Math Applet #2- Grades 6-8 Fractions- Adding

1. Fractions- Adding file:///Applications/MATTI/NLVM_en/locales/en/doc/fractions/addingfractions/teacher.html

2. This applet helps students with adding fractions. It gives the students a fraction and they have to find equivalent fractions. After they do this they have add the fractions together so that they are coming up with an answer. Students have to find the same denominator in order for the question to move on to the next step. If they get the answer wrong then it gives them a clue like "You need to fix the numerator". There is a visual above each fraction that shows the fraction in a picture. When solving the answer they have to move the pictures from each fraction into the solution part of the problem. Each step of the way there is a visual which is very useful. The students also have the options to make a problem easier, harder, or hardest. At the end of this applet it says when students feel comfortable to have them try and fill in the answer on a paper.

3. I thought that this applet would be useful when teaching about adding fractions. The visual was very practical because it helped me figure out some of the problems that were on hardest. I know that a lot of students struggle with fractions and this website would be very helpful to do as a minilesson. I really liked this applet because it is good practice for adding fraction. It brings technology into the lesson rather than just doing problems on the board. I think that this website has really great activities that I would want to use in my classroom. These problems make math more exciting rather than just doing the problems on a worksheet.

Math Applet #1- Grades 6-8 Money

1. Source- http://nvlm.usu.edu/en/nav/vLibrary.html

Money- file:///Applications/MATTI/NLVM_en/locales/en/doc/money/teacher.html

2. This math applet is a virtual program that helps students with the concept of money. There are three different types of problem in this math applet. The first one is how much money is being shown on the screen. The students have to count the bills and the coins and type in the answer. The next type of problem the students have to pay the exact amount that it tells you to give. Depending on the problem it will give you different bills and coins that you have to use to pay the amount. An example of this is, if the number was $74. 02. The students only have choices from 5, 10, 20, and 50 dollar bills and then only pennies and nickles. The third type of problem they have is to make a dollar. For this problem they give you the coins that they want you to use and you have to make a dollar.

3. I thought that this was a fun math applet to partake in. It was really interesting to see the different ways that you can make each number that they asked you to make. I think that 6-8 is a little old to be having students do this activity. I also think that it could be a good lesson because students will be looking for jobs soon and might need to know how to make change quickly. There are also a lot of questions about money on standardized tests which might be why they considered this a 6th-8th grade activity. I can see this activity being very useful for ESL students who may not be familiar with the currency. I really like this applet because it is very interactive and I think students would be excited to practice math using this type of program. I would use this in my classroom but I would probably use it for younger kids when I am introducing them to currency.

February Journal #2

"Rubrics at Play" was an article that explained the different types of rubrics and how to use them effectively. There are four different ways that rubrics classified. These are holistic, analytic, specific or general. Holistic rubrics are rubrics that look at the whole performance and each section is usually worth the same amount of points. An analytic rubric focuses on understanding the problem, planning a solution, and getting an answer. Specific rubrics only address one task but holistic and analytic can both fall under this category. They can also both fall under general where the information does not have to be as specific. There was all the steps listed that explained how to create a rubric. The two main points when doing this were that teachers need to use student work and using the assessment task.

I found this article to be very interesting and informative. I did not know that the different types of rubrics were used when focusing on assessing certain things. I thought it was just up to the teacher to decide what rubric they wanted. I also have never heard of teachers letting their students help them create a rubric and decide what to put on the rubric. There were lots of examples that showed the different types of rubric which was useful because then I had a visual infront of me and compare and contrast the different characteristics of each rubric. Another part of the article that was interesting was the teacher's story of creating a rubric. It explains how she took the rubric and adapted it to analyze her students work. I liked this article and I learned a lot about the different types of rubrics and how to create them.

McGatha, M.B. & Darcy, P. (2010). Rubrics at play. Mathematics Teaching in the Middle School. 15 (6), 329-336.

