So in this blog, I wanted to write about some of the key points I took away from the last day and share them all with you and for my future self because I most likely will forget everything.
Highlights of the last day:
1) Pick your battles...I think this means to really focus on what is important for you and for your student. If you choose to pick on everything, I personally think students will loose respect for you because everything annoys and or irritates you which demonstrates that you cannot control your own emotions well. I think also that when you pick your battles well, students will more likely adhere to the rules that you do have in place because you will most likely have a select few important rules.
2) Give time for your students to cool off...give them an OUT
So this point seemed quite interesting to me especially because of the context V put it in. You want to use the "send the kid down to the office" as a last resort because if you do it right away, you will have no other things left to use on the student when they come back or do the same thing again. So the idea I think is to give them warnings, so for instance, a look, a tap, a conversation and finally when nothing else works, then the office.
3) Don't give them only one choice (ex. apologise now to me or so and so will happen)
I think this applies to anything in life when someone bothers you or is giving you a hard time. Ultimatums are never a good option and should never be used in any situation. If a compromise cannot be reached, well maybe you aren't trying hard enough, or being creative enough. I found that in my own personal experience, I tend to use ultimatums when I am beyond livid and I feel like it has to be my way NOW! so being mindful of when you start to feel that rage of emotion get to the point where you might thrown out an ultimatum and use techniques to soften or lower that.
4) Don't give them feedback in front of their peers.
Conversing with parents:
#1: Don't go into the conversation with judgement, go in with a mindset of "how can we make the situation better?". I think realising that parents are sending you the best thing they have each and everyday as V pointed out is extremely important to be cognisant of. It also ties in with the fact that each and every person is being the best version they believe they can be. No one wakes up and lives life thinking I am going to be the worst version of myself just for the heck of it. People put the best they have everyday given their circumstance and situation.
Some cool quotes I liked were"
"Don't let perfection be the enemy of action"
"An engaged student is a managed student"
Thanks again V for an awesome 3 weeks! Truly had a blast in your class and won't ever forget the experience!
Saturday, 23 July 2016
Wednesday, 20 July 2016
Phil and Bonnie's Oscar award nominated short film
hey guys, so for our first assignment, we decided to utilise the SAMR model and make a video on growth and fixed mindsets. Check it out!
https://www.youtube.com/watch?v=9k1W9Bp7Qk8
https://www.youtube.com/watch?v=9k1W9Bp7Qk8
Tuesday, 19 July 2016
Article Discussion- Balance is Basic
Okay so today was my day to lead the discussion and the article I read was Balance is Basic. What I gathered from the article was the emphasis on having math be a balance between 3 core ideas. These ideas include understanding mathematical concepts, being able to compute math and lastly being able to problem solve or apply the math. Near the end of the article, they add in 2 more accessories which were engagement and reasoning. Engagement being the idea that the individual will want to try harder questions and push themselves beyond their limits because they are "engaged" in math.
So I completely agree with what the article is saying, it makes perfect sense and is totally logical in what it's attempting to argue. All three aspects it touches on are key to a persons understanding and "relationship" with math. The article nicely points out that if a student memorises how to multiply fractions, one must strictly go "straight across" and multiply. Simple. Answer is done. Vice versa, if you want to divide, all you must do is flip the second fraction and go straight across. It is easy to do these simple tasks, however if you don't understand the reasoning behind it, then you are missing the fundamentals of mathematics. Additionally when more complex math is introduced and you don't have a solid foundation, well I think you might be in trouble.
This was also highlighted in class today when V asked us to multiply 18 by 5 without using a pen and paper. I mentally calculated the 10x5 and added it to the 8x5. When Phil mentioned that he wrote it out in his head like a typical multiplication setup, and carried the 4, I agreed that is what should happen. Here's the thing, I couldn't explain why that happens...it just does! It wasn't until V actually explained that the 4 represents 4 (10's) that I was like OHHHH!!! ding ding ding!!! But in my 28 years of existence, I didn't know that and I never cared enough to ask...until now that is.
Another thing V mentioned in class today was that you cannot come into class assuming that students have the same level of math interest or ability as you do. He spoke to the fact that when he was growing up, he was fortunate enough to have a father that asked him solely about math and this in turn might have helped him succeed in math. So not having that notion that all students will have even a fraction of interest in math will help us as educators to try to see things in different way and motivate us to come up with various ways of explaining something.
