# data[].attributes.body
This was used on our last day of Math Buddies that lead great discussion in the morning group with Kevin

# data[].attributes.headline
Productive Struggle Quote from: “Intentional Talk: How To Structure and Lead Productive Mathematical Discussions” (Kazemi and Hintz) Page: 111

# data[].attributes.subject
Productive Struggle Quote from: “Intentional Talk: How To Structure and Lead Productive Mathematical Discussions” (Kazemi and Hintz) Page: 111

# data[].attributes.body
“Engaging in discussions about puzzling mathematics allows a teacher and his or her students to take stock of what makes sense and work through stumbling blocks together.”

Citation: Kazemi, E., & Hintz, A. (2014). Intentional talk how to structure and lead mathematical discussions. Portland, Me: Stenhouse.

Justification: The idea of working through these “stumbling blocks” will help you as a teacher understand and realize what works and what does not work. This will help engrave knowledge that you have built from previous experiences and things that have worked in past situations that you can think back to.

# data[].attributes.headline
Compare and Contrast: Productive and Nonproductive Struggle with Math Buddies at Wilmington Elementary 

# data[].attributes.subject
Compare and Contrast: Productive and Nonproductive Struggle with Math Buddies at Wilmington Elementary 

# data[].attributes.body
Within my two groups of second graders with Mr. Nugent at WASD, I learned how to handle both productive and nonproductive struggle. With my morning group of boys, they seemed to try their hardest on most days when given the task of the day. With my afternoon group, the three students never wanted to work and this was the example of nonproductive struggle. For the morning group, they struggled through noticing the difference between nickels and quarters because of the size on the screen they were looking at. They understood that all four coins had a different monetary value but they couldn’t understand the faces of the coins for the two coins. They would count the nickels as $0.25 and quarters as the same. Working through we would show many different pictures of the two coins and eventually with some frustration and turned off cameras, they knew the difference in the coins.

On the other hand, there was nonproductive struggle each day with the afternoon group except for the last day. These students would always be distracted and would try to distract Chrissy and I to not teach them mathematics. It never worked. We always persuaded them with games at the end if we finished but the three students used the chat to create conversation among each other. It was always “I’m hungry!” or “I am tired”. They would not do anything unless persuaded with games.

I learned that productive struggle will help students not only learn how to adapt out of hardships, which will help them in the future, but also I learned how to work through nonproductive struggle in the classroom.  It helped me better myself as preservice teacher to work on classroom management. I know when I was in Sharpsville I had to work through some struggles with my classroom when they would get distracted when Faith and I would come into the classroom every morning instead of doing their morning work of the day.

# data[].attributes.headline
Video Explaining Quick Tens Lines Example

# data[].attributes.subject
Video Explaining Quick Tens Lines Example

# data[].attributes.body
Citation: 1St grade addition strategy: Quick tens. (2014, March 27). Retrieved April 29, 2021, from https://www.youtube.com/watch?v=o8zgbF8bp3k

# data[].attributes.headline
Reference to EngageNY Grade One Mathematics

# data[].attributes.subject
Reference to EngageNY Grade One Mathematics

# data[].attributes.body
Citation: Grade 1 Mathematics. EngageNY. (n.d.). https://www.engageny.org/resource/grade-1-mathematics-module-1.

# data[].attributes.body
When Faith and I came into the school on the first day (April 6th) the students were learning how to solve addition problems using quick ten lines. Being new to teaching mathematics, this was very intimdating and stressful since I did not know what these lines were. After observing the teacher teaching the lesson for one day and then watching how the students completed the lines, I learned how to actually complete these "quick tens lines". Even though this was a new concept to me, it was intriguing to learn a new way of representing a problem. Normally I would draw out the base ten blocks and then count the individual “blocks” on my paper. This way taught me that if in the number 14 there is one “10” in the number and four “1s”. You would draw one line which represented the “10” in fourteen and then four circles. You would then move onto the next number, the “25”. You would draw two more line that represents the two “quick tens” in 25. You would then draw five “X” over top of the four circles. You would then add up the lines to make thirty and then add up the circles and “X” to make up the nine. The answer would then be thirty nine.

I would use this as one of many ways to represent mathematical thinking. Students should be introduced to multiple ways to represent their thinking and this is why I would like to teach this in my future classrooms.

# data[].attributes.body
After going back to this chart that we have previosuly used in ECE 321/322,  I learned that establishing clear goals of what I am trying to teach will make it easier to stick to the learning goals that are needed to be met by the specific state standards in which I will be teaching in.

Citation: Principles to Action NCTM. (n.d.). Establish Mathematical Goals: Principles to Action. Establish Mathematical Goals. http://rapps.pbworks.com/f/1-TeacherStudentActions-EstablishGoals.pdf.

