This blog will be talking about the CCSS M standards and the process standards and how they all intertwine. A lot of these standards tell us the same thing. We especially found that out when doing our poster activity today in class. It showed that a lot of them are intertwined to almost every single one of the other set and vice versa. It is important to know how important it is that these two sets of standards intertwine because when you start planning and teaching lessons you will want to make sure that you are keeping that in mind. One of the most interesting things that came up out of both sets of standards, to me, was communication. This tells me, and the rest of my classmates, that we really need to be paying attention to how we are wording things to our students, and how we need to model that skill so our students know what to do.
Another big concept that was brought up a lot was the reasoning portion of the sets of standards. This is important because if the students are not able to reason and understand exactly why a mathematical concept or idea works the way it does, than they will experience frustration as they get further along in their academic years.
All in all, I noticed that for each one of the process standards, at least one of the CCSS M standards. I found that very interesting because it has really opened my eyes to how I need to be planning and going about the problems that I will be giving and preparing for my students. By seeing how these sets of standards connect, I also see how important modeling the right thing for my students is. I feel like, if we as teachers don't show the students what they need to be doing, than we are ultimately setting them up for difficulties. This goes for when the students use manipulatives etc. as well. The main beauty, as previously mentioned, is that when you hit one set of standards, you are more than like hitting another standard from the other set which makes the lesson twice as rewarding.
Tuesday, May 27, 2014
Monday, May 26, 2014
Video Analysis 1
This blog will be a video analysis. The video that I will be analyzing is a lesson that deals with cost analysis, and it was called "comparing linear functions". The planning was with the teacher and observers collaborating and talking about the two previous activities that had been done, which lead them to the conclusion that they needed to do this particular activity that they were going to do in the lesson. During the planning, they also discussed that they would have to cover any confusions or misconceptions that the students might have during the lesson. The specific activity is called DVD plans.
The actual lesson the teacher went through with the students step by step. He had the students look at how they constructed their table and started it. Then he had the students open their packets and look at different students tables. As he had them look at the work, he had the students talk to their partners and see if the data that they were looking at made mathematical sense, and ask themselves why the data did or did not make sense. The students found out that even though the data may not have matched the plan, it still could of made mathematical sense. One of the students brought up the concept of zero. The class had a discussion about whether there should even be zero listed in the data. Most students saw that there should be zero listed because even if you do not rent or buy any movies you are still paying the flat rate for the month. One of the big confusions that the students had was the plan where it was the $13 plus $1 per extra rental. I noticed though that the students eventually realized this concept and became not as confused about it. I also noticed when looking at student work from the two previous cost analysis activities before this lesson I noticed that on the second page there was lots of confusion. Some of the students did not even answer any of the questions.
The faculty debriefing was very interesting. It consisted of the teacher and three observers. The teacher discussed how the students had the instantaneous connection to the prompt. Along with that, he discussed how he wanted to delve deeper into that connection for next time. The three observers then discussed their groups that they were observing. The first observer said that she noticed that one of the students set his data up in three charts, which she found interesting. Along with that, she said that the idea of just what a t-chart is etc. needs to be discussed more thoroughly next time and compare whether they are the same, different, etc. The teacher than discussed how he would like to discuss the idea of zero more with his students, and that he liked the fact that his students brought that idea up. They, as a group, also discussed how maybe the teacher should just include all of the charts into the packet instead of having the big posters up on the board, because the ones one the board the students rarely referred back to compared to the packet in front of them. One of the implications that I noticed was the whole t-chart situation. It seemed like he automatically thought that all of his students knew exactly what a t-chart was etc.
Overall, I thought the video was an excellent resource and was utilized perfectly. It shows just how important collaborating can be by having the observers in the classroom, and involved in the planning and reflection processes. The video especially is an excellent tool for reflection in many areas. For example you can tell where certain things may not have gone as you had planned. A perfect example was the confusion about the t-charts, and the kids not using the big posters like he had thought. This also proves that by debriefing with the students, you can also find out just how much growth they actually made, and just what ideas need to be revisited. I also liked how the video was split into segments. It allowed me to look at them a lot closer, and it made it easy for me to watch certain parts more than once when I needed to.So, all in all it helped me realize just what I need to do when I start teaching math, and it also taught me some things that could be adapted.
