Reflection: Curriculum Plan

The process of making the curriculum plan was as time consuming as I thought it would be. Knowing we were planning for three grades, for four domains, for four quarters each I figured we would need to spend a lot of time on it. That being said, I did not think we would spend as much time as we did. We started off working through each column together. Coming up with ideas together and writing it down one step at a time. After a few hours, I took the initiative of working ahead on the concepts of what is being reviewed, the objectives, the format of our document, the justification, and the CCSSM Standards and NCTM Standards. It worked out really nicely because Hallie and Kaitlin were able to bounce activity and task ideas off one another, do research and talk with me while I worked ahead. Once I finished I was able to help them again on an even better level. The process was really eye opening and made me see ways I want to work in the future. It was nice thinking of having control over the three grades, since each only works with addition and subtraction, we could come up with a potentially "perfect plan" that would help the students fully develop to be prepared for the multiplication and division work of third through fifth grade. I don't know how often school's actually do this, or teachers work together to make these plans but when I really think about it, it's a brilliant idea. We just wrote about the importance of teachers knowing what students worked with before their grade and what they will work with after. This process helps teachers see and understand where they students are going and where they have been. This knowledge will help teachers across the board better prepare their lessons, knowing what the students have experienced. I believe our group worked really well collaboratively, and each of us has an issue of wanting to put the details and the precision. I think this can be seen in our work. I would like to work more on long-term activities, even for our young grades, because I do believe that is an area of weakness for me.

Watching the videos in class, even our own, helped see all the ways these plans can be displayed and organized. We had the ability to present it to the class however we wanted, so seeing the girls talking to the camera in various locations, adding in videos of other people was cool because I did not think of doing it that way. Seeing the group writing on the table was really awesome because it was a creative way. Also, they didn't have to worry about what they looked like...I only say that because critiquing our own video I cringe watching myself talking. It is funny though because it's eye opening, you see things you do or say and the next time (hopefully) you don't do that. I looked at my paper a lot out of discomfort more than not knowing what to say. I have been working with the standards so much I should be able to tell anyone anywhere how we incorporated them but due to nerves I spent a lot of that portion looking at my paper. I know now that I will have to focus on that even more next time. 

Reflection: Standards and Classroom Changes to Deepen Math Learning

As the lead teachers in our classroom it is important that we include the CCSS-M Standards of Mathematical Practice (SMP), NCTM Process Standards, have student engagement, active learning, and math discourse. Through ETE 339 we have learned about each of these and their importance.

CCSS-M Standards of Mathematical Practice (SMP)
I had to work with the CCSS-M standards once before and it was pretty brief compared to the work we have done in this course. I feel much more confident in understanding how each of the eight standards work and their importance. Some of the standards have even caused me to look further and research their meaning to make sure I understand them to the best of my ability. I think when we focus on them or have them known it will help our classrooms become a better learning environment. After working with these standards it became apparent to me that they can be worked with together and really help the students master the material at hand. For example, if we start our students on focusing on using appropriate vocabulary (attending to precision) at younger grades such as kindergarten the students will become more comfortable and will be less likely to confuse terms later.

NCTM Process Standards 
I believe that the process standards are similar to the standards above because these five also work together to help the students master the skills. We have communication, connection, and representation. If a classroom is set up correctly the teacher can incorporate all of these standards in lessons. I also feel more comfortable with these standards and have found myself thinking about them more when coming up with lessons. I want to make sure we are hitting all of them to make sure the students are getting the most out of lessons. When all the standards are hit, mastery of the material is bound to happen. Also, again starting at a young age students using these skills will be able to use them even more as they age and develop.

Student Engagement
Student engagement is the motivational strategies we will use as teachers when presenting information to the students. This involves lessons using technology such as Smartboards and apps. It also includes having lessons that require the students to use inquiry or have self motivation. Class discussions can also help motivate the students and using their ideas for the lessons will stimulate engagement. Any teacher can go up to the class, present the information, write on the board, assign the worksheet. A teacher who makes the lesson rich, and engaging, will have better results. Students will want to learn and pay attention because there is self motivation and excitement. Thankfully we covered strategies in this course on how to make sure we do this. This includes our technology lessons, manipulative work, and group work.

Active Learning
I believe this also goes with the above student engagement. This is where the students are doing hands-on work when using their new information. This can be seen in classroom discussion, experiments, use of manipulatives, projects, etc. Active learning is when the students are doing versus just listening to the lecture. There will be times when students need to just listen but more often than not we can make learning active, especially in math class! Students will appreciate the work more and want to pay attention and learn. Technology helps, we have apps and applets that can be used which are stimulating but also beneficial to the lesson.

