that is something I would really want to work to break down. I would never want one of my students thinking, " I cannot do this because of my gender". I really look forward to the day when I can make lessons that work towards creating students with a positive math mindset.

reflecting

Course Wrap Up! For Mathematics 

This course was a very beneficial experience. I have enjoyed learning how to teach mathematics. I came into the course very afraid of what would be expected, because it had been so long since I did math. I have found a lot of very beneficial games and activities from this course.

I also found the textbook to be incredibly useful. The textbook often detailed misconceptions, activities, and very useful observations that previous educators had witnessed. I loved the textbook because it covered all the bases. It was also extremely useful in showing us how to teach mathematics. 

My views on mathematics have changed so drastically. I am still very afraid to teach, but now I feel more prepared. I did not have the skills or knowledge I did before taking this course, and am very happy to have had this experience. 

This week in class we played a very fun math game that can be applied to any kind of holiday or special event. We really loved it as a class and I cannot wait to try it out. The game was a strange version of Battleship. The class was supposed to place the little boxes of options onto a grid and then as the grid squares were called out, the students X out the boxes and either gain points or rewards or lose the numbers they have gathered. I thought this was super fun and hope to get a chance to use this in my placement.

This week in placement I got to see another open question where students tried to answer questions about how two cylinders have the same surface area and different dimensions. From this question, I noticed a lot of students struggling to understand the difference between 2D shapes and 3D shapes. The students were attempting to calculate the 3D shape of the cylinder without realizing the surface area meant it wrapped all the way around. They tried to calculate it as two circles and one rectangle. The teacher eventually brought out a soup can to demonstrate. It was awesome to see some students had already created their own manipulative using paper. This helped them a lot. 

I am really looking forward to exploring math more and am thankful for the knowledge this course has taught me. I know that I have much more learning to do, but now I am excited instead of scared. 

there is 100% chance I am writing a blog right now ... (week 10)

     This week is all about probability! I actually like the topic of probability because I always remember doing fun activities such as rolling dice, flipping coins or playing carnival games. But using the actual mathematics behind probability is a bit more complex than just games!
     One of the things I feel probability really strongly assists in is demonstrating the relationships between numbers. When Michael did his presentation, he explained that most students can have some basic misconceptions about probability variations. If you flip a coin 500 times, you still have a 50/50 chance of it being heads or tails. There is not other option, and regardless of how many times that coin is flipped, the odds remain the same.
    Another aspect we discussed was taking this information and graphing it or placing it into charts. In my placement class, they are always using T charts or other visuals to show their work. The student seem to really thrive when they are given a clear display of the numeric relationships in chart format so I am constantly looking for new examples. I will definitely be borrowing these ideas when it comes time for my placement.

"Trapezoid" Varsity Tutors. 2016. Retrieved from http://www.varsitytutors.com/advanced_geometry-help/how-to-find-the-area-of-a-trapezoid

    In placement, the students are still working on area and conversion. They really like seeing relationships between numbers, and we have continued through math strings. One of my favourite lessons was based around an open problem with the grade 7's. I had the opportunity to split the class up with my associate teacher, and he taught the grade 8's a lesson, while I supervised the grade 7 math problem. He called it an "open problem" and it was basically a generalized question that there were no real, cookie-cutter answers to. I cannot recall the full question, but know the students had to attempt to find a formula that would calculate area of a trapezoid. There was not any more information given. From this, they split into pairs and tried to come to a solution. It was great to see the students work through the problem on their own. They did want help and guidance, but not too much. They knew to channel their frustrations, which was so great to see. I also liked the concept of giving students freedom to explore in mathematics. I feel that students need to understand and make up their own relationships when it comes to numbers. To see these students work through a problem with very little guidance, and come together to learn off of each other, was the kind of math problems I hope to implement in my classroom one day.
     I found this resource from the same author as our textbook, I would love to read more about open questions and see the impact they have on our students.

measurement (it rules!)

This week started with me preparing for my presentation on measurement! We had no in class session this week, so I had to adapt my presentation to fit a smaller group. It was interesting to see how being adaptable is still one of the skills I am learning. I naturally like to plan ahead, so when my plans change, I sometimes don't know how to accommodate those changes. I am still learning!

