Wednesday, December 6, 2017

Annotated Bibliography


Drijvers, P., Kieran, C., Mariotti, M. A., Ainley, J., Andresen, M., Chan, Y. C., ... & Meagher, M. (2009). Integrating technology into mathematics education: Theoretical perspectives. In Mathematics education and technology-rethinking the terrain (pp. 89-132). Springer US.

Hohenwarter, Markus. (2001). Geogebra Online, GeoGebra.

Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and teacher education21(5), 509-523.

Shaffer, D. W., & Kaput, J. J. (1998). Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education. Educational Studies in Mathematics37(2), 97-119.

Trouche, L., & Drijvers, P. (2010). Handheld technology for mathematics education: flashback into the future. ZDM42(7), 667-681.


Thursday, November 9, 2017

Some links for annotated bibliography

Some quick comments: the article poses some very important and difficult questions regarding the integration of technology into mathematics education. For example, considerations such as: should technology be used to enhance already existing paradigms in mathematics education? Or does the integration of technology include the need to create new pedagogies and teaching practices? What about technology creates a need for new ideas?

This article introduced some preliminary terms, i.e jargon, from the academic sphere of education. It used these terms and ideas to expand and explore the effect technology has on these pre-existing understandings. There is a case study of a teacher who encounters various difficulties and discusses based on anecdotal circumstances how we ought to efficiently and effectively get the benefit in teaching that technology can provide.

This paper does a very good way in theoretically separating different types of technology as to highlight what specific properties enhances mathematics education (and education more generally) and which properties have already inhibited this process.

This is a free online software available through an arbitrary browser. This is an example of something that is open-source and incredibly useful for educational purposes: how technology can bring about accessibility to knowledge instead of creating a culture where the ruling class disproportionately has access to more. 

This article has some specific examples in how handheld technology is mimicking some more traditional uses in mathematics education. It uses opinion based arguments and highlight some different perspectives. 

It is an interactive computational environment, in which you can combine code execution, rich text, mathematics, plots and rich media. It is free!!!!! And also illustrates the immense usage of coding for scientific and artistic purposes. These sorts of platforms are great resources for students to know about, be trained in, and have access to. It is incredibly important that it is open source, easy to use, and actually brings about mathematical and computational understanding.

This page presents some opinions from students on how technology enhances or inhibits their learning. Seeing as all the technological pedagocial content knowledge  is ultimately shaped by the students themselves, it is important to consider different student perspectives. 

Not an academic source, but it does pose some interesting counter perspectives on how technology in the classroom currently exists and the consequences of it not being implemented in a thoughtful and pedagogical way. 



Thursday, October 26, 2017

"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.

Thursday, October 19, 2017

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

Thursday, October 12, 2017

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


Tuesday, October 10, 2017

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.