Week 6

Growing Success [online image] 2014 http://bit.ly/2edxWqD

This week was the sixth and final week of our time together in Math II and to be honest, I feel as though this semester FLEW by. This weeks class was focused on assessment, but more importantly, on providing students with descriptive feedback and report card  comments. One thing that Pat brought up in class this week really stuck out to me and it is something that I think will definitely influence the way that I mark and provide comments to my students. The comment that Pat made that really stuck out to me was something along the lines of providing students with just marks does not improve their performance. When you mark a child's work and only provide them with a mark or a grade, that is all they are going to care about. If the student scores high, then he or she is happy and that is all that matters. Conversely, if a student scores very low, when he or she sees their mark, they are going to be overwhelmed with anxiety or apathy, depending on the student. The student will very rarely care to think about where he or she went wrong. Instead, Patricia explained to us that it is much more effective to provide students with comments on their work as the main focal point of grading, and have the mark itself as a secondary piece of information. IF the comments are the focal point, then the student can see where they need to improve/where they made a mistake based on your comments, and thus they are able to perform better next time by applying your comments. I really think that this type of formative assessment will prove to be very successful in the classroom. We also covered writing report card comments and how we should structure our report card comments. In class we took part in a math conference that I thought was informative as each table group was given a piece of work and we were responsible for commenting on the quality of the work. We all rotated around the class, and I found this useful because it really opened my eyes to how other people in the class mark, and by seeing how others look at the same piece of work, it helps to broaden your own understanding.
This week Paddy and McKenzie were responsible for leading their webinar that was focused on report card comments and grading. I think that the two did a great job of leading the webinar, as well as providing excellent insight and research/resources links for us to access when we are in placement and in our own careers.
Reflecting on this, my second year of Mathematics in teachers college, I can confidently say that I am not the same student teacher that walked into Patricia's class two years ago. When I first started teachers college I was intimidated by teaching math. However, after Math I and my first placement, which was a math classroom, I actually was kind of disappointed to learn that I would not be in a math placement this year. I feel as though I have become very comfortable with teaching math which is a huge change from when I first started. Patricia has done an amazing job of providing us with the information, resources, knowledge, and confidence to become effective math instructors.

Math Blog Week 5

In this weeks class there was a main focus on the concept of blended learning. Before teachers college I really did not have any idea about what blended learning was. I obviously figured it was something like mixing two or more styles together in the classroom but I now think that I have a much better grasp of what blended learning is, and how to incorporate it into the classroom. My first encounter with blended learning was the first year courses in the bachelor of education program at Brock. We were told that we would be partaking in blended classes, which meant that the first two hours of class were in the physical classroom, while the last hour of class would be spent online doing activities on our own. My first understanding of blended learning was just this, online and in class work used together. However, I have come to learn that blended learning is much more than simply two hours in class and one hour online.

Blended Learning, 2014 [online Image] http://bit.ly/2ejKO06

Pat had us go through some resources in class this week, and fill out a booklet with information about blended learning. My personal definition of what blended learning is as follows, both teacher led, and student led and focused activities; both in class and online modules in which students are responsible for their own learning. Blended learning is more than just technology, although technology can be a major tool used in blended learning. Rather, blended learning is about the teacher stepping back, and allowing the students to really take control of their learning on their own, whether it be through inquiry, or technological applications that the students use individually or group work where the students have to regulate and govern themselves.

Our online module this week was focused on the premise of teaching mathematical concepts rather than memorization of formulas, as well as the importance of intuition in math, and using visual representations and drawings to help students understand. I have found these online modules to be very enlightening to me as Jo Boaler does a great job of explaining these concepts. I particularly liked the idea of teaching concepts rather than memorization. There are really only a few basic mathematical concepts that are built upon and added to, as we advance in our mathematical career. If we are successful in teaching our students to understand these basic concepts, moving up in their mathematical career will be easier for them as they have a strong base understanding of the concepts needed to be applied in advanced math. Understanding these concepts allows students to have enough knowledge to be able to rely on their mathematical intuition, which is an extremely useful mathematical skill that we use almost everyday.

Lastly, this week was the week Peter and I were responsible for leading our peers in our webinar. We chose to tackle the issue of financial literacy and I think we did an amazing job. Our main focuses were that times have changed since we were in school, and there is a much bigger focus on financial literacy. This is due to the influx of entrepreneurs entering the business sector, as well as the general population taking more control over their personal finances rather than just allowing the bank to take care of everything. We also wanted to focus on fun student centered ways to incorporate Fin. Lit into the classroom (Real World game I was sent by my T.A), as well as providing students with math that they will actually use in their everyday life, and that will give them a head start when they enter the real world in terms of knowing concepts such as mortgage rates, RRSPs etc. Instead of recapping our whole webinar I will provide a link to the video below. If you also would like more information regarding the Real Game, feel free to comment or email me and I would be happy to send some information along.

Week 4 Blog

For this week’s class we were responsible for reading two resources that were focused on creating and administering mathematically rich tasks to the students in your math class. The resources were found on the website NRICH and were very informative regarding what exactly is a Rich Task, and the benefits they have when presented to students as opposed to the more traditional tasks of the past.  In Monday’s class we covered some great concepts and went over what it is to create rich mathematical tasks. Some of the important information that I recorded was that Rich tasks provide students with multiple starting points, which allow for students to jump in and start wherever they feel most comfortable. In addition, there are usually extensions within the problems, meaning that there is usually a second part to the question where you have to use the information found out in the first part, to solve the second part. Another concept that we covered that goes hand in hand with Rich tasks are open tasks. Open tasks are tasks that do not have one exclusive right answer. These types of questions allow students to work on their intuition, reasoning, and logical thinking skills; as long as the students can support their answer logically in an open question, they are right. I thought that there was one quote from the, “What is a Mathematically Rich Task,” resource that did a great job of summarizing what a Rich Task is.

“Rich tasks open up mathematics. They transform the subject from a collection of memorised procedures and facts into a living, connected whole. Rich tasks allow the learner to 'get inside' the mathematics. The resulting learning process is far more interesting, engaging and powerful; it is also far more likely to lead to a lasting assimilation of the material for use in both further mathematical study and the wider context of applications.”

This quote leads perfectly into the videos that we had to watch for this week’s online module. The main point in one of the videos is that math is really only built upon a small number of main concepts. And it is upon these main concepts that all other advanced math is based off of. Therefore, if we are able to teach out students to grasp these few main ideas or key concepts, then when they move forward in their academic career they have a strong base and knowledge upon which they can build. The understanding of these main key concepts, also allows students to be able to think intuitively about math. This was another video that we had to watch online this week. Intuition is a major part of everyday life math as well as math in the classroom, it deals with proportional reasoning and logical thinking, and is a skill that is essential for success in math; it allows us to make quick judgments and estimations about math, which help us in solving the problems. Implementing Rich Open tasks in the math classroom places the importance on Enduring understanding. We, as teachers, need to be moving towards implementing more open and mathematically rich tasks in the classroom, rather than the black and white traditional problems that many of us experienced during our early academic careers.

            This week Adriana and Kathlene ran their Webinar on differentiated instruction.

Diff. Instruction. [online image] 2014, http://bit.ly/2dK0jLW

I think that the two of them did a great job at running the webinar and providing good insight into implementing DI in the Math classroom. However, I have been finding that these online webinars are very unreliable and whether it be audio or video issues there almost always seems to be some sort of issue in the process of carrying a webinar out. That being said, the two ladies did a great job of carrying on throughout the technical difficulties and were able to think quickly on their feet to fix the problems.