Week 3

         This week in Mathematics class we were responsible for reading a monograph issued by the Ontario Government as a part of the Capacity Building Series entitled, Differentiating Mathematics Instruction. As you can probably tell from the name, this monograph was focused on the importance of differentiating instruction in the math class. The monograph contained three main points which were: Focusing Instruction on Key Concepts, Using an instructional trajectory/landscape for planning, and Designing open and parallel tasks. One of the first things that the reading states, however, is the importance of knowing your students and their zone of proximal development. For us, as teachers, to be able to effectively differentiate in the math classroom, we have to be aware of where each of our students are, their abilities, and what they need to improve on/where they need to be. This resource also gave a number of great tips on how to go about achieving the three steps in differentiating for students in the math class. One of the points that really stuck with me is teaching mathematical key concepts rather than a specific curriculum expectation. For example, if you are trying to teach how to solve a simple multiplication question, to allow for easier differentiation, you should teach the concept behind multiplication. Such as Multiplication has many meanings (e.g., repeated addition, counting of equal groups, objects in an array, area of a rectangle), The resource provides some great illustrations and more key concepts behind multiplication that I think prove to be very useful when thinking about how to differentiate.

Hemant Meena, Parallel [online image] 2012 http://bit.ly/2d04xxd.

            Another point from the resource that we spent a significant amount of time in class on was designing open and parallel tasks. Parallel and open tasks allow for everyone to participate in math activities regardless of where they are in their zone of proximal development. For example, in class Patricia put up two similar but different questions. The two questions were very similar and required the same processes to solve it, however, one of the questions had numbers and values that were a little simpler compared to the other. For example, one question could ask for what 50% of 27 is and the other could ask what is 28% of 27. By doing this, the students who might struggle with finding out 28% of 27 can still be involved and solve a problem, and maybe after completing the simpler question, they might move to the more difficult one. As long as the key concept behind the two tasks is the same, this type of differentiation can be highly effective. Patricia’s question about the jeans was a great example of this. Patricia asked us to come up with our own price to insert into the question. This is a great open problem as it allows the students to pick their own difficulty. For example, if you pick an unusual price, or one with decimals, it will make solving the problem more difficult than if you picked a whole number that is easily divisible.  I think that open questions and parallel tasks such as these are a great too to use in your classroom. Not only does this allow students to be active participants in their own learning it also makes the task of differentiation easier on teachers. If you can make it a habit to provide two parallel questions or open questions in every lesson you really don’t have to do much more differentiation as you are providing the same information to everyone in the class, and regardless of their zone of proximal development they will be able to participate.

            The videos in the Online module this week were also very informational and of value to us as aspiring math educators. This week the videos were focused on mistakes, and how making mistakes is such a crucial part of learning, especially in the classroom. In the videos, Jo actually points out that when we get a question right, we are not growing our brains at all. However, when we make mistakes, our synapses start firing and we create new connections in the brain which leads to better understanding and thus, learning. I also thought it was interesting that Jo stated her mathematician colleagues are some of the slowest math thinkers that she knows. I always associated being fast in math class with understanding the material the best and being the most efficient at solving problems. However, Jo states that there is no evidence that states that the faster you are at solving a math problem; the better you are at math. Rather, those who take long to solve a problem are thinking deeply about the problem. We should be encouraging our students to take their time and to think deeply about the concepts behind the equation/problem and to not worry about how fast they are able to solve the problem

            This week Jessica and Danielle hosted the first of the webinars. Their focus was on inquiry in the math classroom, and the two of them did an amazing job. While all of us are still trying to figure out the technology, the two of them handled all the glitches well and were able to present a clear and concise webinar. What I liked most about the webinar was their use of the interactive Google docs where everyone worked on the same sheet. I think Peter and I may have to make use of that great idea in ours. Overall it was a massive success and they definitely set the bar high for the other presentations.