Math Discourse and Syntax -
Math discourse is how the students talk and write while syntax would be the symbols and vocabulary the students use. I will be 100% honest and say these are two concepts I am still really learning about. I am reading the edTPA handbook to make sure I understand the two. From what I understand discourse is how we allow our students write and talk in terms of our mathematics lessons. This again can relate to the process standards and CCSS-M Standards of communication and attending to precision. We are asking our students to use precise accurate vocabulary to present their ideas and justifications. Syntax is the words and symbols we use in our classrooms. This includes the knowledge of graphs and tables for example or symbols such as less than or greater than (<, >). Even though I am still working with understanding these concepts I understand that by using them accordingly we provide our students with the chance of deepening their knowledge and appreciating math more.

Coming into this course I wasn't expecting to have a huge change of mind for math class but to be honest I really did. All of these concepts were ones I could have thought about before but never really did. We learn the importance of communication, the importance of the standards and process standards deepening how lessons, I learned about discourse and syntax. If we use these ideas/principles/standards we will provide lessons with such richness our students will be engaged and appreciate mathematics. I am happy to work with this information and it inspires me and motivates me to get back into my own classroom. 

Reflection: Technology

In all of our education classes we hear time and time again how important it is to incorporate technology. I could not agree more. As times are changing technology is making such an impact on our society. Using these tools enriches our assignments and motivates the students to be working with tools students find intriguing and even fun. Over the past six weeks we have used the SmartBoard, Blogs, Apps and Applets. I really appreciated the SmartBoard work because we don't cover it in any of our classes and there are just so many options on it. I love that we each had opportunity to find or show something on the board to the class because there are things that not all of us knew or though about. I loved the idea of using the dice but putting words on them and asking for the definitions. I love the SmartBoard and sadly think a lot of schools that could use them can't afford them and schools that do have them do not use them to their full potential. I think change is hard, so for teachers to adapt and make lessons using the board might be time consuming but I think it is worth it. Next we have our blogs, which provide a lot of opportunity for reflection. This tool has helped me self-assess and really evaluate work and articles. I think this would be a nice tool to have for older students (especially because I think blogging is trendy? maybe I don't really know but I think it's a thing).  The apps and applets we researched were awesome because we got to show each other lots of different ideas we have. I didn't think about games that other people in class did or some of the applets people chose that they made geared towards their domain. These were out of the box ideas I really liked.

I think it is important to have technology in our lessons and classrooms because this generation is very technology stimulating. At the rate technology is going, when used correctly, lessons can really be enriched. 

Reflection: Assessments in Math

Over the last six weeks we have covered many types of assessments with class discussion, reading articles and activities. We learned about traditional, student centered, open-ended, portfolios, conversation, self, peer, formative, and summative.

Traditional assessments is the type of assessment I only knew about before teaching. This type of assessment consists of tests and quizzes. It is an easy cut and paste assessment, the student is either right or wrong and showing all their work on the document shows their understanding. Now, tests and quizzes are not bad but there are many other types of assessment that provide teachers with a deeper understanding to their students and a richer experience for the students.

Student-centered assessment was a new type of assessment for me to really think about. I understood it to be inquiry based, where the students are working to answer their own questions on the material. The teacher is able to see where the students are at with their understanding. Student centered classrooms provides the students with opportunity to be engaged and motivated to work on their work. I still want to look into student-centered assessments more because there are parts that don't make 100% sense but I think this also comes with time and working with the material more.

Open-ended assessments are awesome in my opinion because they are authentic and provide the students with opportunities to communicate their understanding. Communication proves mastery of the concept, if a student can clearly justify and explain their work (that is done correctly) they are on the way to mastery...but I will mention that again in a few paragraphs..when talking about assessment using conversations! When we give students problems that can be answered a variety of ways we are letting them use problem solving as well. The students can see the multiple ways, or later learn about the other ways, and pick which they think is best or which they can do best. Starting the open-ended assessments at a young age helps students build that confidence needed. This really makes the lesson rich and interesting for the students.

Portfolios are also wonderful tools. I think they take a lot of work but are reasonable. Again, as we work with the material more we can build these great templates for portfolios to use year after year. I think it provides the teacher a wonderful group of work to see where the students started and ended, whether we are using it as a unit, a lesson, a quarter, etc. I also love the idea of having students reflect on their own work. Even at younger ages this will provide students with another wonderful opportunity to build their understanding and communication skills.

Conversation is obviously one that I really like but it also can be found in any part of the day, activity, other types of assessment. Teachers can have one-on-one conversations and hear what a student thinks is a good justification or just to identify what the student is thinking. Teachers can allow group conversation and through observation the teacher can hear where the students are at, how they are problem solving, and thinking through the project. The teacher can also have whole class discussions which will help her assess where the students are and what work needs to be taught better or more in depth. Again, conversation helps students work on being able to communicate what they are thinking and practice justifying their work.

Self-assessment is nice because it gives students the opportunity to reflect on their own work. Having done it myself in this class, it's nice to go back, take ideas learned in class, and fix what we want to. It is also a good skill to have in students because they always need to check their work before turning it in. Self-assessments provide opportunities for the students to motivate themselves and strive to give their best work.

