Doing Math
1. Weekly Work
Exploring “Games and Math”
I wanted to try to dedicate my weekly work to playing math games this week. I thought that it would be a good idea to do this because I haven’t really explored the possibility of learning math through game play. I think that math games can be a very reliable and effective way for students to learn math.
I wanted to try different levels of learning by increasing the difficulty of the game play.
The first game that I played is called “shape shooting triangles” I think that this math game would be a really good game to introduce to students as they are just getting comfortable learning different types of triangles. The objective of the game is to identify different types of triangles as quickly and accurately as you can within the time allotted. There are all different types of triangles as well as angle measures. I think that once your students got really good at identifying the different types of angles and types of triangles, they would eventually outgrow this game but it would be a really good one to introduce the objective of understanding and identifying triangles and their angle measures.
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/triangles_shoot.htm
The next game that I tried was called “Baseball Geometry.” When I first played this game I thought that it was going to be a really good one because not only was it incorporating sports into the game but it also seemed as though the math was going to be very detailed. I played this game for about 15 minutes and couldn’t quite figure out how to really play it and do well. This game focused mainly on naming triangle sides, such as an ABC triangle. I think that this game might be alright for students that are experienced in playing computer games but I believe that if you tried to do this with the whole class it would not go well because there are so many aspects you have to pay attention to and it could get confusing as well as overwhelming to students.
http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw41554
I think that this game was really fun! This game is fast paced and challenging. The goal of this game is to hurry and grad as many triangles as you can and out them into their correct classification basket. There are A LOT of triangles and you have to go fast but make sure that you are correct, or the score starts completely over. I like this game a lot, its challenging but not because there are so many rules and aspects to the game, the speed aspect of the game is what makes it challenging, also this particular game would encourage competition within the student. The student is always going to try to beat the last score achieved. I think that this game would be a great game for studnets to play for a few minutes to brush up on types of triangles once they already know them. I do not think that this game would be very good to introduce types of triangles just because the speed of the game might overwhelm the students. Overall I think that this was my favorite game!
http://www.math-play.com/classifying-triangles/classifying-triangles.html
Considering that I have not played many if any math games at all, not even in high school or elementary school, I was hesitant to accept the idea of “math games.” I originally thought that a math game would either be really boring or really confusing and I may be able to come up with a better math game that my students would love. After actually giving some of these games a chance I realize that they really can be an effective way of learning. Some of them were actually fun and challenging!
2.
How Big is BIG
Response to lecture: to be totally honest, i was not impressed with the talk. I thought that it was kind of boring and hard to connect with. I think that what he was saying did have a certain importance. I think it is essential to live well as he was saying, but i just think that he didn't tie it into teaching very well and a lot of what he was saying was hard for me to relate to teaching. I also thought that it was dull because he mainly just read off of his power point and it got to the point where it was thinking "I could've just read this presentation myself." Nothing against him, like i said, i think that a lot of what he was say does have importance i just was not able to connect with the lecture personally.
24/20130 Comments
Response to lecture: to be totally honest, i was not impressed with the talk. I thought that it was kind of boring and hard to connect with. I think that what he was saying did have a certain importance. I think it is essential to live well as he was saying, but i just think that he didn't tie it into teaching very well and a lot of what he was saying was hard for me to relate to teaching. I also thought that it was dull because he mainly just read off of his power point and it got to the point where it was thinking "I could've just read this presentation myself." Nothing against him, like i said, i think that a lot of what he was say does have importance i just was not able to connect with the lecture personally.
How big is BIG?
I really liked this story.
I think a few questions that it made me think of were
1. if the smallest thing in the whole world are electrons, protons, and neutrons are the smallest thing that we know of, and the biggest thing that we know of is a star, how many electrons, protons, and neutrons are in one star?
2. if we found the answer to that question, and we had an actual number we could figure out my next question which is, Since humans are right in the middle between the biggest and the smallest how many humans could we fit in a star? Would it be half of the number of electrons, protons, and neutrons that could fit in a star?
3. In the book, it says that humans are right in the middle of the biggest thing and the smallest thing. I wonder if that is true? It would seem as though we are much more near the small end of the spectrum when comparing to things like the sun and the stars.
How big is BIG?
I really liked this story.
