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1. What are some obstacles to creating change in the mathematics classroom at the elementary level?
   There are many obstacles to creating change in the mathematics classroom at the elementary level. These obstacles can be minor such as the teaching not feeling confident when teaching the subject. The educator can also feel overwhelmed with the material that they may have to teach and the assessments they must give to test the students knowledge. Another obstacle is that the students can be at different levels of mastery. Some students may need more guided help. The language can also be a barrier to learning mathematics. Some problems require the students to read the question and then solve by either showing the work or writing a sentence explains how the work is done. This can be difficult for ESL students who are just beginning to learn the language.

   How can these obstacles be overcome or interrupted?
   These obstacles can be overcome by going at the students pace. There is no point in bombarding the students with all the material just to test them on it and have them fail because it’s to much to grasp. Another strategy to overcome these obstacles are having the students help each other. The educator can also come up with a way to establish comprehension. Practicing similar problems can also help.

2. The textbook is not the student’s world, the world is the student’s textbook. Everything in the real world is a valuable teaching resource. Therefore, teachers should make full use of various conditions in teaching, create realistic problem situations for students that are conducive to learning, guide students to observe life, and make them eager to learn and enjoy learning. Interesting problem situations can attract students’ attention and stimulate their interest in learning. They are derived from the problem situations in students’ lives. They are conducive to enriching students’ life experience, discovering math problems in life, better solving math problems, training analysis and solving problems. The ability to question reflects the practicality of mathematics. However, the classroom has limitations. Children’s understanding ability is limited. As a teacher, you should try your best to select the content that students can understand for teaching. Implement diversified teaching. Each teacher has his own different teaching methods. Primary school mathematics teachers should combine relevant regulations and requirements to create a distinctive classroom teaching model. For example, it can adopt the education model of students discussing in groups, the teacher’s questioning and students’ rushing answer model, the practical classroom teaching model, etc. Teachers can compare the pros and cons of various educational models, and select educational models with good effects, or combine various models to create an educational model suitable for their own teaching. Only in this way can elementary school mathematics classrooms be better activated, and students’ interest and imagination in learning can be stimulated.

3. Some of the preconceived notions I have about what a high-quality mathematics classroom looks alike are well prepared supplies such as rulers, markers, calculator, and informational boards in classroom. These notions come from my experience growing up as a student in school and working with children as a teacher. It might sound like a simple daily supply that students need every day in school, but everything has its purpose. I would expect to have magnetic ten-frame set, number tiles, Lego bricks, base ten blocks, dice, double sided XY axis dry erase mats, playing cards, plastic patter blocks, counting bears, 100s chart and teaching clock. All these supplies are for both students and teachers. I believe it is important to have informational boards around the classroom, so students know where to look at when they need to remember the words, formulas, or name of the function. All the knowledge and supplies need to be visible and available for everyone to be considered as a high-quality mathematics classroom.

4. I thought that the class on September 1 was structured well. It was interactive and allowed us to work with our peers which I feel like is more helpful than working alone because you are able bounce ideas off each other. I also like the activities we did as a classroom because the professor was very supportive when we told her our different views of counting the dots.
   Coherence is a shift that can help us learn about methods and contents. I believe it can help us learn better because linking content/methods throughout the semester/grades will allow students to see how it is essentially not them just learning multiple new topics, but rather subtopics to a larger picture. When they think of one method they will link it to another and another which can help them down the line as they go to middle school, high school, and college.

5. Overall in today’s circumstances it is difficult to conform to learning. During class I enjoy our break out room sessions. We have time to solve our problems individually, working alone can be more convenient at times. It might be efficient because you can work on the project at your own pace and have complete control over the entire process. The purpose of group work is to demonstrate how being sociable improves learning. You must not only listen to other people’s perspectives, but also compare and contrast findings and strategies. Another person’s point of view will persuade you to rethink your findings. This is something that I will make sure to include in my classroom. Some things that might be difficult in a classroom would be the difference in time students take on their math problems. Some students may need more time than others. Group work can facilitate this because they will get direct help from their peers.

6. Question : What are some obstacles to creating change in the mathematics classroom at the elementary level? How can these obstacles be overcome or interrupted?

   Some of the obstacles to creating change in the mathematics classroom at the elementary level is due to not have enough resources to support the students learning process. In addition to student mindset so at the elementary level either students love math or hate it, they know they are good at it or not good at it …… and this will creat a mind set that might creat obstacles to creating change in the mathematics classroom. In some cases it might be hard to connect math to real life. Sometimes the teacher objectives are not clear, or her lesson plan doesn’t include all students who vary in their abilities.

   So one way to overcome these problems is for teachers to have clear expectations from their students, as well as setting clear goals/ objectives, differentiate in their lesson plan to include all students who vary in their ability.

