Group Reflection on Standards Project

I am really grateful for this project. I had learned about the different standards before but it was nice to actually dive into a couple and really get to know them. I learned that modeling with mathematics included really life situations and the use of manipulatives. It was cool to read articles how the article have related situations so closely to the lives of their students. Next Hallie and I have look for an express regularity in patterns. I really liked this standard although it can be hard for some people to really understand what it is aiming for. I think this is such an importation skill for learning math. I like to look at it in terms of building block. As the student is learning different math shortcuts their level base for math is increasing and increasing. I look forward to using and applying these standards along with the rest of the standards with my future students.  

Video Clip: Word Problem Clues

1) The planning, including tasks, core math and challenges, and questions for teacher reflection

I thought it was really cool that before the teachers were just observing in Tracy's classroom that they all meet and had some time to learn about and hear about what they were going to be observing during that lesson. They were provided with background knowledge on the overall classroom performance with math. I really liked that they actually took some time to look at and try the math problems themselves. I think this is something that some people forget to do, it is important to make sure what we are asking them to do is doable and makes sense. Without doing the math problem themselves maybe the teacher would not have realized how hard it really is for some students to draw pictures for some of the problems. It was interesting to hear her explain how the students just see the numbers and automatically just start adding, they are not taking the time to read the actual problem at hand. This was interesting to me because I never really would have thought that they would just skip the reading part of the world problem. I could understand if they misunderstood the message but just not reading it at all is something new or me to keep on my radar. Tracy really stressed that she wanted her students to make sure they knew what they were writing down and if what they wrote down made sense. She explained how she wanted the students to understand how their numbers, pictures, and words need to all make sense and connect together. This is something that the students were having some difficulty with. I also really liked how she said that she tries to avoid using the word "wrong" because she realizes that this can discourage students to keep thinking and trying. I really agreed with her on this point. Yes there is such thing as a right and wrong answer but we as teachers need to keep our students motivated to learn and show them that they are headed in the right direction. If we just say "No, wrong" well maybe they were wrong but they were close... and now that student has lost their drive to keep going. 

Tracy asked the observers to document any muttering they heard among the students. She stated that this would help her to better understand the students thinking process later when they were shared with her. I thought that was a really cool request from her, because it is hard to catch every students side conversations and outside thoughts. Having more people in the room can make this an easier task.    

2) The lesson including student debriefing, along with success and misconceptions and student work

I really like how much time she spent with the students walking them through the different thinking and processing skills that this math problem was asking them to use. This was the first time that I saw a math lesson start out on the carpet. This really stuck with me because I feel like a lot of teacher always think that math needs to be done at their desks while you stand at the board and write on it. I think doing it the way that Tracy did sets the students up for a better thinking palate. They are sitting at the carpet and have that time to think and verbalize their thoughts. Then when they go to their desks they get to use those thoughts and turn them into process skills and thoughts. 

I also really liked how she pulled examples from students in the classroom and how they all knew to respect each other's work. This is something that Tracy had to have worked with them on before hand and this is something I would like to do with my future students as well. I think it helps them really notice there is more than one way to think and process problems and by seeing it done amoungst their peers with hopefully stick with them better. I also like that while see what doing that she used post it notes show the students what was where and to make the students really be specific with what they were saying they were seeing. 

When Tracy asked them to look back at their work, I thought it was a really cool idea that she used photocopies of the original work of the student and also asked them to use a different color pen. This allowed the students to see their base and how they need to build and improve from what they have already provided. This is also some thing I want to use with my students. More often than not I have seen where a student just erases all the work they have done when they know it is wrong, instead of building off what they have discovered. It actually drives me crazy when I see students do that... 

I liked that she then provided the students with some new and different math problems to see if they could apply what they just learned to accomplish a new task. This is something important, because instead of just ending the lesson with "oh yes now they get it more", Tracy built on it and made the lesson to come to "let me make sure they understand it more by having them show my and apply what we have discussed through different but similar problems". I loved that!!!     

3) The faculty debriefing and implications for instruction

I found it really powerful that Tracy was able to be an accurate reflector of the lesson. She stated exactly what she thought and how the lesson went. I found it very cool that she was able to right off the bat notice what did not go as well as she planned and also how the lesson formed into a little bit of a different lesson. I think as teachers we need to always be able to look at a lesson and understand that it is okay for that lesson to be morfied a little bit as long as the overall main goal is still on track. Which is what I would say happened with Tracy's goal. She wasn't able to get through as much as she had wanted, but that is because she needed to spend more time on certain specifics with some students to make sure they understood and we comprehending the problem. As teachers we need to recognize when we need to slow the pace down to make sure we are keeping all of our students on track. 

4) Explaining your thoughts on the overall use of the video. 

I found this video to be really useful. I have provided my individual comments on specifics throughout my entire reflection. I learned a lot from this video and can not wait to incorporate these math techniques in my future lesson as well. I would also just like to comment on the fact that Tracy used outstanding Math vocabulary with her students. This is so important! Students need to know the proper way of speaking the math language and they are never going to learn that if it is not being used around them. Tracy did an excellent job with that!!! 

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Count On It: Congruent Manipulative Displays

By: Joe Morin and Vicki Samelson

Summary of Journal 

This article's focus was placed on the use of math manipulatives in the classroom. Most of the time people think that math manipulatives in the classroom could only better a student's understanding of a topic, it would never render their learning. However the authors of this journal go into great detail as to how manipulatives CAN have downsides. This article goes on to explain how manipulatives should and should not be used in the math classroom. They start out by saying that it all depends on the cognative level of the student. If the student does not understand the idea of "representation" through the use of manipulatives, you will need to build the student to that level of congative ability first. They then develop the understanding of how students transition from standardized manipulatives to semiconcrete manipulatives. The article address how the use of manipulatives can lead to major distractions with younger children because depending on what you pick to use as the item they can have a hard time seeing it as a learning tool rather than a toy. Another idea that they spent a lot of time on was the idea of Conceptual Congruence; which deals very closely with students understanding the base 10 units. They provided an example of how to properly use base 10 manipulatives with younger students. Long story short all aspect of the 10 units need to visually present for the student to understand. The present ones and the empty spaces that would build a full unit of 10.  

