Math out loud and Orchard Garden Exit slip

The math out loud and orchard garden field trips were quite the unique experience and provided some useful thoughts on the use of field trips in mathematics education.

There are some clear distinctions between the classes in classrooms versus classes on a field trip. First of all, the learning in most cases is way more kinesthetic.  Your actually physically involved in the lesson.  Similar to coaching sports, you can only accomplish so much through talking, writing, or showing videos.  At some point you have to get out in the field and start doing.  In mathematics or physics, field trips can be a great way to accomplish this. Secondly, the learning is more attached and relational.  Not only because field trips are less frequent, but also because of the hands on experience.  Finally, field trips are simply a different venue.  You need change to see growth in your students.  Much like in weight lifting your not going to see any gains if you keep doing the same thing over and over again.  You need to be constantly shocking the body so that it doesn't get used to the routine and doesn't peek/flat-line.  Field trips provide this "shock."          

I think field trips are a great tool for education for various reasons.  For one, the repetitive nature of a classroom lecture can be quite boring and uneventful!  Field trips are something new and exciting, they disrupt the everyday routine and they are a great way to "hook" students in.  Students learn in many different ways, field trips have the ability to easily hit on all learning aspects, visual, kinesthetic etc.  I remember in grade 12 we went to play land for our physics class and we had a simple worksheet to work on that dealt with kinematics and momentum.  Of course it was fun because it was play land, but we had a lot of fun actually doing the worksheet itself.  Going from doing problems and having to imagine it in your head or seeing a diagram on a sheet of paper versus actually going out and physically seeing the problems on such a large and real scale is something that a classroom can't provide.  Another benefit is that field trips can act as way to teach new concepts or reinforce those previously taught.  Not only are field trips a good way to hook students in, they are also a good way to provide real connections between the material in class and the applications to a real environment.  There are some obvious problems with field trips though.  The logistics and administrative aspects are one hurdle, and the amount actually learn't by students is another.  Are the students having fun while learning.  Or just having fun? Or neither?         

I thought the orchard garden was not as useful as the math out loud performance.  It was a great idea to try and connect biology, botany, art, and mathematics through using the orchard garden but I didn't seem to connect with it.  I found myself caught up in the drawings themselves versus the applications they had to mathematics.  I didn't connect with it.  I think this type of problem regardless of field trip or not will present itself to certain students.  You're not going to be able to connect with all your students consistenly.  However I am sure this was and could be very helpful to a lot of students, especially those who already have an interest in the other disciplines.  On the other hand, I found the math out loud performance to be amazing!  Using drama to convey certain mathematical topics was something I have never experienced before.  It had just the right amount of humour and entertainment to keep most students interested and it was the perfect length.  From a teaching perspective this could be a great introductory hook to get kids to see the real world applications of mathematics and it can be a great way to connect those who are interested in fine arts.  Going in as a student I actually learn't a few cool facts like the ratio of meandering river is pi!!! I was quite entertained.              

Ancestral genres of mathematical graphs

Reading Susan's article "Ancestral genres of mathematical graphs," has not only made me eager to pursue further knowledge on the importance of incorporating historical and cultural relations to mathematical graphs but it has also raised interest for using "multisensory pedagogies" and "making cross disciplinary connections" to help students connect better with mathematics.  I think this ties into the idea of relational and instrumental understanding.  Prior to all these readings my views on mathematics education were narrow and one dimensional.  Particularly skewed towards the instrumental side.  However, it seems as if using multisensory pedagogy and making connections to other disciplines and history provides great benefits.  The power of actually knowing and understanding the mathematics far outweighs linear memorization.  Susan provides a great example of this in her graphs and gestures project.  I wrote a reflection at the start of the program in another class and I was convinced that we should be isolating mathematics as it's own unique discipline and that the way we should teach it should be instrumentally(mainly because this is the way I was taught).  Maybe I am just easily persuaded but after only 3 or so short weeks my original opinions are still remotely present but I am definitely swaying to the other side of the pendulum.            

Susan focuses more specifically on the cultural, historical, and human equivalences with respect to mathematical graphs.  Who knew the "up-right," "down-left," positive, and negative of graphs were so heavily influenced through our culture, history and so many other factors!!  After years and years of working with mathematical graphs I still found this quite intriguing.  Bringing this knowledge to a young student could provide the insight and motivation needed to enjoy mathematics.  Even though the article more specifically focuses on mathematical graphs, I think this can be translated to other subjects within mathematics.   




