Year 2, Blog Post 6: EDBE 8P54 (Monday, 23 October 2017)

Good Day Bloggers!

Objective:

For this week, it is my objective for this blog post to present my responses to questions, ideas and information presented this week in the course EDBE 8P54 at Brock University! For our sixth week of Math 8P54, our class focused on blended teaching and learning, touching on forms of assessment. In our forum post, I watched a video about the connection of math to real life application made by both nature and animals. What a diverse learning week!

Blended Instruction: A Necessity for Engaging Mathematics 

For the first activity of the week, we focused on blended instruction tools we could use in our future classrooms to differentiate instruction! We first watched a video about blended learning, and then worked in groups to determine the basics of blended instruction. Following this, performed five minute presentations on our findings. I thought the practices were interesting, and I could see myself using some of these blended instruction tools in my future classroom. 

GeoGebra Activity: Using Software to Construct and Draw

While we did not yet get the chance to navigate the GeoGebra Site, we did watch our instructor explore how to use GeoGebra and constructing a square. I drew a personal connection from this activity to a software I had in grade ten drafting class called AutoCad. In this software, we made architectural designs, and explored methods of construction through the architectural tools. I really enjoyed this class, and I am glad that todays students have an opportunity to explore tools such as GeoGebra through making objects such as squares and examining the theory behind the constructs through application! I think this is a step in the right direction for students to take examples they can relate to and explore for themselves. 

Life Examples Beyond the Formula: A Forum Post? 

This short video relates math to real life application. Specifically, the formation of a snowflakes and spiderwebs. In the snowflake construct, each snowflake is unique, yet its water particles follow a similar hexagonal pattern. Spiders also use math intuitively, as they create their spiderwebs by first connecting two points, then as quickly as possible they form circles combining the webs to one another in a spiral motion. The spiral expands outward more quickly the more the spider weaves it.
I thought this video to be quite interesting, as it encompasses the use of math in both nature, and intuitively between humans and animals alike. Math is everywhere, can be connected to most anything, and in our future classrooms it is important to connect aspects like this to student learning. Building connections is so important in education, so why not allow students to see beyond the formula and connect to real life examples?

Math in Life

Final Thoughts:

In this week of mathematics study, I have learned concepts and tools associated to blended teaching and learning in mathematics, touching on forms of assessment. In the Forum, I watched a video about the connection of math to real life application made by both nature and animals, and realized the continued message being presented in our class. Without engaging thought, tying meaningful mathematic process to opportunities for connections through blended instruction, students can hardly be expected to have a positive attitude and look at the tasks at hand in a multi-representational manner. Students must have these experiences to continue connection outside of the classroom, and isn't it fascinating to allow students to be able to reflect on their connections through nature, animal mathematic intuition, and other topics they are passionate about?

Thats all for now Fellow Bloggers! Until next week :)

Year 2, Blog Post 5: EDBE 8P54 (Monday, 16 October 2017)

Good Day Bloggers!

Objective:

For this week, it is my objective for this blog post to present my responses to questions, ideas and information presented this week in the course EDBE 8P54 at Brock University! For our fifth week, our class was on reading week. However, we focused on our forums this week, consisting of making sense and intuition, drawing and representing, and ideas vs memorization.

Making Sense and Intuition = Engaging Mathematics 

In my forum post for this week, I spoke about the importance of making sense and using your intuition in mathematics, in order to gain a deeper understanding of the problem being solved. I realized how important it is to reflect on the mathematics questions being asked, and to apply other experiences to make sense of the problem at hand. In the video Making Sense in Math, the viewer is encouraged to make sense of the problem; to make/draw real-life connections to their learning, by using genuine intuition to solve the problem being addressed. In an interview with Sebastian Thrun, he said that with many of his projects, he becomes emotionally invested, drawing personal connections and engaging into the problem beyond the realm of formulas and equations. 

