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20 Comments

1. Some obstacles to creating change in the mathematical classroom at the elementary level is trying to re-engineer a way to simplify the math learning process while keeping in mind it must be easy to understand by the Elementary level. I see many ways today’s math has changed from when I was in school and I honestly struggle to understand why they made the process so long and drawn out when you can easily just like up the numbers and do the math. My dad was a whiz in math because he spent his time in school memorizing times tables, etc just like I did and these kids learn to break math down into simple easy to understand ways which is also easy and makes mental math easier, but if they have to show their work, it will take longer doing it their way instead of doing the simplified way. I have no issues with today’s math methods, but I know they confuse me, which means it definitely is not easy for a majority of elementary students to understand at first. I personally prefer using scenarios to understand math, which would allow me to work through the obstacles of creating change to the mathematical classroom, since understanding how to do real world math will make it easier to understand the new methods. I also would teach math in a way I understand easily, but teach the more complex methods I struggled to understand as well for those students who will understand it faster than I did trying to learn it. (Sounds complex to understand when I explain it like I just did, but I know not everyone is as slow of a learner as I was, so I need to account for the students who aren’t challenged enough in my class.)

2. ANN-MARIE CHAWDHURY
   EECE 350
   WEEK 2
   What preconceived notions do I have about what a high-quality mathematics classroom looks like? Where do these notions come from? Whom do they serve?

   I would assume that a high-quality mathematics classroom has students who are proficient in math. I would like to see students who are engaged in the lesson and eager to learn. The teacher should be able to teach out of experience and knowledge, instead of regurgitating a textbook to students. The lesson should be inspiring and students should be expected to apply what they have learnt from the lesson into more meaningful peer and group discussions. The teacher should make it an open discussion where students get to interact and not just sit and take notes. Students should be an integral part of the lesson planning in the classroom as well. The teacher should be able to work with differentiation in order to meet the needs of students with disabilities. There should be room in the lesson plan to tailor the lesson. There should always be positive teacher/student interactions, making room for students to feel comfortable to share thoughts and ideas. There must always be different types of visuals pertaining to the lesson throughout the classroom. Teachers and students should be aware of the standards and expectations that the lesson should follow for that grade. The teacher should try to stimulate students into deeper thinking and more thought provoking questions. Students should be encouraged to discuss and share with their peers and teachers what they have learned. The teacher should encourage students to delve deeper, apply, explore and question everything in math class. Students should be equipped with problem solving techniques when they are faced with a task. The teacher should model so students can follow, in order for them to grasp concepts and follow along. Directions should be straightforward and simple, students should not be confused as to what is expected of them. The teacher should regularly check for focus and understanding by doing frequent assessments. The teacher should provide a plethora of resources so students can have a wide exposure to different forums of learning. The teacher should make notes of what works for some students and what works for others, in an effort to understand that each child learns differently and how best to help him or her. The teacher should align her lesson plan to meet the State standards and appropriate lessons according to grade level. The students would be the ones benefiting from a teacher who is organized, knowledgeable and meets the administrative and State standards. The teacher would also benefit if her students are actually applying what they have learnt to their everyday lives.

3. From the time I have spent studying to become an educator and the somewhat limited experience I have working with children in various after-school programs and summer camps, I believe I have identified two obstacles to positive change from occurring in the mathematics classroom at the elementary level. They are the rigidity of the math curriculum and the general attitudes of adults towards mathematics. While I am certain that these are not the only obstacles preventing positive changes to mathematics in our elementary classrooms, they are the ones I have noticed over the years.
   Firstly, while the elementary math curriculum may not seem rigid or static in a vacuum, especially considering the changes it has experienced over time, I still believe it can be greatly improved upon. When compared to the curricula of other subjects, I feel as if teachers have limited freedom in how they teach and what they can teach in mathematics. This, in turn, would limit the freedom in how students learn and what they can learn in mathematics. As demonstrated in our last class session, how we learn about and perceive math is a highly individualized process. I can also attest that this variability is also present in higher-level math, which is why I believe it is detrimental to limit the flexibility in how teachers teach and how students learn math at the elementary level. Additionally, it is important to keep in mind that this degree of flexibility/freedom can also vary greatly between states, districts, and schools.
   I recall a poster that was displayed in the hallway at the school I worked at. It warned parents to be careful of what attitudes they displayed towards math in front of their children, as their children’s attitudes towards math will be highly reminiscent of it. While this poster was pasted on the walls of the second floor of the school, where few if any parents ever saw it, I do believe it conveyed an important message. How the adults who are prevalent within children’s lives treat math is highly indicative of how those children will perceive and view the field of mathematics, and this includes their teachers. For example, a parent who tells their child that the way they are learning a concept is tedious and convoluted and that schools have complicated math for no good reason may have just discouraged their child from trying their best in math class. I often see and hear the sentiment among teachers/upcoming teachers that math is difficult and that they have never been good at math, but to hold this negative sentiment towards math and to bring it into the classroom will only be detrimental to students.

