Prompt #5

Prompt#5: Discuss what role you believe technology will play in shaping the classroom of tomorrow, and describe how you will keep your technology knowledge base and skill set up to date as a classroom teacher.

I think technology will play a major role in shaping the classroom of tomorrow. Digital textbooks are starting to become popular already and I feel that in the future schools will move from paper textbooks to online textbooks. I am sure that when I am a teacher I will have to go to different workshops and conferences to keep my skills up to date and to learn how to use the best pract for technology. Right now I am in a classroom that frequently uses a smartboard and it has been a huge learning experience for me because I have never used one before. I am starting to create my lessons for novice on a smartboard and during my teachers plan period I practice giving my lesson while having students interact with the smartboard. I am open to learning different types of technology and programs in my lessons because I think that they will help keep my students engaged.

Prompt #4

Prompt #4: Review the ISTE Standards for Teachers and discuss how you plan to integrate technology in your classroom in order to enhance the teaching and learning process and achieve the five educational standards identified by ISTE for teachers.

I plan to use technology in my classroom when students are researching information. I also plan on using technology when I am teaching my students new information whether it be history, spelling, math, or science. I think it is important to use technology during math because then you are not just doing math problems on the board. Using technology for math forces you to do something different that the normal instruction out of a math book. The computer has different sources that can make things easier for children to understand. An example of this is atoms because there are so many websites that have models of atoms that break it down and make ite easier for student's to learn. I think technology will help with promoting citizenship and responsibility because you can easily find different resources to show students how other people live. There are also many different ways you can use digital tools to assess students while having students assess themselves. Having check points on power points would help students manage where they are supposed to be at and seeing if they comprehend the information.

Prompt #3

Prompt #3- Review the ISTE Standards for Students and describe how you can apply the current use/role techonolgy plays in the day-to-day life of students (to include social networking) in your classroom to help achieve the six educational standards identified by ISTE for students.

Giving the students different options on how to do projects or presentations will help the students achieve some of the standards of ISTE. If students are not limited to using just power point or just microsoft word it is allowing them to think outside of the box and helps them problem solve which are two standards of the ISTE. When I am a teacher I hope that I will have a smartboard in my classroom because then I feel like I can have interactive and engaging lectures. I do not want to limit technology in just my lectures but I would use it to do presentations like webquests infront of the whole class and all the students would be able to see what was going on. I think that computers and smartboards when used the correct way and not over used are great tools that engage kids in learning. Student's get excited and want to go up to the smartboards and draw on them or high light things. I am not really sure how I would include social networking in my classroom. I know that when I am a teacher I will use blogger.com for students because I like that you can follow your other classmates posts.

Prompt #2

Prompt#2- Identify how technology has been used in classes you have taken as a student, at all levels from elementary through college- providing examples of efficacious and inefficacious use of technology.

When I was a student in elementary and middle school technology really was not used that often. We would have to take acclerated reading tests on them but other than that the teachers did not really use them a lot in the classroom for instruction. It was not until highschool that teachers were really using computers. I used the computer for an advanced reading class that had a program that the teacher would use that took you through different stages to help you learn better ways to read faster, which was helpful. Power points were also being used for lectures that teachers were giving. This was both a good and bad thing because it would be easier to take notes, but other times teachers would read directly word for word off of the power point. I think it made class a lot more boring because the teachers would do that and not use any other way of instruction in their classes. In college a lot of teachers only lecture using power points and it is hard for students to learn because it is so monotonous and you have listen to it for the whole class period. When we had to create a webquest in ETE 353 I thought this was a very good way of using technology because there are so many different things that you could include to have students do rather than just having them read notes off of a power point.

Prompt #1

Prompt #1: Discuss the role technology has played in each of the following periods of your life: as an elementary student, in middle/school/high school, and in your adult life.

In elementary school we had computer lab class once a week. In this class I learned how to type and use different Microsoft Word programs. When I first started typing I did not like it because they would put a box over our hands so we would not look down at the keys. I would rarely use my computer to complete my homework in elementary school. There were a lot of math and reading programs and games that I played on the computer during elementary school. An example of this was Math Blaster, I used this program to practice my addition and subtraction skills and had fun while doing it!

Middle school is when I really started using technology. In 7th and 8th grade I was enrolled with a technology class with the media teacher. I loved this class because we learned to use a videocameras, microphones, teleprompters, green screens, and different audio visual equipment to put on the morning announcements. It was a lot of fun learning how to use this equipment because we were allowed to use it for projects that we were doing in other classes. I used a computer for most of my homework and papers. I knew how to use powerpoint but we did not really have a lot of projects where we needed to use computers to present. During this time I learned how to use Microsoft Excel. Sometimes I would go to work with my mom and she would have me put numbers in to Excel and do different types of spread sheets for her.

In highschool I used the computer a lot for homework, presentations, and to look up information. I also used the computer for networking which is something I never did before.

