In this article(Promoting equity through reasoning), published in Teaching Children Mathematics, the students are asked to work together and collaborate to find the best possible solutions. The teacher tool the time to walk amongst the groups of students and ask questions that helped widen the students understanding about how to approach the problem. The use of manipulatives (Cuisenaire rods) was an asset that the teacher had the students work with. The use of the Cuisenaire rods was a good tool for the students to use because it gave them an example in front of them to work and find different solutions. The students that were working with the Cuisenaire rods were part of an after school program to help them understand how to go about looking at the class’s material. The after school program incorporated 24 students that were African American along with Latino. The main focus of the program was for the students to focus and build upon their own sense of mathematical thoughts. The students were working together to come up with their solution. Several representations were used in each student’s explanations and were used to back up their claims and prove to the other students. The author’s main focus for the teaching portion was for other teachers to make use of different tasks. Also, teachers must give the students choices that will be easy for them to relate to. The choices will give the students more of an opportunity to explain to their classmates why and how they went about their reasoning. Group work amongst the students is highly encouraged as this will help make the material more public and bring about more class discussion.
I found this article interesting and a great tool/asset that I could use throughout my future career. This article helped me understand the meaning of promoting equity through reasoning. I can see myself implementing some of the author’s ideas on this subject in my future classrooms as long as the students that I am working with will benefit from these methods.
Mueller, M. F.; Maher, C. A. Promoting equity through reasoning. Teaching Children Mathematics, Volume 16, Issue 9, Page 540. Retrieved from: http://my.nctm.org/eresources/article_summary.asp?URI=TCM2010-05-540a&from=B
Saturday, May 1, 2010
Wednesday, April 28, 2010
Technology Reflection
There were many different technologies that have been utilized throughout the semester in this math methods course. Some of the main technologies that were utilized were the use of smart boards, scientific calculators, sketchpad, WIKI, online blogging, and Google docs. My favorites of these were when we made use of the smart board, along with the sketchpad presentation in class.
I am currently novice teaching and it was nice to have a little bit of a background in the uses of smart boards. Unfortunately, the school I am attending only has one smart board available which is located in the computer room. To make use of the smart board, the teacher had to reserve computer lab time for his/her class. It was still nice to show my cooperating teacher some of the basic uses of the smart board for his future reference.
The sketchpad would not have been of much use for me while novicing since I was teaching 8th grade social studies. However, I found that the use of the sketchpad would be a good tool for students that need a visualization of something they are creating. This tool allows the students to make use of the term hands on minds on, because they not only are using their hands to manipulate the shapes and figures on the pad, but they are also thinking through it with their own ideas.
The calculator day was nice because it showed us in class exactly how much one could do with the calculator and it also familiarized us of what could be done. Students sometimes do not know how to work a scientific calculator, but if it is used correctly, it could prove to be a great learning tool for the students. Like all technologies used in the classroom, the teacher must be able to understand what it is the technologies is supposed to do and how to present it to the students.
Google docs were something that I did not really enjoy too much throughout this class, but without them I would not have made it through the course. There was so much group work going on that it was tough for us all too meet every single time we had to complete an assignment or project. Instead of meeting in person we would create a Google doc where one could add their thoughts and ideas to the page and it would save it so everyone else would be able to see the work that was added. It was really nice to have all of the data compiled in one master document so when we were ready to convert it back to a word document all you had to do was cut and paste. It was sometimes frustrating though because the formatting on the Google docs would be different than that of Microsoft Word and you had to spend extra time re-formatting, but in the end, the Google documents proved to be more beneficial than I though they would be mainly because of the nature of the course workload that incorporated lots of group work.
Lastly, but not least, the blogging site has been very helpful for me throughout this course. I never thought I would see the day that I turned into a blogger, but at least I can say that it was for educational purposes. The blogging site was helpful because it gave us the opportunity to look at every student’s perspective and thoughts about the material we were designated to blog about. I was able to read information posted not only by those students who are in my class section, but also the 10:30 A.M. section. The information was helpful because I received lots of insight about the class projects and assignments from my classmates and didn’t have to go mainly off of what I thought and felt about the assignments.
I am currently novice teaching and it was nice to have a little bit of a background in the uses of smart boards. Unfortunately, the school I am attending only has one smart board available which is located in the computer room. To make use of the smart board, the teacher had to reserve computer lab time for his/her class. It was still nice to show my cooperating teacher some of the basic uses of the smart board for his future reference.
The sketchpad would not have been of much use for me while novicing since I was teaching 8th grade social studies. However, I found that the use of the sketchpad would be a good tool for students that need a visualization of something they are creating. This tool allows the students to make use of the term hands on minds on, because they not only are using their hands to manipulate the shapes and figures on the pad, but they are also thinking through it with their own ideas.
