My Weekly Report and Reflection #6:

     After looking back on this math course, I have learned a lot of from all of the instructional forums, and blogs. Unfortunately I learned more from these online-based assignments, than the traditional lecture-based format of learning. This truly shows that there is now a "21st Century" based learning process that is being instilled within not only today's youth, but also my generation as well. The picture below relates to the 21st century based learning in today's society. 

Image retrieved from: http://21stfair2010.wikispaces.com/file/view/whiteboards.jpg/163632339/396x258/whiteboards.jpg

     In the last class, my partner and I had the opportunity to deliver a 30 minute presentation, with regards to "financial literacy". The purpose of this lesson was to facilitate a beneficial lesson to my peers to explore a topic that was not "traditionally" taught within  the Math curriculum. What my partner and I decided to deliver was a "real-life" application of financial literacy. This lesson was based around real-life financial literacy such as "money management, life planning, and setting life goals". Reflecting back on this lesson, I should have delivered a more interactive lesson, relying more on the interactive sections within the lesson. 

     Three important things that I have learned from these Online Modules include:

1. Math is a universal language
2. There is no such thing as a "Math Person"
3. A growth mindset is the best mind set to have (making mistakes, makes the brain grow) 

     Math overall is something that you practice throughout your life, and people should not be discouraged from continuing to learn math. Everything we do in life, somehow involves math and we should always be looking to expand our math understandings. One idea that stuck with me throughout this course was, "there is no such thing as a math person". Anyone can learn math, they just need to be willing enough to put in the time to properly understand the big ideas when it comes to Math. Last but not least, a growth mindset is essential for understanding Math. The interesting fact with this statement is that making mistakes actually helps our brains grow, and makes us become a more reflective math practitioner. The video below just consolidates the idea that Math is a "Universal Language". 

     

     Throughout the lesson, we participated in different lessons that go over the different instructional applications of the math strands:

• Number Sense and Numeration
• Measurement
• Geometry and Spatial Sense
• Patterning and Algebra
• Data Management and Probability 

All of these strands can include a 21st century approach to learning, integrating technology within the classroom. One of the effective ways I saw this done was integrating the use of an iPad within the classroom as an instructional tool. The students can go on an app on the iPad and answer questions with regards to different Math problems. Math is an ongoing skill that needs to be constantly reflected on and improved upon in order to ensure life-long learning of math. 

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My Weekly Report and Reflection #5

    This week, there was a clear connection to the online resources (visual aids) and manipulations while answering mathematical problems. During class time, we went through a lot of online mathematical resources such as GeoGebra, that could be used within the classroom setting, giving students a visual, and a manipulation for algebraic problems. These students were able to manipulate the shape that they made with respect to the co-ordinate graph. If the students had to do this by hand, there would be no way for them to figure out the interior angles as quickly as this app does. The picture below represents the segments and shapes that you can manipulate using this resource.

Retieved from: https://www.geogebra.org/images/landingpage/landingpage-icons-tryout.png, on October 12, 2016

     During this class, we discussed a lot of different topics with regards to differentiation within the classroom, and methods to help students with memorization and mathematical equations. This lesson was extremely difficult for me to understand, because I understand mathematical problems with writing them out on paper, in order to make sense of them. With this UDL (universal design for learning), it often comes with a couple of road bumps. Some of these road bumps include, not taking into account all of the"outdated" ways of learning such as the old fashioned "pen-and-paper" method. Students who are used to having  a visual representation in front of them are now forced to make sense out of a diagram displayed on the overhead projector. Another possible road bump is not having access to technology within the classroom, and not singling any student out for not having a technological device.  

Retrieved from: https://z4zao2x5yv31zz19n46kfiid-wpengine.netdna-ssl.com/wp-content/uploads/2016/04/17125152.jpg, on October 12, 2016

      Overall, the main message behind this lesson, is that there are useful applications of using technology within the classroom to supplement your lesson. There are many other ways to answering math questions than the traditional "pen-and-paper method" and memorizing formulas. There is a huge variety of online resources that teachers can use in order to supplement their lessons. In no way should the lesson solely consist of JUST technology, but there should be a technological aspect included within the lesson to "spice" up the lesson so to speak. It will be interesting to figure out which resources work best within my teaching practice, allowing different students to gain a whole new perspective on answering math questions. 

My Weekly Report and Reflection #4

     This week's Math class had a lot of useful activities, understanding what interleaving was and how  it related to a rich performance task. All of the tasks we did within class required a "higher-level of learning" and reasoning, requiring the students to have a "growth mindset". Every task we did within class, was extremely rich and needed to be executed with a partner, which allowed every student to "talk" about the strategies that they used in order to answer the questions. In the previous forums, "talking about the strategies" is one of the most effective ways for students to not only learn themselves, but to learn from others as well. This strategy was very effective when introducing the concept of "Interleaving practice" into the curriculum. Interleaving practice means that students do not answer questions in a blocked format, but in a randomized format. Our instructor achieved this by having us go around the room, completing various "stations" that required us to think of different strategies in order to answer the questions. The Problem below goes over a mathematical solution to explain the concept of "growth" utilizing multiplication, addition, and problem solving skills.

Heartwell, 2016

     Another station that we were asked go go to was the "spiral" station, drawing flower like objects from using the tool below. An extension of this could be (Where could this technique be used in the real-world, or how many times does it take the pencil to go around a whole 360 degree rotation). This tool was extremely interesting to use and visualize the different colours that could be incorporated into this. This was an extremely rich performance task for the class to complete.

Heartwell, 2016 

     Rich Performance Tasks (RPT) require "open-ended and higher-order thinking" questions that need a thoughtful application of knowledge and skills in context. They establish authentic contexts that reflect the genuine application of knowledge, and students are motivated by "real-world" applications. RPT's when used in assessment enable teachers to gauge student understanding and proficiency with complex processes, not just measuring discrete knowledge. They are suited for the 21st century learner, weighing heavily on the 21st century skills such as, critical thinking, problem solving, collaboration, communication, and technology use. I experienced this when our teacher asked us to expand mixed fractions such as 3 1/4 and 2 5/6 and find the range between the two numbers. The teacher approached this question with decimals in mind, where I took a different approach and expanded these numbers. I found a common denominator and expanded, 68/24 to 78/24, any number between these numbers would fit. the teacher noticed this technique, and I had to explain to the class on the board. These problems intrigued me because I have a strong previous understanding of improper fractions. A real world application of this could be with lumber with buy a certain amount of lumber to cover the perimeter of a fence. These problems were a good way to address the 21st century learner skills, and should be incorporated within the classroom as readily as possible.