The actual lesson the teacher went through with the students step by step. He had the students look at how they constructed their table and started it. Then he had the students open their packets and look at different students tables. As he had them look at the work, he had the students talk to their partners and see if the data that they were looking at made mathematical sense, and ask themselves why the data did or did not make sense. The students found out that even though the data may not have matched the plan, it still could of made mathematical sense. One of the students brought up the concept of zero. The class had a discussion about whether there should even be zero listed in the data. Most students saw that there should be zero listed because even if you do not rent or buy any movies you are still paying the flat rate for the month. One of the big confusions that the students had was the plan where it was the $13 plus $1 per extra rental. I noticed though that the students eventually realized this concept and became not as confused about it. I also noticed when looking at student work from the two previous cost analysis activities before this lesson I noticed that on the second page there was lots of confusion. Some of the students did not even answer any of the questions.
The faculty debriefing was very interesting. It consisted of the teacher and three observers. The teacher discussed how the students had the instantaneous connection to the prompt. Along with that, he discussed how he wanted to delve deeper into that connection for next time. The three observers then discussed their groups that they were observing. The first observer said that she noticed that one of the students set his data up in three charts, which she found interesting. Along with that, she said that the idea of just what a t-chart is etc. needs to be discussed more thoroughly next time and compare whether they are the same, different, etc. The teacher than discussed how he would like to discuss the idea of zero more with his students, and that he liked the fact that his students brought that idea up. They, as a group, also discussed how maybe the teacher should just include all of the charts into the packet instead of having the big posters up on the board, because the ones one the board the students rarely referred back to compared to the packet in front of them. One of the implications that I noticed was the whole t-chart situation. It seemed like he automatically thought that all of his students knew exactly what a t-chart was etc.
Overall, I thought the video was an excellent resource and was utilized perfectly. It shows just how important collaborating can be by having the observers in the classroom, and involved in the planning and reflection processes. The video especially is an excellent tool for reflection in many areas. For example you can tell where certain things may not have gone as you had planned. A perfect example was the confusion about the t-charts, and the kids not using the big posters like he had thought. This also proves that by debriefing with the students, you can also find out just how much growth they actually made, and just what ideas need to be revisited. I also liked how the video was split into segments. It allowed me to look at them a lot closer, and it made it easy for me to watch certain parts more than once when I needed to.So, all in all it helped me realize just what I need to do when I start teaching math, and it also taught me some things that could be adapted.
Article 2 "How did the answer get bigger?"
For this particular blog, I will be discussing an article from the journal Mathematics teaching in the Middle School. The name of the article is "How did the answer get bigger?" This article addresses the fact that when students begin to work with dividing fractions, they tend to have trouble comprehending the idea that the answer could be bigger than the dividend or divisor. So a big point of this article is that number sense includes your students understanding the significance of the size of the fraction. Another big point is that your students need to understand the connections between the whole and an individual fraction and between other fractions.This article also talks about how your students need to have a flexible mind to understand certain concepts involving fractions.
This particular article is important for fifth to sixth grade because those are the academic years when students start getting into dividing fractions. This is important because up till these academic years, students are only use to doing whole number dividing, which is why it makes it difficult for the students to understand the concept of how an answer got bigger. You can certainly implement this in the classroom by using several of the strategies mentioned in the article. Most of them include the use of manipulatives. I have noticed the more I research different topics and articles in math that hands on and the use of manipulatives are very popular strategies. So, to implement this in your classroom, according to the article, please remember to look at multiplying and dividing fractions from the areas of modeling, equivalence, and symbolism. An example would be to use individual cubes to show the division in a visual sense so the students have the opportunity to physically see how it turns into a big answer.
This particular article is important for fifth to sixth grade because those are the academic years when students start getting into dividing fractions. This is important because up till these academic years, students are only use to doing whole number dividing, which is why it makes it difficult for the students to understand the concept of how an answer got bigger. You can certainly implement this in the classroom by using several of the strategies mentioned in the article. Most of them include the use of manipulatives. I have noticed the more I research different topics and articles in math that hands on and the use of manipulatives are very popular strategies. So, to implement this in your classroom, according to the article, please remember to look at multiplying and dividing fractions from the areas of modeling, equivalence, and symbolism. An example would be to use individual cubes to show the division in a visual sense so the students have the opportunity to physically see how it turns into a big answer.
