Tasks in a math class

Tasks in the math classroom

Today in class, we did a very interesting task. It was called the "s-pattern," and it involved a series of figures that increased in number. Although there were different questions asked, we were able to do as many or little as needed, as long as we all answered the question: "Determine an equation and explain how it relates to the visual figures provided." I found it very interesting how diverse the steps taken were by everyone in the class. Some people saw the visual pattern instantly, others manipulated the figures, and others went straight to creating a number chart and finding the pattern from there. However, we all came up with an equation and how it related to the figures, even if we took different paths to get there. I thought this was amazing to see, as it reinforced the idea that not everyone's minds work the same way, and that is more than okay. It also showed that although some people are good at following rules to get formulas, they are not good at visually seeing what those numbers look like, and although others are not good at getting the numbers quickly, they have a much better understanding of what the patterns actually mean.

I think a task like this is amazing for a classroom ! Regardless of what path people took, they were able to start out with what they were comfortable with, and then forced to work on their weaknesses as well. As I have talked about in other blog posts, I think this is extremely important. I am a firm believer that understanding the concepts and not just following formulas is a way better way to retain math skills, for the rest of students lives. It teaches students to problem solve and makes them realize that there is always more than one way to solve a problem.

Personally, I do not remember much of any class, unless I came up with the answer myself before following a formula or specific instructions. I found that if I was given the opportunity to explore ideas and felt safe being wrong, then a much deeper understanding was formed. Since I mostly took academic courses, where teachers did not embrace this idea as much, I found I forgot the content of the course as soon as I wrote the exam at the end of the semester. However, I was lucky enough to have a physics teacher who fully embraced the idea of self-exploration. Before he ever taught content, he got us to try problems on our own, or at least make us think of possible solutions first. He wasn't a big believer in just handing us formulas to use, and it helped me immensely. I was able to remember so much of what he taught me even once I left high school, that I found physics in university easy for the first year.

All in all, I hope to be able to instill this kind of thinking in my classes throughout my career as a teacher. I hope to be able to establish a safe space, where students enjoy the process of learning and don't feel like any subject is all about memorization.

Technology in a Math Classroom

Technology in a Math Classroom

Today we talked about numerous ways in which we can incorporate technology into our lessons. Most of my math classes were just straight lectures, with little visuals, hands on equipment or technology, and I truly believe I missed out. I missed out because my teachers were more concerned with the fact that we could get the right answer, and they didn't have a strong focus on truly understanding why we were doing what the formula said. However, my brain does not work like that. Sure I can follow formulas for the semester that I need, but then the concepts, along with the formulas, vanish from my head. This is not ideal ! However, I found A LOT of the technology and games we did in class made me have to think about why I do what I do. For starters, I loved the website "desmos.com". It contained so many pre-made, FREE games for all sorts of different math concepts. Although we started with a "guess who" type of activity on the site (which was fun), I kept looking and discovered the game Marble Slide, which I found fantastic ! It has different stars placed on the screen, and a sample graph with the graphs equation. The student then has to change the equation, to change the shape of the graph, in order to be able to hit all the stars following the curve with a marble that is dropped from the top. It reminded me of a game I used to play on long car rides called "cut the rope." Anyways, what I loved about the marble game, was that it was fun, interactive, and a great visual. It allows students to see in real-time, what different manipulations to a graph equation, does to a graph. It challenges them to know what they need to change, in order to hit all the stars. However, its all random, so they won't be changing the maximum for 5 questions in a row, then changing the width for the next 5 questions, which I found to be the case when I was in high school following a textbook. It makes them think critically and understand all aspects of a graph. However, it also gives you unlimited tries, so it allows them to experiment and see what different parts of the equation are for, without embarrassing them. As well, I believe it would encourage students to want to learn, as the more they know, they faster they can complete levels. It also allows them to practice math, perhaps without them even realizing how long they are doing it for.

Below is the first screen the students get:

Below is the fixed equation and graph, as well as the marbles being launched to see if all the stars will be hit:

Although there were numerous other games and examples, I don't want to drag on. All in all, I believe that technology should be incorporated into math classes. Not everyone learns the same, so visuals, kinesthetics, and games are important. If we can get students to understand why things are the way they are, or even to just enjoy math class, then I think that is a big success ! What are your thoughts on technology in a classroom? Should it be avoided, slowly incorporated, or fully embraced?
That's all for now !
Miss Sydor

Learning for all

Learning for all !

Today in class, we talked more about differentiated learning, but more specifically about how to create an environment that works for everybody. To me, the environment should be safe and inclusive which would allow all students to feel comfortable, be able to ask questions and be wrong without being embarrassed. This sounds good in theory, but how can someone achieve this? Some possible ideas include utilizing personal white boards, as they allow students the safety to fully erase their answers, as well as the idea of "Pairing and Sharing". This means students turn to their elbow partner, to either work together or even just compare answers. Students then gain confidence in the fact that at least one other person is thinking like them, and in reality, makes more students participate in class. Liisa also gave us a list of positive norms in a math class which I think are quite valuable.

In case it is a little too small to read, the norms state:

1) Everyone can learn math to the highest level

2) Mistakes are valuable

3) Questions are really important

4) Math is about creativity and making sense

5) Math is about communicating

6) Depth is much more important than speed

7) Math class is about learning not performing 

To me, a few of these resonate more than others. First, mistakes are valuable ! I personally find that the questions I make mistakes on the first time, are the ones I remember longer. These mistakes usually mean I need something explained deeper, which means I'll understand it better than something I just followed a formula for. Therefore, I will understand why something is the way it is. This means I can logically understand why I am doing a formula, and will remember the concept even once I leave the classroom. This also ties to point number 4- Math is about creativity and making sense. If students are able to come up with the correct answer in a creative way, it means they are understanding it in a way that makes sense to them. Just because they didn't remember a certain formula, doesn't mean they don't understand the concept. It means, they understand the deeper meaning, and there brains may work differently. This is actually a wonderful thing as it indicates they have problem solving skills, which to me are much more important than memory skills. Lastly, I love the point that math class is about learning and not performing. I sincerely hope I will one day be able to get that across to my class. I don't care how many mistakes are made, or how slowly I need to go through things, as long as every student is able to learn something. 

In the end, my students are going to remember how they felt in math class, more than how much they learned. Therefore, a safe, inviting environment will be much more important than the concepts, and is something I will strive for everyday.