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.
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