# data[].attributes.headline
Establishing Mathematical Goals to Focus Learning

# data[].attributes.subject
Establishing Mathematical Goals to Focus Learning

# data[].attributes.body
Throughout the semester, I have learned the proper way to create an objective. Before I always thought that you needed to have a specific degree to which you want to the students to do. I always made the objective extremely direct (as shown in the image below). Now after being in an actual classroom, I realized that objectives should be based around your classrooom, not an exact number. In my first mathematical lesson plan (for preschool on shapes), I stated that seven out of the eight shapes that the students are learning would be correctly labelled and described by the end of the lesson. After peer, professor, and co-operating teacher feedback I learned that have a set number in the objective should not be used. Having a set number does not always mean that they are going to obtain that. I could have changed this objective to state "Out of the shapes that are being learned (Label out all shapes that are being taught in the lesson), preschool students will be able to identify and describe the shapes using manipulatives, an art activity, and full class dicussion. This makes the objective still directed to the specific lesson but not as set in stone with having the students label at least "seven out of eight" for example.

# data[].attributes.headline
Predesigned Worskeets Compared to Self-Designed Worksheets

# data[].attributes.subject
Predesigned Worskeets Compared to Self-Designed Worksheets

# data[].attributes.body
After what I learned in Mrs. Elser's first grade classroom, I learned that there is a difference in enthusiasm and participation in predesgined worksheets based around the EngageNY online curriculum and the self-designed worksheet that included student names and interest off of Canva. When I taught the lesson on "Subtraction Word Problems", the students seemed very excited to flip through the four page booklet that had their names in the word problems. They kept asking, "Can we do the problem with _____ name in it?" I had to not pick favorites when choosing the two example problems to work through together as a class. I picked the first and the last page to throw them off since they believed that I was just going to do problems one and two. The students really enjoyed creating the sentences since they got to incorporate their peers name in the sentence. The sad part of the whole EngageNY curriculum is that they had to work on the quiz that did not have any student interest in mind. I saw that when the students work the day before on the predesigned worksheet that they did not want to continue on. With the worksheet that I created, they wanted to keep working on it if theey had more time before their next tasks. Students came back the next day with all four problems completed and even drew pictures of their friends and the objects in the story problem. It was amazing to see the difference in enthusiasm as well as participation when a little bit of student centered examples were used.

I decided that this is somehting that I would like to try to implement a little more than what I saw at Sharpsville. Mrs. Elser explained to me that it was an amazing idea but they most likely would not have enough time to make new worksheets, keys, and quizzes all from scratch each year and that is why they stick with the normal EngageNY worksheets and quizzes. It is all dependent on time and preparation. I hope to have the time to create worksheets that have student interests involved in the assignments.

# data[].attributes.body
My goals as a mathematics teacher are as follows:
1. To create an enviornment where the students feel safe and want to learn.
2. To incorporate the idea of "productive struggle".
3. To further my mathematical knowledge year by year to be the best I can potentially be.
4. Have a wide variety of ways to solve a problem for the different types of learners.
5. To be a supportive, understanding, and caring person for all students.
6. Use student interest while creating assingments.

# data[].attributes.headline
My Beliefs About Mathematics Teaching and Learning:

# data[].attributes.subject
My Beliefs About Mathematics Teaching and Learning:

# data[].attributes.body
Before coming into ECE TLL block I was scared and feeling uneasy about teaching math to young children. We are now the future educators that will be teaching the next brilliant minds of America. After learning all of the important topics from ECE 321/322, I realized that my stress and worries are normal but with planning and alot of preparation, I can do it. After the book club converstations that I had with my group, I realized that just like anything that you want in life it will not come easy to you and you must try your hardest. I now am not as scared as I once was of teaching math and will be more comfortable once I get more opportunities to practice what I know. Math Buddies with WASD really was the glue that bonded my love for teaching mathematics this past semester.

# data[].attributes.body
Before this course, my knowledge of mathematics was very low. I knew what I did in high school but coming to a different state to learn what they are doing in school was stressful to say the least. After this course (ECE321/322) I learned that even if you are not the best mathematical thinker, you still are a mathematical learner and thinker! Everyone can learn math, it just might be different from what you learned. It is all about adaptability.

# data[].attributes.headline
NCTM: Implement Tasks That Promote Reasoning and Problem Solving

# data[].attributes.subject
NCTM: Implement Tasks That Promote Reasoning and Problem Solving

# data[].attributes.headline
NCTM: Build Procedural Fluency from Conceptual Understanding

# data[].attributes.subject
NCTM: Build Procedural Fluency from Conceptual Understanding

# data[].attributes.headline
NCTM: Support Productive Struggle in Learning Mathematics

# data[].attributes.subject
NCTM: Support Productive Struggle in Learning Mathematics

# data[].attributes.headline
NCTM: Establish Mathematics Goals to Focus Learning

# data[].attributes.subject
NCTM: Establish Mathematics Goals to Focus Learning