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

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.

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. 

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

Week #7 Blog

Hello everyone, and welcome back!

It is crazy to think that we are basically half-way through the semester and course. This is just a constant reminder that soon enough we will be in our placements teaching mathematics to elementary school children, which is nerve-racking. Although this makes me worried, every class is an opportunity to improve in the subject while reminding myself that I must have an open-mind to contribute to a positive growth mindset.

 

The Hidden Opponent, 2019

Previously, in last week's class we learned about number sense and numeration - proportional thinking/reasoning, which were explained during learning activity presentations. These presentations were extremely relatable and applicable to real life situations, specifically while discussing the importance of rates, ratios and percentages. During the presentations, fellow teacher candidates related mathematical concepts to recipes, maps, driving, money and other. 

This is important when connecting to the math curriculum because under Number Sense and Numeration, students must have a "general understanding of number and operations as well as the ability to apply this understanding in flexible ways to make mathematical judgements and to develop useful strategies for solving problems" (Ministry of Education, 2005, pg. 8). With this being said, math is important in all aspects of life because of the ability to use every day in the real-world. As for educational purposes, teachers have an ability to show students that these math applications are essential and important in life, and will most likely help engage students when being taught.

[2] Ontario Ministry of Education, 2005.

This week during class, we learned about Integers. During the learning activity presentations, a variety of manipulative's were used, such as money (i.e., quarters), number lines, and a deck of cards. When participating in the activities, it was our job to better understand integers, their importance and how they are incorporated in our lives daily. For example, one of the presenters mentioned that integers are seen in golf scores, temperatures, money, sea levels, and many others. 

iPractice Math, 2013. 

Moreover, a fact that I learned that I didn't know before was whole numbers can be integers, but integers aren't always whole numbers. Additionally, discussed was how there is a rule that "two negatives don't necessarily make a positive". We used number lines to determine this theory, specifically when looking at adding, subtracting, dividing and multiplying integers. Specifically, when taking two negatives, there is still a possibility of it adding up to stay negative. I.e., -10 + -5 = -15. When talking with my group and participating in the activity, it was always clear and evident to us that this was the rule. However, we can't remember why this is and we weren't sure the reasoning behind it. 

Online Math Learning, 2018. 

Finally, as mentioned earlier, I have learned from other students the importance of keeping an open mindset. Each interaction with students and the experiences with mathematical concepts are learning opportunities that assists in the development as a teacher. Overall, I have realized that I am always learning, as a student and as a teacher. Therefore, the key take away from this week is that learning from other students is essential in my future teaching practices, whether that be elementary or fellow classmates. This is to help set my students up for success, which can be done by making real-world connections that are related to mathematics. 

References:
EduGains (November 18, 2010). Big Ideas Questioning K-12: Proportional Reasoning. Retrieved from http://www.edugains.ca/resources/LearningMaterials/ContinuumConnection/BigIdeasQuestioning_ProportionalReasoning.pdf

iPracticeMath (November 25, 2013). Integers in real life. Retrieved from https://blog.ipracticemath.com/2013/11/25/integers-in-real-life/

OnlineMathLearning (2018). Integer Rules Song. Retrieved from https://www.onlinemathlearning.com/integer-rules.html

[1] 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

[2] Ontario Ministry of Education (2005). TIPS4RM Continuum and connections proportional reasoning. Ontario: Education Ministry. Retrieved from http://www.edu.gov.on.ca/eng/studentsuccess/lms/files/tips4rm/TIPS4RMccpropreason.pdf

The Hidden Opponent (2019). Instagram. Retrieved from https://www.instagram.com/p/B35I3T1Hfln/

Week #5 Blog

Week 5 already? Boy does time ever fly when you are having fun! 