The calculator day was nice because it showed us in class exactly how much one could do with the calculator and it also familiarized us of what could be done. Students sometimes do not know how to work a scientific calculator, but if it is used correctly, it could prove to be a great learning tool for the students. Like all technologies used in the classroom, the teacher must be able to understand what it is the technologies is supposed to do and how to present it to the students.
Google docs were something that I did not really enjoy too much throughout this class, but without them I would not have made it through the course. There was so much group work going on that it was tough for us all too meet every single time we had to complete an assignment or project. Instead of meeting in person we would create a Google doc where one could add their thoughts and ideas to the page and it would save it so everyone else would be able to see the work that was added. It was really nice to have all of the data compiled in one master document so when we were ready to convert it back to a word document all you had to do was cut and paste. It was sometimes frustrating though because the formatting on the Google docs would be different than that of Microsoft Word and you had to spend extra time re-formatting, but in the end, the Google documents proved to be more beneficial than I though they would be mainly because of the nature of the course workload that incorporated lots of group work.
Lastly, but not least, the blogging site has been very helpful for me throughout this course. I never thought I would see the day that I turned into a blogger, but at least I can say that it was for educational purposes. The blogging site was helpful because it gave us the opportunity to look at every student’s perspective and thoughts about the material we were designated to blog about. I was able to read information posted not only by those students who are in my class section, but also the 10:30 A.M. section. The information was helpful because I received lots of insight about the class projects and assignments from my classmates and didn’t have to go mainly off of what I thought and felt about the assignments.
Manipulative reflection
1.) How do you hold every student accountable?
Students must understand that the use of manipulatives is for their pure benefit. Having concrete examples in front of them is something that could prove to be very beneficial for some students to learn from. Holding every student accountable is something that must be done day in and day out while teaching with manipulatives. Students need to know that everyone in the group must be contributing in one way, shape, or form. Take for example today in class when Dr. Grant called on me and told me that I better be helping Debrell out with the writing portion of the class activity. I believe that Dr. Grant had done this on purpose to make sure that I was being held accountable for the work that was being produced throughout the class activity. In the younger grades it would be a little bit different though. I would make it a priority that each student realized the importance of using manipulatives in the classroom activities. Manipulatives give each student to express a concrete example of what they are trying to explain to anyone that wants to listen and learn.
2.) Why do they say “hands on, minds on” instead of just “hands on?”
Hands on minds on talks about the use of manipulatives and how the students are not only working with the tools with their hands, but they are also thinking through what they are trying to create. When I think of hands on activities, I think of a teacher showing a model and the students having to reconstruct that model with their own tools. Hands on minds on incorporates the students own thinking and gives them a chance to think more critically about what they are trying to create or explain. When I was younger I absolutely loved the opportunity when I was given something to manipulate (play with). In school I would look forward to the free time when the teacher would allow me to work freely with the tools provided throughout the classroom. I was able to do what I wanted and in the end I was able to explain my reasoning for coming up with what I made. When I think of hands on minds on I think back to the days when I was able to work freely and make up my own assumptions. Students that are given the opportunity to express themselves and come up with their own ideas and expressions will one day be very creative.
3.) How are the process standards incorporated into the use of manipulatives?
The in class activity that we completed in class today was a prime example as to how the process standards are incorporated into the use of manipulatives. We were each given a partner and had to complete an exercise that incorporated the use of pretty much all of the process standards. Students are going to need to use communication to talk amongst one another and come up with the correct approaches to soling the problems in front of them. Connections are made in ever aspect of the use in manipulatves as the students must be able to connect what content standard the aspect connects too. Also, students should be able to connect how the use of manipulatives relates to their real life situations. Reasoning and proof will be used often also as the students must show their proof as to how they came about their reasoning. The process standards will always be a huge part of mathematical situations, the hard part is figuring out how and when to use them appropriately.
Students must understand that the use of manipulatives is for their pure benefit. Having concrete examples in front of them is something that could prove to be very beneficial for some students to learn from. Holding every student accountable is something that must be done day in and day out while teaching with manipulatives. Students need to know that everyone in the group must be contributing in one way, shape, or form. Take for example today in class when Dr. Grant called on me and told me that I better be helping Debrell out with the writing portion of the class activity. I believe that Dr. Grant had done this on purpose to make sure that I was being held accountable for the work that was being produced throughout the class activity. In the younger grades it would be a little bit different though. I would make it a priority that each student realized the importance of using manipulatives in the classroom activities. Manipulatives give each student to express a concrete example of what they are trying to explain to anyone that wants to listen and learn.
2.) Why do they say “hands on, minds on” instead of just “hands on?”