Article #1 "From whole numbers to invert and multiply"
For this post, I am going to discuss an article from the journal Teaching Children Mathematics. The article name is "From whole numbers to invert and multiply." This article talks about the different standards that get developed in grades 3-6 when it comes to dividing fractions when you need to use the inverting property. This article talks a lot about using various strategies to use when going about teaching these standards to your students. One of the strategies was using modeling to show whole number division. Another strategy that was discussed pertaining to modeling was the partitioning model. Other areas that were discussed throughout this article were multiplicative inverses as unit rates, visualizing fractions, and understanding the invert and multiply algorithm. As you go through this article, you can certainly see how these standards build upon one another in order for the others to be understood in the upper elementary level as mentioned previously.
This article is important because this article helps teachers realize the importance of making sure that the students at their grade level understand the concepts before moving on so their students can be successful throughout the later school years. You can also certainly implement this in you classrooms, especially in grades three through six because that's what grade levels this particular article is targeting. This article also makes you realize just how important manipulatives can be when it comes to those harder concepts for your students to grasp. This is also true for the hands on aspects of this manipulatives. So, in conclusion, you need to implement this by making sure you use manipulatives to help students grasp any concept that might be difficult for them. An example would be the invert and multiply concept from the article.
This article is important because this article helps teachers realize the importance of making sure that the students at their grade level understand the concepts before moving on so their students can be successful throughout the later school years. You can also certainly implement this in you classrooms, especially in grades three through six because that's what grade levels this particular article is targeting. This article also makes you realize just how important manipulatives can be when it comes to those harder concepts for your students to grasp. This is also true for the hands on aspects of this manipulatives. So, in conclusion, you need to implement this by making sure you use manipulatives to help students grasp any concept that might be difficult for them. An example would be the invert and multiply concept from the article.
Sunday, May 25, 2014
NCTM Process Standards
There are several NCTM process standards that are listed on the NCTM website. However, for the purpose of this blog I will only be discussing five. The first one is problem solving. According to the article, problem solving means that you are having your students participate in a task or problem where the solution is unknown in the beginning. It talks about how if students have good problem solving skills they are able to analyze the situation. This also helps them naturally become able to ask questions that are based on the situations that they encounter. You, as the teacher, play an instrumental role in helping the students develop problem solving skills according to this particular process standard. This means that the problems that you give students need to be engaging, create an environment that allows the students to experience and share their successes and failures, and discuss why the failures worked out that way. You can certainly put this into practice when teaching. An example the article gave was middle school students given different fruit juice mixtures to see which one is fruitier to introduce the topic of proportions.
The second process standard that I will talk to you about is reasoning and proof. This particular process standard is important because students need to know why a particular process or mathematical concept works. This standard is also important because this standard is used across the content areas. One of the biggest things with this standard is that it needs to be developed as the students progress throughout their school years. You can do that by having your students consistently use it in many contexts. You can implement this in your class by making sure that you are reviewing the concepts consistently all year so that they are confident and able to build on it the next school year.
The third process standard that I am going to discuss is communication. Communication is also a process standard that is important no matter what subject you are talking about but especially in math. This is because if you are not precise in your communication it will be all confusing to your students when you are explaining the concepts. This means that you need to make sure that when you are explaining a new concept to your students, or if students are explaining a justification for an answer to you, or if your students are labeling that you are correcting them if needed so they know the correct precise communication skills for math. You also need to make sure that you encourage your students to express themselves clearly and effectively especially as they get further along in school. There is also lots of benefits to your students working collaboratively together. This is because,according to the article, the students get the opportunity to see the perspectives and methods of their fellow classmates. They also,according to the article, should become more aware of their audience as they continue to get further along in their school careers. You can implement this standard into the classroom by correcting students when they are not using the correct communication. You can also implement this standard by making sure that you personally are modeling the correct communication so that your students know what to do.