After sitting through this week's class I felt refreshed and updated with concepts in mathematics that I hadn't focused on or thought about for quite a while. During the first few weeks of class, I was a bit nervous about the semester, especially when thinking about the math "assignments". I was definitely overwhelmed with how the course load was organized, but have settled in, and am now starting to relax. Lately, I've realized that the most important aspect of teaching is how students learn in their classrooms and the different/varying abilities. Rather than how we are going to teach the students, how do the students learn best? Although I am still uneasy and uncomfortable teaching math concepts to students, I am keeping an open mind and making sure to stay engaged during both my math class and at placement, to learn the best strategies and methods in the best interest of students' learning. 

JUMP2MATH (2019).

For example, during the four learning activity presentations we explored different ways to learn and practice fractions. I was intrigued by how Sarah used geometric manipulative's because not only did I feel engaged to complete the lesson however, it brought back memories from elementary school. Also, I enjoyed John's cross-curricular lesson plan activity that included using a musical representation in regards to learning fractions as music notes. Although I do not have a music background or am familiar with how notes are used as fractions, I found the knowledge that he provided was helpful and informative. Overall, fractions are an important concept of number sense and numeration for everyone to know in order to solve problems that occur in daily, in real-life situations (MOE, 2005, pg. 88-89). 

For the past two weeks, we have started getting into placements. I am at a public school with a grade 4/5 split. The varying level of abilities in math is interesting and surprising as I observe. I found that a majority of students don't quite understand mathematical concepts. However, when students are attempting questions that the teacher provided them with I see different and individual strategies, which is helpful for me to comprehend the student's abilities for future practices. Also, this experience is rewarding because I get to interact with students and attempt to help them with math, which for once I can do. This makes me remember and reflect that my growth mindset is continuously and positively changing, as well as and preparing me for the future. 

Adapted from Carol Dweck, Mindset: The New Psychology of Success (2014). 

When connecting all of the courses from school, a growth mindset has been discussed by many professors. I find that I have a great growth mindset because I have always been open to challenges and trying to build my life experiences to be successful. When it comes to math I try to remember that it's not always going to be easy. Although there are some components of math concepts that I struggle with, I try my hardest to work through the problem even when I am having trouble. The main goal is to continue being positive through my journey and believe in myself. Finally, words of advice in building a growth mindset:

1. Learn from your mistakes
2. Effort is essential
3. Setbacks are apart of life, especially when TRYING to LEARN
4. Have an open mind, to allow for critical and constructive feedback 
5. Embrace your outcomes and failures; this is an opportunity to learn and grow
6. Work hard - always!

Resources:
Dweck, C. (October 9, 2014). YouTube: Developing a Growth Mindset with Carol Dweck. Retrieved from https://www.youtube.com/watch?v=hiiEeMN7vbQ&app=desktop and Cohort: EDBE 8F01 Teaching in the Ontario Context. 

Jump2Math. (2019). Math Shop. Retrieved from https://jump2math.ca/product/pizza-fraction-floor-graphics/

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

Week #3 Blog

Hello everyone.

Hopefully I can refresh everyone about what we learned last week (Week 2), and the variety of different math aspects that I'm going to reflect on.

One concept that I am becoming more familiar with is the two strands of education for content expectations, which are overall expectations and specific expectations (OME, 2005, pg. 7). After attending some of my other classes I have noticed that overall expectations and specific expectations are used in a majority of subjects with very similar concepts. Additionally, in mathematics, there are strands of subgroups taught to students throughout the primary and junior grades. These strands include number sense and numeration, measurement, geometry and spatial sense, patterning and algebra, as well as data management and probability (OME, 2005, pgs. 8-10). The purposes of the strands are to help focus on specific aspects of knowledge and skills and are taught and assessed to help further develop the students learning. With this being said, students are expected to explain and show a high level of understanding concepts through problem-solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating (OME, 2005, pgs. 12-17).

When looking back to our first-class, professor Forbes discussed how students need to be proactive as opposed to reactive when it comes to learning new subjects, especially math. This is because students tend to view math negatively if they are having trouble learning a new concept or have been discouraged in the past. Also, professor Forbes addressed that everyone has certain strengths and weaknesses, which is okay. But that the most important aspect of learning is to have the courage to take on new challenges with an open mind and be adaptable.

