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23 Comments

1. I thought class was structured in a very organized way. Every lesson ran smoothly, and class was extremely enjoyable and fun to be a part of. Throughout the class, we took time to go over any questions and answers that we might have, worked in groups, and learned various ways to solve an equation. I appreciated working in breakout groups because it allowed us to go over our homework together and help each other whenever we were stuck. Some of the questions in the homework I was confused about, however, through my classmates, I found so many new ways to solve these math problems. Not only were the answers just spoken, but they were also drawn out for us which was helpful for visual learners like me. In the next portion of class, we learned about “Number Talks”. When learning about Number Talks, we counted dots, and found multiple ways that students can count these dots. For instance, the way I counted to dots can be called a “pig snout” or another way a student counts them can be called “dice”. Structuring a math class where students can be creative with their thought process allows students to feel as if they have ownership and grasps their attention. I believe this class was mainly student-centered because us as students were the ones finding ways to solve an equation or using our background knowledge to find answers. This class would have been beneficial to me when I was younger because it gives me confidence whenever I don’t feel so confident.

2. What did you think about the way that class was structured today? What shifts can help you learn the content and methods?

   I like the structure of today’s class. I enjoyed working in groups going over the task. I think talking about the math problems and discussing how to solve the problem helps me understand better. I liked seeing different methods of solving a problem. Using different methods can help determine what works for me. I also liked that instead of changing the topic we stayed on it to make sure we understood it throughly. The way the class was taught gives me an idea of how I would want to teach my future students.

3. The class was structured in a very positive way. I enjoyed being placed in a group to discuss the homework assignment and view how others have solved the equation. I believe that this is the best way to go over homework because if a student misunderstood the assignment, they will ask their classmates questions and see it from their point of view. Also working with my group mate to find answers together was very useful. There are many students that have trouble with math and working with others can really help them see it from a peer’s perspective.

4. What did you think about the way that class was structured today? What shifts can help you learn the content and methods?
   The class was structured in a very positive way. I enjoyed being placed in a group to discuss the homework assignment and view how others have solved the equation. I believe that this is the best way to go over homework because if a student misunderstood the assignment, they will ask their classmates questions and see it from their point of view. Also working with my group mate to find answers together was very useful. There are many students that have trouble with math and working with others can really help them see it from a peer’s perspective.

5. Some obstacles to creating change in the mathematics classroom at the elementary level are that students perceive math as too challenging and it is not worth the effort to even try to understand. Usually, students have a fixed mindset about their math level, such as thinking they are “bad at math” or “good at math.” One way to overcome this is to teach students about the importance of a growth mindset which would encourage motivation and engagement. This would enable them to develop an optimistic point of view of themselves as well. Another obstacle is that many teachers were taught math a different way. Personally, I was taught math completely different than the common core math standards taught now. Therefore, I need to learn the common core standards of math and keep up to date to be able to effectively teach my students. Another obstacle is that teachers do not have enough resources to be able to teach math to diverse learners. Teachers have to seek materials and resources to meet specific standards. Moreover, many students have a hard time grasping basic concepts needed for building an understanding of another topic, and oftentimes the teacher has moved on to the next lesson. Therefore, giving students exit tickets or allowing them to explain their thinking can show the teacher whether or not the students understand the concept or needs more help.

6. Some obstacles to creating change in the mathematics classroom is that some teachers are set in their old ways and not open to current pedagogical best practices. As a result, what they believe is the best method may not be the best optimal for their students. Teachers need to be open to approaching lessons in different ways until they find what works best for students. Another obstacle is that a lot of the time, lessons are taught in a lecture method in which the teacher goes over a lesson with students and the students just listen and take notes. While it is important to explain things to students, it is easy for students to get lost in the lesson.
   I think it is important to include real life examples that students can relate to when teaching math because it can help them put a concept into perspective and help them form an understanding. It’s also important for students to be involved in a more interactive and student-centered approach. I think it’s important for student’s to always be asked their logic and reasoning behind their responses to math problems. If the teacher can understand how the students think and come up with answers, then it can help the teacher better develop lessons and activities fit for the students. It’s important that students share with their peers because they might explain something in a way that helps a fellow peer develop an understanding for the material.