Hands on minds on talks about the use of manipulatives and how the students are not only working with the tools with their hands, but they are also thinking through what they are trying to create. When I think of hands on activities, I think of a teacher showing a model and the students having to reconstruct that model with their own tools. Hands on minds on incorporates the students own thinking and gives them a chance to think more critically about what they are trying to create or explain. When I was younger I absolutely loved the opportunity when I was given something to manipulate (play with). In school I would look forward to the free time when the teacher would allow me to work freely with the tools provided throughout the classroom. I was able to do what I wanted and in the end I was able to explain my reasoning for coming up with what I made. When I think of hands on minds on I think back to the days when I was able to work freely and make up my own assumptions. Students that are given the opportunity to express themselves and come up with their own ideas and expressions will one day be very creative.
3.) How are the process standards incorporated into the use of manipulatives?
The in class activity that we completed in class today was a prime example as to how the process standards are incorporated into the use of manipulatives. We were each given a partner and had to complete an exercise that incorporated the use of pretty much all of the process standards. Students are going to need to use communication to talk amongst one another and come up with the correct approaches to soling the problems in front of them. Connections are made in ever aspect of the use in manipulatves as the students must be able to connect what content standard the aspect connects too. Also, students should be able to connect how the use of manipulatives relates to their real life situations. Reasoning and proof will be used often also as the students must show their proof as to how they came about their reasoning. The process standards will always be a huge part of mathematical situations, the hard part is figuring out how and when to use them appropriately.
Tuesday, April 13, 2010
Error Analysis Reflection
The in class activities related to error Analysis was helpful for me to understand how and why students make some of the mistakes that they do. Being a good teacher takes time and efforts put into knowing the material that your students are learning. The error analysis activity gave us the opportunity to look at methods and approaches that will help solve problems. Students that misunderstand material will need a good explanation as to why they were incorrect with their response. To be able to give a student a proper response and explanation means that the teacher needs to know the steps needed to complete the problem correctly. I learned through this activity that too many times when a teacher shows a solution to a problem, they give the justification of, “and this should be done this way because it has always been done this way.” A teacher must be able to tell the student why that certain thing happens and not just tell them that the reason is because it has always been that way. Error analysis is something that I will be dealing with day in and day out when I get into the teaching field. This experience has helped me understand a few proper ways to go about helping a student understand the mistakes that they have been performing.
Monday, April 12, 2010
April Journal #2
The second article I reviewed was found in the Teaching Children Mathematics journal. The main focus of the article was to express to its readers that the use of cognates while teaching can give all students more opportunities to learn. Students that have prior schooling in their native language before beginning their schooling in the United States could benefit from the cognate teaching approach. This approach could prove to be tricky because there are both friendly cognates which are the useful ones, and then there are false cognates that mean two different things in their languages.
If found this article interesting because it is material that is new to me. I have never heard of the cognate teaching approach, but from the sounds of this article, I can see this being a good teaching tool to know. I feel that I would be better prepared to deal with the diversity of my students and help them learn to their full potential. Having the ability to relate to the whole spectrum of my students will be important when I am faced with multiple races and backgrounds in my classroom.
Gómez, C. L. (2010). Teaching with Cognates. Teaching Children Mathematics, Volume 16, Issue 8, Page 470 retrieved from:
http://www.nctm.org/eresources/article_summary.asp?from=B&uri=TCM2010-04-470a
If found this article interesting because it is material that is new to me. I have never heard of the cognate teaching approach, but from the sounds of this article, I can see this being a good teaching tool to know. I feel that I would be better prepared to deal with the diversity of my students and help them learn to their full potential. Having the ability to relate to the whole spectrum of my students will be important when I am faced with multiple races and backgrounds in my classroom.
Gómez, C. L. (2010). Teaching with Cognates. Teaching Children Mathematics, Volume 16, Issue 8, Page 470 retrieved from:
http://www.nctm.org/eresources/article_summary.asp?from=B&uri=TCM2010-04-470a
April Journal #1
The first article I reviewed was found in the Mathematics Teaching in the Middle School Journal. The main focus of the article was to express to its readers the importance and uses of technology in the classroom. The author pinpointed the main purposes for using technology while teaching mathematics. The author also expressed how technology could be used to get the students more engaged in real-life mathematics. Technology capabilities have caused us to re-think how we are going to present material to our students. It also has helped make learning mathematics more engaging and improved the value of mathematics education for both students and teachers alike.
I felt this article expressed many quality ideas and examples as to how the use of technology can improve mathematics teaching all-around. The author talked of specific ways that could be used to implement good uses of technology while teaching your students. This information will prove to be helpful as I progress through my teaching career since technology will keep improving over the years. It will always be helpful to keep up-to-date with the uses of technology and how I can implement its uses in my classroom.
