Saturday, May 1, 2010
May Journal Article
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
Wednesday, April 28, 2010
Technology Reflection
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
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
Monday, April 12, 2010
April Journal #2
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
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
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 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
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
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
http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm
Math Applet Blog: Pre K-2
http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm
Wednesday, February 10, 2010
MTMS Article Summary
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
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
Friday, January 22, 2010
Instructional Games With Calculators - Wallace Judd
Judd, W. (2007). Instructional games with calculators. Mathematics Teaching in the Middle
School 12 (6), 312-314.