As an adult I use the computer to research things, to keep track of my banking, and for all of my classes. Last year a girl spilled water on my computer and I was without it for a month. This month was extremely hard because for me to access a computer I would have to go to the library. I watch tv on my computer and check my mail constantly and this incident really made me realize how dependent I am on technology.

When I am a teacher I am going to use technology in my classroom because I think that it helps get students engaged. When I was in elementary school computers were not as popular as they are today and teachers were still using them in their classrooms for different activities and projects. I think that the internet is a very useful tool to have which is why I am going to incorporate it into my lesson plans.

Journal Article- May

This journal article was about fractions in a fifth grade classroom. It talked a lot about math specialists and how they are working hard with teachers, students, and administrators about math curriculum. The teacher was teaching her students about how parts of a fraction are equal sizes using pattern blocks and multilink cubes. It is called the funky cookie activity because it uses all the shapes to represent a whole. The students would separate the multilinks into groups to see the relationship parts of a fraction to the whole part of an object. After doing this activity the students understood that all of the parts were equal. The specialists work very hard to cooperate with the teachers to give them the best activities for students to be particpating in.

I thought that this was a very interesting article about how teachers work with specialists. When reading I expected that there would be more information about the students and the activity. The article went into a lot of detail about the specialists and how they are creating different lessons and activities for teachers that they work with to give to students. It was interesting learning about this because when I am a teacher I would like to work with a math specialist in my classroom. I am not very strong in math and I think that having a specialist would really benefit me when I am teaching math. Overall, I thought that this was a very informative article and I learned a lot about how to teach fractions.

Ellington, A., & Whitenack, J. (2010). Fractions and the funky cookie. Teaching Children Mathematics. 16 (9), 532.

Manipulative Blog

1. How do you hold all children accountable when you're using manipulatives for an activity?

All children can be hold accountable by giving them their own manipulatives to have in front of them. When children need to get manipulatives you can have them come up to the class by groups or seating and have students take all of the manipulatives for their group. At the end of the activity you can have students put away their manipulatives. If students have their own manipulatives and the teacher tells them to put away their manipulative they have the responsibility of putting their manipulative away. By having this procedure and expectations in the classroom the teacher is holding all students accountable.

2. Why do people say not hands on they now say hands on minds on?

I think that people have changed the saying because before when they would say hands on students would just be playing with the manipulatives. It is important that students have their minds on so that they are understanding the concepts that the teacher is trying to get across. In order for teachers to do this I think they should allow the students some times to get used to the manipulatives before they start teaching because if you do not let the students play around with the manipulatives, the whole time you are trying to teach the students will be playing with them and not listening to the points you are trying to make.

3. How do process standards fit with the manipulatives?

The manipulatives connect with all of the process standards. They stand for representation because each manipulative is representing some kind of concept. When students use manipulatives they are using communication whether it is with other students or the teacher. It does not have to even be verbal they might be writing something about a manipulative. Students are consistently making connections when using manipulatives, they might be learning new concepts and connecting it to prior knowledge. Teachers can also use manipulatives to reason and proof. The manipulatives could be used to prove a theory or new concept that a teacher is teaching in class. The manipulatives also could be used to problem solve. An example of this is that chippies could be used to represent an equation and they have to solve the problem using the chippies.

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.

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.

Article- Aiming for Understanding: Lessons learned about writing mathematics

The article states how hard it is for teachers across the country to get students communicating about math whether it been infront of people or on paper. Teachers need to get students to feel comfortable with writing about math they cannot just give them a piece of paper and a pencil and expect them to do it correctly. The author says that students need to be provided with support like graphic organizers, demonstrations, and modeling, tips for improving written work, and specific lesson on ways to more effectively write or describe ideas (O'Connell, 2005).

Cooperative learning was a main part of the study that the teachers from the college level and elementary level noticed when working together. The student's benefitted because it allowed them to come up with more ideas from talking to another person. Being with a partner was a non-threatening environment because they did not have to share with the whole class if they did not want to. Problem solving activities were also another concept that was written about in this article. The students were writing out how they were solving the problems and it helped the teacher a lot because then she could follow the students logic step by step. The author stated that problem solving used to be an assessment tool but now they were using it as an instructional tool (O'Connell, 2005).

There were many good and bad examples of the communication process in this article. It helped for me to see where these elementary teachers were making mistakes and why they were getting so frustrated when their students could not explain the answers. This article was very interesting because it had a lot of different concepts that explained how students could using writing when doing mathematics. There were examples of what the teachers did in their classrooms and how they fixed the problems that they were having with their students communicating their answers through writing. Over all, I really liked this article because it showed me not only good techniques when trying to get students to communicate about math, but also the bad techniques that some teachers are using.

O’Connell, S. R., Beamon, C., Beyea, J. M., Denvir, S. S., Dowdall, L. A., Friedland, N. G. and

Ward, J. D. (2005). Aiming for understanding: Lessons learned about writing

mathematics. Teaching Children Mathematics 12 (4), 192-199.