I think a few questions that it made me think of were
1. if the smallest thing in the whole world are electrons, protons, and neutrons are the smallest thing that we know of, and the biggest thing that we know of is a star, how many electrons, protons, and neutrons are in one star?
2. if we found the answer to that question, and we had an actual number we could figure out my next question which is, Since humans are right in the middle between the biggest and the smallest how many humans could we fit in a star? Would it be half of the number of electrons, protons, and neutrons that could fit in a star?
3. In the book, it says that humans are right in the middle of the biggest thing and the smallest thing. I wonder if that is true? It would seem as though we are much more near the small end of the spectrum when comparing to things like the sun and the stars.
TEACHING MATH
1. 11/03/20130 Comments
Ineffective Vs. Effective teaching
I recently had a bad experience within a student teaching placement. I was already thinking about doing something similar to this concept but the recent event that i just went through makes me want to do it that much more. So here it is, the TOP 5 things that turn an ineffective teacher into an effective teacher.
#1: Trust- Normally, i think that this one would be a given, but i continue to be astonished at how often trust gets looked over. I think that it applies in more than one way throughout teaching. Obviously, it is absolutely crucial to earn that trust within your students. If your students do feel like they cant trust you, and that you have their best interest at heart, you might as well forget it. But another big part of that puzzle that i personally struggle with is having trust within myself. Especially if we are specifically talking about math. My abilities in math can be extremely scary when i think about it. I often am scared to really get far into the subject with students because i am afraid that i will get lost and confuse them even more. So i guess what i am boiling down here is that yes, it is very important for the teacher to develop the trust with the student but it's also just as if not more important for the teacher to be able to trust that they are a great teacher and have the ability to do some great learning.
#2:Time- Throughout my school experience i had the advantage of having teachers who probably would've stayed all night to help me if they had to and i had the advantage of having teachers who would barley give me the time of day. Although back then i absolutely did NOT view having those teachers as an advantage, i realize now that it was. My junior year in high school i had a teacher for honors English. He had a reputation around the school for being extremely mean and often embarrassing his students. Most kids avoided taking his class all together but some got stuck with him, like me. Throughout this class we had to read Shakespeare and all kinds of readings that were not the easiest to understand without some guidance. I, as well as all of my classmates, dreading going to that class every day because he would embarrass us all. He would randomly call on us to answer one of his questions and if we didn't have the "right" (in his mind) answer, he would call us out that we didn't read, or we don't get it etc. even when we were trying. If we were stuck, there was NO WAY we were going to go ask him a question. He would offer no support or be available if someone did muster up the courage to ask him a question. Basically, what he taught me is that i need to make myself available at all times for my students. I want them to feel like i care about their well being and to know that no matter what i will be their resource at anytime.
#3:Collaboration- I feel like this one is a big key to being an effective teacher. I think being a good teacher is like being a good comedian, don't let your material run dry! If the students have heard and seen this act a million times, they are going to tune out. I think its crucial to be able to get online or talk with peers in the school and see what other teachers are doing. There is something so awesome about seeing or hearing a good idea and being able to change it and make it better for your students. It also keep you as well as your students on your toes. the teacher wont get stuck in a rut of teaching the same way, and the students wont become bored and get stuck in a rut of learning the same way.
#4: Flexibility- With that being said, i believe that flexibility goes hand in hand with collaboration. Teachers need to be able to get a new idea a shot, bring it into their classroom, try it, if it works--> don't just leave it at that, think about a couple things: 1. How well did it go? 2. Is there a way that i can make changes for the activity to go any better? 3. Was each and EVERY student engaged or just some? If it doesn't work--> I would think about 1. Is there a "saving" this activity? 2. Should i just throw it out completely? There have been times where i had what i thought was the coolest lesson plan ever and it totally tanked with my students. I don't think that teachers should get too attached to the lessons and activities they do. I am not saying that if one is awesome you shouldn't use it again, i am just saying that even though it is awesome, could it be better? each time you use it, could it be better?
#5: Variety- I know that this is easier said than done, but it is important. Basically, each student learns a different way at a different pace in a different level. That means that as teachers, we should be able to teach in all those different ways. Back to my English teacher, he felt the only effective way to teach was to have us do the material, then quiz us on it in class. Look how that turned out, I hated the class, and i feel like i didn't learn anything.