In terms of my discussion, I wrote 4 questions that I asked my group.
We had some interesting discussion, and I will just touch on a couple of the questions that I asked. So in terms of the first question, some mentioned that they disagreed with the article in that you don't need to have all 3 aspects fully developed because we don't use all three everyday. We also have the lovely thing called the internet and Google at our disposal if we need to look some rule up that we have forgotten. Another member said that she wished she had a stronger computation skill set because she finds that she struggles with some basic math arithmetic like being able to currency convert. In my opinion, I think ideally one should have a balance of all three aspects, but does this mean that you are going to fail miserably in life if you don't? Of course not!! I didn't know why I had to carry the little 4 in today's class yet I managed to get an A- in first year calculus. So to me you can still succeed even if there are some tiny minor gaps....(please let me know your thoughts on this!)
For the second question, I think we mostly agreed that it would make our lives a bit more challenging only because we have been trained as professionals to see things as separate entities. So for example when we are marking students work, we always separate the knowledge, application, thinking and communication pieces. We are conditioned in society to have things organised and in their own compartments but I think once you get over seeing math as these three aspects that one MUST focus on and instead try to see it as a holistic approach, it might be slightly easier. We also mentioned that for some standardised testing, they are very much set up in a way where everything is compartmentalised and separated which might again make the transition tougher.
So I completely agree with what the article is saying, it makes perfect sense and is totally logical in what it's attempting to argue. All three aspects it touches on are key to a persons understanding and "relationship" with math. The article nicely points out that if a student memorises how to multiply fractions, one must strictly go "straight across" and multiply. Simple. Answer is done. Vice versa, if you want to divide, all you must do is flip the second fraction and go straight across. It is easy to do these simple tasks, however if you don't understand the reasoning behind it, then you are missing the fundamentals of mathematics. Additionally when more complex math is introduced and you don't have a solid foundation, well I think you might be in trouble.
This was also highlighted in class today when V asked us to multiply 18 by 5 without using a pen and paper. I mentally calculated the 10x5 and added it to the 8x5. When Phil mentioned that he wrote it out in his head like a typical multiplication setup, and carried the 4, I agreed that is what should happen. Here's the thing, I couldn't explain why that happens...it just does! It wasn't until V actually explained that the 4 represents 4 (10's) that I was like OHHHH!!! ding ding ding!!! But in my 28 years of existence, I didn't know that and I never cared enough to ask...until now that is.
Another thing V mentioned in class today was that you cannot come into class assuming that students have the same level of math interest or ability as you do. He spoke to the fact that when he was growing up, he was fortunate enough to have a father that asked him solely about math and this in turn might have helped him succeed in math. So not having that notion that all students will have even a fraction of interest in math will help us as educators to try to see things in different way and motivate us to come up with various ways of explaining something.
In terms of my discussion, I wrote 4 questions that I asked my group.
- Do you agree with the article in the sense that we need an equal balance of all 3 strands of math: understanding, computation and application? Justify your answer
- In what ways does this way of thinking about mathematics make your job more challenging or difficult?
- What issues do you see arising with having this model as a standard model for all math teachers?
- In what area of math (out of the 5 mentioned- understanding, computation, application, reasoning, engagement) do you feel is your strongest and why?
For the second question, I think we mostly agreed that it would make our lives a bit more challenging only because we have been trained as professionals to see things as separate entities. So for example when we are marking students work, we always separate the knowledge, application, thinking and communication pieces. We are conditioned in society to have things organised and in their own compartments but I think once you get over seeing math as these three aspects that one MUST focus on and instead try to see it as a holistic approach, it might be slightly easier. We also mentioned that for some standardised testing, they are very much set up in a way where everything is compartmentalised and separated which might again make the transition tougher.
Lastly for the third question, we discussed that because it isn't explicitly stated in the curriculum that math should be thought of in this way, it might be challenging for some teachers to accept. I sort of struggled with this argument because I took the article to be somewhat of a guiding tool as opposed to "this is how it needs to be done" tool. So I took from it that you can still teach everything in the curriculum but make sure you are looking that students are able to understand concepts, can compute math and critically think on their own. We also jokingly said that many math teachers will be retiring and when they do, then this whole shift will occur because many are still very focused on the computation aspect of math.
So here is a picture from today's exercise on how a simple multiplication question could be seen in a different way.