In my opinion, my strength when it comes to mathematics is problem-solving. However,  I know my greatest weakness is selecting tools and computational strategies, improving these would help me to become more successful in mathematics. During this course I will be keeping an open mind to develop a growth mindset, to improve my ability to learn computational strategies and use them in a future teaching setting.

As I reflect, I think about how excited I am for the entirety of this course. Math was a subject that I enjoyed learning in elementary and high school more than the other subjects that were taught. However, I found that my teachers also made it fun while incorporating ways to enhance student's learning. Moreover, during the last class, I was more engaged than in the first week due to the excitement of Jeopardy. I felt that utilizing this tool was informative and a clever way to teach some mathematics concepts. When I become a teacher I will look back at the enjoyable moments I had as a student during math and the array of feelings I had while participating in the different types of games. Therefore, I would like to use these ideas in future educational practices to teach students important mathematical concepts, while at the same time making learning meaningful and fun.

Resources:
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

Welcome Post

Hello everyone!

Here is my first post for the welcoming week so that my you as my classmates can get to know me better.

My name is Mackenzie Robinson and I am a teacher candidate in the consecutive junior/intermediate stream at Brock University. I previously did my undergraduate degree at Laurentian University in the Bachelor of Sport and Physical Education program, receiving my Bachelor of Physical and Health Education. My first teachable is physical education and I have a second teachable in science.

I am from Collingwood, Ontario. I have a love for nature and spend a great deal of time outside hiking, traveling, and reading. Luckily, I am 10 minutes away from Blue Mountain where I participate in a lot of physical activity in both the summer and winter. Also, I have been playing many sports since I was young. I grew up playing basketball, baseball, volleyball, rugby, and swimming. While attending Laurentian I was grateful to be a member of the varsity women's basketball team for all four years of my undergrad and even winning the Pride and Tradition Award and Most Valuable Player, as well as the Ontario University Athletics- Tracy MacLeod award for perseverance, determination, and unwavering spirit.

As for the two blog posts that caught my attention, they are: Engineering a Better Engineering Student and How I went from High-school Slacker to Passionate College Student. These first blog was appealing for me because I learned that many high school students who dream of becoming engineers don't. According to the blog about a third of students who enter into the engineering program fail out. The major problem for failing is because those students have a limited knowledge of mathematics, specifically calculus, which is actually required for a majority of classes (Hopkins et al., 2016). Interestingly, when reading further in depth, the author talks about how he completed a scientific study using an experimental group vs. a control group in a precalculus class to determine if manipulating the spacing of quiz questions vs. massed over a 4 week period, will it influence a students learning capability? Overall, after reading this blog I was surprised at how testing methods can contribute to the performance of individuals and how many engineering students fail because they are unable to pass calculus. I am fascinated to know and possibly research more into how math subjects, such as calculus, algebra, and functions correlate with and are applied to science concepts.

The second blog was also appealing to me because I was curious to read more on how someone went from being unmotivated and slacking as a student to a hard working and determined "new" type of student. I connected with this article in a sense because of how one person can influence future decisions. Throughout my entire education from kindergarten till even now, I have had one individual in particular who was my teacher and coach, and has had a positive influence on my life, specifically as a student. It was interesting to read that the author of the blog started with a mindset of being a waitress, to working at a gym and deciding to apply to school, getting a scholarship for college and then applying to university for a bachelor degree and changing the course of her studies. This person never gave up and continued learning even when she could have just kept her regular job.

Finally, for this course I am really looking forward to re-learning new concepts that I will be able to teach my students in the future. Personally, I feel that this course will be the most intriguing course that I am taking because of the engagement that will take place for a majority of the projects. I am extremely interested in completing the learning activity presentation, where I will be choosing a strand in the mathematical curriculum and lead my peers through a 10 minute learning activity.

Good luck to everyone this semester and in their classes!