Assessment Journals

Open-Ended Assessment
Questions are considered open ended when there are multiple ways to solve it as well as multiple correct answers. Creating these types of problems is time consuming and often difficult. These questions are much more difficult to come up with. You have to be sure when creating these problems that the students will understand what the question is and that they need to show how they came up with their solution. Implementing these questions on assessments in my classroom would allow for me to gain a better understanding of where the students are at in their understandings of the topics.

Assessment Options
There are many different types of assessments for teachers to choose from. Assessments are designed to help students learn as well as to help teachers to see what the students are understanding. Assessments should be chosen specifically to evaluate students on each topic. Using the same type of assessment over and over is not useful to the students or the teacher. By using different types all of the time, the students will be able to demonstrate their strengths in different areas and the teacher will be able to get a clearer picture of the students' current performance levels.

Understanding Student to Open-Ended
This article focused on several different student responses to the same question. Their responses showed that the students who were in sixth grade were able to thoroughly explain their processes in writing. The responses also give the teacher a great understanding of how the students are working through the problems. Asking for an explanation of how the students found their answer is a great idea. I think that this will even help the students, because they may notice that something does not quite make sense when they are writing their explanations, which gives them a chance to go back and make adjustments.

Conversations
This article starts out with a great example of why classroom discussions are valuable. The students are answering questions aloud which lets the teacher know that some of her students are confused about a topic before the one which they are currently working on. This allows for the teacher to go back and clarify that basic topic and then continue to move on. Conversations in the classroom can be helpful in directing instruction. The teacher can listen to how students explain various topics to see where they need the most help.

 Portfolio Assessment
When I think of portfolios, I think of something that shows growth and development. After reading this article, I realize that there are more things to look for in math portfolios than growth. Students can show their attitude, problem solving skills, growth, writing, and connections all in a portfolio. Portfolios can be assessed based on their organization as well as the math content within them. I think that portfolios are a great assessment tool which can be shown to future teachers to help understand the levels of their new students. This is also a great thing to show to parents so that they can see the growth as well.

NAEP Reflection

I really enjoyed this assignment. I found it so interesting to be able to see so many different student responses to the same problem. I think that it was valuable to be able to see how greatly the thought processes of students can vary, even within the same grade level. I enjoyed picking out specific samples and judging them to determine what score should be given. It was very eye opening to try to assess them based on the rubrics provided. Many of the rubrics were vague or had overlapping ideas for different scores. I think that the rubrics could have been more specific in order to allow for more objective assessment. I think that creating a plan of how to continue student learning after their work on the problems was also quite interesting. We chose three students who had very different abilities and showed different strategies in solving the problem. This caused it to be slightly challenging to create a plan of what to do next for the class as a whole. I think that this was an authentic activity because in our future classrooms our students will always have varying abilities and talents.

Video Reflection #2

This video starts out with the teacher asking the students what they know about multiplication and division. The teacher allows the students to talk to each other and then asks them what ideas they have about the two operations. I think that it is a good idea for the students to talk out the ideas that they have with their peers, however, the students may not have been ready to do this just yet. I think the teacher could have taken a little more control in guiding the conversations at this point in the lesson.
Next, the teacher asks the students to complete some mental math problems. She then has the students discuss with their peers again about how they solved the problems. During this time of sharing strategies, many misconceptions were shown. Students seemed to get confused between different operations and were unsure of which to use when. The teacher discusses the different ways which students solved the problems. The teacher shows show the students could use drawings to enhance their answers. When the teacher asks the students to write about what they will remember about Charlie's way they need a lot of guidance to come up with something to write down.
During the faculty debriefing the teacher talks about how the students all said that division is related to subtraction. I also found this to be very interesting because that is not what I would have thought to say. I agree that the students must have heard that somewhere or simply thought that since multiplication is similar to addition, division must be similar to subtraction.
Overall I found the video interesting. I think that there could have been more guidance and structure in the lesson, but I also like the large emphasis on their individual exploration.