Monday, 18 July 2016
Thinking Tools and Manipulative
So today's class was quite fun and entertaining for me for a couple of reasons. It was the first time in a long time that I used manipulatives to assist me in expanding and factoring quadratic equations and also just solving binomial expressions. For me it was extremely helpful and solidifying seeing the expressions in the form of these little tiles because before today, (x+2) always was just something that was written and almost slightly abstract to me but today I got to work with just that!
So it was really easy to see what 2(x+3) looks like in real form and when you actually make it with the tiles, one can easily see what the expanded form looks like and I think that could really help students who need some sort of visual to understand concepts.
So in the reverse, if you wanted to factor the expression, then in that case, you would be given the area of the tiles and you need to come up with the Length and Width that would form that pattern. So in order to do that, you first need to manipulate the tiles so that they make a square/rectangle shape once you have your square made, then its easy to see what you need to put in your x and y axis to make the square. Overtime you start to notice a pattern with these perfect squares where if you have x^2 and an equal number of x values, then you know how many small white tiles you need to fill up the remaining space.
What I also really liked was using the hanging number line to demonstrate to students how expressions would sit on a number line. So it is super easy to create, all V did was hang up 2 pieces of string one on top of the other. On the top string he put a paper marked 0, and on the bottom he put 0x.
From there he would show an expression, so for example 5x + 2. And he would ask us, where would you put this on the number line? We would answer, the bottom line because it has a variable in the expression, and then we would have to decide, does it go the right or left of the 0x. After that he would tell us that 12 corresponds to the expression and put the 12 directly above the expression on the number line without variables. From there he would hold up another piece of paper marked 5x and ask again where would we put this and why. From there, what would be the corresponding value for 5x and we would answer 10.
This image above demonstrates 3( 2x + 1) 3 white tiles on the left side, 2 green for 2x
This demonstrates the number line
So it was really easy to see what 2(x+3) looks like in real form and when you actually make it with the tiles, one can easily see what the expanded form looks like and I think that could really help students who need some sort of visual to understand concepts.
So in the reverse, if you wanted to factor the expression, then in that case, you would be given the area of the tiles and you need to come up with the Length and Width that would form that pattern. So in order to do that, you first need to manipulate the tiles so that they make a square/rectangle shape once you have your square made, then its easy to see what you need to put in your x and y axis to make the square. Overtime you start to notice a pattern with these perfect squares where if you have x^2 and an equal number of x values, then you know how many small white tiles you need to fill up the remaining space.
What I also really liked was using the hanging number line to demonstrate to students how expressions would sit on a number line. So it is super easy to create, all V did was hang up 2 pieces of string one on top of the other. On the top string he put a paper marked 0, and on the bottom he put 0x.
From there he would show an expression, so for example 5x + 2. And he would ask us, where would you put this on the number line? We would answer, the bottom line because it has a variable in the expression, and then we would have to decide, does it go the right or left of the 0x. After that he would tell us that 12 corresponds to the expression and put the 12 directly above the expression on the number line without variables. From there he would hold up another piece of paper marked 5x and ask again where would we put this and why. From there, what would be the corresponding value for 5x and we would answer 10.
This demonstrates the number lineSunday, 17 July 2016
Assessments and Evaluations
So learning the different types of assessments, how to gather evidence of student learning, and then being able to practise creating an evaluation was helpful to me. I found it useful going over the different forms of assessment because sometimes I get them mixed up.
The one thing that really stuck out to me during that class was the sunflower exercise where we had to first solve the task at hand and then create an evaluation for it. I found that rich task very fun to do because it provided me with just enough information to do the assignment and yet still make it challenging. I also got to use Desmos to see what sort of graph some of the equations (or expressions? I still get them mixed up!) looked like and that was fun because it was a resource that actually came into handy! I really liked the task because it wasn't just math per se...you had to understand and apply the math to a real life situation. So for example, if you had an inverted parabola where the graph clearly isn't a linear relation, you would have to think of which scenario would best describe that particular parabola. So you couldn't just simply state that the plant was placed in sunlight and grew accordingly. One would have to take into account that it started off growing quickly but then as time passed, the growing slowed down exponentially- so maybe, just maybe the plant was initially placed in highly radioactive soil that mutated the organism to grow wild, like that bean stalk story, but then it got uprooted and planted in soil that had been over irrigated and lacked essential elements. Again this goes back to what Dan Meyer had said about math being credible and real, existing outside the four walls of a classroom.
