Accessibility in Education:

-Dynavox-picture board/speaking tool

-Dragon natural speaking

-Kurzweil 3000 and Firefly

-Reader Pens

-Talking Calculators

-Alpha Smart (writing aid)


*ASK for help. LEARN about these technologies*

*As an educator, make sure your lessons are accessible for ALL of your learners….really think about WHAT is it that the students are learning*

*by emphasizing technology, we can appeal to the widest student audience.


Off the trail

Posted: December 1, 2013 in The root of the matter
Tags: , ,



“…mathematics teaching which possesses an ecological sensibility also provokes an awakening for that which is yet unknown. This kind of awareness re-cognizes mathematical environments, mathematics, teaching and learning to be coemergent events, events that can only be brought forth as they occur moment-to-moment.”


As the first four months of term come to a close, I find myself more open and accepting of mathematics than I have ever felt in my twenty six years of life.  This class has been so interesting and unique: I admit that I expected to be given full lesson examples and ‘real world training’ like so many of my other teacher education courses. This never happened, and I am so very thankful and appreciative I was given a different experience. Jennifer’s job is to push us to think about how we, as future educators, are going to teach our students; why we will teach certain concepts, and how our perspective affects our students. Our goal should not be to become a replica of Jennifer and teach her activities (for that is robotic); our goal should be to take the knowledge we all acquired during our 4 months together and connect it to our individual teaching philosophies and then create holistic teaching activities that are meaningful, connected, and leave our students wanting more. This is one of my goals.


Are you going to be a giant, wizard, or dwarf?


What about a different character? What about a mermaid?

No, replied the other person, you have to choose from the giant, wizard or dwarf-there is no mermaid option.

The above is an excerpt from Jennifer’s chapter on “Spaces for unpredictable mathematics.” If we think of the giant, wizard, dwarf and mermaid as metaphors for mathematical learning, we can view the above exchange as an educator asking students to be “boxed” into a category of mathematical learning; one that does not make room for mermaids(who stand for the unpredictable).

Jennifer argues that “…it makes no sense that definitive categories or endpoints in children’s mathematical explorations would be desirable or even realistic…”

I wholeheartedly agree with this statement: WHY are we creating constraints and trying to push student’s thinking in a directed outcome? To me, this seems akin to rats in a maze, searching for the one correct outcome. That is not learning, that is projecting your desired outcome onto someone else for the sake of maintaining your perspective or ideal. Instead, we need to focus on discovery-based learning, where the teacher is a sort of “guide on the side,” and students take on greater responsibility for their mathematical learning; giving way to quantitative literacy. Through these two means, students understand the role that mathematics plays in the world. This type of learning and teaching will allow for the resurgence of mermaids; who are dwindling in numbers.

So, after writing on how I enjoyed “Notes on a Triangle,” I read the chapter on Re-viewing and Seeing Differently and discover that it is about the film and how the students studied the triangles from the film clip! (Funny how things work in life…) I especially like the chapter’s section on how the students noticed that numbers could be triangles: not only were the students constructing triangles from numbers, but they were also forming patterns. Once the students noticed their pattern (the relationship between the increasing length of the hypotenuse and the total number of dots needed to construct the triangle), they were able to use mathematical language and symbols in order to predict the next number in their triangular sequence.  This exploratory lesson allowed for a natural progression to take place in the classroom;building on students’ prior knowledge of triangles affords them a better opportunity to make real world connections (triangles made from squares, soccer drill formations, pyramids, etc.)  I was then reminded of a word from earlier in the year: oikos. Jennifer’s students were creating a sort of family with their number sense: They were able to relate to, and understand that the mathematics they were attending to was connected. The students also seemed to view the classroom as a family, or home: They were confident and comfortable exploring and questioning their environment.

When I become a teacher, I want my students to feel like their classroom is a type of home. I want them to feel comfortable asking questions and challenging themselves. To do this, I need to create an environment that fosters problem solving and open ended questioning. I want to make mathematics more hands on, more interactive, and more engaging; it is through discovery that deep connections can be made.

Sidenote: Notes on a triangle has a partner: dance squared-here is the link:

Math Centres

Posted: December 1, 2013 in The root of the matter



Today’s class focused on math centres.

Jennifer had a few key teaching points that I am including in my journal so that I don’t forget them!