The fourth process standard that I am going to discuss is connections.Connections, according to the article, is important because it helps students come to the realization that mathematics is not a set of isolated skills. It also helps kids understand that it relates in someways to the other core subjects. As the students go along in their school careers, they should, according to the article, come to expect and exploit the connections using what they have learned in one area for justification on how something does or doesn't work in another area. You also, as a teacher need to make sure that you have the connections that the students can make in their real lives as well. You can implement this standard in middle school, for example, when you have them collect graph data. This is also true in social studies. An example will be when going over measurements on a legend of a map of the united states, and you are trying to figure out which state has the biggest land area, etc.
The fifth and final process standard that I am going to discuss is representation. According to the article, this is important because it allows your students to communicate mathematical approaches, arguments, and understanding to themselves and others. It also is important because it allows students to recognize the connections that can be made between similar topics to the one they are studying, and apply those concepts to real life like situations or problems. With this particular standard, you need to make sure that you let your students represent their ideas in their own way even if it is not the standard way to do it. This is so that it makes sense to them. However, the article says that you should still teach the standard way to do it so that way that still get that opportunity to see it. You can implement this as a teacher by having the students represent a math problem such as 16-4 by drawing pictures. You can tell them a standard way to do them but don't take away points when grading if they do it differently but get the same answer.
The second process standard that I will talk to you about is reasoning and proof. This particular process standard is important because students need to know why a particular process or mathematical concept works. This standard is also important because this standard is used across the content areas. One of the biggest things with this standard is that it needs to be developed as the students progress throughout their school years. You can do that by having your students consistently use it in many contexts. You can implement this in your class by making sure that you are reviewing the concepts consistently all year so that they are confident and able to build on it the next school year.
The third process standard that I am going to discuss is communication. Communication is also a process standard that is important no matter what subject you are talking about but especially in math. This is because if you are not precise in your communication it will be all confusing to your students when you are explaining the concepts. This means that you need to make sure that when you are explaining a new concept to your students, or if students are explaining a justification for an answer to you, or if your students are labeling that you are correcting them if needed so they know the correct precise communication skills for math. You also need to make sure that you encourage your students to express themselves clearly and effectively especially as they get further along in school. There is also lots of benefits to your students working collaboratively together. This is because,according to the article, the students get the opportunity to see the perspectives and methods of their fellow classmates. They also,according to the article, should become more aware of their audience as they continue to get further along in their school careers. You can implement this standard into the classroom by correcting students when they are not using the correct communication. You can also implement this standard by making sure that you personally are modeling the correct communication so that your students know what to do.
The fourth process standard that I am going to discuss is connections.Connections, according to the article, is important because it helps students come to the realization that mathematics is not a set of isolated skills. It also helps kids understand that it relates in someways to the other core subjects. As the students go along in their school careers, they should, according to the article, come to expect and exploit the connections using what they have learned in one area for justification on how something does or doesn't work in another area. You also, as a teacher need to make sure that you have the connections that the students can make in their real lives as well. You can implement this standard in middle school, for example, when you have them collect graph data. This is also true in social studies. An example will be when going over measurements on a legend of a map of the united states, and you are trying to figure out which state has the biggest land area, etc.
The fifth and final process standard that I am going to discuss is representation. According to the article, this is important because it allows your students to communicate mathematical approaches, arguments, and understanding to themselves and others. It also is important because it allows students to recognize the connections that can be made between similar topics to the one they are studying, and apply those concepts to real life like situations or problems. With this particular standard, you need to make sure that you let your students represent their ideas in their own way even if it is not the standard way to do it. This is so that it makes sense to them. However, the article says that you should still teach the standard way to do it so that way that still get that opportunity to see it. You can implement this as a teacher by having the students represent a math problem such as 16-4 by drawing pictures. You can tell them a standard way to do them but don't take away points when grading if they do it differently but get the same answer.