Soucie T.; Radovic N.; Svedrec R. (2010). Making Technology Work. Mathematics Teaching in the Middle School, Volume 15, Issue 8, Page 466. Retrieved from:
http://www.nctm.org/eresources/article_summary.asp?from=B&uri=MTMS2010-04-466a
I felt this article expressed many quality ideas and examples as to how the use of technology can improve mathematics teaching all-around. The author talked of specific ways that could be used to implement good uses of technology while teaching your students. This information will prove to be helpful as I progress through my teaching career since technology will keep improving over the years. It will always be helpful to keep up-to-date with the uses of technology and how I can implement its uses in my classroom.
Soucie T.; Radovic N.; Svedrec R. (2010). Making Technology Work. Mathematics Teaching in the Middle School, Volume 15, Issue 8, Page 466. Retrieved from:
http://www.nctm.org/eresources/article_summary.asp?from=B&uri=MTMS2010-04-466a
Wednesday, March 24, 2010
Tests and Quizzes: Examining an assessment strategy on high school mathematics achievement
Shirvani, H. (2009). Examining an assessment strategy on high school mathematics achievement: Daily quizzes vs. weekly tests. American secondary education. 38 (1), 34-45.
In this article, Shirvani describes the information that she has found out pertaining to the assessment methods that include frequent quizzes along with weekly testing. Shirvani explained how the use of frequent testing and quizzing proved to be helpful for the students to retain the information being taught to them. Shirvani had many examples as to how these types of assessments prove to be positive learning tools for the students. Examples expressed, but are not limited to:
• Helps monitor
• Builds motivation
• Produces engagement
• High retention rate
• Reduces anxiety
• Leads to higher student achievement
The article also explained that the assessments being administered would help the student with their problem solving skills. There were many connections that were made relating directly to mathematics along with real life situations. The process standards along with the principles relating to school mathematics were expressed abundantly throughout the scholarly article. From the research, I have found that tests and quizzes can prove to be helpful learning tools for students to learn from as long as they are used in the correct manner.
In this article, Shirvani describes the information that she has found out pertaining to the assessment methods that include frequent quizzes along with weekly testing. Shirvani explained how the use of frequent testing and quizzing proved to be helpful for the students to retain the information being taught to them. Shirvani had many examples as to how these types of assessments prove to be positive learning tools for the students. Examples expressed, but are not limited to:
• Helps monitor
• Builds motivation
• Produces engagement
• High retention rate
• Reduces anxiety
• Leads to higher student achievement
The article also explained that the assessments being administered would help the student with their problem solving skills. There were many connections that were made relating directly to mathematics along with real life situations. The process standards along with the principles relating to school mathematics were expressed abundantly throughout the scholarly article. From the research, I have found that tests and quizzes can prove to be helpful learning tools for students to learn from as long as they are used in the correct manner.
Tuesday, March 9, 2010
March Journal Summary #2
The second article that I reviewed was found in the Mathematics Teaching in the Middle School and was titled The Value of Guess and Check. The author states that guessing and checking encourages the development of problem-solving skills by forcing students to try and make sense of the material involved. Having the students gain a better understanding of quantitative relationship is also one of the main goals shown throughout the article. Word problems can never be underestimated while students are learning new concepts. By giving the students the opportunity to guess and check helps them look deeper into the problem and eventually understand it more. Eventually, the goal is to have the students not go through the process of guessing and checking each time a problem comes about, instead they will know how to go about the problem faster and more efficiently. This will not only help the students learn more material in a shorter amount of time, but will give the teacher more time to look at and help students in problem areas. “Guess and check is a powerful problem-solving strategy that can connect a conceptual understanding of word problems with a symbolic representation” (Guerrero, 398).
The value of guessing and checking has always been important to me. Through my educational career I made use of the guess and check method on many occasions. I have learned that by guessing and checking I look deeper into a problem and it helps me understand it more fully. This is an aspect that I would like to incorporate in my own classroom someday. The more a student looks into a problem, whether it is a number problem or a word problem, will be better for them in the end. Hopefully, as my students travel through their academic careers they won’t have to guess and check as much as they did when they first started out. My reasoning behind this is that they understand how to go about a problem quicker and more efficiently. There is a strong possibility that this method will be incorporated in my teaching atmosphere in the future.
Guerrero, S. M. (2010). The Value of Guess and Check. Mathematics Teaching in the Middle School. Volume 15, Issue 7, (392-398).
http://www.nctm.org/eresources/view_media.asp?article_id=9176
The value of guessing and checking has always been important to me. Through my educational career I made use of the guess and check method on many occasions. I have learned that by guessing and checking I look deeper into a problem and it helps me understand it more fully. This is an aspect that I would like to incorporate in my own classroom someday. The more a student looks into a problem, whether it is a number problem or a word problem, will be better for them in the end. Hopefully, as my students travel through their academic careers they won’t have to guess and check as much as they did when they first started out. My reasoning behind this is that they understand how to go about a problem quicker and more efficiently. There is a strong possibility that this method will be incorporated in my teaching atmosphere in the future.
