"Problem Posing", "Assessing Problem solving thought", and "Assessment Design:Helping Preservice Teachers Focus on Student Thinking"

             For this blog, I will be discussing three articles. The three articles are call "problem posing", "assessing problem solving thought" , and "assessment design: helping preservice teachers focus on student thinking". The first article I will be discussing is "problem posing". This article is all about how problem posing has not gotten the attention it deserves in recent years. However, according to the article, it is now starting to receive more attention. The author talks about how if they are wanting this to be part of mathematics classrooms, then there needs to be criteria about how we are going to assess this both with problem posing and of problem posing. The author then goes on to say how there are three criteria that should go into the assessing of this. They are quantity, originality, and complexity. Each of these are explained in full detail. The article concludes by saying that assessment is a very important part of math, and that as it becomes more widely used in the classroom teachers need to make sure they are looking at the ways they are assessing it.
           The second article I will be discussing is "assessing problem solving thought". This article deals with the fact that this author thinks that teachers should go through the assessment process first before they have their students do the problem. According to the author this is to help teachers understand and go through the problem themselves and see how their students might go about doing the problem. It also goes into detail on how to create a good rubric to use to assess your students. It also discusses the difficulties that might be associated with the assessment process. The big thing from this article is that we as teachers need to make sure that we are not letting our emotional attachments to the students get in our way from assessing what is actually on the page that the students have demonstrated.
               The third article that I will be discussing is "assessment design: helping preservice teachers focus on student thinking". This article is all about an assessment project that a woman  designed for preservice teachers so they can understand that math "should make sense to students." Each person involved in this project had to go through a specific process that involved picking out one of the CCSSM content standards to focus on. Their job was to focus on this standard and evaluate how the students were thinking about the content they were teaching. They then had questions that they were to be asking themselves as  they were evaluating their projects. They even had one woman give her testimony as to how her experience was while going through the process of this project.
               I personally thought all three of these of these articles were eye opening. They really made me think of how important assessment really is when planning any sort of lesson. I will certainly have to implement some of these projects and ideas into my own classroom especially the one that pertained to preservice teachers as I will be student teaching this fall. These will certainly help me be a better mathematics teacher throughout my teaching career!

"Connecting the threads of area and perimeter"

                This blog will be about the article " connecting the threads of area and perimeter". It is from the March 2014 issue of Teaching Children Mathematics.This particular article was all about a quilt project that can be done pertaining to the subject of area and perimeter. The author starts out by saying she got the idea for this quilt project because her students would always ask when they would ever use what they learn about perimeter and area. So, that go her to thinking that she needed to find a way to give the students more real life connections when it came to perimeter and area. This is where the quilt project came into play. The students where to go through a process. Then once they went through that process they had to get it approved by the author before they could start the actual construction of their quilt square. During the process though, it allowed the author to go around and do formative assessments on her students to see if they completely understood the project and what was being asked of them. This worked out extremely well because not only was she able to help struggling students get back on the right path, but the also gave her the opportunity to let the students conversate and collaborate with their fellow classmates if they had questions. She was also able to address all of the common core standards as well as all of the CCSSM standards relating to this project. This project took a week to complete.
                     This article was very interesting to read. I was very impressed to find out how to incorporate more real life connections when it comes to perimeter and area. It also really opens your eyes when it comes to how creative you can  be when it comes to hitting those standards. I also really loved how you don't even need very many materials when it comes to planning this project. I will certainly keep activities like this in mind when it comes to certain subjects like perimeter and area to where my students will always be able to make those real life connections to things they might not think they will ever use.

"Decimal Fractions: An Important Point"

               For this blog I will be discussing the article " decimal fractions: an important point." This article is from the March 2013 issue of Mathematics Teaching in the Middle School. This article starts off talking about how decimal points are a point of frustration for students. This is because, according to the author, students  have a lot of misconceptions about the decimal point. The author then goes into some background knowledge to help us gain some insight into how the author came about in looking into this subject of decimal point fractions. The author even gives some research to back up why students might have misconceptions about this subject. The next part of this article is about different strategies that came about from investigating and researching this subject. It even has a nice table to look at that has four misconceptions on it and explains them in a couple  different ways on the table. Those four misconceptions are longer is larger thinking, zero makes small thinking, shorter is larger thinking, and money rule. This article also talks about different student samples of work, and some of them shown on different tables.
               This article was very educational and eye opening for me. I was certainly one of the students who struggled with decimals and fractions growing up, so I am glad that I have this article to take notes on and utilize if I am ever teaching this subject or helping a student with this subject. I also love how it give samples of student's work to understand what the author is talking about. This article also made me realize just how important decimals and fractions are to everyday thinking and life. I will certainly implement this into my classroom by making sure that I have those common misconceptions learned, so that way if I see my student struggling I will have a nice starting point to go from. I will also be watching what strategies I use when teaching this subject and try some of the other strategies mentioned in this article to make sure all of my students succeed!