7. One obstacle stuck in the way of changing the teaching of mathematics within the classroom is the usual lack of time teachers have for students to fully understand and grasp the concepts they are being taught. Oftentimes teachers are forced to rush through lessons and then give homework and tests based on materials students were never able to fully learn and understand because of the absence of time in providing extra care and thought into these lessons. Another obstacle is the lack of teaching aids and materials within schools. There are often not enough provided resources and materials to help students learn to the best of their abilities. As teachers, we have to find ways to overcome these obstacles and struggles. One way could be asking for donation of material and time by students to sit with them after class if they are having trouble within a topic and fully explaining and developing the concepts and ideas.

8. To me, a high quality mathematics classroom would look like a class with a variety of functions and tools that can provide clear understanding to all students. This would look like charts, vocabulary words, examples of the topic that is being covered around the classroom to model correct work, and tactile learning tools. There would also be things to make it more interesting like colorful posters and worksheets that involve puzzles, some type of art and music making. These notions come from my own classes as an elementary level student, and the tools that I noticed helped me learn math more effectively. Math has never been my strongest subject but the activities that stood out to me the most that I still remember to this day were the interactive activities like making a grocery store budget, counting coins, the math puzzles that required solving problems to get a piece of the puzzle, and anything fun like these activities. Children like to do things they find entertaining, and while math may not in and of itself be the most creative subject, there are ways to make it fun and attention grabbing, especially for those students who may have a hard time maintaining their attention to math or simply do not enjoy it. This would serve the students the most because it would give them long lasting memorable ways to learn topics they need to know for the future. I intend to be the teacher who provides interactive and interesting math lessons because those are the teachers I appreciated most when I was in school.

9. Some obstacles that may arise when trying to create change in the classroom is that students may not be confident about their math skills. A child’s self esteem and confidence in their education plays a huge role in their academic success. Another issue that may arise is that teachers may not be familiar with kid culture. Kid culture is what they are interested in such as video games, shows, activities, and current trends. This is an important thing to take into consideration because it helps with student engagement and performance. Last year, on social media, a teacher went viral for including the popular game Among Us in her 5th grade math class. The teacher included the games characters and concepts. The students worked together to choose the “imposter” in each set of expressions. She reported huge success with this game. This may be difficult and challenging as it includes keeping up with what students are interested in but these changes can help students improve their math skills.

10. Mathematics in the classroom at the elementary level seems so simple, yet there are many obstacles that get in the way of students succeeding and growing. I think one of the obstacles could be that teachers are unwilling to adapt to changes in mathematics and how it is taught. From my personal experiences growing up, I remember being taught math from a young age to know “tricks” and to simply remember how to commutate things rather than how to think and evaluate a situation critically. I think to overcome this, teachers must be willing to learn themselves while they teach students. Teachers need to be willing to expand their concept of mathematical thinking and problem solving, and they must acknowledge that students may not always grasp their ideas the same way. Students may find their own paths and solutions, and as long as they are not doing anything incorrect in the process, their method CAN (not saying it will) be just as valid. Another obstacle is that very often, tied into math is reading and comprehension skills. Some students while they may be good with numbers, may not necessarily be good at reading and understanding word problems. This can hinder their ability to understand and tackle higher level math as they grow older. Therefore, it is important for teachers to not necessarily see math and reading as completely separate. Rather, to tackle this, teachers must know their students and accommodate for them so that they can receive the necessary scaffolding and help they need.

11. What are some obstacles to creating change in the mathematics classroom at the elementary level? How can these obstacles be overcome or interrupted?

    When creating change in the mathematics classrooms, some challenges may arise and there are very good reasons why. For example, some students that enter your classroom may have had bad experiences with this subject. They may have had a teacher that was not understanding of the way that they learn and see numbers or was very strict with going about solving problems and doing it a certain way. Some students might not have fully gotten an understanding of what they were learning, and that can make it difficult and frustrating. Therefore when they come to school the next year they might not be looking forward to when it comes time to learn about Math. Their confidence may be lower than you expect and there will need to be more time and understanding into getting the students more comfortable with the material. By determining what they like and how they see certain problems, numbers, or operations you can get a better feel of how they see Math and build a curriculum that will support their view of Math, making it something they look forward to. Another way is making connections to their interests so make Math more exciting and relatable. Allowing students to fully comprehend what they are reading and seeing, practicing and working together will also build a comfort and confidence in themselves when solving mathematics problems. Group work allows for strident a help each other and ask questions they might not ask the teacher themselves.

12. An obstacle that can hinder change in the mathematics classroom at the elementary level is not having the proper resources. By not having the proper tools that students need, teachers are limited to what they can do, and this can negatively affect students’ learning. This obstacle can be interrupted by looking for free resources that are available online and looking for creative ways to teach the topic even when the resources are limited. To add on, in some cases teachers might have all the resources available and they will be ready to create change, but the workplace environment might want them to complete things in a specific way. This can result into teaching in the same traditional methods, instead of teaching the way they want to. Another obstacle to creating change in the mathematics classroom is that the student enters the classroom with a negative attitude or with poor behavior. This is an obstacle because they already believe that math is hard and since they don’t like the subject, it means that they might not want to try. This obstacle can be interrupted by showing the different ways that math can be exciting and teaching math in creative ways that motivates them to always try their best. Lastly, another obstacle that can disrupt the process of creating change in the mathematics classroom is time management. During the elementary years, teachers will want to make sure they are preparing their students with the proper mathematics knowledge and skills. The obstacle would be that teachers have to make sure they find a way to teach the topics effectively or else students will not learn them, and they’ll begin to struggle. This obstacle can be overcome by having a basic outline for the school year and making sure that it’s flexible in case any changes need to be made.