February Journal #1

The article "Story Boards for Meaningful Patterns" from Teaching Children Mathematics was about using story boards to get students to recognize patterns. The article states how important it is that students learn patterns, functions, and relations from the time they start prekindergarten to senior year of high school. The authors give different types of patterns and examples of how to use the patterns in this article. The teacher says that rhythmic patterns can be used simply to get students attention and spelling patterns are used when teaching writing. The teachers used snap cubes when teaching her lesson and let the students use their own snap cubes when building their own patterns and placing them on the storyboards. The students would use the storyboards for the different patterns and then create it with the cubes and have to present them to the class. When the students were talking through their patterns and stories that they created some of the students would catch the mistakes that they made and fix them. The article explained how the teacher should be modeling storyboards. It showed what the teacher was doing wrong and how she could fix that so her students could better understand the patterns.

An interesting part of this article was how the college professor came in and helped this teacher to make her lesson plans better. When she first taught the lesson a lot of the students were not understanding the patterns that she was teaching. The observation teacher said that if the students attach meaning to the patterns by having to explain it orally that the students might understand more which I thought was interesting. The teacher came back to observe at a later date and the students made a connection that she was the "pattern lady" and showed her the new patterns that they made. This article reminded me a lot of the process standards because the teacher was incorporating communication, connections, problem solving and reasoning and proof. I also realized how important self evaluation is to teaching a lesson and that teachers need to be doing this frequently.

Dubon, L.P. & Shafer, K.G. (2010). Storyboards for meaningful patterns. Teaching Children Mathematics. pp 325-329.

Review of two PBLs

1. Name and Summarize Each PBL

PBL #1 Lounging Around Summary
I thought that the problem of this PBL related to the students a lot and that they would be interesting in solving it. Even though the PBL is math based it incorporates science, language arts, social science and fine arts. The day to day schedule was in depth and related to the question. The guiding questions seem very helpful and applicable to the seventh and eighth grade students. The PBL is very step by step and detailed for each activity that the students have to complete. The minilessons really related to the main topic of the PBL and I think that the students would want to complete them. The students are not just completing worksheets everyday one day there was a speaker and another day they used magazines and computers to look for designs. There was a lot of technology and connections being made through out this PBL.

PBL # 2 Hawaiian School Carnival Summary
This PBL was about a carnival fundraiser that the students were participating in to get 30 new computers, educational software, and a smart board. The PBL had activities that incorporated safety to building things like a playground. There was lessons that incorporating scaling in to the lesson which would be very useful to the math and geography. The lesson on the budget and comparing prices was very helpful and I think that they could be applied a lot to real life. You will have use these things in everyday life. The presentation day the students were presenting blue prints, graphs, figures, and models. There were a lot of strong connections being made in this PBL.

2. PBL #1 Strengths and Weakness
There are many strengths to this PBL because it incorporates many different subjects that relate to the topic. The activities in this PBL are very engaging and the students will want to do them because it directly relates to them. This PBL does not just focus on part of the activity it goes into all the aspects of creating the lounge. The weakness of this is that there is not a lot of reasoning and proof of why the students are doing what they are doing. I think that the creator of this PBL could have done a better job of making the students prove why they are doing each activity.

PBL #2 Strengths and Weakness
I did not find a lot of strengths to this PBL. The activities were really well explained and went along with the subject but they did not seem that exciting for the students to participate in. I thought that the topic could have related more to the students. I do not think the students would be really interesting in having a fund raiser. The creator of the PBL said that the it used higher level thinking but I did not see very much of it when going through and reading it. The guiding questions are not organized and kind of random and most of them did not really relate to the topic.

3. Compare and Contrast the two PBLs.
The first PBL was very well organized and well thought out. I thought the topic and activities were very interesting to the students that were participating in them. There was a new activity almost everyday unless there was a work day where students were continuing to work on a project. The objectives seemed to relate to the assessments. The second PBL activities did not seem to relate to the topics. I did not like the PBL problem to begin with but maybe the students would have been interested in having the carnival. This PBL also seemed very unorganized. The connections that they were trying to make did not really connect to the topic.