Peer-assessment is also nice when we did it in class. Again, we are provided with ideas we might not have thought about. We talked about how this is hard for students at younger levels because the teacher is going to have to go back and re-assess the work if it is a formal assessment such as a quiz. This type of assessment can be done in pairs where the students work together to make their work better.

Formative and Summative assessments will be used. Formative is on-going and regular used, such as through class discussion. Summative assessment would be the tests, quizzes, etc. that provide a grade. It is important to have the formal and informal assessments. Teachers need to make their observations to help justify a student's grade.

As teachers we will be using assessments constantly. It's important for us to remember the variety of options we have to assess our students and the strengths and weaknesses of each. I hope to always provide rich experiences for my students and opportunities to provide and show their growth and development. 

Manipulative Reflection

I really liked the activity in class seeing all the main manipulatives classrooms have. Some I have never worked with and others I have worked a lot with. It's cool to think about the ways you can use one manipulative to cover all or most of the domains. When people see unit blocks they might just think for counting or measuring but it was cool to hear what other people thought of. We even tried to come up with a way to use it and money. A concept that might be confusing but do-able. It was really eye opening and made me appreciate all the manipulatives, the simple ones and complex because we might end up in a school that can't afford every type but seeing what other groups did and my own showed me how we can find ways to make it work.

Students understanding deepens with manipulatives because they make the concept real. Students who have a hard time visualizing can manipulate objects will really grasp the concept. That being said even for students who can visualize, having manipulatives right away helps students see the concept. I could not imagine teaching addition, or even counting without manipulatives. Students can take concepts learned from manipulatives and use them later once the concept is grasped. Students should not always need the manipulatives and one day will be able to do the work without them. Teachers can assess students' understanding and growth by observation of the students and scaffolding. In the beginning the teacher will have to model and guide the students on using the manipulatives appropriately as the students begin to understand the concept they won't need to be guided or follow the teacher. When a student can use the manipulatives independently that shows he or she is understanding the concept. Students will work in groups a lot and the idea or lesson can very easily not be understood by each student and in groups its easy to have one or two students doing the talking, maybe one or two who kind of get it and one who is just sitting there following but not really grasping the concept. As teachers we will need to make sure we are watching all students, and asking questions to specific students. We will know who are leader students are, the ones always trying to ask questions, but we will want to make sure we check in with each student. This can be done through quick conversations and observation.  Teachers can also use this to assess the student's depth of understanding. I think group work is awesome, students can talk, work ideas off of each other but it is important to have individual work on the concepts as well. Students can improve their problem solving skills with manipulatives using inquiry. Teachers can present a new lesson, give manipulatives the students are comfortable with or a variety of manipulatives and ask the students to solve the problem using those manipulatives. 

Reflection: Error Analysis

Using the More Errors document, we had to see students' sample work and figure out where the student went wrong. As I started going through the problems I thought it would be really easy to get the answer I needed, see where the student went wrong. That was not always the case. Even for some, when I could obviously see where the student went wrong I struggled with why he/she did what they did. It was nice talking it over with some classmates because we do see things differently. I think if this were to be a problem in my own classroom I would be much more comfortable because I know the students and the material. It also brought to my intention all the ways students can misunderstand directions. Not to always talk about my experiences, but I definitely did not think about how if a direction is given in a way where any misunderstanding can happen....you will have a handful of students going in the wrong direction. As teachers we have to think ahead of times of instances this can happen and how to avoid them or at least be prepared for them. 

Reflection: Assessments in Math

I think it is really easy to say assessing math is done through critiquing a student's work. An outsider of the teaching major/career would probably assume this is the only way to assess where a student is. To be honest, a few years ago as a Health Science graduate I would have assumed that's mainly what teachers use to assess students. I just never thought about the variety needed to assess students because it was not what I was expecting for my teacher. Even though I taught preschool students it became apparent how multiple options/opportunities to assess the students. First I assessed the students one-on-one multiple times during the school year. This was to see initially where the students were with previous knowledge, how far they have come, and how they finished the school year. I quickly critiqued this process by adding in class activities and observation. The power of observation and conversation. I truly love that through conversation we can see where one student is, or the whole class! I also was working on a portfolio for my class if I were to have stayed an additional year. I just loved the idea and wanted to material all there to analyze and assess. Formative and summative assessments are two names we hear a lot in the major. Formative assessments are on-going, constantly happening. This is through observation, conversations, asking questions, activities. Next summative assessments are at the end of lessons/units and give an opportunity for overall learning. We have worked with rubrics a lot. I have made several for classes and have had them used for my work in a lot, if not all, of my classes. I have a love/hate relationship with them. I do like having all the details in front of me for what I need to give to the teacher. I think in the beginning I struggled making my own so I have rubric anxiety. :) They are growing on me though.

It's definitely crazy how one year of teaching and then a year of being an education major have made me see so much more. I definitely appreciate it all a lot more and always am fascinated to hear the ways we come up with to assess and work with students.