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.