March Journal Articles

This article was about the value of the guess and check method. It explained how this method could be used when doing word problems at the middle school level. The author explains that teachers need to be using this method because it helps deepen students understanding of quantitative relationships and help increase the students problem solving skills. The guess and check method help students to break down each word problem and put it into everyday language rather than just reading the math problem. Students use the table to help them organize the different parts of a problem. The guess and check methods helps students to use reason when finding the answer to the problem that was given to them. When students become familiar with this strategy they can adapt it and have their own way of using for different problems.

I thought that this was an interesting article to read. The guess and check method seems very useful when teaching students about problem solving. There were many examples of charts and tables that students used when organizing their guess and check system. This method is a way for students to understand what the math problem is saying because they are breaking it down and learning from an answer if they guessed it wrong. They have to look at their answers and reason them of why it is the right or wrong answer.

Guerrero, S.M. (2010). The value of guess and check. Mathematics Teaching in the Middle School, 15 (7), 392.

This article was about using technology when teaching students about polygons. There are many different kinds of polygons and a lot of students do not realize that shapes likes squares and triangles can be found in the different types of polygons. The website has a lot of different features that can help students to identify polygons better. The paintbucket tool also helps the students with polygons beause they can draw different conclusion from the different colored polygons. The article also states that students are engaging themselves with polygons by using the technology. They can interact with the polygons by having them on the computer and play around with the polygons to see the different kinds that they can create.

I thought this article was very interesting because I have never really thought that much about polygons. By doing this activity on a computer the students are able to make different kinds of polygons. The computer gives them the ability to try to come up with different solutions. Some of the shapes that are in the article are not polygons and it allows the students to see why they are not. I think that this is a good activity because the students are engaged with the polygons they are not just learning what a polygon is out of a book. Another interesting thing is that students can take different shapes like squares and put them in a polygon and see how many squares fit in each polygon or triangles. I would use this activity in my classroom because I feel like the students would get more out of this lesson rather than from me teaching them on the board. Overall, I thought that this was really interesting and would use it in my classroom.

Edwards, M.T. & Harper, S.R.(2010). Paint bucket polygons. Teaching Children Mathematics. 16 (7), 420.

Video Analysis #2

Activity
This activity was about students starting with graphs and they make up stories that go along with each graph. Then they have to present the stories that they created to the class. The students had to learn about the different parts of the graphs in order to tell their stories. They were also learning how to do functions while doing word problems. The teacher helps them out in their groups when they are doing their word problems. She goes around to each group and answers the questions that they have.


Question 1- Lesson Analysis #2: Describe what the teacher does to support learning while students are working groups
While the students are working in groups the teacher is walking around and make sure they are understanding. When the students came up with the wrong answer the teacher said "Lets re-read the question" they were on the right track they were just interpretting the question wrong. They ended up coming up with the right answer to the question without the teacher helping them. One group did not get the answer and the teacher broke the question down and said "What am I looking for?" Next, she said "Lets look at week one." She was breaking down the problem in to steps so that the students could figure out the first step and then be able to figure out the rest of the problem with out the teacher doing the whole problem for them.

Question 2- Reflective Task #2: Describe how the teachers questioning, and the manner in which the student responses are handled, contribute or do not contribute to a positive classroom learning environment?
The teacher asks a question then lets the students answer, then she will ask another question based on the answer that the students just gave. She wanted to know what the students had already figured out in the problem and then try and challenge them with a new question. When the student answers she says "Oh you are so great!" and then asks if he can explain his answer. She is encouraging her students to answer because she is so enthusiastic about it what they are saying. Then she goes on to the next part and asks students how she would write this part of the problem and they tell her how to do it. She is discussing each step of the problem and making sure that the students are understanding.

Question 3- Reflective Task #1 Describe the nature of the evidence of student learning, e.g. answers, explanations, questions. etc.
You can tell that the student was learning because she went in front of the whole class and correctly explained the solution to the problem. One student answers the question wrong and then she asks where did you get that from and tries to lead the student on the right track. After she asks the student a couple more questions he explains his reasoning and is on the right track. The students are explaining the way they are coming up with the answers which shows that they are understanding the problems that they are learning. The teacher is constantly asking questions so that the students have to answer and explain how they are coming up with each answer and the other students need to understand. She tries to ask different questions to get him to go in to even more detail to explain how he came up with each answer.


Reflection
I thought that the way this teacher used questioning was very effective. She also used a lot of discussion for each problem that the students needed to figure out. She talks to the whole group of students but switches off on what students she's calling on. I did not like how there were so many videos of the same thing going on. It would have been better if it was one long video of different kids answering questions to figure out the problems. I liked how this teacher was so enthuisastic I think that it made the students more interested in trying to figure out the problems.

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.