A Frayer Model for Real Numbers

Here is a sample of something that I worked on to develop a better understanding of numbers. I had found a project to develop a numberline for real numbers, but was needing something a little more to help personalize my own understanding. So, I took a Frayer model for real numbers and developed the idea as a cover page in my visual journal for the actual numberline.

I found several resources for the numberline project...
http://mathequalslove.blogspot.ca/2012/09/real-number-line-project.html
http://motivate.maths.org/content/complex-numbers-and-argand-diagram
https://educationalaspirations.wordpress.com/tag/the-real-number-line/

I found that it was quite interesting to work on this project, developing thoughts about where numbers would fit and how to represent them. One of the most interesting moments was developing algebraic functions to represent numbers. In the past, I have not necessarily considered math as a creative process, but I am coming to realize that given the opportunity, students who are able to create and develop their ideas in many different ways are able to communicate those ideas more clearly.

I am developing more confidence in my mathematical abilities by creating visual representations of my learning. Another thing that I discovered was quite interesting when I started looking at the algebraic functions was that I did not have to limit myself to a single dimension on the numberline. Further investigation lead me to the Argand diagram, and the possible development of a dimensional number line. But that is a project for another day...:-)

Exploring Math Teaching

I have been seriously considering the aspects of teaching over the past few months, and have been looking into several methods and aspects of why math is perceived as being hard...

A bit of my history and opinion...

I loved school when I was younger, but when I was in grade school, learning the multiplication tables was stressful in that my teacher played cassettes that blurted out questions that, to me at that time, seemed to go lightening fast. I did learn the majority of them, and I am fairly good at mental calculation, though I am not as fast as some...when given time to work on things in later years, math was great fun.

In my Jr. High years, I had a wonderful teacher, Mr. Sealy, who was a fabulous teacher and encouraged me greatly. He would explain and explore concepts that seemed to be in a near alien language. He would do it with such care and precision that the meanings and understanding were accessible to (I like to think) everyone in the class. It is this aspect of learning that I have been curious about through University and that is coming to the forefront of my understanding of teaching.

One study that I worked on in University was that of places having their own internal jargon, and that unless and until you are in that place, be it a place of business or a classroom, you may not know the language, or jargon, that is commonly used. I have found this holds true for a great many people upon entering a new workplace or environment, and the amount of jargon can be quite considerable. In respect to math, there are teachers that sometimes use different jargon when teaching and/or there are students that have a hard time catching on and retaining the jargon. I have discovered that this is an area of growth for me. The language of mathematics is something that I continue to explore and develop an understanding of.

Like the teacher in Charlie Brown, when a teacher starts speaking about mathematics in mathematical jargon, students may find the language inaccessible, and all they hear is "blah blah blah". In the process of personalizing learning, it is vital that the language of mathematics be accessible to all students as something that they can relate to and something that they are exposed to regularly so that they can develop a more comprehensive understanding of the many ways of expressing something mathematically. When students and teachers are able to communicate effectively in a mathematical language, learning becomes more meaningful.

In the ongoing development of my own understanding of the language of mathematics, I am working on some readings, including Van De Walle's Elementary and Middle School Math- Teaching Developmentally, the "Murderous Maths" books (fun learning, my kids love them) and working on developing a visual journal for math vocabulary. I am also re-discovering my joy for algebra (yes, it is actually fun!)

It is a great endeavour, and one that I hope to be able to share with students over time.

Meaningful Substitution...

Ah, the joys of learning never end...especially if you are a teacher.

I have been fortunate to be signed on as a substitute teacher with a few different charter schools in my area, and am quite enjoying the experiences that these opportunities provide. Though I am still searching for a full time placement, it is wonderful to have experience in a variety of classrooms. :-)

Thus far, I have taught in both elementary and middle schools, from traditional classrooms to visual and dramatic arts programs to phys ed, and have enjoyed every single day. I find that the most challenging part of being a substitute is not that of behaviours, but that I want to ensure that I am supporting the students and teacher in a manner that is consistent with the classroom learning.

One concern that I have heard from regular classroom teachers is that they do not want to just have a class where the students and substitute are doing "made up" work. I agree wholeheartedly that as a substitute, I would like to know that the work that I am doing with the students is valuable. For my own personal growth, I do try to put a bit of my own ideas and style into the lessons. I love it when a teacher provides me with the lesson plan in advance, and there is that opportunity to become acquainted with the plan. One teacher provided me with the opportunity to plan an art project with her options class, while I brought in additional materials to enhance anther project students were working on in another class. It is taking those moments and opportunities, I think, that really helps the students to understand that the substitute is not just there to babysit them while the teacher is away.

As a substitute, it is important to challenge your boundaries and become comfortable in many different teaching environments. After all, you never know when opportunity may come knocking at your door...