Making Sense and Intuition

Classroom Connection = Brighter Futures 

In our classrooms, we should strive to strengthen the idea of making connections, deeper thinking, and concept formulating; for students to become further engaged in the problems at hand. As educators, we play a huge role in determining this outcome, facilitating learning in an enjoyable way. Students are then able to look inward for a solution, and propose deeper understanding to the process. In my future classroom, I hope to implement this style of thinking in order for students to enjoy mathematics, and appreciate its functions in our everyday lives. 

Thats all for now Fellow Bloggers! Until next week :)

Year 2, Blog Post 4: EDBE 8P54 (Monday, 2 October 2017)

Good Day Bloggers!

Objective:

For this week, it is my objective for this blog post to present my responses to questions, ideas and information presented this week in the course EDBE 8P54 at Brock University! For our fourth week, our class focused on guidelines for producing rich mathematics tasks for students, continued our exploration of mathematics problems and student mindset, and through our forum posts identified the
importance of communicating our reasoning to our peers! In addition to this, my partner and I have created our webinar together. What a jam-packed week of learning!

Rich Task: A Necessity for Engaging Mathematics 

For the first activity of the week, we focused on a reading for rich tasks and mathematical process expectations! I would not have guessed that so many rich tasks would have so many different attributes that we could incorporate int he classroom. I realized that this portion was important to incorporate into my own classroom, as students need to be engaged, make meaningful connections to mathematics in a differentiated way to promote a growth mindset. One of the ways for differentiation was provided to us through means of an online game where the purpose of the game was to make a square out of the dots before our opponent. This game was both engaging to students, and helped some students learn about spacial awareness and producing shapes in a strategic manner. It also produced some frustration, as many students were not able to succeed in making a square before their counterpart, and I personally was only about to win one game of approximately twenty. Games like this hold an importance in our classes, as long as they are presented in a way that will promote mathematics growth. 

Exploring Problems: Engaging Students in Mathematics

To promote rich tasks in the classroom, we played games such as 'Which One', worked out the 'finger counting problem', and 'small number counts to 100'. I particularly enjoyed the Finger Counting Problem. In this mathematics problem, we as teacher candidates were assigned small groups to work out the problem on our hands, to count on our fingers from 1 to 100 and discuss which finger the number 100 landed on. We started on our pinky fingers, and moved one finger at a time to our thumbs (5) and then reversed our count (without counting the thumb twice), continuing this count to 100. As an educator, one thing I really liked about this problem was that students were drawing connections from something as simple as their hands, and performing a thought process that would have never been connected before this problem. As a class, we found that the answer to this problem was the pointer finger (finger beside the thumb) would equal 100. 

Reasoning, Communication, Oh My!

This problem was directly linked to my forum post this week, and this is why I chose to elaborate on it here in my blog post! In this short video shown below, number flexibility, mathematical reasoning, and the importance of learning and collaborating in mathematics was outlined. Professor Uri Treisman of Berkley performed a study on the high failure rate in mathematics class, finding that those students who were unsuccessful chose to work on math on their own, while those who were regularly engaged in mathematics discussion in and out of the classroom were able to surpass the majority of the students. In response to his research, students that had difficulty in mathematics were given the opportunity to join mathematics groups, and in a year, their performance dramatically improved. As educators, we can initiate these discussions, as well as incorporate an atmosphere in which students feel comfortable about the subject through the promotion of a growth mindset and differentiation in instruction.

Talking About Math

Final Thoughts:

In this week of mathematics study, I have learned the importance of communicating with others about mathematics to achieve better results for ourselves. As was outlined in last weeks blog, through this repetition (in this case talking about mathematics problems in every day discussion), students can drastically improve their knowledge and become more comfortable in the subject. We as educators have a huge role to play in this, as we are the ones who are initiating rich tasks with the objective to provide positive process expectations for our students. Without engaging thought, that ties into meaningful mathematic process grounded in problem solving and opportunities for connections through differentiation, students can hardly be expected to have a positive attitude and look at the tasks at hand in a multi-representational manner. Students must have these experiences for them to continue connection outside of the classroom.

