"Embodied learning"

One interesting aspect of mathematics is that although the theory is quite abstract, the intuition behind it usually results in observations from the physical world. Being able to use all of our senses to engage with the presence of mathematics around us is certainly one way to bring about these intuitions in students and in ourselves. The article presents some interesting ways in which mathematics can be embodied, but in particular I found the discussion with crocheting a hyperbolic plane quite interesting. A hugely important consequence of mathematics is that it breaks complex abstract ideas, such as the hyperbolic plane, into a set of parameters that uniquely define the structure. Knowing these parameters gives one the ability to re-construct these ideas through theory as a means of proving things, or in the actual physical world. Certainly if one understands the structure enough to see and understand how we might create a physical representation of it, one probably understand or at the very least has a better understanding of the mathematics behind it. The concept of creating physical objects with mathematics is certainly one way I would in-cooperate embodied learning in my classroom. Further, as much as I would love to have everyone pursue mathematics in academia and add to the rich and beautiful subject in that way it seems as though it might be more practical to show how engineers and computer programmers design and construct using mathematics.

Entrance Slip

Hey Susan. I didn't get a chance to read the article, I don't have access to a stable computer setup so I am doing everything between classes. Here are my answers, slightly late.


1) What are your "student bird" and "teacher bird" thoughts about assigning percentages or letter grades in the assessment of student work? What do the grades indicate? How are they arrived at? Whose purposes do they serve? What are positive and negative aspects to giving grades? to be assigned grades by an instructor?
As a student I found percentages really encouraging and I had a way to see how I was doing relative to my peers. I never had any particular talents other than mathematics so being able to reach perfection was a nice inflation for my ego. I recall getting 100 in pretty much every math course since Grade 9. From a student perspective I would say most people aim to do the bare minimum to pass and are pretty satisfied with anything in the mid-range. This was my attitude, anyways, for subjects other than mathematics. I think for most people they find grades do not accurately assess their aptitudes or perhaps do not feel a need to prove this qualities that they possess with often time arbitrary numbers. Grades indicate a lot if they are praise in some way... perhaps a lot less if they do not seem to act fairly.




From a teacher stand-point I think precise number grades in mathematics are detrimental to the goals of deep abstract understanding, complex problem solving, and exercising technical cognition. In mathematics when the emphasis is on how many multiple choice out of 100 one can answer correctly we are putting a number on a student's ability to be a very quick and precise human calculator. I think if we genuinely focus on the wide spectrum of skills mathematics can give we need to have grades which fall within a range as opposed to a precise number. Assessments should be designed not to bring down a student, but rather give opportunity to illustrate and explain how they use mathematics to think about a posed problem. It's hard to stick a number on that... it doesn't seem to encourage the continued use and exploration of students' ideas.

2) What are some of the unintended side effects of grading? How do grades and marks in themselves format the social relations and learning situations in a classroom, a school, a district?

A huge hurdle for teachers is the fact that you are really being used for the ruling class. Time and time again we see backlash from highly influential people surrounding the idea of adjusting school such that people who are disadvantaged can also prosper. When a parent is concerned for their child, most times this concern is genuine and well-founded, bu they are striving to allow their child to have the same or more economic freedom as they do. The problem is, these students with supportive parents are already substantially more likely to obtain that irregardless of what we teach at schools. Some students this is not the case, and I think marks harm those people.


3) Could you imagine teaching math and/or science without giving grades? How could a teacher encourage learning without having an emphasis on grading

Exit slip

I think the use of film is good in a classroom setting especially as a tool to represent marginalized demographics in various areas. That being said, I am quote critical of using tactics that further push gender on subject areas in school even if the aim is to be more inclusive. I think making things gender neutral is the first step of accomplishing a welcoming environment. Playing off a gender stereotypes in a counter intuitive way can be dangerous in so far as attaching gender with any subject. We schould teach outside of gender.

Exit slip

Exit slip - Orchard Garden

Our lesson in the Orchard Garden last Thursday was a lot of fun. Being outside and breathing in fresh air is almost always good for the soul, but even more so when it is coupled with a clear sky and warm weather. The Orchard Garden really brought out creativity in the students, but further creativity in the instructor.


Changing the teaching setting from a classroom to something else grants access to different instructional instruments. This access results in lessons that are more dynamic and exercise different strengths and weaknesses within the students. For example, the drawing exercise worked on looking at the geometrical elements present in both man-made structures and things that result arose from nature. Even though some student would really excel in a drawing activity such as this due to their previous experiences with art, all students will be able to make connects between math and the special world around us. Further, there is no need for an specific mathematical background and allows for open-ended questions, something often lost in traditional conceptualizations of mathematics education.


I thoroughly enjoyed our field trip to the garden and it certainly made me more open minded to using non-conventional education tools whose use might not be immediately obvious.

Orchard Garden

Garden based learning is one of many ways in which we can try and introduce non-traditional components into the class room to try and create a multi-dimensional learning setting. The article mentions how changing the setting to a more social one allows for personalized pace as well as a natural setting to integrate cultural aspects. This is a welcoming setting for a lot of demographics who are often marginalized and under-represented in schools. Further, something like a community garden fosters enthusiasm toward a mutual goal that both implicitly and explicitly brings about aspects of education. I also think that a garden brings about opportunities to explore the real-world applications and observations that exist in nature, thus putting subject matter in context. Gardening is a practical skill that connects people with the environnement and can be a practical life skill as well, all while bringing about a means to teach various subject matters.