         

"On becoming a reflective teacher"

After reading “On becoming a reflective Teacher,” one of the main points that stuck out to me was was the openmindedness trait. Grant and Zeichner say that “you not only ask why things are the way the are, but also how then can be made better,” and this really caught my attention. Upon entering the education program I was expecting to learn effective strategies, styles, and methods of teaching. Of course I still expect this, but now I hope to consciously challenge some of those and see if I can insert my own flair and offer improvements. The story about Mary Smith was also quite intriguing to me. I have gone through similar experiences in coaching when you have certain athletes that don't want to be there, or they simply don't see the value in certain concepts you are trying to teach them. There have been times when I have given up on these athletes. There have also been times when I have been more persistent and optimistic with these specific athletes, eventually bonding with them and gaining their respect. This is way more rewarding then just giving up. I can see how this will relate in a classroom setting and I am sure it will happen more frequently because most athletes are motivated, where as a lot of students aren't. I look forward to opportunities like that.

Even though this paper may be outdated, for the most part the concepts are relevant.

I think being a reflective teacher is still, and always will be what we should strive for. Students in 1980 were unique and different much like the students in 2012 are unique and different. Being a reflective teacher takes into account each unique individual and is able to adapt accordingly. We have to be willing to challenge what we already know, we have to be open to new ideas and concepts, and we have to be able to evolve. Being a teacher entails being a student as well.

Going into our practicums it seems as if Grant and Zeichner agree that we should be asking our teacher sponsors questions as to why they do the things they do. Will certain teachers get agitated if we keep peppering them with questions?? Should we just cooperate and go with the flow while asking these questions to ourselves?? Or is it important for us to learn what kind of teacher we have and then cater to them?? For me personally, I think it will be important to interject our own style while taking in and soaking up what they have to offer.

Exit Slip Sfard Article

Our group discussion focused a lot on cultural differences in the way we teach math.  Our western system is more tailored to specific students needs and learning abilities where as somewhere like china has a more linear system.  Which one is the best? I don't think we know the answer to this but I think the best we can do is to just adapt constantly.  The "westernised" system seems to be at least trying to get better constantly by making changes to the way we educate.  We are always doing a little bit of trial and error.  In our group we discussed an aspect of the pendulum swinging back and forth we our education system may be doing, but at the same time this pendulum is moving forward in the right direction.  So if you can imagine the pendulum going back and forth along the y and x axis but at the same time it is moving forward along the z axis as we get closer and closer to reaching a "perfect" system.  These educational systems are constantly changing on this pendulum much like our sense of fashion is.

Thoughts and Reflections on Sfard's "new clothes -- and no emperor"

EDUC 450B Response to Anna Sfard article

“As a dressmaker, I can only strive for solutions that are good for now”

This particular quote stood out to me because I think she is trying to convey that mathematics education, research in mathematics education, and education in general is constantly changing much like the trends of the fashion world are always in flux. One day what you're wearing might be considered fashionable but three months from now its considered faux pas. As a “dressmaker” we only look for solutions that are the current trend, often neglecting past or future intentions. There will never be a set answer key to mathematics education research. This whole concept was very interesting to me and I tend to agree with Anna! Will we ever find a solution to mathematics education? Is there a “perfect” way to teach Math? Although I would like to be optimistic and say yes, there is just no way we will ever conquer that. Humans are incredibly diverse. We all learn differently, think differently, and react differently. For as long as this remains true(I doubt it will ever change) and as technology continues to develop, there will always be a constant need to continue research in mathematics education. As humans grow so do the ways we teach. Certain trends may come and go but for the most part mathematics education is constantly evolving. Or at least I think it is?? Looking back at when I was in high school I can't remember a single class that wasn't taught with chalk and a chalkboard. But now I look around and math is being taught online, through youtube videos, using powerpoint slides, by incorporating different disciplines etc. These are the solutions that we think are good now, it will be interesting to see what solutions we think are good 20 years from now?

As soon as I finished the paragraph ending in the quote mentioned above I found myself re-reading it 3 or 4 times to try and really grasp what Anna meant. Whether or not what I stated above is a correct interpretation of the quote, I found that this article got me asking myself quite often why is it important to teach math and why is it important to do research on teaching math? I hope as I go continue on in the program I will be better suited to answer these questions.

First post

Hey everyone, this is my first post