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.

Week 2 Reflection

This week we were responsible for reading three different articles regarding mathematics and different mathematical concepts. The first document that we were responsible for reading was the “Paying Attention to Mathematics Education, K-12” which was issued by the Ontario Government. In this document 7 foundational principles for Improvement in Mathematics are laid out as follows:

1.     Focus on Mathematics

2.     Coordinate and Strengthen Mathematics leadership

3.     Build understanding of effective Mathematics Instruction

4.     Support collaborative professional learning in Mathematics

5.     Design a responsive Mathematics learning environment

6.     Provide assessment and evaluation in Mathematics that supports student learning

7.     Facilitate access to Mathematics learning resources.

These principles were issued serve as a guide for planning and implementing improvements in mathematics teaching and learning and as support for Math programs and changes that school boards are already implementing. The first principle states that teachers must focus on the curriculum in terms of what they are teaching, as well as what the students should know and what they will learn in the upcoming years. The 2^nd principle focuses on ensuring that, the teachers, as well as the board members, principals etc are all aware of effective mathematics instructing techniques and can engage in conversations with the teachers about how to improve etc. This leads to the third principle, which is building an understanding of effective math instruction for students to become successful in the 21^st century. The 4^th is to ensure that you and your fellow teachers are working and learning together when planning math units etc. The last three principles are focused on creating a responsive learning environment for the students, providing students with assessment and feedback that supports their learning and lastly ensuring that students have access to varying learning resources. I thought that this was a valuable resource because not only did it provide principles for improving your mathematics pedagogical ability, but it also gave specific examples regarding how you could go about achieving this improvement.

The second document that I read was, “Paying Attention to Proportional Reasoning K-12.” This document was focused on proportional reasoning and why it is so important to Mathematics education. I always knew that proportional reasoning was important, but it wasn’t really until I read this article that I realized that we really do use proportional reasoning in so many different situations, in, as well as outside of, the classroom.  Teaching a student to really understand proportional reasoning gives them a logical lens through which they are able to look at the world. Proportional reasoning involves a number of different aspects and concepts and this document does a great job of providing examples of these concepts and explanations as to why they are so important to the greater concept of proportional reasoning.  The document also lists the strands within the grades that are related to proportional reasoning as well as sample questions so you can focus your teaching. One last piece of this document that I found useful was the inclusion of sample EQAO          questions for grades 3 and 6.

Strand of Math. Proficiency. 2001, Journal. http://bit.ly/2cAdzUY

Lastly we were responsible for reading, “The Strands of Mathematical Proficiency.” This document describes the 5 strands of math proficiency as Conceptual Understanding, Adaptive Reasoning, Strategic Competence, Productive Disposition and Procedural Fluency. The document describes these different strands in detail whilst providing examples of each. The most important piece of information from this document is that fact that it is stated that these strands of mathematical proficiency are not stand-alone concepts. Rather, they are intertwined, much like a rope, and when put together they result in mathematical proficiency.

There were three things from class this Monday that really stuck with me.  I think that the personality colour test that Patricia briefly touched on would be a great activity to lead your class through at the beginning of the year to establish the different learning styles and thus be better able to tailor your lessons to meet your specific class/student needs. I also thought that the hate example was a great refresher on the concept that everyone looks at math differently. While one person may prefer to think of the problem algebraically the other student may want to think about it visually etc. Finally, the video about the shepherd’s age really resonated with me. I was interested in this video because it showed me the problem with much of the math instruction in today’s classrooms. Students are taught to really think and understand the problem/question they are being asked. Rather, they instantly start looking for numbers, which they can use as clues, to plug into an equation and reach an answer. This is the difference between Understanding vs just Doing. We have to be teaching students to really think about questions they are being asked and to try and understand the problem/question first, and then try and solve, rather than just looking for information to plug into an equation that does not make sense.

Blog Post #1

This week was the first week back to school after summer and the first class of my final year of teachers college is math. Last year walking into Patricia's class for the first time I was definitely a bit intimidated by the thought of having to go through math again. However, this time around I was way more calm and ready for the experience. Last year was great for me in terms of my learning of math and creating a growth mindset in my own learning journey. I feel like a created a great base last year to which I will be adding this year, strengthening my understanding of math and how to be an effective mathematics teacher.

This week we started class with Pat having us play a game on our computers where you had to move squares into a designated area with ascending levels of difficulty. As always, Pat does a great job of using activities like this as minds on activities which lead into a lesson. The point of this game, in my opinion, was to show the importance of teamwork and patience. Patience is incredibly important to have as a teacher as you have to be able to be patient with your students while they are learning and mastering new concepts and techniques. Another very important aspect of this game was the fact that it allowed you to go back and redo a level or undo a single move. In terms of mathematics and learning in general it is so important to make mistakes as this actually helps you learn better. Jo Boaler actually spoke about this in one of the videos that we were responsible for watching as homework this week. She explains that as we make mistakes our brain is firing off synapses and creating new pathways and connections within itself which helps us learn and strengthen our mind and understanding of an issue/math problem etc. Encouraging students to make mistake and remaining patient with them as they are working through their mistakes and the learning process is part of developing a growth mindset in the students; by supporting them patiently you are helping them to understand that they are capable of completing any task, even if they struggle with it at the beginning. There is a reason why erasers are on the back of pencils, we should be encouraging our students to make mistakes!

Pencil, Sept 11 2016 [online image] http://bit.ly/2c3DjKb

Another great takeaway from our first math class of the year was in a video that we watched called 'Ever wonder what they would notice?' I enjoyed this video because it presents a great idea about how to lead discussions and lessons in the class. Right now most classrooms and lessons are based on finding out what kids don't understand and then teaching them. Instead, this video was explaining that we should be asking kids what they wonder about, not what they don't understand. By asking the students what they are wondering about a certain topic you are more likely to actually spark genuine interest in the students which will lead to a better learning experience for them. The video said to use a Wondering Vs Noticing handout about topics in the classroom in which the students write what they notice about a  topic/idea/concept on one side, and what they are wondering about that same issue/topic/concept on the other. This allows us, as educators, to really understand what our students want to learn, as well as how much our students already understand about a topic, sometimes intuitively. This also supports the importance of creating a growth mindset in our students. By having them wonder about what they want to know they are motivating themselves internally to learn about a topic. Lastly, the other videos that we had to watch during the online module were great in terms of getting my mind back into the groove of thinking about growth mindset not only in math but throughout all of my courses. I really enjoyed watching the Math Myths and Stereotype videos as I thought it was interesting to hear the stereotypes and myths and compare them to my own personal experiences and thoughts about math.

Year Two

Welcome back to my Math Blog!

Here I am writing in my Math blog in my final year of teachers college. I cannot believe how fast the time has gone by. In a few months me and my fellow classmates will be finishing our journey through teachers college and will be certified teachers. This is both and exciting and somewhat scary thought; the real world is closing in on us quickly. Much like last year I will be using this blog to write about what we have learned from Patricia and in our math class as well as posting useful resources and commentary on math ideas and topics.