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Sunday, November 24, 2019

Week #11 Blog

Math is More than Numbers!

Bittersweet Endings

Hello everyone,

Can you believe that the end of the semester is next week already? Because I definitely can't. When first beginning the semester, I was deterred by the idea of "making math meaningful". However, as time went on, I realized that making ALL subjects meaningful is essential for students to successfully learn. Over the last 10 weeks of this math class, we have learned a great deal on how to teach and how not to teach in our upcoming future placements.



For this class in particular, I found that participating in the weekly learning activity presentations were beneficial for learning strategies. Specifically, I will reflect on these to assist in my future teaching practices. For example, it was interesting to see the different ways that each of my fellow teacher candidates presented their math activity in terms of the actual activity. Every student provided a handout/worksheet, while some students used manipulative's, others took their own spin on the activity, and a few people tried connecting their activity to real-world connections. For instance, last week during the presentation on Data Management and Probability, Daniel mentioned a few different types of "real life probability", such as the weather, sports strategies, insurance options, politics, games and recreational activities, and others.




How Is Math Used in Daily Life?

When growing up I found it extremely challenging to make real-life connections with the math concepts being taught. Now, I have learned there are a variety of ways to use math daily in improving important life skills. Recently, I have tried incorporating math into language, problem-solving, spatial, way-finding, memory, financial, and critical thinking skills.


Problem Solving Skills
As we have learned in the past 10 weeks of class, problem-solving skills is a highly stressed concept for the process expectations in math. As stated in the Ontario Curriculum, “is the primary focus and goal of mathematics in the real world; increases opportunities for the use of critical-thinking skills; and allows students to use the knowledge they bring to school and helps them connect mathematics with situations outside the classroom” (2005, pg. 12). Additionally, these problem-solving skills are used in most word problems that require a combination of simple mathematical operations. With this being said, students are anticipated to think through these problems carefully. When this happens, students incorporate these newly learned concepts to apply them carefully to approach problems from a variety of perspectives” (Mathnasium, 2018).

Language Skills
I remember in high school how challenging mathematics was as a subject, especially with learning complex calculations and manipulating numbers. I always had difficulties completing algebraic expressions, calculus equations, and advanced functions. However, while learning the process of math at an academic and university level, I realized there are valuable language skills being implemented. For example, students are expected to read through a word problem or are to listen to the teacher while they explain solutions for each equation, with specific steps to get there. With this, students are constantly improving their language skills in essential ways.

Spatial Skills
For as young as I can remember, my mother emphasized the importance of learning basic spatial skills. As I continued to grow up, she was always on my back about how essential this aspect of math is. Mathnasium states that “with appropriate instruction, students can better recognize the sequences, understand how objects fit into and move in space, and comprehend spatial relationships between people and things” (2018).

Way-Finding Skills
Personally, I know that my way-finding skills are above average. I find this ironic because mathematical instructions play a significant role in students developing their practical abilities and go hand-in-hand with spatial thinking. In terms of math, students naturally enhance their way-finding skills through navigation. When improving these skills of navigating through buildings or cities, it requires them to learn about directions and distances at the same time (Mathnasium, 2018). For myself, I have always been trusted with giving instructions and following directions, especially without using a map.

Memory Skills
Math has been known to help with a variety of critical memory skills, specifically supporting the development of auditory and sensory memory. As concepts of certain strands are taught each year, students are given problems which assist in procedural memory and rule-based memory, through standard formulas and calculations. Additionally, when students begin to understand visual and numerical patterns, they start developing pattern recognition (Mathnasium, 2018). Overall, these types of math concepts are advantageous for enhancing short term and long term memory, and will be significant in future situations that deal with calculations and formulas.

Financial Skills
In my opinion, it is common knowledge that math is helpful when learning basic financial skills. Unfortunately, some individuals have troubles transferring mathematical concepts over when learning about finances. Although I struggle in a majority of math subjects, such as algebra, calculus, and functions, I am thankful for my impressive data management and probability skills, especially when dealing with statistics and finances. Additionally, financial skills are probably used the most in life daily. For instance, elementary students apply their skills to determine sales, such as the total amount on a receipt, subtracting the amount owed to determine the final change that is due. As students age, in middle and high school, they learn more complex equations, such as calculating interests for savings accounts. I currently use my financial skills to create budgets, calculate my expenses and revenue and set financial goals while attending university.

Critical Thinking Skills
Finally, critical thinking skills is probably the most important concept for life in general. Critical thinking is used everyday for a variety of situations that is required for problem solving on the go, especially with analyzing complicated problems. Students are expected to use these skills in thinking independently and making reasonable choices. In relation to math, students are taught mathematical concepts in thinking abstractly and symbolically, which is important for critical thinking. Overall, with developing critical thinking skills, people are able to assess risks more effectively, which leads to better decision making in their professional careers in the future (Mathnasium, 2018).


