Week 3: Report and Reflection

What I was primarily fascinated with this week was the way our brain learns and interprets math. In the video below Brain Crossing, Jo Boaler explains what brain crossing is, she says that pathways of our brain light up when we think about symbols and numbers and other pathways light up when we visualize, draw, or estimate with numbers. And when both of these pathways cross, when we think of numbers and start visualizing and drawing them, that is the most powerful math learning.

https://www.youtube.com/watch?v=qZBjub36Bvs

In class Friday we preformed two activities that got us using visualizing and drawing with numbers. The first activity the class divided in half and on separate boards created addition and subtraction problems we thought to be difficult and then had to rank the other groups questions from hardest to easiest. Between the two groups rankings, there was a commonality that fractions seemed to be ranked the hardest because of different denominators. Personally, on the spot I can not remember how to solve fractions at all, having not taken math in about 6-7 years. So for me to find this the hardest was stemmed from not understanding the underlying principles to find an algorithm that could be written on the board.

Board reads: "Too much extra work to make them all the same" and "the common denominator is extremely hard to find."

Our second activity was with base-ten blocks and using these manipulatives to show the different outcomes of ways we can find answers. For example, we were asked to represent with the blocks 56-23. They way I would approach this was to have my 5 longs and 6 units and take away 2 longs and 3 units to come up with my answer. Mathieu presented a different method to the class where he took another set of 2 longs and 3 units and compared it to his 5 longs and 6 units and took away from that to get his answer. His method was more of a visual comparison, where mine was more of an approach of applying the logic that we new each long represented 10 units. In the end, we both came up with the same answer, just in different ways.

These examples in class all relate back to the main ideas represented in this weeks reading. That there are many procedures, or algorithms, for adding, subtracting, multiplying, dividing, etc. The traditional methods we use is just one algorithm and not necessarily better than the others. It is valuable for students to participate in learning activities like the ones above so that they have the opportunities to invent their own procedures and to see the procedures others come up with. It was valuable to the class when Mathieu presented his different approach with the base-ten blocks.

As teachers we should be aware of the alternative and multiple algorithms our students may come up with. We should not worry about how to present these algorithms or how many to present to our students, as long as procedures are taught with meaning to the principles of operation, students can invent their own algorithms themselves. We should let students continue the use of their invented algorithms, and encourage them to record in whatever way is meaningful to them as long as it is understandable by someone who is reading it. Our role is to provide students with the understanding to the underlying principles of the problems and with the appropriate language used in mathematics so that they are able to think more holistically about numbers and how they work.

Week 2: Report and Reflection

I believe there is a stigma with mathematics. When the subject of math comes up most people connect that with negative experiences. I know I do that myself, and the majority of our class announced in their introductions that they were not the best with the subject or have not done it in a while, and there seemed to be some nervousness in that. Also in our social culture math seems to be viewed with the same hesitancy for the subject, in the video Hollywood Hates Math we are presented with streams of clips from different movies where math is something that adds to their character development. Math either takes a back seat, or characters present that they're not good at math, or they are the "freaky math girl," these all add to a negative stereotype of how our culture views math.

https://youtu.be/3uYBoWH3nFk

Regardless of these issues, as teachers our job is to find ways to make mathematics accessible to learn for all students and in a way that will serve them throughout their lives. Teachers and students, as well as parents, all play a part in the curriculum responsibilities so that students will meet the expectations, and more importantly understand the material. Students must bring a willingness to learn and teachers and parents should be their for guidance and encouragement through their process. Parents as well should be discussing the work with their child at home and becoming aware of the curriculum and expectations. They should communicate with their child about their progress and stimulate their interest in mathematics.

As teachers, we must develop appropriate instructional strategies that will help students achieve and develop appropriate methods for evaluation so that students are provided with numerous opportunities to be able to solve problems, reason mathematically, and relate their knowledge and skills to the world around them. We must teach our students to understand, not memorize and regurgitate things that do not make sense for them. Teach them that the answer is only a product and the solution is evaluating the whole thinking process itself. But also understanding ourselves that people can learn better when they are able to connect, and using human experience as a way for students to relate their knowledge and understanding to what makes sense in their world.

The curriculum outlines overall expectations and specific expectations, our five strands of content expectations (or our "big ideas") and our process expectations (problem solving, reasoning and proving, reflecting, selecting tool and computational strategies, connecting, representing, and communicating).

But as a teacher it is important to be able to use different instructional techniques in order to relay these expectations into the class room. Group activities are helpful and game techniques can be used in the classroom, students together are like investigators while teachers provide prompts and facilitate learning so that the students may draw conclusions on their own. For example the Handshake game on Friday's class, allowed us to get up and have social interaction by introducing each other (relative to real world experience) along with the "Think, Pair, Share" strategy allowed us to think on our own, share pair up with a partner to see if we had similar views and come up with conclusions to share with our group. Professor Mgombelo also facilitated our learning during our discussions with prompts so that we were able to collectively find the answer. I found this technique extremely effective for a student like me, who needs extra minds around when learning math and interactiveness, since I find it more complicated on my own. The picture below I found was a good basis for math literacy, to understand math we must know that it is grounded in problem solving, find the most efficient way to understand that problem, understand how we come to an answer, and relate it to personal experiences so that it becomes meaningful.

http://www.emsisd.com/Page/27599

Resources:

1. Ministry of Education, The Ontario Curriculum Grades 1-8: Mathematics, 2005. https://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
2. Dr. Joyce Mgombelo. J/I Math Lecture 2 [In class lecture]. 2015 September 19.

Introduction: Welcome!

Welcome to my blog for EBDE 8P29 - Teaching Math! My name is Julia Chamberlain and in this blog I will be reflecting weekly on the pedagogy of math, ideas for learning, and integrating the classroom discussion into a basis for understanding how we teach and how we learn.

I think that there is a stigma when it comes to learning mathematics, that we ourselves can over complicate it and maybe cannot experience learning it to its full potential. I want to use group dynamics for problem solving, through games, activities, and discussions, we can find solutions together and create problem solving techniques.

In this course I am already beginning to learn that it does not matter of your background or experiences in mathematics because we all have the ability to learn it, we just all learn in different ways at different paces. I hope to gain from this course the knowledge to teach the subject, class room techniques, and also create a large scope of activities that can be used in the classroom to better the teaching of mathematics. As we learned in class today, there is a difference between not knowing the solution and just not having found it yet!

Me!