Reflection on Errors.

The errors were very interesting to do in class. I learned a lot because I have never thought about looking at students work before and trying to figure out a pattern in what they are doing wrong. This was the first class in my college career that has done that and I think that it should be done in other classes as well. It's important to see where your students are missing something or not doing something right. It is a teachers job to help their students learn new concepts first you have to look at the problem in their shoes to see what they are seeing and how they are looking at the problem I liked doing these in class it was very helpful to look at the different mistakes that students were making. There were some errors that I could not figure out and my group members had to help me and talk me through it. Sometimes I might need to ask other teachers to look at a students work when I am a teacher if I cannot figure out the pattern of the work that a student has. I think analyzing student work is very important and doing it in this class really helped me.

The errors also went along with the presentations that we did in class where we had to figure out how to grade the students work. This was really hard and frustrating but I feel that my group and I decided on the right way to classify their answer. It still took a lot of analyzation on all of the students work that they were doing, which is why I think that this activity also went along with the errors. Analyzing students work is vital to being a teacher and I think both of these activities were extremely helpful in preparing us to do that.

Technology Blog

There were many times that we used technology throughout this class. Computers were the main piece of technology that we used both inside class and outside of class. This course was basically a hybrid course because we spent so much time on the computer. I have never done anything with a wiki or a google doc before and I really liked doing those in this class. I have now started doing google docs in my other classes because it makes group projects so much easier since you do not have to find a time to meet. It allows you to work on it separately even though you are not meeting together. We used the forums on sakai and emails to communicate with each other and to send in assignments. There were many other computer programs used in this class like Microsoft word, excel, powerpoint, inspiration, geometers sketchpad and panopto. The NCTM website was a very helpful website and I really enjoyed reading the articles on there because I learned a lot from them.

In the actual classroom the smartboard was another piece of technology used. I have never used a smartboard before and after using it in this class I really want one. It is a tool that is interactive with the students and seemed to make teaching a lot easier. I liked that students can just write on it like it was a chalk board I thought that was so cool. There was also a camera that we used one day in class. This camera was a really neat piece of technology that we had in the classroom. I was trying to think of ways that this could be used in the math classroom other than the number line activity. We could have also used this for the measuring with a non-standard tool activity. It would have been interesting to watch everyone go around the classroom measuring the different objects. Calculators were another tool that was used in the classroom that is technology. We did a calculator activity in class and I have never used a calculator that was not graphic that could do all of those different types of problems.

April Journal Articles

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.