Sometimes I don't really realize how much I actually use probability every single day. For example, yesterday I had a class at 10am, and my exact thought running through my head as I'm lying in bed is, "What are the chances that there is going to be an in class activity today? Will I lose points if I keep sleeping?" That is just one example of me thinking about and analyzing the probability of a certain situation.
For a homework assignment in our coursework, it was to make a comment on Facebook about probability that we recognize in our everyday lives. A really good example that I read, was about the chances of me guessing on a multiple choice test and actually getting it correct. If there are four choices on the test, A,B,C,D, there is a 25% chance that I would get it correct. Which is terrible probability for a test if you ask me. But another chance to increase your probability of getting it right is when I may eliminate a choice all together because I am certain that it is incorrect, then I am guessing between 3 different choices and my chances increase to 33%.
Another good example that I noticed was the weather. In Michigan, everyone knows that Michigan weather is out of wack, so we usually don't rely on the probability of a certain weather occurring. Our type of weather varies from hour to hour, so this is an example when probability is harder to calculate.
Overall, probability happens in our day to day lives when we don't even realize it, and that is what concludes us to become critical thinkers.
Thursday, April 20, 2017
Monday, March 27, 2017
FMN & WMAAA
The past few weeks of class, we have been spending time with students ranging from kindergarten to 8th grade. This was a neat experience for me, and placed at a really convenient time as well. I spent some time in classrooms because of my courses but not much, mostly just observations. It was very cool to be able to make up our own game for family math night and see how students and their parents were able to react to it, and also give us their feedback.
While at the WMAAA a few weeks back, we had an activity given to us to work on with the students. But it was nice to not have to worry about the organization portion of it and just work on the teaching parts, and getting to know the students. Personally, I met 3 boys who were all in 6th grade, two of them were best friends and one of them was just sitting at the table. And with the 45 minutes that I was able to talk to the, I learning so much about every single one of them. They were not afraid to tell me what they liked most, what they didn't like, etc. And it was nice to just sit back and listen while working on the activity.
Overall, being in the classroom these few times was refreshing. It was just a little reminder as to why we all stay up late finishing projects, studying, finishing up endless lesson plans, etc. It makes everything worth it.
While at the WMAAA a few weeks back, we had an activity given to us to work on with the students. But it was nice to not have to worry about the organization portion of it and just work on the teaching parts, and getting to know the students. Personally, I met 3 boys who were all in 6th grade, two of them were best friends and one of them was just sitting at the table. And with the 45 minutes that I was able to talk to the, I learning so much about every single one of them. They were not afraid to tell me what they liked most, what they didn't like, etc. And it was nice to just sit back and listen while working on the activity.
Overall, being in the classroom these few times was refreshing. It was just a little reminder as to why we all stay up late finishing projects, studying, finishing up endless lesson plans, etc. It makes everything worth it.
Sunday, February 26, 2017
Sandwiches?
Walking into class last Tuesday I was very interested on what we were going to be talking about that day in class. I had previously checked the google document before class to see what we would be doing, and was very curious as to why the picture of the bagel with the jelly in it was important.
As a Subway employee, I feel confident in saying what is and is not considered a sandwich. I was relieved that the whole class agreed that a pizza was not a sandwich. I really think that I would have gotten really worked up if someone thought it was.
As a table, we agreed pretty quickly with what we considered to be a sandwich, so that was a relief. But as each group started to be put up their ideas on the board, I started to think more deeply to what would be a sandwich, specifically with the quesadilla. Yes, a quesadilla is a food with two sides of bread substance and filling in the middle, but is that considered a sandwich? I still am not sure at this point, part of me believes that it is according to my definition, but another part of says that there is no way that I could ever go into a restaurant, look at their sandwich menu and see that is quesadilla is listed below. And I also started to question, if a pastry or danish was considered a sandwich. Yes, both of these match the definition that me and my group created, but personally in my mind I consider them to be a dessert food, and I think that all sandwiches should be a "lunch" food.
Through our discussion in class, I also noticed that a lot of people were altering their definitions or changing their minds to what they thought was considered a sandwich in the start of the class. I believe that this relates to math in many ways. People often think of one way to do math in the start of a problem or issue, but then as they work through it they notice that there is a different way of approaching the problem. This even happens in our everyday life. Math is everywhere.