I found that creating the evaluation part was a lot trickier than doing the task itself because creating an evaluation forces you to think about all the steps you have to take to solve the problem. It makes you have to go back and think well what was my initial thought? Then what did I think once that part got figured out and so forth. It's funny how fast your brain operates when you are engaged in solving a dynamic problem...all the steps in thinking happen so fast and organically that you don't even realise what's happening and how you came to your conclusions.
The only sort of confusion I still have is if you want to create Learning Goals with your students, so that they feel more included in their learning journey, how does one do that when curriculum expectations are clearly defined? So maybe I have this wrong, but are Learning Goals taken from the Curriculum expectations? And if they are, how do you tweek and alter them with student input? Any clarification is greatly appreciated!
The one thing that really stuck out to me during that class was the sunflower exercise where we had to first solve the task at hand and then create an evaluation for it. I found that rich task very fun to do because it provided me with just enough information to do the assignment and yet still make it challenging. I also got to use Desmos to see what sort of graph some of the equations (or expressions? I still get them mixed up!) looked like and that was fun because it was a resource that actually came into handy! I really liked the task because it wasn't just math per se...you had to understand and apply the math to a real life situation. So for example, if you had an inverted parabola where the graph clearly isn't a linear relation, you would have to think of which scenario would best describe that particular parabola. So you couldn't just simply state that the plant was placed in sunlight and grew accordingly. One would have to take into account that it started off growing quickly but then as time passed, the growing slowed down exponentially- so maybe, just maybe the plant was initially placed in highly radioactive soil that mutated the organism to grow wild, like that bean stalk story, but then it got uprooted and planted in soil that had been over irrigated and lacked essential elements. Again this goes back to what Dan Meyer had said about math being credible and real, existing outside the four walls of a classroom.
I found that creating the evaluation part was a lot trickier than doing the task itself because creating an evaluation forces you to think about all the steps you have to take to solve the problem. It makes you have to go back and think well what was my initial thought? Then what did I think once that part got figured out and so forth. It's funny how fast your brain operates when you are engaged in solving a dynamic problem...all the steps in thinking happen so fast and organically that you don't even realise what's happening and how you came to your conclusions.
The only sort of confusion I still have is if you want to create Learning Goals with your students, so that they feel more included in their learning journey, how does one do that when curriculum expectations are clearly defined? So maybe I have this wrong, but are Learning Goals taken from the Curriculum expectations? And if they are, how do you tweek and alter them with student input? Any clarification is greatly appreciated!
backward design and rich tasks
So one thing that intrigued me in class was the soda pop problem. I felt interested and captured the moment the video started. It was so strategically short, simple and to the point that even the student who HATES math would be intrigued by it. I felt like a lot of students would guess that the wider glass had more soda, and even when I showed my engineer partner the video, they too guessed the wider cup only because the real answer they figured wouldn't be so obvious. When I watched the video, it was clear to me that regardless of whether the creator was trying to fool you or not, the skinnier glass clearly had more! Sometimes the answer is just that obvious, and no one is trying to trick you :P
Anyway I took a lot from watching the video clip of Dan Meyer as he explains about the different aspects to creating a good rich task for a student. He explains that there are 3 Acts and though I cannot exactly recall all of them, he says that in order to make a question or problem more alluring, we need to give as little information as possible and make the students figure out what information they need in order to solve the problem. So the idea is that we give them the problem they need to solve first; let them think about it, sit on it, ferment with it, rather than giving them all the information and tools they need and then asking the question in the end, because all the guess work is already done.
Another thing he mentions that intrigued me was the idea of math being credible. So often we do questions in the textbook and look to the back to check whether we answered correctly. Though that can work for some students who don't need that extra motivation, it's not appealing to all students. This idea of "does math work?" is so interesting because I think once students can see for their own two eyes that math is real and legit, they will learn to appreciate it more. So in the water filling example Dan uses, he gets the students to guess how long it will take for the jug to fill. Rather than calculating it and checking your answer, he says, lets actually test it in real life and see what we get. I honestly never thought that something as simple as video taping an experiment would make a difference, but it really does because it puts math into something that is tangible, rather than having it be this abstract thing that doesn't really apply to real life.
