Curriculum Plan Reflection

Although this project was very intense, I really learned a lot and enjoyed completing it. This is something I have to get used to doing because I will some day be teaching math in my own classroom and have to plan out exactly what I will be teaching. For me, the most difficult part of this project was getting started and figuring out what we were going to teach and when we were going to teach it. We decided to split it up into four 9-week quarters. For each grade level, there were 5 standards, so we decided to teach 1 or 2 standards per quarter and it ended out working very well. I was fun trying to find different activities for my domain and also the semester long projects. It was more difficult to come up with semester long projects for the older grades because they cover so much material throughout the semester and it was hard to incorporate all of the standards. Getting the video to work and getting it right on the first try was very stressful. We were having technology troubles with iMovie so we had to use another program and that added unnecessary stress to the project. I thought all 4 of us worked really fairly together throughout the entire project of planning, creating projects, and filming the video. The work load fell more on a couple of us, but in the end it all worked out! I liked the opportunity we had to watch all three groups' videos. I thought it was interesting how different each of the groups interpreted the assignment. All three of the presentations were very different, but they all got the point across! Out of all the projects, this was the most beneficial because once we begin teaching, we have to know how to create a yearly, quarterly, and then more detailed plan for our curriculum.

Manipulative Reflection

• How do you know students deepen their understanding while using manipulatives?
• Students can deepen their understanding using manipulatives because it is hands on and the students are involved in the process of learning. When students are actually able to create and represent objects using manipulatives, they are able to visually see the process and are better able to understand the math concept.
• How do you know if the students can transfer their understanding from manipulatives to other situations?
• I will know if a student is able to transfer their understanding from manipulative to other situations by asking different types of questions during the activity while walking around the classroom and then  having a class discussion. Students will be able to discuss and compare and contrast different ideas that came up during the manipulative lesson. Listening to the discussion will allow me to see if the students were able to take away information from the activity. I could then have the students split up into groups and see if they could solve a real world problem utilizing their knowledge from the manipulative activity.
• How can you assess that understanding or growth?
• I could lead a class discussion about the topic, then let the students work with the manipulatives, and then have a closing discussion. This way I can see what thoughts and ideas existed before and after the manipulative activity to see what growth was acquired from the manipulatives. 
•  When students work in groups, how do you hold each youngster accountable for learning?
• I think it is important to assign roles to each student in a group (recorder, directions, and two people using the manipulatives). Then every few minutes I would rotate the roles. This way each student has the opportunity to be hands on with the manipulatives, give ideas and directions as to how to use the manipulatives, as well as listen and record the group member's ideas. By setting these roles, each student has a job to do within the group. This was each student is accountable to learning and participating within the activity.
• When students work in groups, how do you assess each youngster’s depth of understanding?
• I could assess their depth of understanding informally by walking around the classroom and listening to each group as they work together. I could also assess more formally by having the students submit a reflection assessment as well as answer a few questions regarding the topic covered by the manipulative activity as an exit slip.

Classroom Changes

There have been many changes to a math classroom in Illinois lately. With the recent introduction of the Common Core Standards, to having CCSSM standards, and the NCTM standards, it can be intimidating how many standards teachers need to be aware of when teaching math. The Common Core State Standard-Standard Math Practice or SMPs are eight different standards that teachers should be aware of and have included into their math activities. These 8 standards are: make sense of problems and persevere through solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, model in mathematics, use tools strategically, attend to precision, look for and make use of structure, and lastly, look for and express regularity in reasoning. Teachers will need to be sure to integrate all of these standards into their math curriculum no matter what grade level they are teaching. There are 5 NCTM standards for math. When I was in middle school, it didn't matter how we came to the answer, as long as we got to the correct answer. The NCTM standards as well as the SMPs want the students to explain their thinking and reasoning and justify as to why their solution is correct. These standards make students who are more aware of their math abilities and know how to problem solve. Even if students gets an incorrect solution, they can look back at their work and reasoning to see where they ran into a problem. The NCTM standards are: problem solving, reasoning and proof, communication, connections, and representation. I am glad this class has taught me so much about the different standards. I have been given the time to really become familiar with these standards before I have to be responsible in teaching them to my students. This will prepare me best when going into my own classroom once I graduate and become a teacher in my own classroom. 