I think that the math point of this topic, is to think about how different ideas can fit into different or multiple categories. For example, in one of my SBAR's I included a Venn Diagram about how different 3D shapes can fit into multiple categories or none at all, and I believe that this is what that activity was proposed to show. This is a fun example of showing students how different and similar some math concepts can be all in one instance.
As a Subway employee, I feel confident in saying what is and is not considered a sandwich. I was relieved that the whole class agreed that a pizza was not a sandwich. I really think that I would have gotten really worked up if someone thought it was.
As a table, we agreed pretty quickly with what we considered to be a sandwich, so that was a relief. But as each group started to be put up their ideas on the board, I started to think more deeply to what would be a sandwich, specifically with the quesadilla. Yes, a quesadilla is a food with two sides of bread substance and filling in the middle, but is that considered a sandwich? I still am not sure at this point, part of me believes that it is according to my definition, but another part of says that there is no way that I could ever go into a restaurant, look at their sandwich menu and see that is quesadilla is listed below. And I also started to question, if a pastry or danish was considered a sandwich. Yes, both of these match the definition that me and my group created, but personally in my mind I consider them to be a dessert food, and I think that all sandwiches should be a "lunch" food.
Through our discussion in class, I also noticed that a lot of people were altering their definitions or changing their minds to what they thought was considered a sandwich in the start of the class. I believe that this relates to math in many ways. People often think of one way to do math in the start of a problem or issue, but then as they work through it they notice that there is a different way of approaching the problem. This even happens in our everyday life. Math is everywhere.
I think that the math point of this topic, is to think about how different ideas can fit into different or multiple categories. For example, in one of my SBAR's I included a Venn Diagram about how different 3D shapes can fit into multiple categories or none at all, and I believe that this is what that activity was proposed to show. This is a fun example of showing students how different and similar some math concepts can be all in one instance.
Monday, February 6, 2017
You CAN do math.
In this blog, I am going to be reflecting on chapter one of Jo Boaler's textbook, "Mathematical mindsets." Her purpose in this book is to unleash student's potential through creative math, inspiring messages and innovative teaching.
I am going to be completely honest with you. Growing up, I was good at math. I don't know if I just got lucky with good teachers, or if my mind was "made" to do math, or what, I just wasn't sure. Through elementary school, I kept up well, catching on pretty quick to most math concepts, and succeeding in showing what I knew to my teachers. Throughout middle school was similar and when I got to high school, something was different. It got harder for me, I wasn't sure if it was the content, or the teaching of the certain concept, or if other students were just understanding it better and faster than I was, but I felt belittled by it all. It may have been that I always did so well without trying that much, and then as I got older math starting to become my effort-filled subject form day to day.
Then my senior year I enrolled in AP Calculus 1.
That was probably the hardest class I had taken throughout all of high school. Before that class I thought that with effort, I would always do well in math, but that class proved me wrong. I put my all into the first test, and got a 94% on it, not bad, right? WELL, the second test I got a little too confident and came out with a 51%, that was like a stab in the gut. I thought I was supposed to be good at math? It felt like I knew what I was doing, but I guess not.
I didn't let that second test score discourage me throughout the rest of the year. It made me want to push myself harder, and get the grade that I thought I deserved.
I believe that all students should have this type of mindset when it comes to mathematics. They should not walk into math class, and immediately think, "I can't do this." As teachers our job is to positively encourage students to do well and always try the best that they very can. And that is all that we can ask from them. No student should every be considered "unable" to do well in mathematics. This may be because some teachers doubt their own math skills, and as teachers if we go into teaching with a negative attitude, our own students will pick up on those comments, and come to the conclusion that they are unable to do math too.
I believe that growth mindset is an important aspect in a child's education. They need to be able to understand that they are capable of growing in their knowledge and obtaining anything that they put their mind's too. I believe that mathematics can sometimes discourage students because they get frustrated and such, but as teachers we need to be able to explain to them that growth is obtainable for everyone in every subject.
"Students may be unready for some mathematics because they still need to learn some foundational, prerequisite mathematics they have not yet learned, but not because their brain cannot develop those connections because of their age or maturity. When students need new connections, they learn them." -Jo Boaler
I am going to be completely honest with you. Growing up, I was good at math. I don't know if I just got lucky with good teachers, or if my mind was "made" to do math, or what, I just wasn't sure. Through elementary school, I kept up well, catching on pretty quick to most math concepts, and succeeding in showing what I knew to my teachers. Throughout middle school was similar and when I got to high school, something was different. It got harder for me, I wasn't sure if it was the content, or the teaching of the certain concept, or if other students were just understanding it better and faster than I was, but I felt belittled by it all. It may have been that I always did so well without trying that much, and then as I got older math starting to become my effort-filled subject form day to day.