Anyway I took a lot from watching the video clip of Dan Meyer as he explains about the different aspects to creating a good rich task for a student. He explains that there are 3 Acts and though I cannot exactly recall all of them, he says that in order to make a question or problem more alluring, we need to give as little information as possible and make the students figure out what information they need in order to solve the problem. So the idea is that we give them the problem they need to solve first; let them think about it, sit on it, ferment with it, rather than giving them all the information and tools they need and then asking the question in the end, because all the guess work is already done.
Another thing he mentions that intrigued me was the idea of math being credible. So often we do questions in the textbook and look to the back to check whether we answered correctly. Though that can work for some students who don't need that extra motivation, it's not appealing to all students. This idea of "does math work?" is so interesting because I think once students can see for their own two eyes that math is real and legit, they will learn to appreciate it more. So in the water filling example Dan uses, he gets the students to guess how long it will take for the jug to fill. Rather than calculating it and checking your answer, he says, lets actually test it in real life and see what we get. I honestly never thought that something as simple as video taping an experiment would make a difference, but it really does because it puts math into something that is tangible, rather than having it be this abstract thing that doesn't really apply to real life.
Mindsets
So after reading the article and getting to know my fellow classmates a bit better, I have come to realise that most people have been brought up in a fixed mindset (phew, I am not the only one). But what's remarkable is that all my classmates, myself included can safely say that we are now aware of the consequences of having certain mindsets. It's impossible to change your upbringing and the conditions that you were exposed to growing up but now that you are aware of the way you think, you can consciously more often think about your thinking and the thoughts you have.
For myself, I love learning about this sort of self growth/awareness aspect because it can translate into so many areas of our lives, not just in education. Before learning about this mindset business, I thought I had it all figured out...well I thought I had myself all figured out (ohh the good old days of being in your early 20's) but I could totally see certain behaviours arise whenever change occurred. To make a long story short, I essentially didn't like challenge and yet I craved it at the same time. I didn't like challenge because I was terrified of not succeeding and being seen as inferior. I didn't like the idea of people seeing me "try" because I thought of myself as being "special" and "different" and one who didn't have to try. Looking back on it now, it was extremely draining living in such a mindset, because you basically were forced to live in this box and never stretch or grow out of it. I think all of this stemmed from my parents and perhaps even some educators telling me I was such a good, smart student in high school and like the article said, I placed all my self worth on that.
Now a days, because this concept has been reintroduced to me, I find myself analysing my automatic thoughts and reactions to when things don't go my way. And I ask myself, am I thinking in a fixed mindset? Am I not taking the risk because of how others will view me? Am I not speaking my opinion in fear of how I may be perceived? etc.
So to tie this back to education, I think the best thing you can do for a student is to create a space where students feel like they can share and ask questions. Praise effort and reinforce that hard work and effort are essential to success, whatever their form of success may be. I think it's crucial to value perseverance and resiliency because when you enter the "real world", you aren't going to be validated by a grade and for some that can be tough to deal with.
For myself, I love learning about this sort of self growth/awareness aspect because it can translate into so many areas of our lives, not just in education. Before learning about this mindset business, I thought I had it all figured out...well I thought I had myself all figured out (ohh the good old days of being in your early 20's) but I could totally see certain behaviours arise whenever change occurred. To make a long story short, I essentially didn't like challenge and yet I craved it at the same time. I didn't like challenge because I was terrified of not succeeding and being seen as inferior. I didn't like the idea of people seeing me "try" because I thought of myself as being "special" and "different" and one who didn't have to try. Looking back on it now, it was extremely draining living in such a mindset, because you basically were forced to live in this box and never stretch or grow out of it. I think all of this stemmed from my parents and perhaps even some educators telling me I was such a good, smart student in high school and like the article said, I placed all my self worth on that.
Now a days, because this concept has been reintroduced to me, I find myself analysing my automatic thoughts and reactions to when things don't go my way. And I ask myself, am I thinking in a fixed mindset? Am I not taking the risk because of how others will view me? Am I not speaking my opinion in fear of how I may be perceived? etc.
So to tie this back to education, I think the best thing you can do for a student is to create a space where students feel like they can share and ask questions. Praise effort and reinforce that hard work and effort are essential to success, whatever their form of success may be. I think it's crucial to value perseverance and resiliency because when you enter the "real world", you aren't going to be validated by a grade and for some that can be tough to deal with.
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