W33K [(-3) + (-2)] x (-1)

Hey Math Friends!

Welcome back to my math blog! This week was an even busier one for me. In our math class we had to work on a math assignment that required us to review the Ontario Math Curriculum in order to observe and analyze student volunteers. The activity had us focus on math content expectations, i.e) analyzing equivalent fractions and probabilities, and specific math processes that students are required to have while working on their math problems. Math processes are ways in which we deconstruct a problem and arrive to an answer and examples include connecting, problem-solving and reflecting. Additionally, this week we explored integers and our teacher candidate presenters had some excellent activities for us. I will also be sharing my two favourites!

Ryan McGilchrist. (2008, March 26). EQAO [Image]. Retrieved from https://www.flickr.com/photos/shinealight/2371533586

Our EQAO Deconstruction Assignment

My math assignment this week was based on a Grade 6 EQAO sample problem. This assignment took a lot of critical thinking and analyzing. I had to make sure that I understood the curriculum expectations in Grade 6 and I needed to dig deep into my own understanding of mathematical processes as I first worked through the problems my self. It was challenging for me to identify exactly what I was doing and why I was doing it, as opposed to just writing out an answer as I usually do. After I analyzed myself, I was able to apply what I learned about the mathematical processes and analyze my two students as they completed the questions. The students were members of my family and it wasn't surprising that we all used very similar processes and ways of getting to the answer. This assignment allowed me to learn that as a math teacher, we all come from different backgrounds and we all have different schemas. This means that teachers need to be aware of the diverse student minds in their classroom and cater their lessons and math problems accordingly! It was a great assignment and this made me think about my role as a math teacher in the junior-intermediate classroom one day.

Integers

This week in class, we moved away from fractions and began exploring integers! Integers in the Ontario Curriculum are introduced in Grade 7 and are built upon in Grade 8. We had some excellent presentations and activities this week. For my group's activity, we had a worksheet where we referred to a number line and a small lesson on integers before starting our questions. I would definitely incorporate a small lesson into my worksheets to help guide my students, especially for more abstract concepts like integers. This worksheet had critical thinking questions and was for independent work! I also really enjoyed another activity that consisted of solving a magic square where the diagonal row was given and thus every column must add to (+2). I liked this activity because it reminded me of sudoku! Lastly, we played a fun integers game called Orbit Integers on Arcademics. This game helped me pick up my speed when answering basic integers questions!

That's it for this week friends. Join me again s0000000000n!

Teddy

Richard Stephenson. (2012, June 25). Numbers below zero [Image]. Retrieved from https://www.flickr.com/photos/richardstep/7438001520

W33K (2+2)

Hello math friends!

Eric Gjerde. (2006, February 23). Pentagonal tiling ideas [Image]. Retrieved from https://www.flickr.com/photos/origomi/103452651

It has been around a week since I've last posted and I do have some interesting updates! In this post, I will focus on two things. First of all, I'll talk about how the video I shared on my last post has impacted me and how I am applying what I've learned every single day. Secondly, I will be talking about what we've done in math class this week and I will be discussing my fractions presentation. Hope you enjoy this week's post!
     

Class Connections

Now, I would like to start things of by mentioning how math this past week has been super engaging for me. I have been seeing math everywhere since I watched the interesting video that I shared with you in my last post! I'm trying to work my brain these days and visualize mathematics so that I can develop my spatial reasoning. I will have to admit that I am not the most talented when it comes to understanding how objects relate to each other in the 3D space and working on it over the past few days has been interesting! An example of me using this practice would have been during my placement with my associate teacher. She had prepared an activity where students were looking at several circles that were divided by 4, having some of those quarters coloured in purple. The question she asked was for the class to calculate how many purple circles could be made in total. I tried not to count them and started moving the shapes together in my head to get the right answer! It was a Grade 4/5 math question, however, I was happy that I chose to visualize the problem instead of use an algorithm! I can't wait to find my self in another situation where I can fine-tune my spatial reasoning and improve my overall three dimensional insight! I'll definitely keep you posted, math friends.