After constructing all of these i realize that there is a big difference in effective teachers who make a difference and ineffective teachers who create problems. As a future teacher i want to be someone that students remember
2. Perseverance in Math
On Friday when I heard Professor Golden say that Perseverance in math is a common core standard i was actually shocked. I don't know how many student can relate to me on this but i can personally say that there was absolutely no opportunity or chance to "persevere" in any of my math classes.
So i looked into the standard and it basically says that students should be able to look at a problem and construct a plan as to how they are going to solve this problem instead of jumping right in. I also says that once students get "stuck" instead of just giving up and looking for the answer right away, they should be confident that if they think about it a little bit longer in different ways, they will eventually reach a conclusion. I find this shocking. To be more clear, i think that this standard is awesome and has great intentions, but i do not think that it is being met in regular high schools on a daily basis. At least if regular high schools are anything like what i went to. My middle and high school math experience were exactly the opposite of this standard. If a new concept was introduced, we would work on a problem or two as a class, get the routine down and memorized, and then do some on our own. I cannot honestly say that i remember having to struggle my way through a problem even 1 time. It was always "here is a problem, here is how you do it, try one, quiz on Friday." I know that that sound horrible but that is honestly what i thought was normal. Having to think deeply in M221 and struggle our way through problems is totally new grounds for me. I don't think that my teachers were lazy, i think it was a matter that they knew that they had to rush through material in order to get through what the state required them to get through. In no way am i blaming this on my teachers. I think that this problem comes from the standards that they have to teach. There is so much pressure of what they have to teach and how fast that they have to get through it that i don't think that there is any time to honestly let a class think and struggle their way through one problem for the whole class. That is viewed as a class wasted. What they fail to see is that the student will have actually LEARNED the material, they won't just be memorizing for the quiz or test that is coming up.
Perseverance in the class room seems like a really nice standard but i don't believe that it is taught and practiced enough. I hope to find a way to a happy medium in my class. I hope to find a way to give my students the opportunities to persevere and struggle through a problem but still meet the demands of the state standards.
1. Weekly Work
Exploring “Games and Math”
I wanted to try to dedicate my weekly work to playing math games this week. I thought that it would be a good idea to do this because I haven’t really explored the possibility of learning math through game play. I think that math games can be a very reliable and effective way for students to learn math.
I wanted to try different levels of learning by increasing the difficulty of the game play.
The first game that I played is called “shape shooting triangles” I think that this math game would be a really good game to introduce to students as they are just getting comfortable learning different types of triangles. The objective of the game is to identify different types of triangles as quickly and accurately as you can within the time allotted. There are all different types of triangles as well as angle measures. I think that once your students got really good at identifying the different types of angles and types of triangles, they would eventually outgrow this game but it would be a really good one to introduce the objective of understanding and identifying triangles and their angle measures.
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/triangles_shoot.htm
The next game that I tried was called “Baseball Geometry.” When I first played this game I thought that it was going to be a really good one because not only was it incorporating sports into the game but it also seemed as though the math was going to be very detailed. I played this game for about 15 minutes and couldn’t quite figure out how to really play it and do well. This game focused mainly on naming triangle sides, such as an ABC triangle. I think that this game might be alright for students that are experienced in playing computer games but I believe that if you tried to do this with the whole class it would not go well because there are so many aspects you have to pay attention to and it could get confusing as well as overwhelming to students.
http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw41554
I think that this game was really fun! This game is fast paced and challenging. The goal of this game is to hurry and grad as many triangles as you can and out them into their correct classification basket. There are A LOT of triangles and you have to go fast but make sure that you are correct, or the score starts completely over. I like this game a lot, its challenging but not because there are so many rules and aspects to the game, the speed aspect of the game is what makes it challenging, also this particular game would encourage competition within the student. The student is always going to try to beat the last score achieved. I think that this game would be a great game for studnets to play for a few minutes to brush up on types of triangles once they already know them. I do not think that this game would be very good to introduce types of triangles just because the speed of the game might overwhelm the students. Overall I think that this was my favorite game!
http://www.math-play.com/classifying-triangles/classifying-triangles.html
Considering that I have not played many if any math games at all, not even in high school or elementary school, I was hesitant to accept the idea of “math games.” I originally thought that a math game would either be really boring or really confusing and I may be able to come up with a better math game that my students would love. After actually giving some of these games a chance I realize that they really can be an effective way of learning. Some of them were actually fun and challenging!