4. In class on Thursday, I thought the way that the class was structured that day was a positive experience. When I was going to class, I was excited but feeling unsure because of my task one homework answers. When we went into groups and shared our work with each other, I find that helpful because we get to share our confusion and thoughts with each other to help answer the questions. Then afterward when we went over them as a whole class setting, I find that even more helpful because we’re not only going over at one group’s work, but each of the group ideas on how they thought about the questions. It was a great learning experience and that’s why I called it a positive one because I find it valuable when we make a mistake and learn from each other by working together. I remember learning that it’s ok to make mistakes and we take them in and gain a new skill in improving them. When other groups were showing their answers, I found some common ones in which I realized I misunderstood the question in my part of end. I had to keep rereading the questions and take notes to remember what to look out for next time or even learn to use these new techniques. I find that this shift would help me pick up from my mistakes in learning the content and methods better. Since I’m more of a visual learner, I like how we show our work visually and explain our work. Same goes for any lessons, I like it when we are showing out the work or even providing examples when we trying to show our point of view. In the end, I see that it’s beneficial for both the instructor and the students to learn from each other, and it’s motivating when we use tools like the Cuisenaire rods to connect with our lessons. Using different tools and methods into our lessons would help us see which strategies would be practical and understanding.

5. Class today involved sharing our answers and explaining our methods of solving it to our peers. The teacher also showed support by going around to each group, offering advice, comments, and help. I believe that working in groups helped a lot because we were able to help each other out and view a different perspective of how a problem can be solved. Therefore, I can say that this method would be one of the things that I would like to apply to my classroom. When activities are done in team work it makes the classroom feel more united as well as showing that everyone is here learning together.

6. There’s a lot of obstacles teachers face in an elementary school classroom curriculum, time, faculty etc. For instance teachers have to follow the curriculum the school board has set up for them and that’s what they have to teach and follow all year long and sometimes isn’t fair for them or the students they don’t have an option to teach their way. Another obstacle is the time teachers have a certain time in the day to teach math and then switch right away to another subject students don’t have enough time to process the information or even understand. Teachers might be rushing to teach and also might not have time or the hands to individually help a student or each in every student since she still has to teach a whole class of like 20 students. Teacher will have to work and speak out about what they want in order for them overcome the curriculum and also create ways to allow students to understand the material or work together in groups or partners so they can help each other and the teacher will go around still help everyone but adjust the class for easier support.

7. I really enjoyed the class on Thursday. It was an interesting class and I definitely learned a lot. I really like the methods that the professor incorporates in the class. I think the exercises on task 1 carried easy tasks but also some challenging ones for the students. I really enjoyed working in groups. I believe we can lear so much from each other from working together. We are able to see the different techniques that each one of us uses to find the solution. It is very helpful because we actually help even the ones that are struggling, maybe we teach them an easier method to solve the problem. Another thing that I really like is the technology used in this class. The use of the jam board is a first for me but I see it is becoming so popular as other professor are using it. By using jam board the professor is able to see how the students are working and track their progress. A very important thing in the group work that we had is the teacher coming in to each group and see how we are working and giving us helpful tips in solving the problems. I really enjoyed the new program called mathigon. That helped me solve the problem quicker and more in an organized way. I am looking forward to learn more in this class.

8. In a high quality mathematics classroom, there are a lot of charts and math pictures around as references for the students. There is also a teacher that keeps the students engaged in the lesson and pushes them to expand their knowledge. All high quality classrooms are student oriented because the lesson is to benefit the student. The teacher should always use mathematical representations and facilitate meaningful discussions. One obstacle to creating change in the mathematics classroom is the curriculum. There is almost never enough time to cover what the curriculum expects the teacher to cover and that can affect the student’s grades in tests. Another obstacle can also be the teacher. If the teacher doesn’t plan out their lesson in an effective and fun way then the students will lose motivation. Teachers should always fo their best to make the lesson as engaging they can. I liked the way our class was structured.I always enjoy working with my classmates especially when the assignment was complicated like task one was. I like working in small groups and learning from our mistakes and also knowing that we found the same answer to prove to ourselves that we did it right.