Guerrero, S. M. (2010). The Value of Guess and Check. Mathematics Teaching in the Middle School. Volume 15, Issue 7, (392-398).
http://www.nctm.org/eresources/view_media.asp?article_id=9176
March Journal Summary #1
The first article I reviewed was found in the Teaching Children Mathematics journal and was titled Identifying Logical Necessity. Teachers are used as facilitators throughout the article expressing the importance to make wise reasoning when describing things that happen. The author goes on to state that teachers that know more about the topic regarding logical reasoning are more prone to be able to help elementary students understand the concept. Logical reasoning should not be taught explicitly in throughout a students elementary years, but should instead be presented when an instance occurs that could be related with the topic. Activities used throughout a student's day to day learning should incorporate and encourage students to explain their ideas by reasoning with proof. Proof is vital for a student to grasp onto early in their academic careers since the term is at the root of explaining reasoning and proof. Determining where a student is struggling with their proof statements is something that all educators should master. Mastering this skill will help guide young students throughout K-8 and will prepare them for the next step in the educational careers.
A teacher’s main goal is for their students to learn the material being taught and to have them succeed as they go through their academic endeavors. Students that are able to recognize and explain their reasoning and proof methods will do well as they move on. Teachers must make it one of their main goals to make sure that they are able to recognize and correct a student that is struggling in their logical reasoning. The article expresses numerous activities that will help teachers sharpen their skills in this area and is a great resource that I can see myself looking back to in the future.
http://my.nctm.org/eresources/view_media.asp?article_id=9162
A teacher’s main goal is for their students to learn the material being taught and to have them succeed as they go through their academic endeavors. Students that are able to recognize and explain their reasoning and proof methods will do well as they move on. Teachers must make it one of their main goals to make sure that they are able to recognize and correct a student that is struggling in their logical reasoning. The article expresses numerous activities that will help teachers sharpen their skills in this area and is a great resource that I can see myself looking back to in the future.
http://my.nctm.org/eresources/view_media.asp?article_id=9162
Wednesday, March 3, 2010
Video work #2
The second video work was done for the grade level of seven and focused on “lessons and graphs.” The teacher explains that she made multiple graphs showing different things. The students broke off into groups of their own making and were given a copy of the graph. She wanted the students to be able to come up with their own pattern of the graph in table form and to come up with the remaining values from those that were already existing in the table.
1. Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.
By having the students coming up with their own stories they are able to look at the material in a more personal level. This will hopefully help the students bring more personal interest in the material along with them putting more passion and pride into their work. Taking this information and building it around math hopefully will help the students bring about more understanding of why the connections relate to one another.
2. Propose one or more alternative tasks that might have strengthened the lesson or helped to clarify the key mathematical ideas being developed, and justify the use of this task or these tasks.
The students could have each come up with more than one story and related them to one another. This way they would have had more experience in the comparing and contrasting aspect. Representation could have been used more too which could have been used in ways like building things actively or using the students to build a life-like graph.
3. What criteria do you use to determine whether or not to use a particular task with your class?
I am novice teaching right now in a 7th grade social studies class so I can relate well to this topic. Every time I am about to do a lesson I try to think of ways to connect with my students on a personal level. Also, knowing what my students enjoy learning about could prove to be very useful. This aspect of my teaching will come with time as I learn more about my students as I am around them day in and day out.
The overall use of the video was helpful as it gave a real life example of good teaching. There are numerous things that I could see myself making use of in the future as I go through my teaching career. The movies showed a little light on the things that I could better myself at and hopefully in time I will be able to master quality learning techniques.
1. Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.
By having the students coming up with their own stories they are able to look at the material in a more personal level. This will hopefully help the students bring more personal interest in the material along with them putting more passion and pride into their work. Taking this information and building it around math hopefully will help the students bring about more understanding of why the connections relate to one another.
2. Propose one or more alternative tasks that might have strengthened the lesson or helped to clarify the key mathematical ideas being developed, and justify the use of this task or these tasks.
The students could have each come up with more than one story and related them to one another. This way they would have had more experience in the comparing and contrasting aspect. Representation could have been used more too which could have been used in ways like building things actively or using the students to build a life-like graph.
3. What criteria do you use to determine whether or not to use a particular task with your class?
I am novice teaching right now in a 7th grade social studies class so I can relate well to this topic. Every time I am about to do a lesson I try to think of ways to connect with my students on a personal level. Also, knowing what my students enjoy learning about could prove to be very useful. This aspect of my teaching will come with time as I learn more about my students as I am around them day in and day out.
The overall use of the video was helpful as it gave a real life example of good teaching. There are numerous things that I could see myself making use of in the future as I go through my teaching career. The movies showed a little light on the things that I could better myself at and hopefully in time I will be able to master quality learning techniques.