7. I like the way class was structured. I like that we go over the homework with our classmates first because that way, I’d see if I misunderstood something and it’s fun working together and discussing the work. I also feel that it’s less intimidating discussing work with our peers than our teachers. I like that the entire class is always engaged and interactive. It’s not just you speaking the entire time and showing us a bunch of slides. It’s very student-centered, in my opinion. I really enjoyed doing the multiplication problems because I learned new ways in solving the problem that I didn’t know about or I forgot about. I also like the way you broke down the three-phase lesson plan. It was very informative and it will be useful when writing lesson plans for math. Taking breaks in between gives me a chance to refresh so I really like that because sometimes the amount of information can be overwhelming. Overall, everything is going smooth and your energy is great during our zoom sessions so with your positive energy and these informative and interactive lectures, I’m interested in learning more from this course.

8. When creating a change in the mathematics classroom at the elementary level there may be some obstacles we may face as a teacher. One of the obstacles may be the curriculum teachers have to follow. One of the curriculums teachers have to follow are the common core which makes it more difficult to add change in a classroom. Another obstacle in the mathematics classroom teachers may face is not having the right materials and resources to help the students understand how to solve certain math problems. From my personal experience one obstacle I have faced during math classes is not having enough time to both understand what I have just learned and to practice it in school among my classmates to learn different ideas and methods. Just like our previous class where we were able to solve the question or speak about how we solved the question in a group help me understand more than one way to solve the question. These obstacles can be solved by creating a lesson in which students have more time to understand what they are learning and have time to interact and work together as a class to solve the problems together. This allows students to teach each other and learn from each other’s work and mistakes. I believe this would help because it makes the classroom student centered rather than just listening to what the teacher is teaching and struggling on their own.

9. Class was really enjoyable today. I originally thought a math class would be boring, and confusing, but this class proved me wrong. The structure of this class helps the class run smoothly. I enjoyed working with my peers in breakout rooms. I enjoy working in smaller groups to see how they solved problems and to see their perspectives on the math questions. Sometimes I struggled with a question and my group members explained how they solved the question. I also think hearing what each group thought of was helpful, because we learn about more tricks and perspectives that they have. From this, I learned about many strategies that I have never heard of before. It made answering the problems simpler, and improved my understanding of the questions. I think most of the class was structured as student-centered learning because we were sharing our thoughts and ideas throughout class. We were talking with our groups and sharing our ideas with the class. I think this benefitted us because we have a chance to learn from each other. I also enjoy having a break in the class because after long classes I get distracted. Having class end a little earlier is also helpful because I have time to review and process what we discussed in class. The class seems to go by quickly, which is always a good thing! I like the fact that we also have some asynchronous classes because during this time I can work independently. I am very excited for our future classes.

10. Some high-quality mathematics classroom notions are that “math is hard”, some students feel like once you fail/make a mistake, they are not good at math after one bad experience with Math. This one notion creates many concerns, the notion “math is hard” came from the teachers that didn’t have the right tools and teaching skills to just simply blame math to be the problem, when in reality, teaching our students how to overcome this “math is hard”. Another reason this notion is being carried down is the parents, parents have had their bad experiences which have been reflecting on the student’s math journey. One notion is “Asians are good at math”, which is a racist stereotype towards Asians. There is this variation towards Asian students, there should be an equal opportunity for all students in the classroom without any pressure on a certain race to do well in class and other races not to do well, this creates negative thoughts in students minds about them not doing well in class because they aren’t good at math. Some obstacles in a mathematics classroom are having the student’s attention throughout the whole classroom, keep them connected to the lesson, as teachers, we need to incorporate group work with at least 2 students. This can easily be interrupted if the students get distracted and go off-topic. Learning in math class can sometimes be student-centered, this way they will feel more comfortable and feel like they are in control which will help them stay focused on the work. Class was great just the way it was.