Wednesday, May 21, 2014
Group Noteworthy Ideas about Math and Rich Activities
5-21-14
There were pdf articles that we had to read. The first pdf was called rich activities. This pdf starts off and explains what to consider when looking at whether an activity is rich or not. The first aspect to consider is students age. The second aspect is the student's gender. The third aspect is what the student's expectation of the class is. The last two aspects that are worth considering is the knowledge and experiences that the student might have.This pdf goes on to explain that the student's cognitive demand must be at a higher level. There are four different areas. According to the pdf, they are memorization, procedures without connections to concepts or meaning, procedures with connections to concepts or meaning, and doing math. According to the pdf, we need to be making sure as mathematics teachers that we are not just having kids memorize mathematical facts. This is because, when we, as math teachers, do that are not allowing our students to expand their knowledge and see the whole picture of just what the mathematical concept is or how we got from one point to the next. Another aspect of this pdf is taking into consideration that we really need to look at the problems we give to our students. This is because "looks can be deceiving" so to speak meaning that it might look like a higher level problem, but when you actually break it down and look at it, the problem is really not a higher level problem. This pdf also gives great questions to think about when planning lessons. Some of the questions include in what ways does it build on prior knowledge, previous life experiences, and culture?, what are all the ways the problem can be solved?, what particular challenges might the particular activity present to struggling students and ELL students?, etc.I will certainly keep all of these in mind when I start planning math lessons for my classroom. This also really puts into perspective just how much thinking and reflecting goes into planning a lesson or making sure an activity is rich enough.
The second pdf that I looked at was group noteworthy ideas. This gives different math habits to keep in mind. They are explore ideas, orient/organizing, think in reverse, generalizing, representing, justifying, math language, and check for reasonableness. Each one had a small explanation by them. Also, as you look at each of these ideas, you notice how important each one is to the whole big picture on how students understand mathematics. Without any one of these ideas going through their heads, especially if they are working on a collaborative assignment, they will have difficulty, whether it be great or small, in completing the assignment or task. This is also true, in my opinion, when it comes to planning as a teacher. You need to make sure that you keep all of these ideas in mind, especially when making groups, to help make sure that all of your students can have success in doing the assignment.
Attend to precision and make sense & perservere
5-21-14
There are several CCSS standards when it comes to teaching math to elementary students. The two that I am going to discuss are attend to precision and make sense & persevere. These two, along with the other CCSS standards, will help your students be successful when it comes to math. Also, having the students proficient in these two standards will help their anxiety levels lower when it comes to math.
The first standard I will discuss is make sense and persevere. There are many things that you can say about this standard. The first thing that needs to be said is that not every problem that your students will in contact with will have a clear cut solution to figuring it out. This means, that the students will have to have several chances to attempt the problem. With that being said, you need to consider several different questions when you are examining the types of problems you are giving students. This is because, when you are giving students problems, your job as a teacher is to have your students understanding the many different mathematical concepts so well that you are confident that even if they don't see the solution right away, they will still be able to think through a problem based on what formulas, etc. they already know.
The second standard that I will be discussing is attend to precision. This is important because it pertains a lot to how the students communicate in the subject of mathematics. This includes labeling answers, being clear and concise when using definitions, using definitions properly, etc. This also goes for calculations and procedures. These are particularly important because students need to be specific especially when it comes to, for example, conversions in later elementary years. You would certainly apply this,for instance,in fourth grade when dealing with measurement, units of time, etc. You could take off a point for each time they don't use a label to accompany their answer. You can also relate this to your students everyday lives by getting them involved in a discussion on how confusing it would be to explain to someone increments or specific numbers with no labels, etc.
There are two articles that I read pertaining to these two specific standards. The first article is called "Reasoning and Sense." This article pertains to the standard make sense and persevere. The article gives a very good definition of what the word sense making means. The authors, Kasmer and Martin, say that reasoning and sense making are intertwined. Another good point of the article is that there no is the need to shift from students just memorizing formulas ,etc. and actually understanding the big mathematical ideas that are the foundation in their younger elementary years for when they reach the secondary years. That also hits home when it comes to persevering because if the students are able to fully grasp the concepts or big ideas in the elementary years, then they will be able to persevere and work through much more complicated problems in their late elementary to secondary years. Also, a way to apply this particular standard to your classroom is by creating problems that will challenge the students and make them persevere by having to make sense of the what the problem is asking and think of different solutions to try like in story problems.
The second article I read was "Multidimensional Teaching." This pertained to attend to precision. This article goes into detail on how you need to pay particular the social and cultural aspects of your classroom in order to implement multidimensional teaching into your classroom. This pertains to this particular standard because you are paying attention to fine detail and precision by looking at the cultural and social aspects, which is then modeled to your students through mathematics when it comes to the fine details like labels, etc. This article even gives a teaching example on how to implement this into the classroom.
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