Monday, February 15, 2010
Math Applet Blog: 3 - 5
The math applet that I chose for the grade level third through five included: Communicating about Mathematics Using Games: Playing Fraction Track. This applet involved the use of fractions and the student’s ability to understand how the fraction chart was built. The chart was built in a way where the smaller of the fractions was located on the left while the greatest was on the right. This was done so in a pyramid manner and would have to be discussed and understood by the students before the game began. The ease of use for this applet would be tough for a student that was not familiar with how the fractions compared to one another. This activity would help the student’s progress to a higher learning of mathematics once they figured out the concepts. The students would be assessed by their ability to play the game/activity to the best of their abilities while trying to learn the concepts fully. Students that are having troubles understanding the material should be placed with another student that understands the material, but could explain it in a way that the struggling student would be able to comprehend. The only concerns I have with this applet is that it could prove to be tough for multiple students and eventually hold some students back from moving on to the harder material.
http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm
http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm
Math Applet Blog: Pre K-2
The math applet that I chose for the Pre K – 2 grade level included: Developing Geometry Understandings and Spatial Skills through Puzzlelike Problems with Tangrams: Tangram Puzzles. The main objectives for this applet included the ability to describe figures, along with the ability to see the formation made when the shapes are changed through the buttons located in the applet. The applet has the student use different shapes to fill in an outlined image. This type of task should be very simple for the students to understand and something that they could do on their own without much instruction. The students will have a better understanding of geometry when the time comes because of the background that they received with these different shapes. The teacher can create student discussions by asking them certain questions pertaining to the applet functions. A good example of this would be, “what happens to the shape when you flip it?”. An easy way to assess the students would be to see if they were able to identify and use all of the shapes to fill in their respective outlines. All in all, this is a good applet for the younger students and is a good stepping stone that will eventually lead to higher learning.
http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm
http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm
Wednesday, February 10, 2010
MTMS Article Summary
Mathematics Teaching in the Middle School recently published an article title Calculus in the Middle School?. The main idea of the article is to express to students in the middle school that they can in fact further their understanding of higher education math. Students who have a background in the content area and information pertaining to calculus are found to be more eager and willing to go further in mathematics. The authors of the article also state that there needs to be a change in the way that calculus is perceived among young students. Introducing topics that can be related to higher level math could get the students ready to dive into harder and more advanced math later in their education careers.
This information would be very helpful to me since I want to teach students in late elementary. I could help the students get ready for what they are going to encounter in both the middle school and high school. Getting students eager and excited to learn about higher levels of mathematics could help them in the long run as they travel through their educational endeavors. The article has some good ideas in it, but overall didn’t really jump out at me. I am more so a social studies guy, but the information and ideas expressed are things that I can see myself making use of in the future when teaching.
This information would be very helpful to me since I want to teach students in late elementary. I could help the students get ready for what they are going to encounter in both the middle school and high school. Getting students eager and excited to learn about higher levels of mathematics could help them in the long run as they travel through their educational endeavors. The article has some good ideas in it, but overall didn’t really jump out at me. I am more so a social studies guy, but the information and ideas expressed are things that I can see myself making use of in the future when teaching.
TCM Article Summary
The article titled Transitions from Elementary to Middle School Math posted in the TCM journal expressed the need that teachers need to recognize and help students as they make the transition into the middle school/junior high. Students come across changes made with regards to how the aid materials are presented to them and the difficulty level of the material. It would be best for teachers at this level be aware of all of the challenges and difficulties that a student may run into as they make the transition. By doing this the teachers will be better at preparing the students to leap frog the challenges. The authors also talked about the involvement that the teaching community must have with one another. Having middle school teachers make visits to the elementary schools and having direct communication with the staff could help them understand better ways to help students who are making the grade level transition. Elementary school teachers must also be familiar with what the students will encounter at the junior high level. It would be best for the students to have the opportunity to practice learning at a more advanced level prior to making the transition. Connections will be vital for the students to make and act upon when they are preparing for junior high instruction. If they are familiar with the methods then they will be able to learn to their full potential without having declines in academic achievement. More importantly, the students will be ready to learn and build upon the concepts and knowledge they already have pertaining to mathematics.
This would be very helpful as the students would be very familiar with what will be expected of them in at the junior high level. By having teachers that are prepared to help guide students through their transitions into the upper grade levels then they will have a greater possibility of success. The article stated many good points that I can see myself implementing in my classroom, but the main concept of preparing students for their transition really hit me at home. As a teacher I will want to see my students go on to do great things so it is important to myself that I do all I can to help the students grow.
This would be very helpful as the students would be very familiar with what will be expected of them in at the junior high level. By having teachers that are prepared to help guide students through their transitions into the upper grade levels then they will have a greater possibility of success. The article stated many good points that I can see myself implementing in my classroom, but the main concept of preparing students for their transition really hit me at home. As a teacher I will want to see my students go on to do great things so it is important to myself that I do all I can to help the students grow.