Reflection of Journal 

This was a very interesting article, because I never really knew so much thought went into the use of manipulatives in the classroom. I kind of always thought what the majority of people think: manipulatives always help. However after reading this article that is not always the case. I learned some very valuable concepts from this article. For example, I did not know that for younger students if you provide them with two different types of manipulatives, one for which is physically larger than the other, but smaller in quantity; some students might have a hard time getting past that if asked to state which group has the larger amount. I never really took the time to take a step back and think about the congative development that needs to be present in students when dealing with manipulatives in the classroom. Lastly I also really liked how they stressed the importance of base 10 manipulatives for students. How it is important that all aspects that form a unit of ten are present visually for the student to see and grasp how many units make a "base" of ten. I look forward to carrying this insight with me as I progress in my teaching career. I will always think about this information when it comes time to pick out manipulatives in my future math classroom.  

An Authentic Task That Models Quadratics

By: Lorraine M. Barron 

Summary of Journal

I had the pleasure of reading this journal article that was written in February of 2015. This article was placing its focus on the Common Core Standard number 4: Modeling with Mathematics. There was a team of teachers that wanted to create an authentic problem situation for their students. They also wanted the problem to fulfill the Common Core Standard for High School math dealing with non-linear functions. The teachers wanted to make sure that the problem was relateable to the students current lives, so they based it off of a school fundraising project that many of the students shared a passion in. The problem had to deal with selling muffins for the fundraiser. The students were placed into groups and then presented with the problem by their teachers. They were then given 90 minutes of work time to figure out the problem and create a visual representation to go along with their findings. The teachers created a very inquiry based learning environment for their students. If the students asked questions the teacher did not give an answer but yet guided them in a different direction by posing more questions for the students to think about. Once the time was up the students were then asked to present their findings to the class and explain what, why and how they did what they did. Once all the groups had presented the teacher followed it up with a closing of the topic. They explained what non-linear graphs are and how they are important to know about. They told the students about maximum and minimums. The last thing the teachers asked the students to do before their time together came to an end, was each student did a quick write. Their version of quick write is each student writes a question that they either still have about the material or a question they have about the material they learned and how it is related to future learning. The very last part of this reading is the teacher's and their self-reflection. They reflect on the on going thought: is it worth spending the extra time with your students to do an inquiry lesson? They then go on to say: yes it is. Throughout their later lessons for this topic they felt that their students really remembered and knew the information better than if they would have presented it in a different manner.  

Reflection of Journal 

I found this journal to be very interesting. I had learned a lot about inquiry skills and how to write an inquiry lesson for science topics, but I had never looked at it from a math standpoint. I really liked that the teachers picked an inquiry based problem that was not only relateable for the students, but also a current issue with their fundraiser. I believe that this allowed the students to be dedicated to finding the answer because they wanted to figure out how to help save their fundraiser in real life. I also really liked that the teachers stated that they picked the problem they did because it can be solved in a variety of different ways. This allowed the student to make sense of the problem in whatever way works best for them and their group members. Another aspect that I really like what that they allowed each group to present their findings to the class. While presenting the students had to explain why they did what they did. The reason I liked this was because when students are able to explain what steps they took and why this demonstrates higher level learning, which is usually closely related to a better retention level as well. I also really liked that the teachers explained how if a group was unable to reach an understanding or conclusion while presenting they would "parking lot" the idea and come back to it later at the end of class. Lastly I never would have thought to do a quick write or an exit slip for math class, but I really liked how they used them. They just asked the students to write a question that was still on their mind about the topic they worked on for the day; all the other quick write I have seen require more that the students write more than one sentence. However for a math lesson that allows the teachers to see how their students feel I think that the way they did the quick writes was perfect. This is something I will use with my future math students someday.       

Article Related to Standard: Look for an Express Regularity in Repeated Reasoning

Why Play Math Games? 

http://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/Why-Play-Math-Games_/ 

Summary and Examples: 

- Games helps students develop reasoning and and understanding 

- They create engaged learners in a positive learning environment

- Allows for the students to explore other math patterns, values and concepts 

- Guide students towards computational fluency 

- Games support a School-to-Home connection. The parents can play the games at home with their child to help improve the child's skills. 

- Group games can allow for the teacher to walk around and observe the students' methods and reasoning. She can take note of each student's progress and ability level. 

- Fluency requires a balance and connection between conceptual understanding and computational proficiency. 

- Drilling students with tests and worksheet all the time will not allow them to learn the skills as well as using a math game. 

- However games without efficient strategies being used are useless and should not be used in the classroom. 

- Be cautious of games that would cause the students to memorize the answers and not develop skills and concepts. 

- After playing the game have the students complete/do some sort of reflection. 

Important Ideas about Standards

4: modeling with mathematics 

- model real wold applications to mathematics 

- choosing and using appropriate math methods and skills for the problem at hand 

- visually representing mathematic questions, reasonings and solutions 

- engaging students with a variety of different of modeling problems 

8: look for and express regularity in repeated reasoning

- patterns in mathematics help to develop students' reasoning 

- helping students to find efficient methods to problem solving 

- developing regularity in calculations can help students recognize irregularities due to mistakes.