Manipulative Activities Reflection

By doing the manipulative activity in class, I now have a better understanding of the types of manipulatives as well as their uses. After examining several different types of manipulatives, I now have a better idea of the kind of manipulatives I would like to have in my classroom. I saw some manipulatives that we used today, such as pattern blocks and snap blocks that I would like to use in my classroom. Other types of manipulatives I saw were not so versitille and I would not nesecarily want to use them in my classroom. I believe that manipulatives are essential to use in math classes, as well as other subjects. I believe that all students can learn but they all learn differently, manipulatives are a great teaching tool and great for visual learners. When students use manipulatives, they deepen their understanding by being able to physically use something to represent a mathematical concept. Students deepen their understanding by connecting a math problem to something real, they can use the manipulatives and mess around with them to understand the mathematical problem. In order to determine if students can transfer their understanding from manipulatives to other situation you must gently ease them away from using manipulatives. By having the students use manipulatives on a regular basis to solve math problems, you slowly ease them away from using the manipulatives until they say they do not need them anymore. Once the students stop using them and realize they do not need them anymore, that is how you can assess their understanding or growth.

Technology Reflection

Throughout the course of the semester we have used several different types of technology. A lot of the technology we have used I was completely unaware of or have never used before in my life. Some technology such as email and Sakai I use on a regular basis for my other courses and general Bradley information. However, most of the technology used within this course was completely unfamiliar to me and I learned a great deal from. First, we used Wiki, which is something I had never heard of before in my life. Since we did use it towards the beginning of the semester, and only a couple times, I still need to become familiar with it but it will definitely be something I will further investigate. We also used Prezis and Jing videos throughout the semester, which I had never heard of or used before either. I will be using one of these forms to make a video for my portfolio which will be the true test if I indeed learned how to make a video properly. I had never made a video for a class before, and I found them to be extremely beneficial. They re-iterate the purpose of the assignment in a visual way. Videos are important to make when we are teaching if we have students that are visual learners. I can also see it being beneficial as a teacher if we are absent and can put our lessons onto a video, or if a student is absent we can do the same thing. Throughout the semester, we have been using Blogger to write blogs about various things. I had never had a blog before, but I found it extremely easy to create and use throughout the semester, with a few mishaps here and there. I think blogs can be useful within the classroom to keep students and parents updated. Now that I know how easy it is to make and use, I can see myself using a blog to keeps parents informed of classroom activities. I think using Blogger is more appropriate to communicate through versus a social website such as Facebook. We also used Smart Board every day, almost, to sign into class. I have heard of teachers using SmartBoard for this purpose but have never seen it done, I was glad to get the experience in using SmartBoard for this purpose. Overall, I think we used more types of technology within this class that I have in all of my college courses combined. Although at times it was frustrating, since technology can be somewhat unreliable, I found it extremely beneficial. By being experienced with all of these various types of technology, I will be able to use them within my own classroom. It is important as teachers to remain current in the education trends, which will always be involved with technology. Technology is a major part of education today and it is going to be essential as a teacher to remain current and know how to incorporate technology within the classroom.

Video Analysis 3

"Looking Behind the Numbers"

1.) Purpose of Activities:
The videos were taken in an 8th grade math classroom. The students were examining mean, median, mode, and range by using real life statistics. The students first were to find the statistics of a players on a basketball team and were to determine the MVP. They determined the MVP based off of the mean, median, mode, and range they calculate with their classmates. The students then wrote a letter to the basketball coach explaining statistically why that player deserved to be MVP. The second task the students were given was to calculate the mean, median, mode, and range of the hours spent watching the Olympics. Once the students completed that, they were given mystery sets of data to analyze and figure out various means, medians, modes, and ranges.
2.) Connections to Process Standards:
Throughout these videos, I saw several process standards being demonstrated. One standard that was used from the beginning task was reasoning and proof. The students has to mathematically reason why one player should be the MVP of the basketball team. The students has to use their statistics that they figured, to make a viable argument why that person should become MVP. Going along with the letters, another standard I saw being used was communication. Communication was demonstrated by the students writing letters to the coach to mathematically reason why the player should be MVP, as well as the students communicating by working together in pairs and as a class to construct the mean, median, mode, and ranges for various sets of data. The students had to communicate with one another, as well as the teacher, in order to solve the problems and communicate their individual data results. The students also were problem solving throughout the videos. They were given problems with sets of data and were required to solve the problem using various methods. During the ending tasks, the students used methods such as "guess and check" to solve their mystery problems. A main standard I saw being used during these videos was connections. The entire concept of this lesson was making outside connections  to the real world. By using real world data from a real basketball team and from Olympic data, the students could connect to the mathematics they were using. Also, by writing the letter to the coach and doing peer editing, the students were making interdisciplinary connections as well.
Connections to Standards of Mathematical Practice:
There were also quite a few standards of mathematical practice being demonstrated within these videos. One standard that is easy to see being used was constructing viable arguments and critique the reasoning of others. The students demonstrated this standard by writing the letter to the coach about which player should be MVP and having to reasoning and construct a viable argument as to why. The students also peer edited each others letters, therefore they were critiquing one another. Another standard I saw being used was making sense of problems and persevering in solving them. Students demonstrated this when they were trying to solve the last task by using various mathematical techniques such as "guess and check" to solve the mystery problem. A third standard I saw being used was using tools appropriately, this was demonstrated when the students used their calculators to figure out the mean, median, mode, and range easier.
3.) Reflection:
I greatly enjoyed these videos. I thought making the connections to the real world by using basketball player statistics and using the Olympic data was a terrific idea. I can really see students being engaged and wanting to solve problems using this type of data. I also thought writing a letter to the coach and making interdisciplinary connections was fabulous, not only did they write the letter but the students peer edited it also. I particularly liked the Olympics activity, I am doing an Olympic unit in my novice teaching classroom. Although second graders cannot do this type of math, this would be wonderful for a middle school classroom. This would connect wonderfully to an Olympic unit, especially if the Winter Olympics were currently on.