Technology

Technology in the classroom is always changing. I remember having chalkboards in the classroom when I was in early elementary school. Then we switched to whiteboards. I also remember having the giant carts with overhead projectors and the clear transparencies teachers used to write on. Now, classrooms are equipped with SmartBoards, iPads, ELMO projectors, smart response remotes, and computers. There are so many ways teachers can use technology to engage their students and to make learning fun. Even if schools don't have the funds to have all of the technology styles out there for their classrooms, I think the most useful are computers, smart boards, and the ELMO projector. I have learned so much about the SmartBoard just from being in this class. It can be used in so many different ways and makes learning more interesting! Students love coming up to the front of the room to get a chance to use the board. This is definitely a great tool to use in any classroom. The ELMO projector is a digital camera that displays whatever is placed in the view of the camera onto the smart board. This is very useful when demonstrating how to complete a task on a recording sheet, or when reading a word problem passage together. I would definitely use as many technology tools as I can for my math class. I also enjoyed learning about all of the apps and applets. There are amazing apps and applets teachers can use in the classroom on the smart board, computers, or tablets that incorporate the mathematical standards. These provide new and fun ways for students to learn the math curriculum.

Assessment in Math Reflection

Assessments in math can come in all different varieties, just like assessments in any other subject. In math methods we have learned many beneficial assessment styles and tools other than homework grades, quizzes, and tests. There is a big push for switching classrooms over to inquiry based learning. This learning style is best assessed by a rubric. In methods, we have learned about the importance of a strong rubric that has different levels that are very clear and also the rubric needs to not be biased. My two favorite assessment styles are performance based assessments and portfolio assessments. Performance based assessments allow students to take the knowledge of the topic and apply it to a real world situation. Portfolio assessments allow students to see the physical growth of their learning by collecting various assignments throughout the semester or year. These assignments are much more meaningful to students because they are applying what they have learned. The traditional tests and quizzes are also important, however these mainly assess memorization and don't represent the depth of knowledge a student may have when compared to all the levels of Bloom's Taxonomy.  In my classroom I want to have a variety of assessments for mathematics. 

Error Analysis/Reteach Reflection

I really enjoyed completing this activity. I found it fun and very interesting. It was a lot harder than I thought to identify the mistakes the students made. It was also eye opening because I never realized some of the strange ways that my future students could possibly misunderstand math applications. I really liked that we were asked to think of a way to reteach the coordinating topic for one of the students. It made me think of a different approach to take in order for them to better understand how to complete a problem. This is an important practice that I think some teachers forget. If a student does not fully comprehend the material being taught, I believe it is extremely important for teachers to revisit it. I think teachers tend to  avoid re-teaching material because they feel that it will take away time from other content that needs to be covered. While this is true, it is also the incorrect approach because many mathematics concepts builds upon one another. Students won't be able to learn new material if they don't understand the previous material.  As a future teacher I will look for these possible errors or misunderstandings with my students and reteach when necessary.   

Assessment Articles

Getting Started with Open-Ended Assessment

This article is addressing some different ways of assessing math in the classroom. The articles focused on the difference between multiple choice and performance based assessment and how performance based assessment is better. It talks about using open-ended problems to assess math students' work. I like this idea, because with the many possible solutions to the problem, students may think outside the box to find a strategy to solve the problem. Open-ended problems allow teachers to see the students thinking process and allows them to help the students where they struggle.

Sbord of Assessment Options

The article is addressing problem solving. Problem solving is a huge part of the math curriculum. It also talks about the different ways math can be assessed. This is often referred to as the menu choice. This article mentions how even though multiple choice may be an okay assessment, performance assessments with accurate rubrics are a much better tool to assess whether or not a student is able to apply the information in a real life situation.

Understanding Student to Open-Ended Tasks

This article is addressing how open-ended questions can work in a math classroom. I really like this because I believe that it allows students to really vocalize their thought process for the math concept. This also allows the teacher to feel like they are better able to understand and student’s understanding.  The teacher in the article had students explain what area was in their own words. This allowed the teacher to see what each student was thinking and how they were able to think or reason throughout the problem based on what the student wrote.

Assessing Students' Understanding through Conversation

This article is addressing the importance of conversation in the math classroom. The article is addressing how based on conversations in the classroom the teacher might need to change the plans for the day. For example, this teacher was able to realize that her students were struggling with some of the properties of a rectangle, so instead of moving on she created a small mini-lesson on the spot to help improve her students’ understandings of the topic. I really like the idea of assessing the conversations that take place in a classroom I believe that it allows for the teacher to reflect on her teaching methods based on how well the students are speaking about the topic they just learned. I believe that this is allows for the teacher to create stronger lessons and for the students to speak up about their understandings. 

An Experiment in Using Portfolios in the Middle School Classroom

This article was talking about a teacher who decided to implement portfolios as a way of assessment in her math classroom. Portfolios are an important tool that allow teachers as well as students and parents to see the mathematical growth of the child. I love this idea of having a folder where the student can reflect back on their work. I also liked how this teacher used a certain criteria to assess the portfolio so that this was a project that encouraged the students in mathematics, instead of discouraging them. She allowed the students to pick the materials they felt should be in the portfolio and then they had to so some sort of reflection with them.