Then my senior year I enrolled in AP Calculus 1.
That was probably the hardest class I had taken throughout all of high school. Before that class I thought that with effort, I would always do well in math, but that class proved me wrong. I put my all into the first test, and got a 94% on it, not bad, right? WELL, the second test I got a little too confident and came out with a 51%, that was like a stab in the gut. I thought I was supposed to be good at math? It felt like I knew what I was doing, but I guess not.
I didn't let that second test score discourage me throughout the rest of the year. It made me want to push myself harder, and get the grade that I thought I deserved.
I believe that all students should have this type of mindset when it comes to mathematics. They should not walk into math class, and immediately think, "I can't do this." As teachers our job is to positively encourage students to do well and always try the best that they very can. And that is all that we can ask from them. No student should every be considered "unable" to do well in mathematics. This may be because some teachers doubt their own math skills, and as teachers if we go into teaching with a negative attitude, our own students will pick up on those comments, and come to the conclusion that they are unable to do math too.
I believe that growth mindset is an important aspect in a child's education. They need to be able to understand that they are capable of growing in their knowledge and obtaining anything that they put their mind's too. I believe that mathematics can sometimes discourage students because they get frustrated and such, but as teachers we need to be able to explain to them that growth is obtainable for everyone in every subject.
"Students may be unready for some mathematics because they still need to learn some foundational, prerequisite mathematics they have not yet learned, but not because their brain cannot develop those connections because of their age or maturity. When students need new connections, they learn them." -Jo Boaler
Sunday, January 22, 2017
Patterns? Patterns.
Math is an interesting subject. Certain individuals interpretations of it, differ intensively. For example, some may say it's strictly numbers and formulas, others may include that there are letters involved, and few amounts would include patterns in their descriptions. So are patterns a part of math? Of course they are! Patterns may not be in most peoples descriptions of math, but if they were to be asked if patterns were a part of math, they would agree that they are. It just takes a second for some people to realize what concepts outside of numbers, formulas and letters, are incorporated in math.
For us teachers, incorporating patterns into our math curriculum is very important. Patterns are present in many different branches of math. Such as formulas in geometry, to long division, etc. Students are performing pattern-like tasks everyday in their math lessons, homework and tests. They just might not be aware of it at the time.
Being able to teach our students how to recognize patterns all around them is very important.
For a simple example with practicing the differentiating of patterns, students can be given four images and decide 1. which one does not belong or 2. what each image has different from the alternate 3.
Why is this important? Patterns are a way of life, we see them each and every day even when we don't even realize it. We want our students to be able to go home and tell their parents how they recognize and analyze different patterns, because when they do, we know that they fully understand that single concept of math, and as a teacher, that is an important milestone. As students are recognizing these patterns, i want them to be thinking about how math is involved, and this will help them realize how important math really is and how we use it every single day. This will help answer their questions, of "why is this important, I'm never going to use it?" And being able to answer WHY to that question, is a huge step in education.
Let's practice and give it a try!
For us teachers, incorporating patterns into our math curriculum is very important. Patterns are present in many different branches of math. Such as formulas in geometry, to long division, etc. Students are performing pattern-like tasks everyday in their math lessons, homework and tests. They just might not be aware of it at the time.
Being able to teach our students how to recognize patterns all around them is very important.
For a simple example with practicing the differentiating of patterns, students can be given four images and decide 1. which one does not belong or 2. what each image has different from the alternate 3.
Why is this important? Patterns are a way of life, we see them each and every day even when we don't even realize it. We want our students to be able to go home and tell their parents how they recognize and analyze different patterns, because when they do, we know that they fully understand that single concept of math, and as a teacher, that is an important milestone. As students are recognizing these patterns, i want them to be thinking about how math is involved, and this will help them realize how important math really is and how we use it every single day. This will help answer their questions, of "why is this important, I'm never going to use it?" And being able to answer WHY to that question, is a huge step in education.
Let's practice and give it a try!
Answers:
Top left- Not a digital clock.
Top right- Specifies whether its AM or PM. The others are not stated.
Bottom left- Hour is at 8, the others are at 9 o'clock.
Bottom right- Minute is at 32, the others are all at 31 minutes.
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