Grade 7/8 Math Curriculum

Grade 7/8 Math Curriculum

Today in class, we learned about the grade 7/8 math curriculum for two reasons. One, was because we are going to be qualified to teach them as I/S teachers, and two, because it shows us what theoretically, our grade 9's should know when they get to us. I think reason two is good enough reason to begin with as the curriculum shocked me! First, I had no idea that grade 7 and 8 students were suppose to be taught so much. Their curriculum for math really does have so many different needed learning blocks to get them off to a good start in grade 9, yet that is not always the case. As you can see in the picture below, we cut out all the expectations that would lend themselves to good starting blocks for one aspect in grade 9, and the list in grade 7 and 8 is massive!

I was also shocked, as I learned this class that not all grade 7 and 8 classes have rotary, Ie. specialized teachers teaching different subjects. Rather, the students have the same teacher for all courses. I seem to have been one of the lucky few that did go through rotary as a middle school student, and looking back, I believe it was definitely for the better. As a teacher, if I had to teach all subjects, I could definitely see myself, unknowingly, favour certain subjects over others just on the basis that I have more knowledge in them. Personally, I wouldn't really be that useful in teaching history or English, in comparison to math and science. In others cases, I find a lot of middle school teachers grew up terrified and uneasy with math, so I wouldn't be surprised if unknowingly, they pass on those same feelings or even just put less emphasize on learning those skills. To me, this is a shame.  Math is so important and a good basis is key in later success. A prime example of a poor start was my brother. He used to be very strong in math, until he had a teacher who couldn't see things from a different perspective. He did not like how my brother approached questions as it wasn't the same way as him. One day, this teacher told him he wasn't good at math, and never would be. This small act when he was a child changed his whole path. He kept telling himself he couldn't do math throughout school, and never had any confidence in it. To this day, he still believes he cannot do math, and refuses to do any job that involves money or even simple math. Although this occurred in grade 9, not grade 7 or 8, I believe the same thing can happen when teachers unknowingly have a bad attitude to teaching math in younger grades.

What were your experiences with math in middle school ? Did you have rotary or just one teacher and how do you believe it affected your life of mathematics ?

That's all for today,
Miss Sydor

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. 

Differentiated Learning

Differentiated Learning:

Today we learned about differentiated learning and how it looks in a math classroom. For those of you who may not know what differentiated learning is, in short, its providing many different ways for students to understand and explore the same concept, in the same classroom. Most people may not believe this is a good idea for math, or that it should only be done in an applied or college course, as academic and university courses just need to learn content to move up in the world. This is not true at all ! It is so valuable, in all courses and levels ! Even in our class today, many teacher candidates went straight to the numerical and algebraic versions of equations, as after university math, that is what they are most comfortable with. To me, this shows how much more important it is for us to explore concepts in visual ways, as it makes our understanding of concepts so much more concrete and gives us a deeper understanding of the number math we are doing. Sure we can get the correct answer to numerical problems, but do we actually understand why those answers are right ? Or are we just really good at following formulas and inputting values?

This actually leads me to my next thought, and something that really stuck with me in class. By using differentiated learning, we can challenge all students at the same time. For those who understand the numerical equations, they can start with those and then move onto the picture equations, and those who understand the picture equations can use those to assist them in getting the numerical equation. Those students who believe they are too good for picture equations, probably just aren't comfortable with them, and should try them at least a few times before throwing in the towel. As well, if its group work, those who are good at one version can work with those who are good at a different version, and hopefully help each-other in a student based, cooperative learning environment.

Learning with visual tools

Learning with visuals:

I feel as if people don't give visual tools enough credit. Today we used many different manipulatives in order to learn different math concepts, and I found them extremely helpful. Although I would be able to do the math without them, they make things much easier and quicker to comprehend. I especially found the coloured shapes useful for fractions. For people who don't yet understand how to do fractions and common denominators, they are extremely easy to use. At first, we didn't even think about the fact that we were finding common denominators, but instead, had fun trying to make the different shapes out of the number of specific shapes we were given. Then, when we had to think of the exercise as a teacher, I realized what the topics we were actually learning were. This made me realize that it would be an excellent way to get students engaged who don't normally like the thought of math. Many students have the potential to do well in math, but just don't see the use in learning it. I feel that if a lesson was started this way, they would be able to practice and get confidence without realizing it, and would hopefully follow the lesson much better afterwards. However, you would definitely need to clean the tiles up afterwards as (just like we discovered), they can be very distracting and too much fun to play with !

Introduction to me !

Hello math teaching community and beyond !
Welcome to my blog, I hope you enjoy it and find it useful !

To get started... a little about myself:
I am a new teacher candidate, who hopes to teach both math and chemistry, so yes writing is not my forte.. you will have to bear with me though as I do believe I still have useful, thoughtful ideas to share. The purpose of my blog is to share with you my learning process and thoughts on how to teach math. I will explore many different views, and how one way of teaching is not always the best. I mean, can you imagine if we only learnt a single way throughout all of school? Oh how boring that would have been. I also hope to explore the many ways students think, especially when trying to connect the abstract formulas we use in math, to the concrete examples of where it could be used. I find many people think math is useless after they have learned basic algebra, but that is not true at all! The logic of math problems and the problem solving skills you learn are useful in so many scenarios in life. For example, I work as a waitress, and the number of times my coworkers cannot figure out how many people can fit at a table without counting each and every chair, or whether or not their reads at the end of the night make sense, kills me! If they just took the time to think it over logically, or did some simple algebra, it would all be easier. However, due to many different scenarios in their lives, they have come to the conclusion that they are not good in math, and therefore, have no confidence in themselves. My number one goal as a teacher, especially in math and chemistry, is to instill a confidence in my students that allows them to enjoy the learning process of subjects they may have been previously told they are not good in, and allow them to see how math really is related to the real world.

In our class today, we had to look over the high school math curriculum. What I found most interesting was the way learning goals and objectives were written. I had assumed that the goal would always just be to be able to get the correct answer using the modules you teach. However, it contained so many different verbs! Yes, the correct answer is always good, but the curriculum planners also want those answers shown in many forms. They want students to be able to describe answers in words and sketches, connect answers to the real world, justify why its the answer, and even define what their answer means. I believe this is an amazing thing! It makes students think of there answers as more than just numbers and following a formula. It makes them need to see why they are getting the answers they're getting, and use critical thinking skills. Lastly, it allows students who may not be able to understand formulas, to be able to express there answers in a different form which may make more sense to them. Personally, I believe this is a major step in the right direction, if teachers actually pay attention to word details they're given.