Fractions Activities

As I also mentioned, this past week in math was when I had the chance to present my fraction's lesson to the math class. It was indeed fractions week and we had a total of 4 teacher candidates present their lessons to small class groups. The goal of the activity was to choose an appropriate lesson from one of our math resource books and present it to our class as if we were doing this activity with junior or intermediate students. The activity I chose was titled, "Dot Paper Equivalencies (3.12)" from the book Van De Walle, J. & Lovin, L. H. (2006). Teaching Student-Centred Mathematics: Grades 5-8. Toronto, Pearson. This activity was primarily catered to Grades 4-5 students and it explored equivalent fractions using an isometric grid paper. Since I was very inspired by spatial reasoning last week, I made sure to choose an activity that used conceptualization and algorithms. I asked my students to draw a symmetrical shape on the grid, divide that grid into either 1/2, 1/3 etc. and being connecting the grid dots in that fractioned area. Then, students began to see how many times they could divide that space using equivalent fractions! So, for example, 1/2 could look like 2/4 then it could look like 4/8 and so forth. I believe the students got to a denominator in the hundreds! I really appreciated how you can both visualize the fractions and use multiplication and division to get to the answers. Overall, I think that the activity went well! My classmates also had excellent lessons. They included matching decimals and fractions together, rolling dice to make 2 fractions then performing an operation to get to a specific answer and lastly comparing fractions to each other.

Next week, I will try to look for more digital photo math problems because applying math in real life scenarios always engages me! Also, I will continue to work on my spatial reasoning game!
By3 4 n0w!

Teddy

W33k 3!

No attribution required. 

Hey Math Friends,

Welcome back to my blog! I would like to start by pointing out that interesting image because it ties in with this week's math concept. The image is that of an x-ray like picture of a human brain with math symbols surrounding it. To me this image represents how using math picturing math as symbols engages our brains at a deep level. This is precisely what we focused on in our math classes this week.

Math and Science (and Your Brain)

As a class we watched a short and interesting video on how connections form in the brain due to the stimulation that occurs when we are practicing math. Check it out in the link above! Additionally, Small (2016) states that, "more and more there is an understanding that students can and should deal with meaningful mathematical situations even if they are complex. Brain research (Caine and Caine, 1991) has established that multiple complex and concrete representations are essential for meaningful learning".

We learned that when students can perform math tasks, they are predominantly activating their right-brain. This is due to the fact that math is content heavy and requires logical thinking and a step process along with an eventual correct answer. Right-brain students perform well in math because they can perform well on math assessments that are naturally more rigid. Now, the interesting aspect is when students begin to activate both hemispheres of their brain and begin using their left brain when solving math problems! When students think about numbers in an abstract manner as symbols and then actually visualize numbers, graphs, processes, this engages the left-brain and makes the entire brain active and engaged!

Since I am a biology major, I love this kind of research and would like to quickly comment on what exactly happens in the brain. According to scientific research, the brain activates and creates pathways that cross between hemispheres and those pathways encompass the entire brain rather than one hemisphere at a time. This is how students learn math the most thoughtfully and carefully. Using the idea of symbolic integration into math is the most powerful form of math learning! For example, students can use their imagination and symbolize math strands like fractions and even algebra! The basic and key steps are to visualize, draw and estimate! The more creative the student gets, the better it will be for their math learning process!

This was a pivotal lecture and video for me personally. I cannot wait to try using this technique more in my own math inquiries and I cannot wait to incorporate them into a classroom! I believe students will be hesitant at first because the task of visualizing numbers and abstract math concepts might be daunting. I completely understand! I will actively try to find resources regarding how exactly students can begin to grasp this idea and use what they learn and like for their own benefits. For now I found a blog that has some interesting 3D and animation visuals at:
http://visualizingmath.tumblr.com/tagged/visualizingmath!
It is definitely a good start and I will look for more tutorial-like resources that can couch the mind of students!