Error Analysis Reflection

After spending several weeks throughout the semester analyzing errors, I feel I have gathered enough data to provide an in depth reflection on the error analysis process. First, I enjoyed looking at common errors children make and further analyzing them to discover not just what their mistake is, but why they're making the mistake. I think it is extremely beneficial as a teacher to take the time to analyze the errors our students make. I can honestly say, I know that as an elementary student I made several of the same type of errors that we analyzed. I am certain if my teachers took the time to analyze my errors, the problem could have easily been corrected. If my problems were corrected rather than just marked wrong, I might not have gotten so discouraged and developed my dislike of mathematics. I also thought by working separately within our tables to discuss what the errors were and then why they were made was helpful. I then thought by sharing our ideas with the entire class to see what we thought of was beneficial as well. There were several times in which my group had thought we solved the error work and analyzed it correctly, but when discussing with the entire class, we were in fact incorrect in our analysis. I learned many things after analyzing the errors, the main thing I learned is that there is always a reason a student answers the way they do. Many of the errors were made from a simple mistake, or misunderstanding, which led to wrong answers. These problems and answers, however, made complete sense to the students. From my experience within this classroom working with the error work, I have been able to use my gained knowledge within my novice teaching classroom. Some of the examples of the error work were mistakes made when doing two digit subtraction, the student did the problem right to left instead of left to right. After analyzing the error work in class and discussing the reasoning behind this type of errors, I was able to notice it right away with my second graders during novicing.These types of errors are extremely common and must be addressed right away in order to succeed with other mathematical operations to come. Luckily, my cooperating teacher is familiar with these types of errors and addresses them immediately. I can see first-hand the importance of analyzing student's mathematical errors in order to help the students be successful down the road.

Journal Summaries

1. Fair Shares, Matey, or Walk the Plank

Wilson, P., Myers, M., Edgington, C., & Confrey, J. (2012). Fair shares, matey, or walk the plank. Teaching Children Mathematics, 18(8), 482.

This article discusses the importance of teaching young children the value of equal-sized groups. By educating children at a young age about equal-sized groups, they will be more likely to excel when dealing with fractions, ratios, and multiplicative operations. This article focuses on a study done on children of all ages that shares a pirate treasure and later shares a cake. The focus of these studies is to see the logic and reasoning behind the way they are sharing the pieces into parts, equal or non-equal. The term equipartitioning is mentioned quite a bit throughout the article, this term refers to creating equal-sized groups or parts of collections or wholes. When children are creating fair shares there three pieces of criteria that should be met: 1. creating the correct number of groups or parts 2. generating equal-sized groups or parts 3. exhausting the collection or whole. When the students shares the pirate treasure they were given different problems, first there were only two pirates and they had to share the treasure. Next, there were more pirates to share the treasure with and the students had to explain their rational. This type of problem and questioning was also in the form of a pirate birthday party and they had a rectangle cake with n number of pirates, then a round cake with n number of pirates to share. The way a student divided the whole demonstrates different knowledge, as well as their reasoning behind it. By justifying their answers, teachers can make connections between fair-share experiences and other mathematical concepts.

I really enjoyed this article and have found several interesting and useful strategies within it. The information given was especially pertinent to me in that I want to teach younger elementary grades. By knowing that teaching fair share problems to young children enables them to be more successful in mathematics down the road, I will be sure to remember this and emphasize this technique within my classroom. I liked the use of pirate treasure and a pirate birthday party, this is something young children would enjoy and can easily be incorporated into a multidisciplinary unit. I also liked that the article gave a couple different books to incorporate when teaching fair share problems, I think using books with all subjects is extremely beneficial and math books are more difficult to find.