Wednesday, February 3, 2010
PBL Blog - Third Step
Example PBL: Hawaiian School Carnival #2
The students in this PBL are trying to raise the money to fund a technology center for their elementary school. The grade level was chosen for the 6th and 7th grade students and fulfills the want and need for some prior knowledge. The strengths of this PBL outweigh the negatives I feel because they focus so much on the process standards. The grade level is appropriate and they are doing something that will affect them directly which fulfills the real life connection. The problem also covers allot of the curriculum that they have either learned are pretty familiar with.
Example PBL: Mall Madness
Through the PBL the students are attempting to build a child based learning area in a local mall. They are given the opportunity to do something that will affect their community directly and perhaps even affect themselves; depending how often they make use of the mall. They will be learning how this problem will affect them personally and relate back to the real life. This type of activity/problem gives the students independence while giving them something challenging. Group work will help the students become better communicators and work better with others. This PBL yet again meets my standards of what a PBL should look like. There are many good qualities throughout this PBL.
Both of these Problems are related in multiple ways. The biggest and most important aspect is that they both relate back to the process standards. The process standards can be seen being acted upon in both PBL's which is why I am so positive for the both of them. I really have not had too much experience in PBL's so it is hard for me to tell what these PBL's are doing wrong. I can tell you however that both of these are getting the students engaged and providing them with something challenging and relatable.
The carnival one I really enjoyed because what they were doing was coming directly back to the school in the ways of technology. I cannot say the same for the mall PBL because they are doing it more so for the community and not their school. I would have liked to see both PBL's be associated with the schools instead of something else.
Both groups did a fine job assessing the students work. There are always so many things that you have to take into account when assessing all the students work so it is hard to have the same thing written down every time. Different assignments call for different measures. All in all the assessments look fine to me.
PBL Blog - Second Step
The students in the article were reading a Harry Potter novel and a problem came up that eventually turned into a math problem. The problem connected Literature to Mathematics, made the problem easy to understand for the students, and connected it to daily life. Sounds like the connections standard all over again! The students were to make a budget list of all the supplies that they were have at Hogwarts School. To bring about the idea of budgeting the class had a discussion as a whole and established the basics of what they would need. Once they began on their own they realized that they were not going to be able to get everything that they wanted. All students were excited to help one another out through the problem. At the conclusion of the problem the students and teacher came together again and gained a greater understanding of how this problem could be related to the real world. The teacher enjoyed this process because she likes Harry Potter and she also could see where her students were making errors and struggling.
It was good for the students to have this PBL because it brought about so many of the process standards into play. Communication was expressed through the class forum and group discussions throughout the problem. Connections were made to the real world while bring together both mathematics and literature. This problem was also very beneficial for the students because they were able to relate to it well. Reasoning and Proof came into play when they had to reason and provide proof as to why they chose the things they did to stay under the budget. They also had to use their problem solving skills all throughout the problem when they chose different items to represent their materials list to head off to Hogwarts School of Witchcraft and Wizardy. Overall, I really enjoyed this article and wouldn’t mind doing it in my class too at some point in time. I enjoy Harry Potter too so I don’t have any bad/negative things to say about this lesson.
Beaton, T. (2004). Harry potter in the mathematics classroom. MathematicsTeaching in the Middle School 10(1), 23-25.
PBL Blog - First Step
PBL stands for Problem Based Learning. PBL's are focused upon things relevant to people today. They ought to be problems that are tough for a person/group to come up with an answer for, but not too hard. With that being said, PBL problems must be given to students who are grade appropriate or have a certain level of prior knowledge that will help them in solving the problem. PBL's hardly ever have an uncomplicated answer as all of the answers must be accompanied with the persons/groups reasoning and proof. Numerous resources will be made use of throughout the process. Problem Based Learning should promote a higher level of knowledge and understanding for all who participate.
Wednesday, January 27, 2010
Video Analysis - Grade 4 (#1)
The purpose of the activities portrayed throughout the videos was to encourage student learning through their own findings. The teacher was there to guide the students in the correct paths, but she stated that her main goal was for the students to find things out for themselves. In this type of environment, both the teacher and the students are learners of the material. Of course, the teacher knows the material well already, but goes about the activities in ways that encourages student involvement and thinking. The teacher spent much of the time having the students explain their reasoning for the answers that they had come up with and always had them "digging" for more information. Questions upon questions were thrown at the students in hopes that they would encourage more analyzing of the material.
(Orchestrating) : How do you determine whether group work is appropriate?
In the first scene of this section, the teacher is working with the students in groups. I feel that the type of activity that they were doing in these videos was very good for group work because each student could learn from another. I enjoy activities where I am able to teach students in groups because I feel that I am able to reach more of them directly. Unfortunately, it may take a little bit of time before the students feel comfortable working together. It was stated that if this activity were done eight months ago that the outcome and flow would have been completely different. I determine if group work is appropriate by how comfortable the students feel together and also how comfortable to students feel towards the material presented for the group work.
