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

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

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.

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.

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.