2. Putting Mathematical Discourse in Writing

Bolyard, J., Lynch, S. (2012). Putting mathematical discourse in writing. Mathematics

Teaching in the Middle School, 17(8), 486-492. 

This article describes a research project in which sixth graders write about their problem solving efforts. A term used frequently in this article, and one of the main foci of the research, is metacognition. Metacognition is being aware of, evaluating, and regulating their own mathematical thinking. The research project was designed by a sixth grader math teacher, she started a pen pal correspondence between her sixth graders and preservice teachers enrolled in a math methods course. The sixth graders responded to a main question and additional open-ended questions by completing a graphic organizer with the following information: 1. the problem's main question 2. potential solution methods 3. the student's work 4. the student's final response. Then, the students wrote a letter to the preservice teachers describing their understanding of the problem, their methods, their reasoning, and their answer. The teacher then sent the preservice teachers the letters and the graphic organizers. The preservice teachers responded with feedback on the student's work and explanations and questions further explaining their efforts. For students that understood the problems, the preservice teachers asked higher-order thinking questions to further enhance their understanding. The last step in this cycle was for the students to respond to the preservice teachers questions. Based off of this correspondence, the teacher analyzed the areas in which she needed to work on with her students. She found out the students got more out of discussing their reasoning with groups, rather than writing about it. She also discovered that by only doing one graphic organizer per group, instead of per person, this allowed for more discussion which enhanced their problem solving skills. This is one example of how written discourse can provide information for instruction while developing student's thinking.

I thought this article was interesting in several ways. I really liked the idea of having the students write out their reasoning and logic behind problem solving, I think this would be a great way to get students to think about it. I also thought having the students write their reasoning in a letter form to preservice teachers was fabulous. I think this would have been beneficial to both parties and I wish we were doing something like this in our course! This provides better communication skills, especially mathematics communication skills. The students are putting their logic into words and giving reasons behind why they answered the way they did, which further enhances thinking. I found it interesting that the students found it more beneficial to discuss within their groups their reasoning rather than write out their thoughts. I also thought making a graphic organizer with the information was a great idea. There were several ideas from this article that I think would be extremely beneficial to do in a middle school classroom.

Conferences and Interviews: Students lead parent-teacher conferences

This article focuses on student-led parent conferences. It discusses the importance of focusing on a student portfolio during the conference. It is important to have the student chose what to put in his or her portfolio to share with their parents. It is also essential to make a schedule and stick to it. By having a schedule it allows for little off topic conversation and gives the students something to go off of while speaking. Evaluating right away is also important, there are only four main questions needed for a good evaluation of the conference. Another beneficial idea when doing a student-led conference is for the parents to fill out a questionnaire afterwards to get immediate feedback for the teacher and the student. A few things the students did not like was the time constraint and they were unable to previously view their end of quarter reports. Although there are a couple negatives, the majority of the students thoroughly enjoyed student-led conferences. It gives the students, parents, and teachers a better picture of who the student is, who he/she has achieved, and what the students future goals may be.

I enjoyed this article and I think student-led conferences are a great idea. I would love to use student-led conferences in my classroom and I think this was a great article to display ideas about it. The article also gave an example of a schedule for a student-led conference as well as an example of a parent questionnaire. This article displayed many benefits for not only the students, but the teachers and parents as well.

Journal Summaries

1. CCSSM: Getting Started in K-Grade 2

This is the second article in the series which focuses on each grade band. The article first focuses on characteristics in K-grade 2. Next it discusses why teachers may have to change their thinking of mathematics in the classroom. Last, the article offers suggestions that allow teacher to reflect on their implementing CCSSM standards into the classroom. The main domains of the standards that relate to kindergarten, first, and second grade are: operations and algebraic thinking, number and operations in base ten, measurement and data, and geometry. In the article there is a great table that displays CCSSM wording and translates it to student friendly wording. There are some great tips on how to reflect and implement CCSSM into the classroom. The following ways are what is suggested: familiarize, reflect, identify, make, keep, have, at...and several paragraphs are attached to each word with additional suggestions.

This is the second article in this series in which I also read the first article. I am glad the articles are going to focus on each specific grade band. I think these articles are extremely helpful to educators and future educators that want tips on how to successfully implement CCSSM into the classroom. Most districts do not give suggestions or ways to use these standards but simply tell you to implement them. As teachers, I believe examples and strategies are beneficial to look at. I think these articles are great for teachers that want help and need help in implementing and better implementing CCSSM into their classrooms.

2. From Artithmetic Sequences to Linear Equations