(Questioning) : What kinds of questions predominate in your classroom? Single answer? Short answer? Explanation?
The kinds of answers that predominate in my classroom would be short answer. Having short answer questions gives the students the opportunity to always give their reasoning for the answer that they have come up with. Single answer questions I feel do not get the students involved into the material quite enough. Short answer questions also leave the window of opportunity for a two-way discussion involving both the students and the teacher.
(Evidence) : When during a lesson do you check to see what students have learned?
Periodically throughout a lesson the teacher should check to see how the students are coming along. It is always nice to pose questions to them to make sure that they understand the objectives and are on track to complete the lesson correctly. Towards the end of the lesson it would be smart to have a class discussion that includes the students thought processes as they came to their conclusion. Also, it would be beneficial for the students to talk about what they were having problems with and how they eventually found a way around that barrier.
The overall use of the video was very beneficial for me. There was much information throughout the clips that I can see myself including in my own teaching someday. Including the hands-on visualization of the bands toward end of the connections portion was nice to see as I really enjoy activities such as that. Students were able to see how the variables worked, were able to show how the variables worked, and they were able to talk about how the variables worked. There was a little bit of each learning aspect incorporated into the lesson and proved to be very effective.
Exploring the Volume of Mayan and Egyptian Pyramids - M. Alejandra Sorto
Sorto shows how the information presented through out the article relates to the information regarding the connections portion of the process standards. Making up tactics to find out the volume of prisms and pyramids around the world is a major component of the article. I really enjoyed the portion that spoke about having the students make three-dimensional illustrations to help them see and find out solutions related to area and volume. Not only will the students by compiling their information on a sheet of paper, but they will also be actively engaged in the activity as they build their prisms/pyramids. Another major component of the text that I enjoyed was the application of real-life situations and places. Students that are engaged in the activities are linking relationships associated with other areas included throughout their educational curriculum. Prime examples expressed were the relationships built through art, science, and other aspects of daily life. All of the aspects in the course of the article are meant to enhance a students learning and understanding of the material. Also, the connections that the students make from the activities hopefully will stick with them for the duration of their education careers and beyond!
Sorto, M. A. (2010). Exploring the volume of Mayan and Egyptian pyramids. Mathematics teaching in the middle school 15(5), 294-297.
Connections - Process Standards
The connections portion of the process standards outlines three main components that all students from grades K-12 should be able understand use. Through the connections principle the students should be able to familiarize affiliations of mathmatical ideas and use them. Students should also be able to make connections among the mathematical ideas and bring them all together to form the "big picture". Lastly, students should be able to use the concepts of the connections standard in their daily activities and lives. Connecting ideas to the real world is something that can go a long way and is vital as students go through their education careers. Mathmatical connections help students learn how different things are connected in different ways.
Friday, January 22, 2010
Instructional Games With Calculators - Wallace Judd
From the beginning of Judd's article to the end of Judd's article there was a strong message regarding the use of technology and the many ways that technology uses can make learning fun for all. These games could be presented in many different ways to meet a students learning ability. All of the games presented in the article can be completed in less than five minutes and could be done on almost all basic calculators. These games teach students the basics of mathematics along with calculator functions. The relevancy to mathematics is that these games will teach students place value concepts including decimals, counting, and addition. These games seem like they would be a quick fix for a student that has finished his/her work before the rest of the students. A direct quote from Judd stated, "The Mathematics requirements for all of the games are minimal" (Judd, 2007). I look at that statement and see that all students could learn from these games and take advantage of their engaging qualities.
Judd, W. (2007). Instructional games with calculators. Mathematics Teaching in the Middle
School 12 (6), 312-314.
Judd, W. (2007). Instructional games with calculators. Mathematics Teaching in the Middle
School 12 (6), 312-314.
Thursday, January 21, 2010
Principles and Standards - Technology
The technology priciple of mathematics is meant to help further a student's understanding of material presented to them. There are many forms of technology that have been used over the years and are still very helpful tools in the education field. Examples directly expressed in the text were the help of calculators and computers. With the help of technological advances students are able to use the abilities of these mechanisms to make their learning more enjoyable and to make better use of their time. With the aid of technology in the classroom a teacher will have more of an opportunity to reach each student's special needs. The use of technology in the classroom is mainly the teacher's responsiblity. If a teacher does choose to make use of technology in the classroom then they must be able to find a positive way of using it, rather than having it be a negative teaching aid. Technolgy is a component of the education process that becomes more and more andvanced as the years pass. As these advances come about, they give future generations of students the opportunity to learn and to keep raising the bar (climbing to greater hights).
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