4. Critique The Strengths and Weaknesses- Give Examples
The justifying the budget and the guest speaker were the activities that I thought were very interesting for the first PBL. The budget activity would really help students in the future not only for this PBL but for real life situations. There is also an activity about measuring the room and making the model that I think would be useful for math that the students would have to continue to do in the future.

The second PBL had a lot of the same activities as the first one did that I thought were beneficial like the budget lesson plan. Another activity that I thought was useful was the geometry/measurement lesson plan. One of the weaknesses of this PBL was the probability lesson plan. It did not seem that interesting to students and did not relate to the topic of the PBL.

5. Math Focus
I think that math is the main focus of both of these PBLs. Both of the PBLs have a lot of interesting activities that have interesting and engaging ways of focusing on math and other curriculum areas. The first PBL incorporates a lot of algebra and geometry, which I think is very beneficial to the students. There is also simple math like having a budget that would be helpful to students. There are also a lot of graphs that the first PBL uses where students have to analyze and apply data. The second PBL the students had to use graphs, determine areas, and make a scale drawing. Both PBLs were very math centered had a lot of interesting math activities.

6. Assessment
There were many different forms of assessment in both of the PBLs. The main assessment that I saw were worksheets, rubrics, and checklists. I think that both PBL assessments matched up with the standards that were listed. In the end the PBLs were interesting and new ways to teach students things that related to them. They would have learned a lot more from these PBL's then they would have learned from just having a lecture or completing a worksheet.

Problem Based Learning- Journal

1. The article had a lot of interesting points about problem based learning (PBL). It talked about how the constructivist theory relates to PBL's in the classroom. The constructivist theory is where students use prior knowledge to make connections to the new information that they are learning. It goes on to say that in order for students to be successful in solving PBL problems they have to be in a comfortable environment where they are not afraid to express their ideas. They have to relate what they are learning to the experiences in their lives and the things that they have already learned. I thought that this article was very interesting because it talked about how the teacher organized the groups that she put the students in. Next it talked about the order that the teacher went in presenting the PBL to her students. The article also gave questions that students should be trying to answer and different ideas that help the students answer the questions. All student's should be an active member of the group and be sharing their ideas with their group members.

2. I think that there were a lot of strengths to this article because it gave examples for each step that the teacher did for PBL. There was also a part of the article that had student comments and the students responded that they really liked the PBL. I also think that it was interesting that they incorporated the constructivist theory into this type of learning. The part of the article about splitting the students into groups based on their leadership abilities and creative abilities was new to me because no other article I read talked about how teachers actually put their students into groups. The article could have given more information on what the teachers did to prepare for creating a PBL problem. The author makes it sound like it was given to them it did not explain the thought process of the teachers when creating a problem. Also the article could have gone in to more detail about the role of the teacher during the PBL process.

3. Siefert, E.H. & Simmons, D. (1997). Learning centered schools using a problem-based approach. National Association of Secondary School Principals. 81, 90-97.

Problem Based Learning (PBL)

PBL is a type of curriculum that allows for students to figure out the answer from working with the problem. It is a new concept of teaching because it is different than a teacher passing out a worksheet or lecturing. PBL involves students working together in groups and using their critical thinking skills to come up with a solution to a problem. The problems that are used in PBL's connect to real life to make it more appealing for the students. PBL's also require that the students are discovering the answer when working through the problem. Students have to identify what they know and what they do not know and explore different options to find an answer. Students use cooperative learning to complete PBL's because they are working together in a group. When students have come up with a solution to a PBL they should present their results in front of the class. PBL's are generally used when teaching science in the classroom. Teacher's play a different role in PBL they are not just giving the solutions they are helping their students work through the problem.