Process Standard- Communication

Communication is an important part of math, which is why it is one of the process standards. The four points that my group came up with from reading the article were

-Organizing thoughts in order to explain them to others

-Communicating clear and developed thoughts to others

-Reflecting on other people's methods for solving problems

-Expressing concepts correctly

Being able to communicate about math is important because it helps the students to really understand the concept that they are learning by organizing their thoughts. In the video analysis we watched how the teacher used discussion to talk about math. This was a different way to do math rather than having them just do problems out of the book. The teacher and the students were communicating about what they were doing. They were also reflecting on what they were doing and trying to figure out new ways to come up with different words that were worth more points. Communication is such a vital tool for any subject and I think students would like math more, if there was more communication involved. If the students can correctly articulate about math concepts that means they really understood what they have learned. In the standard it said that if students are challenged to think and reason about math and communicate about it, then it will be easier to understand when they have to write it out on paper. Listening to other people talk about math helps students to make connections in there head. I found this process standard to be very interesting because I never knew that teachers should be discussing math. When I was in school I was used to only doing problems out of a book and on the board. By watching the videos and reading this I realized that there are many ways that students and teachers can communicate about math.

Video Analysis #1

The fourth grade video addresses teaching variables to the students. Variables are something new that they have not learned yet and the teacher is trying to get them to understand what variables are. The teacher gives the students a task to create a variable machine. The machine is made up of two strips of paper.

1- Describe how the teacher's questioning and the manner in which student responses are handled, contribute or do not contribute to a positive classroom.

The teacher is asking questions to the students to try and get them on the right track and to see how much of the information they are understanding. I think it definitely contributes to the class because the students are trying to answer her questions. It seems like the students wanted to know more information about what they are learning. I think the teacher asking the questions is a positive way to help the students when they are learning new information.

2- What techniques does the teacher use to determine whether students have learned the material you are teaching?

The teacher in the video just walks around and looks at what her students are doing and why they decided to do that. She is making sure that each table is doing the right thing and observing where the students are at. She wanted the students to make the realization that if they change a letter to another number that it will also be chaning the variable.

3- Describe the primary task in this lesson and identify the mathematical skills and concepts that this task is designed to develop.

The task in this lesson was for the students to create a variable machine where they could create a word that was worth the highest amount of points or the lowest amount of points. The were also using addition and subtraction when they were figuring out how much the word was worth.

Over all, I felt that this video was helpful to me as a future teacher. I will have to be able to use the different approaches that this teacher did like observations and questioning. The students seemed very responsive to this lesson and I think that was a valuable lesson because they had to make connections between the letters and the numbers. I thought this was an interesting way to teach a math lesson and will have to use it when I'm teaching math in the future.

"Provoking Intellectual Need" By Kien H. Lim

This article talked about how students need an intellectual need or internal drive to solve problems. It gives teachers ideas on how to create an internal drive for students when teaching mathematical ideas or concepts. Lim makes it clear that teachers might just teach the information that is going to be on the standardized tests. He states in his article “Although tasks should engage students and align with assessments, they should also cause students to grapple with the mathematics that we want them to learn” (Lim, 2009). I agree with Lim I think that teachers need to make their lessons engaging but at the same time they have to still meet the states standards.

The next part of the article is about the need for prime factorization and least common multiple. There were helpful visuals in the article that helped explain to the reader how to make these concepts interesting when teaching them. It shows the order that the students should go in when completing the problems so that the students could connect what they just did in the first problem to the next problem.

According to Lim “The purpose of an intellectual-need-provoking task is to allow students to use their existing knowledge to, solve a problem, feel challenged because of the limitation of their existing knowledge, and experience the need for the target knowledge to solve the problem” (Lim 2009). I think that this is a vital part to teaching students mathematics. Teachers need to be aware of their student’s prior knowledge so that they are not overwhelming them and that their students are not falling behind. I think that students give up easily when doing math problems, which is why teachers need to have engaging ideas. If teachers do this then their student’s will not be discouraged but excited to learn.

Lim, K. H. (2009). Provoking intellectual need. Mathematics teaching in the middle school

15(2), 92-99.

The Learning Principle

The learning principle explained how students need to learn mathematics through understanding. Today many students are not learning mathematics because they don’t understand it; they are just memorizing the facts and numbers. Students who understand mathematics are able to use it in other subjects and can apply it in different places by the connections that they have made from prior knowledge and new knowledge.

The article also talks about using math in every day life. Children are interested in math concepts when they are younger. They like patterns and shapes and even learn these concepts before they have entered school. Teachers need to take hands on experiences and make math exciting for children to learn and understand. The article states that social interaction can be used to promote the recognition of connections among ideas and the reorganization of knowledge (NCTM, 2004). I agree with this article because I do not think that making kids memorize facts necessarily means that they understand them. I feel that this goes along with what we talked about in class. How teachers still use timed-tests even though research has proved that they are not effective.