9. I thought the class was structured very well. The class was very engaging and exciting. The group work was a good idea because in our groups we were able to come together and compare the work we did for Task One. We also were able to see the different strategies other classmates used to determine the solutions to each question. This helps because as a math student you can begin to understand and learn many other different ways to solving math solutions whether simple or more complex. I enjoyed working on Task One because it had been a while since I was able to sit and really figure out solutions to math problems and using certain strategies like a table to organize my work which for me is easier because I’m a visual learner. The need to think about the steps to take to solving math problems and then being able to explain the work you did is great to be able to help others see your thought process and your way of seeing their thought process which could be the same or completely different. The virtual manipulatives that students were able to use for Task One were useful, I had thought to use them when I completed the task, but I couldn’t figure it out for some reason, so I opted for the old school way of just writing/typing it out. I believe manipulatives are useful tools to help students who are visual learners or to just give students a fun hands-on experience when doing math. It also supports student learning in the classroom.

   The shifts that can help me learn the content and methods is just being able to collaborate with my peers and learning from one another. We are all going into the education field so it’s very helpful to share our thoughts and ideas with one another which could be very helpful for our future teaching. I think also having more visuals and hands on activities helps me learn and better apply myself when learning new contents and methods.

   Overall, I enjoyed the way the class was structured today. The opportunity to work in small groups and being able to see different strategies used to find math solutions. Math is my favorite subject and I really hope to be able to provide high quality math instruction to my students where they are engaged and learning.

10. I think a high-quality mathematics classroom has an outstanding teacher and a group of students who show high performance in mathematics and have the ability to understand the true nature of mathematics. Teachers in a high-quality mathematics classroom have a very explicit learning goal and aim. They usually plan well in the lesson’s structure and have a particular method to motivate students’ interest. The teacher and students have a good cooperation relationship, and the teacher is not always the dominant force. Students have more opportunities for independent inquiry and discovery. The way the teacher uses the textbook is more flexible and creative and covers more methods and mathematics content. Students in a high-quality mathematics class have high intelligence in mathematics. The interest in mathematics is higher enough to lead them to self-explore the mathematics, and sometimes, they will develop a new and unique method to solve the mathematics problems. These kinds of students are the desired talents for the math teacher who wants them in the high-quality mathematics classroom. We will have a high-quality mathematics classroom that only serves these highly talented students during my education time. The difference between teachers in the high-quality mathematics classroom is that they are more enthusiastic about educating these talented students than in the general education classroom.

11. Some obstacles to creating change in the mathematics classroom at the elementary level are the school curriculum and faculty. As a teacher, there’s a curriculum that we need to follow that is given to us by the school. Sometimes, there’s simply no if, and, or but’s. What’s given to you is what you follow and that’s it. If a teacher wanted to create change, they’d have to be able to not fear the repercussions of their actions and prove that their change is for the better. Their change is helping students become better students. They’d have to convince the school and others that change is good. To overcome this obstacle, they’d just have to be confident in themselves and their ability to create change.

    Another obstacle might be faculty. Some won’t embrace change at all and some will. Some might give you a hard time and refuse to be part of the change or your principal might threaten to have you fired for not following the curriculum. There will be so many challenges in your way that you’ll have to find your way around. It isn’t easy to change because everything will stand in your way and the only way to overcome it is to power through it.

    Creating change isn’t an easy task. There are so many steps to creating change and it’s difficult when there’s a curriculum you have to follow. It’s like giving teachers an ultimatum: do your job and follow the curriculum or do what’s best for your students but possibly get fired for changing what’s not “allowed” to change. Creating change comes with so many obstacles and everything seems to be in your way, but at the end of the day, a teacher should do what’s best for their students even if there might be repercussions. It truly isn’t easy being a teacher that has to follow a curriculum with no room to improve the curriculum in their own way.

12. One of the obstacles that prevent change in the elementary classroom is time. Time is an obstacle because sometimes teachers need to cover material in a specific time frame. There are students who learn at a slower pace and they are affected by time because they are not given the time to fully understand the content when new content is already being taught. I think this can be overcome by better assessment and providing students the time they need to understand and not fall behind. Another problem is that sometimes schools want students to solve problems a specific way. I have heard by other classmates that a student they knew was told that the homework was wrong because the child needed to use a certain method for their homework to solve the problems. It is good that students learn to approach a problem through different ways but they should be allowed to use the method that they understand and feel more comfortable with. Lack of motivation is another obstacle because if students are not interested they won’t pay attention and if they don’t pay attention they won’t understand. I think math can sometimes be difficult to make fun and engaging but it is crucial that students be motivated so they can learn. I think this can be overcome by better understanding students and knowing what they like, so that what they like can be used to draw their attention. Lack of motivation can also be overcome by the way work is graded. Having red exes all over students’ work can discourage students and instead of using red exes maybe positive messages can be written down.