-It is important to start with 3d then move to 1d (3d is more tangible for students to look at)

-We are so used to scaffolding, moving up in small increments, and now literature is telling us to look at the whole and move down.

-We need to teach the following areas:

Comparing and sorting


Non-standard and standard units and appropriateness

Estimation- it is developed through experience

Benchmarks: as long as, as heavy as, juice box 250ml, about an hour

Ratios: I’m twice as tall as, half as heavy as

Jennifer also provided us with what educators need to provide in order to create good math problems:

-They must be meaningful and interesting

-Provoke children’s curiosities in creative cognitive and embodied manners (extending their thinking out)

-Be Flexible and Open

-Make use of manipulatives, diagrams, and pictorials

For today’s class, we first learned how to create successful Math Centres, (use once a week with additional help-preview, practice, extensions, can be used for all different grades and mathematical topics, Non-routine problems, adjust the instructions: depending on class competencies, spend entire 20 minutes on each centre.)

We were then able to explore these centres in a hands-on manner (we rotated through 3 centres every 15 minutes.) Being able to work on the math problems during centre time was incredibly eye-opening: I realize how invaluable math centres are to students, as being able to work with a partner and in groups can completely change your own perspective of how something should look (for example, the lidless box activity). Working in the math centres was also a challenge-our group could not figure out Jennifer’s instructions because we kept ripping the most miniscule pieces off of our triangles…which left us with micro pies…After Jennifer came around we all had a great laugh and a good AHA! Moment. As a future educator, I realize the importance of incorporating math centres into mathematics lessons. For myself, I was engaged, enthusiastic, actively problem solving, and was so involved with the activities that I was a bit sad I didn’t get to try out all of them!


During class, we were exposed to a variety of geometry activities that connect mathematics to personal experiences and incorporate visualization, kinaesthetic, and creativity (what am I game, building shapes with marshmallows, body drawings). We also watched a short video, titled “Notes on a Triangle.” The video was wonderful! Students could watch first for visual information, and then re-watch to notice patterning, different shapes, definitions of unknown shapes, etc. I immediately thought of the chapter we had to read for today’s class; as Jennifer stresses the importance of connecting mathematics to it, it being ‘more than human world.’ Thom takes the reader back to the snowflake, and the meaningful activities that formed from the snowflakes. While reading, I could see that the students were knowledgeable and understood the concepts of geometric patterns and shapes. They used mathematical language correctly and fluently and also came up with their own idea of how to verbalize their knowledge of snowflakes: through poetry.

I re-read the chapter several times. I did this because reading the passages made me feel good. I felt like I was peeking into what good teaching looks like. I felt that this is what education should look like: guided exploration. This is what successful teaching and learning looks like. Our cohort has gone on multiple school visits, and I have yet to see what Jennifer writes about in her book come to fruition. However, I know that there are educators who want to change what formal education looks like, feels like and acts like. I know that I will be taking these instrumental lessons from the textbook with me as I begin my teaching journey.


New furniture

Posted: November 28, 2013 in The root of the matter

Complicated thinking assumes that math is a collection of pieces that can be assembled or disassembled in order to understand a concept. I thought of this as a big jigsaw puzzle: each time you put together the puzzle, the outcome is the same; you are not creating anything different.

Complex understanding acknowledges that mathematics is more than a collection of parts and how they work together. “Complex thinking involves understanding the role that is played by the whole is necessarily embedded in social and natural environments.” Each time the pieces are put together, something new is created. This also means that it cannot be easily taken apart, such as when you bake a cake. You cannot simply go backwards in your procedure and end up with your original ingredients. They are now apart of this new thing, called cake.

download (1)

Jennifer then postulates that a complex view of curriculum is needed. Okay, so instead of looking at curriculum as separate, distinct parts we need to consider viewing curriculum as dynamic, flexible, and co-evolving based on interactions between teacher-student-environment. I understand this concept, and I feel that this is the direction learning is headed toward. I am interested in what this curriculum would look like: Would subjects be taught by guided questioning, problem solving and exploration? Instead of distinct subjects (mathematics, art, science) would we view learning as embedding these elements in every learning experience? At the end of the chapter Jennifer likens mathematics to residue, explaining that it “resides seamlessly and all at once with past, present, and future contexts of students’ knowing.” I will admit I feel overwhelmed by this chapter, as you have to completely disregard all previous notions of curriculum and learning. However, the ideas in the chapter ring true for me, and I will work on examining these concepts further.