Video Analysis 2

 This blog will be a video analysis. The video that I will be analyzing is a lesson for fourth grade that deals with multiplication and division, and it was called "number operations". The planning was the teachers and students going over just what constituted multiplication and division.The students had to talk with their partners before sharing as a class. During this time, the teacher was trying to get the students to understand the big idea that the groups were equal.She was also trying to get the students to understand how creating pictures to solve problems worked. Then the students did mental math before the teacher had the students complete the word problem. The specific activity was the students solving the problem of Maria saving $24 and Wayne saved three times less than her.
                  The teacher had the students look at the problem then gave each student a piece of paper that had the problem on it. After each student was given the piece of paper, they were instructed to take it back to their desks and work on it individually for a minute than they could look at their partners. After they students completed the problem, they came back together as a class and discussed ideas and answers.
                     The faculty debriefing was very interesting. It consisted of the teacher and three observers. The teacher discussed how the students had been almost conditioned to understand that multiplication is like addition, and division is like subtraction. Along with that idea, she said that especially the division is like subtraction idea was interesting because most people don't see division as like repeated subtraction. One of the observers brought up the point that peer pressure might have something to do with why some of the students had their answers the way they had them. The teacher than discussed how she had to drag the idea of the equal groups out, and she had to almost prompt them to expand of the addition and subtraction ideas. One of the implications that I noticed was the whole misconception about the 24 or 32 dilemma. It looked like the observers and the teachers automatically thought they would be on the right track. The student debriefing was also useful because it showed just what students knew what they were doing because I noticed that a lot of the same students were answering or sharing ideas during the discussions which is why the teacher had to prompt for other students to share.
                      Overall, I thought the video was an excellent resource and was utilized perfectly. It shows just how important collaborating can be by having the observers in the classroom, and involved in the planning and reflection processes. The video especially is an excellent tool for reflection in many areas. For example you can tell where certain things may not have gone as you had planned. A perfect example was the confusion about the 24 or 32, and the kids relying on their peers answers or peers mathematical thinking at times. This also proves that by debriefing with your colleagues, you can also find out just what ideas need to be revisited. I also liked how the video was split into segments. It allowed me to look at them a lot closer, and it made it easy for me to watch certain parts more than once when I needed to.So, all in all it helped me realize just what I need to do when I start teaching math, and it also taught me some things that could be adapted.

Math Applets

                For this blog, I will be talking about two applets and one app so three altogether. The first app that I am going to talk about is the smart exchange. This is specifically designed for smartboards. However, you can look at them on your computer before you try it on the smartboard. I chose an app on this site that is for the 3-5 grade category. The particular app has to do with fractions it goes through different ways for the students to review fractions. For example, on of the activities on this app is match the fractions. This would be perfect for students to use not only as a review for the test, but also as a way for them to get more practice with fractions if they are struggling.
                   The second app is all about angles and it is designed for grades 6-8. This particular app was found on shodor.org/interactivate. This can certainly be implemented at several times throughout a unit in geometry on angles. This could included using this as a pre-test, using this as a review for before a test, or using it as an intervention technique to give students extra practice. Throughout the app, it gives you different angles to look at and you have to answer how many acute angles you think there are, etc.
                    The third applet is on http://illuminations.nctm.org/. The actual applet is called grouping and grazing. It is designed for k-2. It has different activities that you can do and it involves animals that graze in groups. You can count by 5's, 10's or add/subtract. Again, as with the other two apps, you can certainly implement this in your classroom by having the students doing this several times not only when you are teaching addition and subtraction, but as review and intervention  technique if needed. All three of these apps that I have discussed I think will be great additions to my future classroom and will help so many students succeed to their fullest potential!

Student Work Reflection

        This blog will be about the student work project that my group and I did. It was certainly an eye opening project. I never knew just how much information you can really gather from looking at student work. This includes what their previous knowledge is, what they might still be struggling with, etc.It is important to see this in all of your students work, especially in math, so that way you can make sure that all of your students succeed to their fullest potential. It is also important to analyze your students' work, especially in math so that you are able to plan your strategies to where they work for all of your students to succeed.
         Overall, you need to make sure that you are constantly going over and analyzing your students' work. I know I will certainly implement this as soon as I get into my first classroom. I have also found out that you need to look at multiple works in order to even start getting a handle on the information that the works provide for you. I also realized that it might also be useful to collaborate with other teachers for the same grade because you can have second opinions to think about as you are going through them. You also might find out many different strategies that students might use to solve a problem. The biggest thing I noticed was that interpretation is key when looking at how you classify the samples.

"Thinking Through a lesson" and "A model for understanding"

                  For this blog, I am going to discuss two different articles. The first article is called "thinking through a lesson." I found this article very interesting. This is because the topic of this article is a process that teachers can use when planning a math lesson that involves higher or more complex thinking. It is a three part process. The three parts are selecting and setting up the mathematical task, supporting students' exploration of the task, and sharing and discussing the task. The article then goes into detail about each part, and explains what questions teachers should be asking their students at each part during the process. This article also gave an example of the type of problem that would be great to use this process with. Another part of this article was talking about how you should be looking at your students prior responses and responses to the other tasks you give them so you know how you can help your students succeed even more.
                 The second article was called "A model for understanding." The first item discussed was the definition of understanding. The article gave seven signs that you will exhibit if you truly understand something. They are you are able to state it in your own words, give examples, recognize it in various situations, make connections between that topic and other topics covered or discussed, use it in multiple ways, foresee some of its consequences, and be able to state its opposite.The author also discusses understanding as a process. This process involves organizing and integrating knowledge according to a set of criteria. Another idea discussed is the idea that understanding is also a continuum. This means that students only have partial understandings. The rest of the article goes into detail by explaining how to understand different concepts in math and gives examples to go off of when planning lessons or activities. You can implement both of these articles into my teaching career by taking these processes to heart when I am planning my activities for my students. For example, if I was going to plan a problem that dealt with colored candies in a bag, I would go through these processes. From reading these two articles, I know now that it is important to keep these processes in mind to make sure that I am pushing each of my students to challenge themselves so they can succeed at their fullest potential.