13. When I think of a high-quality mathematics classroom, I envision a group of really smart students who perform really well on everything math related. I believe so many people are intimidated by certain math classes that the only students who actually register for those classes are students who know they’ll be able to pass. Thinking back to when I was in high school the only way you were able to be placed in certain math classes was depending on your grade from prior math exams. I remember in order to be placed in trigonometry you had to have scored a 85 or higher on the algebra regents and in this class it was me and 10 others. These types of classes serve students who are “really good” at math, which isn’t fair, especially if a test score determines eligibility. I know for sure there were students who just got lucky when answering certain questions or who even cheated to get their score above 85 and it’s not fair to the students who really tried but couldn’t hit the 85 mark.

14. Two obstacles that first came to mind regarding teaching math and creating a change at the elementary level could be the following – a childs lack of confidence and easily gives up and the lack of flexibility provided by the school. Every school year teachers get and entirely new batch of students with varying experience with math from the previous year, some may have had a very engaging teacher and they are confident and ready to learn more math. Where as some students have lost all confidence in their math skills, they struggle with the way previous teachers have taught them, so they walk into the school, year discouraged and not willing to give it a try and change regardless of what techniques the new teacher brings. This obstacle can be overcome by starting the year off easily and guide the students into boosting their confidence and learning new strategies.
    The second obstacle that teachers can encounter is the lack off flexibility provided by the school and higher ups above the teacher. As much as us as teachers want to make differentiated lessons, add more time to provide support to our students, some of our curriculums and school wants us to fit so many subjects into our day and leads us to rush from one thing to another and not putting all our focus on one thing from start to finish. A way to approach this obstacle is by approaching your school staff to discuss making your schedule more flexible.

15. Some obstacles that might occur to creating changes in the mathematics classroom at Elementary level is teacher not coming up with a variety of different strategies and methods. Every child thinks and does math problems different then their peers, and have different techniques in order to solve a math problem. Teacher’s don’t always have the time to spend with each student if they need help with something, and there are going to be students who just need a little more help and patience. Another obstacle that children might come across if a change occurs in the mathematics classroom is the ability to do a problem with only one method. Teachers need to understand that children need more then one method in-order to solve anything. These obstacles can be overcome and interrupted by just giving children the extra time they need, teaching new methods, and also allowing children to come up with their own methods to solve math problems. Letting children work in groups can improve their understanding of math problems and allow them to be more open with sharing their ideas with their peers.

16. Some obstacles to creating change in the mathematics classroom at the elementary level includes the unwillingness of the teacher to accept the inclusion of different strategies that the students might come up with in solving a problem. Another challenge that might present itself could be that teachers are not using a variety of techniques or methods to include participation and ensure understanding of the material been presented. Teachers may not have enough time during the class period to spend with students who need more help in understanding the content. I believe another obstacle is that some students are not confident in their ability to master the subject and so they are intimidated to try different techniques in problem solving.
    These obstacles can be overcome by allowing students to be more open to interpret and share their ideas. Also, to allow students to work in groups with different level of competence level.

17. For the most part, changes in the mathematics classroom improve students’ learning ability and conceptualization in math. This change does help students to understand and remember it better and really use the knowledge to solve the question effectively. However, one obstacle that can be faced regarding this change is that the students may struggle and take longer to solve the problem. Rather than to have students to work on multiple, similar questions again and again, each problem is unique which will require them to put in their logical and mathematical reasonings into it. Elementary students, especially the younger grade levels, are not fully developed with the English vocabularies and critical thinking skills. Few ways to overcome these obstacles are to put students into groups or assign them a partner. It would be less fearful for them to solve those problems and may end up with much greater ideas. Also with the teacher’s guided instructions, students can gain confidence to even start the problem. Ultimately, this change will be successful and essential for the students in developing their mathematical and conceptualizing skills.

18. While finding all the possible combinations for all the numbers I noticed a pattern. The pattern is as follows as you are counting from 0 to that number the addend decreases to 0 as that number gets higher. I know I have every possible outcome because I have utilized all the numbers possible to reach 11, 7, 12 and 35. Using a number line may work to show this to students or writing out numbers downwards so the students can see how to do it.
    Creating a pattern with multiple numbers is difficult especially when it comes to creating different combinations. This task has been pretty hard because there is a vast amount of combinations you can make especially when it comes to having so many different number options as well as having different types or options for those numbers. For instance with this example there are 17 number options, but there are also 4 different options of how they can be placed in order to create a purple rod. This question is very confusing for me and I am not understanding it.

    A child’s mind is like a sponge so it is important to engage them in everyday activities that involve some sort of numeracy. This can be done by singing songs, counting, looking at shapes, comparing the sizes of everyday objects which include toys as well.

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