Resources:
Mathnasium (June 08, 2018), Math is More than Numbers. Retrieved from https://www.mathnasium.com/2018/01/math-is-more-than-numbers

Ontario Ministry of Education (2005). The Ontario Curriculum, Grades 1 to 8: Mathematics. Retrieved from http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

Monday, November 11, 2019

Week #9 Blog

How to Make Math Meaningful!

Hi everyone,

What an exciting time of the year, Halloween has passed and Christmas is about 5 weeks away! Keep pushing, you can do this. 


What is geometry and spatial sense? 


Last week our class learned about geometry and spatial sense. This is one of my favourite strands of mathematics because of the interconnectedness of curriculum context to the world. 

Spatial sense is known as "the intuitive awareness of one’s surroundings and the objects in them, while geometry helps us represent and describe objects and their interrelationships in space" (OME, 2005, pg. 10). With this, I learned that spatial reasoning is a key concept in mathematics that is essential when making real-world connections. Students should be able to apply spatial sense to many aspects of life, such as navigating, orienting, manipulating objects, creating or designing objects, moving one's body in space, and many other area's (Ministry of Education, 2014, pg. 4). 

(Melson, 2018). 

Spatial sense is a key concept of mathematics that is required for careers in science, technology, engineering and mathematics (STEM). Now, the acronym STEM has changed to incorporate an A as in arts, to make it S.T.E.A.M. Moreover, spatial sense is just as important in other areas of field work, such as architecture, graphic design, computer science, biology, physics, chemistry, geology, geography, and even medical sciences. Therefore, as an educator, teaching spatial sense is not only necessary for meeting curriculum expectations, however, it is an important concept that is considered a predictor of success in life.

Image result for 2-d and 3-d shapes
Amazon, n.d.

How is this important?

Well, as previously learned about, geometry and spatial sense are important mathematical concepts to consider when looking at 2-D and 3-D shapes. When making real-world connections we see geometry and spatial sense in many aspects of our lives. As already mentioned, geometry can be seen in art, architecture, astronomy and physics, and even geographic information systems (Mehta, 2018). 

Geometry & Spatial Sense in the Classroom

Recently, in my placement, we used geometry to determine coordinates on a graph that made up a shape (i.e., rectangle, square, triangle, irregular shapes, and others). These made all the shapes come together to make a Halloween character. Not only does this type of activity involve geometry and spatial sense however, number sense is important for understanding the values given, measurement is important in being able to count how many squares you need to go horizontally or vertically when given a coordinate point, and patterning and algebra is used to identify and determine patterns in shapes, designs and movements. Additionally, in the junior grades, students are expected to use graphs, as the class did for this activity. The example that was used from class is attached below.

Teachers Pay Teachers, n.d.

This activity was quite enjoyable for the students, and they learned about mathematics in the process. This activity was found on the website Teachers Pay Teachers, which is a valuable resource when trying to find other handouts that help develop students learning while keeping them interested. Also, when taking a look at the website, I found handouts for Christmas too that could be useful when the time comes, as well as fun to participate in. Overall, I really liked helping the students with this math activity because they were extremely engaged and could barely put down the work when asked too. 

Image result for phone with question mark

Where is My Phone Charger?

During one of the classes, a specific presentation stood out to me because of the opportunity the student took to put a spin on the learning activity. Instead of taking the activity straight from the textbook Making Math Meaningful, this student used the activity and added a component of real-life applications, for students to make connections. The activity consisted of using geometric transformation, reflection, rotation, and translation to find a "shape" that was considered the missing phone charger. This activity was interesting, interactive, and made math meaningful in a sense that the students could relate and apply it, well done. 

Finally, I am looking forward to the rest of the semester and cannot wait to implement my learning from this class into my future teaching practices.


Resources:
Amazon (n.d.). 2D & 3D Shapes-Educational Poster. Retrieved fromhttps://www.amazon.co.uk/2D-3D-Shapes-Educational-Poster/dp/B000PHB2GY

Mehta, M. (October 4, 2018). Bytes: Use of Geometry in Daily Life. Retrieved from https://www.toppr.com/bytes/geometry-in-daily-life/

Melson, K. (2018, February 11). KTSM:Young Women’s STEAM Academy hosts open houses for prospective students. Retrieved from https://www.ktsm.com/news/young-womens-steam-academy-hosts-open-houses-for-prospective-students/
Ministry of Education (2014). Paying Attention to Spatial Reasoning: K-12. Retrieved from http://www.edu.gov.on.ca/eng/literacynumeracy/lnspayingattention.pdf

Ontario Ministry of Education (2005). The Ontario Curriculum Grades 1-8: Mathematics. Retrieved from http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

Teachers Pay Teachers (n.d.). Halloween Math Coordinate Graphing Pictures Ordered Pairs - Halloween Activities. Retrieved from https://www.teacherspayteachers.com/Product/Halloween-Math-Coordinate-Graphing-Pictures-Ordered-Pairs-Halloween-Activities-1469797