Thats all for now Fellow Bloggers! Until next week :)

Year 2, Blog Post 3: EDBE 8P54 (Monday, 25 September 2017)

Good Day Bloggers!

Objective:

For this week, it is my objective for this blog post to present my responses to questions, ideas and information presented this week in the course EDBE 8P54 at Brock University! For our third week, our class focused on math problems in the shape of mental math, communicated to one another about our reasoning whether or not to implement this activity into our own classrooms, and made our own classroom games in partners. In our forum posts (in addition to the first week of Webinars!), we looked into the concept of mistakes, and how making them is beneficial to overall learning. I thought that this week was engaging in that the classroom was led often by the teacher candidates, and allowed for interaction with our peers in regards to mathematical concepts and presentation. 

Fluency in Mental Math = Attainable!

Our first activity was a real eye-opener! I would have assumed as a class we would be prepared for mental mathematics, but I quickly realized that the mathematic language of many questions led teacher candidates to a confused state. The activity provided by our professor was quite a simple concept. Every teacher candidate was provided with one question containing a number and a simple word problem. Ex: My number is 10, twice my value plus 2 equals what? With problems such as these, another teacher candidate would have the answer to the first question, and so on until everyone had a turn answering one question. As we saw as a class, this exercise allowed us to practice our mental math, as well as refresh our mathematics literacy. I thought this to be an interesting exercise, but if I were to use this sort of refresher, I would contain it to grades 7 and 8 mathematics, and use it a day before a test for students to draw on their mathematical language skills and interpret what the question is asking of them with increased accuracy. 

We also drew on this concept of mental math through our games we created in partners. My partner and I created a game with the doors of the lockers, adding a similar component to the one shown to us but with a few certain twists. The concept created was meant for a break in the middle of a particularly long lesson, allowing students to have an energizer while simultaneously still studying mathematics. In our activity, we gave each student a post-it, where students had a mathematical equation equaling a certain locker in the hallway. Once each student received the post-it, they were to speed walk to the locker number that equaled their equation. We thought this game to be engaging and stimulating to the concept of mental math; it allows students to get out of their seats and work with one another (as there were groups of 3 going to the same locker). We thought that students of a younger age could benefit from this too should the educator implement a classroom environment that supports safety during this exercise (no running, pushing, etc).

Mistakes? Do You Mean Opportunities For Learning? 

Making Mistakes for the Purpose of Learning

Final Thoughts :

In this week of mathematics study, I have learned that we must consistently utilize repetition in our classrooms when we are teaching any concept. Mental math in problem solving allows for students to gain an approximate value of what they are problem-solving, and thus it is a very important concept. In addition, through mistakes in their values, students are increasing their knowledge, and learning how to come up with an answer, perhaps with even more efficiency. We can connect this to last weeks' concept in regards to growth mindset. Mistakes allow for a growth mindset, when the learner realizes that they are welcome to make mistakes and knows that this is an opportunity for growth. 

Thats all for now Fellow Bloggers! Until next week :)

Year 2, Blog Post 2: EDBE 8P54 (Monday, 18 September 2017)

Good Day Bloggers!

Objective:

This week, I will present my responses to questions, ideas and information presented this week in the course EDBE 8P54 at Brock University! For this week, we threw ourselves into magic = math, and for our online portion, we continued our webinar familiarization and focused on growth mindset in the educational field of mathematics!

Growth Mindset = Positive Experiences in Mathematics:

We as a class have come to realize just how necessary it is to have a growth mindset when studying mathematics; indeed in any subject! For this week, we started our class by completing a card trick. In groups and as a class, we attempted to figure out the card trick through mathematics. The only way the card trick made sense was through factoring the cards and determining how one could come up with three queens and one king. I quickly found the math problem to be problematic for a majority of the class, as most people have not had the experiences of mathematical reasoning at this level for quite some time. Some Teacher Candidates understood through their prior knowledge of factoring, but the majority felt a certain unease towards the problem at hand. In this case, having a growth mindset about the problem and allowing yourself to have some unease can help grow you as a student of mathematics! We all have different ways of learning followed through at alternative paces, but having a growth mindset truly contributes to success; when you can overcome these moments of unease. As a mathematics educator, this is what should be impressed on our students.