Applets & App Review

Applet #1
Catch the Fly
 http://hotmath.com/hotmath_help/games/ctf/ctf_hotmath.swf
This applet is designed to practice working with x and y coordinates. This is just a quick activity that provides simple practice, this is not an applet that the students would need a lot of time to go through. The premise of the game is that you are a frog and a fly lands somewhere on the coordinate plane. You have to type in the coordinates of where the fly is in order to eat it. The applet itself is on a plain grayish blue colored coordinate plane with the frog a vibrant green color. The answers which are typed in by the students are placed on the plane in red for incorrect answers and green for correct answers. The plane is easy to see and has clear numbers which are easy to read.
I think that this applet can be used anytime when the students finish work early or are allowed to have time on the computers. This applet is perfect for middle school students and I think that the students would be entertained by it. The feedback is very clear, the point which the students selected is highlighted until the correct point is selected. The coordinates are also written next to that point to help them see how they are set up. The feedback is immediate and helpful.

Applet #2
Factor-Tris
http://hotmath.com/hotmath_help/games/factortris/factortris_hotmath_sound.swf 
This game adds a math spin to the traditional game of Tetris. In this game, the students select what size blocks will come down based on their factoring of numbers given. For example, the number 72 will show up on the screen, the students then must select 72 units in some way (a rectangle which is 6x12). That rectangle will then come down the other side of the screen in a Tetris type game. This game is really fun and great for middle school aged students.
The main focus of the game is factoring. This is a great way for the students to keep practicing their multiplication and division skills. There is also some spacial reasoning skills required for the Tetris side of the game. This can be used in the classroom again during free time as a skill builder for students.

App #1
iTooch 7th Grade Math
http://www.edupad.com/itooch/middle-school-app/
This app is awesome! It includes so many different topics all geared toward 7th graders. The app is appealing to children and has many bright, vibrant colors. The topics include; numbers and operations, algebraic structures, statistics, functions, and geometry. Within this app, the player starts out answering a few questions from the selected category. After getting these questions correct, it will allow you to take a test within that category. The student can then unlock new levels and tests to take. This game has great sounds and visual effects. It is fun and exciting to play. This is something that the students can play for a very short amount of time or even a longer time because of the way it is set up. The teacher can select what category the students should play in or the students can select whichever they would like. The app is available for Apple and Android devices.

Thinking Through a Lesson Article Reflection

This article talks about Think Through a Lesson Protocol or TTLP. This is something that I have never heard of before and at first sounded kind of silly to me. The protocol seemed to be sort of common sense to me. I think that teachers should be naturally following the three stages of the TTLP without having to really think about it. The goal of teaching is to ensure that students are learning, and I think that this protocol does ensure that, but I do not see why a teacher would need to be told to do this. For example, in figure 2 the section of questions dealing with stage one include, "How will you group students?", "What errors might students make?", and "How will students record their work?". These are questions that teachers should always be asking themselves when planning lessons for any subject.
I think that the TTLP has a lot of great ideas in it, but I think that any good teacher would already be implementing those ideas even without ever even knowing what the TTLP is. I think that asking these questions and providing students with higher-order thinking problems is always a good idea and will benefit the students greatly. If the TTLP can help teachers to do this, I think it is a good idea.

A Model for Understanding Article Reflection

I found this article quite interesting. I think that we, as teachers do in fact need to have a vision of what understanding looks like. This article gives us many ideas of how to check for understanding when teaching mathematics. It was very surprising to me that the article was written thirty years ago, because it is still very relevant today.
I greatly enjoyed all of the example questions that can be asked to check for understanding of concepts, processes, and facts. I think that it is hard to determine whether a student is truly understanding what the material is on a deep level, or if they are simply memorizing what they can and pretending to understand. One example I found to be a good idea was when talking about prime numbers, asking "I have a prime number written on the back of this card; what can you tell me about it?" This is an excellent way to determine if the students truly understand what makes a number prime. The ability to generalize what they have learned and talk about it in their own words will often show that they have a deep understanding.

Rich Task Reflection

Through completing this assignment, I have learned a lot. I realized that there needs to be a lot more thought into planning "rich" activities. It was difficult to find an activity that included parts which would work for all different types of learners. Our task was the "How Big is Barbie?" activity. I really enjoyed working with this activity and changing it slightly to meet the needs for the assignment. I think that this is an activity I could definitely see myself implementing into my classroom one day.

I also greatly enjoyed the activities which the other groups presented. I think that the biggest thing which I learned through all of the presentations was that it is very important to run through the full activity before trying it in a classroom setting. There were some minor hiccups during all three of the activities that I think could have been fully avoided if we had all ran through the activities beforehand.