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! 

let's taco 'bout it ! (and by it I mean patterning and algebra) (week 7)

     

"Let's Taco Bout It" (2016). Pinterest via Hollister Co. Retrieved from https://www.pinterest.com/pin/56154326576907607/

       This week surrounded patterning and algebra. When it comes to algebra, I am automatically lost! I feel like I lack the foundational knowledge to build up my current skills, so I am trying to re-learn and teach myself a lot of these concepts. It has been a challenge.
          We started our learning with a Speed Dating Multiplication number sequence. This activity required us to each start with a number, then pair up repeatedly to have two numbers to multiply together each time. I enjoyed this activity, while I did find it challenging. We were multiplying pretty high numbers, so it our answers were in the thousands. I did like this activity as a "minds on" portion. It got us thinking about multiplication and the relationships between numbers. It is a good example because it can be applied to any grade level. Even grade 3-4's could do this worksheet, the teacher would just give the students smaller numbers to work with.
        While discussing patterning and algebra, one of the things I found was a lot of great activities. The textbook provides a variety of image examples to show patterning. The misconceptions students often had was related to the changes in orientation of a shape. I think this is extremely common, as students often think the way a shape is oriented defines part of it, but this is not the case. Two shapes can be exactly the same but mirrored, or translated. Using manipulative shapes would be a very good way to avoid this.

          One of the things that stood out to me this week was Mohamed's presentation. He was very funny and engaging and I liked the way he presented the equations. I felt like I understood and followed his presentation. One of the main things I was happy he went over was the difference between an equation and an expression. As a student, I struggled with this concept. I often could not identify what the question was asking, which would leave me lost. I liked his distinctions because I think comparing them made them stand out better in my mind. Students would take a lot out of his presentation. I also loved the GOAT! Greatest Of All Time would be a really funny title to introduce to students and let them compete for the title. I also loved that he took the time to relate his examples to real life experiences. I always remember things better when I form the memory around something I already know and understand, so Mohamed's presentation stood out to me after he made the concepts relatable to us as students and educators.
        I also enjoyed Nicole's presentation. She related the Fibonacci equation to the real life Parthenon. This task was challenging and hard to understand, but created a great learning environment. She explained the equation in a very understandable way, and I think if I am teaching that concept I will think back and use some of her ideas. Real life examples stick out in any students memory much more than memorizing an equation will.

"The Parthenon and Phi: The Golden Rule" (2016). Retrieved from Google Images. http://www.goldennumber.net/parthenon-phi-golden-ratio/

      One of the other concepts we discussed was teaching students who are learning or have learned English as a second language. This was very useful and can be applied to any subject area. I love when we discuss problems like this because it feels like very relatable information that I can see myself using out in the classroom. We discussed the challenges that come with teaching ESL students, but also were provided with strategies to consider. I have worked with a few students while volunteering that are ESL learners. I found that cues and gestures worked best for me, as I am already one of those people who talks with their hands. One of the things that stood out to me most of all was the idea of a language directory/ personal language dictionary. I loved loved loved this idea! I cannot wait to try it out. I may even apply it to an English class and make them all do it, regardless of their first language. The idea of students keeping a book that they write words they do not understand, may have heard in a different context, do not really know what it means, feel like they need to engage with it more is so exciting. I think it would be really beneficial to do.

"Lesson Plan ClipArt" 

      So far, I have found the hardest part of planning a lesson to be getting started. I feel like I do not know where to start. I have seen these great ideas, and understand the curriculum documents, and have started to become familiar with the process as a whole, but I still feel unsure about where to begin. It is a very intimidating process, because it comes with a lot of responsibility, and I want to do right by my students. The terminology in lesson plans has also been challenging to distinguish. We have gone over it once in our practicum class, but I still do not feel like I have a clear understanding of the terminology. I am also struggling through picking out curriculum specific and overall expectations, but am learning that and feel like I have clear expectations on that part.
        To make lessons learner-centered I plan on considering my students first when planning a lesson. I will make sure to be critical of ideas and think about my students when deciding whether they will work or not. At its core, lesson planning should first and foremost consider the effectiveness of teaching to these particular students. One cannot just take a generalized lesson plan and apply it to all students because not all students learn the same way. I hope to take each student into consideration when planning lessons.