2.
How Big is BIG
Response to lecture: to be totally honest, i was not impressed with the talk. I thought that it was kind of boring and hard to connect with. I think that what he was saying did have a certain importance. I think it is essential to live well as he was saying, but i just think that he didn't tie it into teaching very well and a lot of what he was saying was hard for me to relate to teaching. I also thought that it was dull because he mainly just read off of his power point and it got to the point where it was thinking "I could've just read this presentation myself." Nothing against him, like i said, i think that a lot of what he was say does have importance i just was not able to connect with the lecture personally.
24/20130 Comments
Response to lecture: to be totally honest, i was not impressed with the talk. I thought that it was kind of boring and hard to connect with. I think that what he was saying did have a certain importance. I think it is essential to live well as he was saying, but i just think that he didn't tie it into teaching very well and a lot of what he was saying was hard for me to relate to teaching. I also thought that it was dull because he mainly just read off of his power point and it got to the point where it was thinking "I could've just read this presentation myself." Nothing against him, like i said, i think that a lot of what he was say does have importance i just was not able to connect with the lecture personally.
How big is BIG?
I really liked this story.
I think a few questions that it made me think of were
1. if the smallest thing in the whole world are electrons, protons, and neutrons are the smallest thing that we know of, and the biggest thing that we know of is a star, how many electrons, protons, and neutrons are in one star?
2. if we found the answer to that question, and we had an actual number we could figure out my next question which is, Since humans are right in the middle between the biggest and the smallest how many humans could we fit in a star? Would it be half of the number of electrons, protons, and neutrons that could fit in a star?
3. In the book, it says that humans are right in the middle of the biggest thing and the smallest thing. I wonder if that is true? It would seem as though we are much more near the small end of the spectrum when comparing to things like the sun and the stars.
How big is BIG?
I really liked this story.
I think a few questions that it made me think of were
1. if the smallest thing in the whole world are electrons, protons, and neutrons are the smallest thing that we know of, and the biggest thing that we know of is a star, how many electrons, protons, and neutrons are in one star?
2. if we found the answer to that question, and we had an actual number we could figure out my next question which is, Since humans are right in the middle between the biggest and the smallest how many humans could we fit in a star? Would it be half of the number of electrons, protons, and neutrons that could fit in a star?
3. In the book, it says that humans are right in the middle of the biggest thing and the smallest thing. I wonder if that is true? It would seem as though we are much more near the small end of the spectrum when comparing to things like the sun and the stars.
TEACHING MATH
1. 11/03/20130 Comments
Ineffective Vs. Effective teaching
I recently had a bad experience within a student teaching placement. I was already thinking about doing something similar to this concept but the recent event that i just went through makes me want to do it that much more. So here it is, the TOP 5 things that turn an ineffective teacher into an effective teacher.
#1: Trust- Normally, i think that this one would be a given, but i continue to be astonished at how often trust gets looked over. I think that it applies in more than one way throughout teaching. Obviously, it is absolutely crucial to earn that trust within your students. If your students do feel like they cant trust you, and that you have their best interest at heart, you might as well forget it. But another big part of that puzzle that i personally struggle with is having trust within myself. Especially if we are specifically talking about math. My abilities in math can be extremely scary when i think about it. I often am scared to really get far into the subject with students because i am afraid that i will get lost and confuse them even more. So i guess what i am boiling down here is that yes, it is very important for the teacher to develop the trust with the student but it's also just as if not more important for the teacher to be able to trust that they are a great teacher and have the ability to do some great learning.