13. What I think about the structure in the classroom in the 21st century is that they are not really teacher center because students are learning by doing and teachers are also acting like coaches to the students in the classroom also of schools do not use textbooks anymore since technology’s is taking over the 21st century. In teaching center, you normally see teachers creating opportunities for students to work in groups, collaboration, and discuss and revise. Some shifts that can helps me as a teacher learn the content and the methods is by using effective teaching strategies in the classroom. Which can be cooperative learning, behavior management, professional development, and technology in the classroom.

14. I really enjoyed the way class was structured. The task one assignment had questions that involved a lot of mental math and thinking. I liked to write everything down so that I could see every combination, or rod and it really helped. The questions made me really think and look at my work to figure it out. I enjoyed the class because I was able to show this thought process and learn more from my classmates. I enjoyed having a partner because I was able to converse with someone on my thoughts and hear their opinions. If it was in a real classroom it would be a lot more beneficial because there would be no internet troubles. I also liked that each group was able to share something from the tasks, because I was able to hear out my classmates and learn their thought processes for each problem. Another thing that helped was that we were able to see your paper and work. In previous classes, it was hard to understand a couple of problems because I could not see it being done.
    There was an intro, we went over the task, we learned more skills, and there was an ending. In my opinion, the class was very engaging and I was always thinking about the questions you were asking. The structure of the class was very beneficial and I enjoyed it. I don’t think there needs to be any big shifts because any confusions I had were clarified, and I gained a lot. Maybe we can be in different groups every time so we can meet new people and have more discussions. I don’t have any other thoughts on this, because I really did enjoy the first class and the structure of it. I learned many new methods of the content we were going over and had fun while doing it.

15. I liked how the class was structured yesterday, due to us all first coming together to review the agenda for the day. I believe this is important because students have to know what to prepare and expect for the class. When we all went into groups to review the first task, I saw it was very helpful, since we shared how we solved the problems and discussed the patterns we found. It also was a great opportunity to ask about anything that was confusing when completing the task. In addition, we compared answers and I noticed that I missed a couple of combinations and my group mentioned that, which was helpful. This creates a supportive environment, which leads into us discussing our techniques and interesting ways that my classmates found the patterns. I liked seeing the combinations in the virtual version of the cuisenaire rods, whereas I used the physical parts of them. This showed me how math can be creative as well by trying many different potential ways to find out the answer. I liked how we reviewed subitizing, as it was discussed in the textbook and that leads into number talks and grouping. It immediately allowed me to connect an activity called Dot Plate Flash, where you quickly show a plate of dots and the children count them. I thought learning about the number talks and different ways to group the dots was interesting, since each person had a unique contribution. This shows that children will enjoy this activity by grouping and creating something with the dots that will help them count faster. In the end, I liked the connection between seeing different ways to multiply numbers and lesson planning, as everyone has a distinct way of learning. Overall, math needs to be made engaging and fun for students to feel they can experiment without risk and experience inquiry learning like we are in class.

16. I really enjoyed today’s class. I think it went very smoothly and it was engaging, which is always important. I think the structure of the class was very organized. I like how we spent some time going over the task. It was very helpful to go over it with some of my classmates. Working together is always impactful to me because it helps me learn more. I really like jam board, and I will definitely be using it in my classroom. It is so fun and interactive, and it is very engaging. I also like the structure because the class did not feel rushed. We took our time on each topic and made it our focus, which I like. I do not like when classes are rushed. I like being able to ask questions and I was able to in today’s class.
    One shift that helps me learn, as I mentioned before, is the group discussions we do. I enjoy talking to my classmates and I appreciate learning the methods that they use. Learning these new methods is important because I am going to need to be able to have a bunch of different methods for when I am a teacher. All students learn differently so I need to have multiple methods. I think another shift that helps me learn is when we use other websites, like jam board. It is fun to share our ideas with each other. It is also a great space to share our work. I only learned about jam board this semester and I love it. The last shift that I want to bring up is the breakout rooms. The breakout rooms are good because you can get personal with a smaller amount of the group. It is nice to talk to 2-3 people and learn more about them. I liked working with the group that I did in today’s class. They were very nice and hardworking, which I appreciate. I like the breakout rooms because I feel like they allow me to ask for help if I am stuck on a specific topic.