         In my presentation I had students draw out their hands on 1 and 2 square centimetre paper, and count how many centimetres their hand was on each paper. From this, I hoped they would gain an understanding of measuring in square centimetres, what square centimetres are, and how to compare two measurements.
         It went pretty well though. It is also very interesting video taping yourself and being able to look back on what you said and did. I think I would edit some things if I did present this lesson again, but I am happy with the activity,  it is always interesting to get students to understand how they can use the world around them mathematically.
         One of the things we learned online this week was investigation is one of the key aspects of measurement. Our professor discussed how students may not have the basic skills of measurement, and I think that is where my presentation would come in! It is a starting point for measurement.
The topic of measurement has many different features, because one can measure a variety of things. This features include measuring temperature, time, area, perimeter, circumference, and volume. One of the resources I looked through while planning my presentation was the Measurements grade 4-6: a Guide to Effective Instruction in Mathematics, Kindergarten to 6. This guide features really good examples for educators. It is laid out with similar sections as a lesson plan, making it super accessible and easy to read. One section that stood out to me is that it provides specific examples on how to scaffold the problems. There are several examples of "scaffolding suggestion" boxes featured in the document that seem really useful. On Page 49, the document suggests ways to connect a linear representation of time to life events that students will understand, in the scaffolding suggestion box. I think these little ideas and suggestions to educators makes it easier for pre-service teachers to understand, and have ideas to reference. I love documents like this because they take away the fear of trying to implement complex topics scaffolded in effective ways.
         I also sat in on Kursten's presentation, and assisted her in filming it! It was a great experience to see her activity. She also did hers on area, but focused on estimating area. Her activity is also a good introduction or refresher for students. In her presentation, the students cut out pictures and estimated their size based on the other pictures they cut out. This was an excellent example of estimating area! I definitely saw how hard gaining a conceptual understand of measurement can be for students.

snakes on a plane (week 8)

This week was about geometry and spatial sense. I actually do not mind this unit. I like thinking of how things can work together spatially. While reading through the "guide to effective instruction: geometry and spatial sense grades 4-6" teaching guide, I found a lot of information that I could see being very useful when it comes time to implement a lesson. One of the concepts that stood out to me was the inclusion of teaching strategies that are effective for this particular math lesson. They included several examples of instructions on what methods to use to teach geometry and spatial sense such as, "carefully planned activities will enable students to build on these [personal] connections and identify relationships between and among the various areas of geometry and spatial sense" (25). The document contained ample information on how to teach, the basis of why students need to know this information, where the information came from, and most important of all, how to connect it back to our students in a way they will remember. I will definitely be using this guide in my practicum. 

"Geometry Pun" (2016). Retrieved from tumblr.com

Geometry and spatial sense are so essential because they are skills that can translate to everyday. We use shapes in our everyday life, and need a sense of where things fit in the world. There are many real life examples and connections to be made on a unit like this. 
One of the things discussed was the misconceptions regarding comparing different units. For example, students need to be made aware to be careful of comparing shapes with different units. In my presentation, I introduced students to measuring perimeter with 2 inch grid paper, and 1 inch grid paper, an example like this would help students to see the difference measuring with different square centimetres can make. (featured in next weeks blog)

I will work to make sure my students have a conceptual understanding of geometry and spatial sense by providing them with a variety of demonstrated examples, and scaffolding the work to make it easier for them to understand. With a unit like this, which has foundations all the way in ELKP, if a student has missed a concept or doesn't quite understand something, they will struggle to build up any understanding. I will also focus on the big ideas. As was detailed in the effective instruction document, "These big ideas are conceptually related and interdependent, and instructional experiences will often re ect more than one big idea. For example, when students create or analyse designs made by transforming a shape or shapes (location and movement), they demonstrate an understanding of congruence (geometric relationships), and of how congruence is connected to the properties of a shape (properties of two-dimensional shapes and three- dimensional cues)."  (16). This quote stood out to me because it demonstrates the way every step of a lesson can affect a students conceptual understanding of the whole. 

I enjoyed the presentations this week because I loved playing with the shapes and seeing how that worked. I particularly enjoyed Ashley's presentation because I felt it was a good lesson for junior learners. I liked the use of manipulatives. Our table actually thought making the shapes and putting them into the bigger diamond was going to be very easy, but it was actually harder as she gave us parameters to follow. 

I also enjoyed learning from James. I liked his trick with flipping the paper to be able to see how shapes are translated and flipped and can move. I tried out the method of doing the exact opposite coordinates, and am happy to have learned that because I feel like I can really use that in my practicum. I do sometimes get lost when it comes to translating shapes and moving them across the grid. While working with students, I often try and get them to cut out a paper or have a physical resource so we can actually work with it, like Jacob did. Overall, I really enjoyed the presentations this week. I have been learning a lot from them. 

This week I am working on my own math presentation on measurement so stay tuned for updates on that!