#2:Time- Throughout my school experience i had the advantage of having teachers who probably would've stayed all night to help me if they had to and i had the advantage of having teachers who would barley give me the time of day. Although back then i absolutely did NOT view having those teachers as an advantage, i realize now that it was. My junior year in high school i had a teacher for honors English. He had a reputation around the school for being extremely mean and often embarrassing his students. Most kids avoided taking his class all together but some got stuck with him, like me. Throughout this class we had to read Shakespeare and all kinds of readings that were not the easiest to understand without some guidance. I, as well as all of my classmates, dreading going to that class every day because he would embarrass us all. He would randomly call on us to answer one of his questions and if we didn't have the "right" (in his mind) answer, he would call us out that we didn't read, or we don't get it etc. even when we were trying. If we were stuck, there was NO WAY we were going to go ask him a question. He would offer no support or be available if someone did muster up the courage to ask him a question. Basically, what he taught me is that i need to make myself available at all times for my students. I want them to feel like i care about their well being and to know that no matter what i will be their resource at anytime.
#3:Collaboration- I feel like this one is a big key to being an effective teacher. I think being a good teacher is like being a good comedian, don't let your material run dry! If the students have heard and seen this act a million times, they are going to tune out. I think its crucial to be able to get online or talk with peers in the school and see what other teachers are doing. There is something so awesome about seeing or hearing a good idea and being able to change it and make it better for your students. It also keep you as well as your students on your toes. the teacher wont get stuck in a rut of teaching the same way, and the students wont become bored and get stuck in a rut of learning the same way.
#4: Flexibility- With that being said, i believe that flexibility goes hand in hand with collaboration. Teachers need to be able to get a new idea a shot, bring it into their classroom, try it, if it works--> don't just leave it at that, think about a couple things: 1. How well did it go? 2. Is there a way that i can make changes for the activity to go any better? 3. Was each and EVERY student engaged or just some? If it doesn't work--> I would think about 1. Is there a "saving" this activity? 2. Should i just throw it out completely? There have been times where i had what i thought was the coolest lesson plan ever and it totally tanked with my students. I don't think that teachers should get too attached to the lessons and activities they do. I am not saying that if one is awesome you shouldn't use it again, i am just saying that even though it is awesome, could it be better? each time you use it, could it be better?
#5: Variety- I know that this is easier said than done, but it is important. Basically, each student learns a different way at a different pace in a different level. That means that as teachers, we should be able to teach in all those different ways. Back to my English teacher, he felt the only effective way to teach was to have us do the material, then quiz us on it in class. Look how that turned out, I hated the class, and i feel like i didn't learn anything.
After constructing all of these i realize that there is a big difference in effective teachers who make a difference and ineffective teachers who create problems. As a future teacher i want to be someone that students remember
2. Perseverance in Math
On Friday when I heard Professor Golden say that Perseverance in math is a common core standard i was actually shocked. I don't know how many student can relate to me on this but i can personally say that there was absolutely no opportunity or chance to "persevere" in any of my math classes.
So i looked into the standard and it basically says that students should be able to look at a problem and construct a plan as to how they are going to solve this problem instead of jumping right in. I also says that once students get "stuck" instead of just giving up and looking for the answer right away, they should be confident that if they think about it a little bit longer in different ways, they will eventually reach a conclusion. I find this shocking. To be more clear, i think that this standard is awesome and has great intentions, but i do not think that it is being met in regular high schools on a daily basis. At least if regular high schools are anything like what i went to. My middle and high school math experience were exactly the opposite of this standard. If a new concept was introduced, we would work on a problem or two as a class, get the routine down and memorized, and then do some on our own. I cannot honestly say that i remember having to struggle my way through a problem even 1 time. It was always "here is a problem, here is how you do it, try one, quiz on Friday." I know that that sound horrible but that is honestly what i thought was normal. Having to think deeply in M221 and struggle our way through problems is totally new grounds for me. I don't think that my teachers were lazy, i think it was a matter that they knew that they had to rush through material in order to get through what the state required them to get through. In no way am i blaming this on my teachers. I think that this problem comes from the standards that they have to teach. There is so much pressure of what they have to teach and how fast that they have to get through it that i don't think that there is any time to honestly let a class think and struggle their way through one problem for the whole class. That is viewed as a class wasted. What they fail to see is that the student will have actually LEARNED the material, they won't just be memorizing for the quiz or test that is coming up.
Perseverance in the class room seems like a really nice standard but i don't believe that it is taught and practiced enough. I hope to find a way to a happy medium in my class. I hope to find a way to give my students the opportunities to persevere and struggle through a problem but still meet the demands of the state standards.