17. I think students in a high-quality mathematics classroom should look full of desire for knowledge, and the teacher has a good plan for the teaching topic, which can be conducive to the positive thinking of the students. Not only that, the activities that teachers take during teaching can allow students to feel and experience the formation of knowledge. Students are not a container for passively accepting learning, but an active explorer and discoverer of learning. These nations come from interest and are the best teachers.
    A clear and reasonable motivation, appropriate and enlightening examples, and targeted references are the keys to being able to teach mathematical concepts and the core of the problem. There are a lot of concepts in books. People who know how to read know every word in the books, but not everyone understands the concepts in the books. Therefore, the activities and examples used by the teacher in the classroom need to be targeted to bring mathematics to life and make students like mathematics. Moreover, as a teacher, you also need to be liked by the students, and then the students will also like the subject you teach. Therefore, keeping friendliness, patience, and equality attitudes to students have become indispensable factors for high-quality classrooms. These nations serve the students, because they are the protagonists in the classroom, and each lesson and teaching plan taught as a teacher is for them to understand and be able to apply the knowledge they have learned in their living.

18. Many teachers will encounter obstacles in the classroom, and some may be due to many factors. For example, some educators will be hindered from in the classroom by curriculums, or advisors that instruct educators to follow a certain method, that they have learned in workshops to incorporate in classrooms. When introducing a new topic lesson in math, teachers are following a specific guideline and instructing the lesson in a matter that is created for them. Such as teaching the child what the problem will look like, show the steps, have the child repeat, and then sending students off on their own. After this is done, teachers are conducted to give quizzes and exams to assess if the child mastered the topic or not.
    Some ways a teacher can overcome this obstacle, is taking the information given to them and incorporate it into their lesson but not using it as a finalization for the lesson. For example, instead of demonstrating the problem in the beginning and going on from there, it’s important to let students explore and begin to think of strategies they can do on their own. Teachers should lead students, observe their thinking skills and prior knowledge, and carry it from there. When a teacher knows the different abilities of the students throughout lessons, she/he will know what certain aspects of the lesson she/he will have to clarify or go over a bit more for the students. And instead of having students take tests and quizzes to determine if they understood the topic, children should be able to complete tasks on the lesson, explaining the steps of the lesson, their strategy, and their conclusion on how they arrived to the answer.

19. Today’s class went really well it was great. It was structured really well. I enjoyed being put into groups and seeing my classmates work on task one. We were able to communicate on how we each completed the task. I enjoyed this because we got to see each other’s combinations and we got to discuss our answers. I enjoyed putting our answers on jam board. I like how it was planned out first we discussed our task one assignment with two other classmates, then we came together as a whole class to discuss what each group answers were. The Professor also gave us her examples which helped me visually see. I learned about number talks which I never heard of which was really a fun way to learn how to group, combine and figure out the answer of a specific question. I will definitely use that when I become a teacher. Professor makes learning mathematics fun and enjoyable. I think it was perfectly organized. Shifts I think that can help you learn about content and methods is really studying the material before class and actually looking at different examples of topics. Studying is extremely important in mathematics. Math has always been a challenge for me. Throughout my school years I would struggle until I thought about what would help get through a specific topic? When it comes to math you have to really study a topic over and over again to fully understand the material. I always study the methods and material before class again to refresh my memory. I also watch videos sometimes on the specific topic if I still do not understand. Another way to shift is if you do not know a specific topic or you have a question ask the professor they are there to help.

20. Some obstacles to creating change in the mathematics classroom at the elementary level are that there are children who already have the thoughts that they are no good at math and are unable to learn math. This type of thinking disables children from wanting to learn even if they are capable. These obstacles can be overcame or interrupted by showing children their true potential and even by teaching when children don’t even realize it. They may believe they cant focus on instruction and are not able to learn because they are not being taught the correct way they can learn. Differentiated instruction could be a huge role in whether a child learns a topic or not. Keeping curriculum and learning practices open to being adaptive is important because of this so children do feel like they are able to understand and learn based on their capabilities and how they process information. This is extremely important to me because it could be the difference in whether or not students are actually learning in the classroom or just waiting to be passed or failed in the next class they get transferred into. These practices could mean an early intervention into children’s lives because we are very well impacting how and if children learn.

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