I cannot wait to see how learning this great research-based technique will improve my own math skills and the math skills I will aim to instil in students! I'll keep you posted, that's for sure.

S33 y0u s00n!

Teddy

Wh4t'5 Up Th15 W33k?

Hey Math Lovers,

The Ontario Math Curriculum

This week was the first time that my class and I had started discussing actual Ontario Curriculum strands in math. We also talked about some great ways to approach math problems and we consulted points of a "problem solving attitude". Examples we touched on included Polya's problem solving processes such as understanding a problem, making a plan, carrying out that plan and reflecting on what went right and wrong. I found this very beneficial to my understanding of math because sometimes I even neglect this way of thinking!

My Thoughts About Math at the Moment

I have to admit that when I see a math problem I obsess over getting the right answer.

I am really opening my eyes and seeing that what I have already learned and have been taught is something that teachers are trying to counterbalance in modern classrooms. As I said in my last post, we are focusing on the process rather than getting the right answer, which is something I was totally guilty of doing! This concept ties in with the article by Ball and Bass titled, "Toward a Practice-based Theory of Mathematical Knowledge for Thinking" where the authors emphasize that although knowing the content as a math teacher is important, how teachers lead lessons and facilitate learning proves to be more beneficial towards students' overall knowledge.

Class Activities

We did an interesting activity in class where we had a problem and we were asked how many ways we can come up with its solution. It was interesting to actually see how many interpretations of the problem my classmates had. Additionally, it was interesting to note that we began to really engage in the process of thinking and problem solving rather than getting to the answer quickly, even though we had already figured it out.  Sometimes it is hard to stem away from the way that you’re used to getting to an answer and this helped me especially, slow down and really think about what was going on. I believe that the way the curriculum is shifting is beneficial because students will develop a fundamental basis of logic and problem solving skills. Sometimes in a traditional math class setting, students feel too much pressure to perform at a high standard, because usually the more correct answers they get, the better grades they are given, so they might acquire performance anxiety so to speak. 

Kelley Stirling. (2016, November 2). Cool looking calculator [Photograph]. Retrieved from http://www.navsea.navy.mil/Media/Images/igphoto/2001665557/

Even with this changing process of math in classrooms, at this moment I still believe that we need to have a mixed system of traditional and contemporary math strategies. I do believe there should be less emphasis on getting the correct answer, however, I still believe eventually getting the right answer is still an important assessment of math comprehension. To support my thought, I raise this question: How will any of life’s important mathematical issues have been solved without getting the correct answer? If students are left with too much freedom, I believe mathematics as a strand in the curriculum might collapse on itself and we will miss the entire point of why we have and need math in our lives!

L0v3,

Teodora

W31c0m3!

Hello Readers!

Welcome to my math blog. Here, I will be chronicling my math adventures!
I decided to take a different approach to my title and incorporate numbers in place of the letters! This way, I truly hope that you, the reader, had some fun with decoding the words. I am sure everyone had no problem with that. Looks like you are quite the math-wiz already!

My goals with this blog are to highlight how learning math can be fun and rewarding. I hope to have a new tip or technique each week and I hope to spread some positivity to apprehensive math minds all over!

Over the course of learning that I'll be doing for my Teacher's College math courses, I really hope to learn new skills and new approaches to teaching math to students. This means that we are moving away from a 'get-the-right-answer'-centred math class to an 'it's-all-in-the-process'-centred math class. We will slow down and focus on the steps and logic behind math problems, rather than the search for an instant and right answer.

Doesn't that sound great? A new world where we can take our time and not have to focus on getting the answer correct right away? I hope that eases some nerves already!

Let's all participate in this movement, help each other in difficult times and get to solving some awesome math problems!

Yours Truly,

Teodora

Teddy's Avatar. August 31st, 2017. Created using PicaFace.