Connecting Experiences:

To me, this sort of growth mindset is comparable to my practicum experiences from last year. Transforming my thought process from university student learning to teaching at the grade 8 level was quite a change, particularly in language and mathematics. I was not entirely sure what to expect from myself and the students, but I knew that having a growth mindset would encourage positive learning in the classroom. I contributed to the idea that everyone had something to offer to the classroom environment, and to mathematics problems, that is no different. With a fixed mindset, students are not able to achieve their full potential, and this can have serious consequences later in their education.

Messages About Math: Promoting Growth Mindset

Reflection:

In this week of mathematics study, I have learned to further use growth mindset for both myself and my future students. Mathematics can have its complications, but through a growth mindset we can continue to grow as students, even to break down complicated fraction questions as was the case in our class this week. By reflecting on the question, looking at it in multiple ways, and looking for patterns in the question, it is easier to produce a solution to a complicated problem.


Thats all for now Fellow Bloggers! Until next week :)

Year 2, Blog Post 1: EDBE 8P54 (Monday, 11 September 2017)

Good Day Bloggers!

Objective: 

For this week, it is my objective for this blog post to present my responses to questions, ideas and information presented this week in the course EDBE 8P54 at Brock University! As this was our first week of Year 2 Mathematics, we went through the course objectives, were introduced to webinars, created Self-Introductions on Sakai, and went through the many misconceptions in the educational field of mathematics!

Card Tricks = Mathematics? 

In our class, we utilized cards to illustrate how mathematical concepts are used in magic tricks. Believe it or not, there are many areas of mathematics that contribute to a successful magic trick! In this case, we were shown a 'simple' card trick. For those of us who had little to no knowledge in regards to the use of playing cards in a magic trick, (myself) I was fascinated with how the trick followed through. The teacher demonstrated the trick with the cards: shuffle the cards, split the cards into four piles, move the cards around in a methodical manner (3 cards per pile) and come up with a Queen on top of all four piles of cards. We as a class then attempted to perform the card trick, trying to identify the mathematical concept that was utilized, and learned from one another to do the trick ourselves.

Card Tricks = Mathematics!

Welcome to the Forum Posts!

As this was the first week of our course, we were introduced to the essential concepts: webinar presentations, the mandatory forum posts, and how to respond to others when they posted a forum post. We as individuals in the class were responsible for completing two forum posts in Math Mindset Module 1, and to react to other forum posts made by our fellow Teacher Candidates. The topics of these forums were: Attitudes Toward Math, Math Myths, Brain Growth, Smashing Stereotypes, and Online 1 Recap. I personally thought the messages from Attitudes Toward Math and Smashing Stereotypes to be interesting, as it is not always clear why many individuals look at math with displeasure. When watching the Attitudes Toward Math video, I realized that many of these misconceptions are in many of Hollywood movies. The message in many of these short clips depicted that if you were good at Math, then your character is categorized in a negative way. Individuals see these movies, and they connect with their characters, and often people relate to the characters that they idolize, and assume that they are not 'good' at math themselves.

Reflection: 

I thought this first day (as well as the forum posts and other reading material provided) to be very interesting, as it allows for us as Teacher Candidates to connect mathematics to something fun (such as magic) and allows us to probe the reasons why many of us feel that we are not 'good' at math. This can very likely be due to the misconceptions of Hollywood films, but I think this is also due to our every day influences such as: Parents, Teachers, and our fellow peers. As future teachers, we can do our part to eliminate these misconceptions, and demonstrate in a fun and positive classroom that math can be fun, and is often directly linked to real life application. 

Thats all for now Fellow Bloggers! Until next week :)