11. An obstacle that might occur when wanting to create change in a mathematics classroom is the strictness of how a child is taught to solve a problem and show their work a certain way. Many schools have a strict set of rules to follow when grading a students work, they have to follow certain criteria in order to give a passing grade to a student. In many cases when it comes to math the answer is either right or wrong there is no in between although the way to get an answer varies among different techniques and strategies. Schools tend to not focus too much on the thought process of getting these answers but rather if the child got the right answer. This obstacle can be overcome by allowing the student to explain how they arrived at their answer. Letting them explain their thought process verbally or writing it down on paper, the steps they took to solve the problem will help the teacher know if the student understands how to solve the problem or part of the problem and their reasoning for using a certain method. Teachers can tell if the students is on the right track and knows the steps to take to solve the problem by doing this. They can also tell where the student went wrong and help them if needed with their reasoning/ideology when solving a problem instead of just dismissing their thought process when they get the wrong answer. This method helps create change in the mathematics classroom by leading to better class discussions about math and helping teachers recognize students thought process and understanding of the material.

12. I loved the way the class was structured, it was fun learning and working together as a class. I enjoyed working in groups in the breakout rooms and the fact that we got to discuss our strategies within our groups as well as with others. I liked how the whole class was able to participate and was very well interactive. We got to learn different strategies from other students, like for example , Rashmit ‘s method of solving the multiplication problem, it was very helpful and will be helpful in the future when we get our own classes because if a student is unable to understand one method, there will always be another method that the student can learn.

13. There are a few obstacles to creating change in the mathematics classroom at the elementary level. First of all, teachers have a common core to follow, which makes it hard to create change in the math classroom, and most of the teachers used to follow the path from past experiences. Besides that, the time we spend in the classroom for mathematics class is not enough. Suppose we are trying to shift the class from a teacher-center classroom into a student-center classroom. Students-center classrooms consume much more time than a teacher-center classrooms. As we all learn from this class, there is always more than one way to solve one question, and every student will have their comfortable ways of solving the problem. Therefore, teachers need to provide students enough time to think, interpret, and share their thoughts and methods with the class. Furthermore, we do not have enough resources and support to create change in the mathematics classroom. Teachers need more materials to create change for math class, such as different kinds of math tools. Therefore, to overcome these obstacles, we need a better lesson plan to slowly making changes in the math classroom. Furthermore, time management of ourselves and the students is essential as well since teachers need to make sure the students learned and understand the materials by the end of the class.

14. There is definitely the challenge of creating a shift from a teacher-centered paradigm to a more student-centered one. When teaching math, the first instinct is to do an I do-we do- you do model. However, this simplifies math and creates students who rely on the teacher extensively rather than take risks and problem-solve independently. As educators, we want to create engaging lessons that reply on problem-solving methods. Obstacles include a looming curriculum and a lack of resources; teachers might be overwhelmed to finish the curriculum. They opt for the easier teacher-centered method because they don’t have the time or resources to imagine implementing hands-on solutions. Similarly, an obstacle might be only viewing a lesson in one way and not reimagining it or thinking outside the box, thus making teachers feel even more stuck in their ways. Realistically, teachers can overcome these obstacles with professional development that provides both new and veteran teachers with strategies and tools to tailor to their student’s needs, focusing on problem-solving and manipulatives. Ideally, teachers would be given more resources and time to create lessons.

15. The way that class was structured today made me really comfortable. I really enjoy doing group work in the breakout rooms because it is less intimidating talking about math strategies with two other people versus the whole class. I have always been shy when it comes to talking about my own math strategies because sometimes, I am nervous that they are wrong or just different than another person would do. I really enjoyed the way we all shared how we counted the 8 dots. I thought it was really insightful to see how we all interpret math in our own ways. It was also really helpful because it allows us to think about math differently and deeper into the problem. I learned a lot of strategies that I did not think about, from my peers. I like when the class is hands on and actually has us doing problems rather than just learning about concepts. Personally, I really enjoyed the way class was structured today.

16. I think the way that the class was structured today was the combination of student-centered learning and teacher-centered learning. In which in my opinion, it is the most effective way of learning, because while the students need to participate and discuss in the class their works, they do not easily get bored or distracted from others. Even though the beginning of the class was teacher-centered learning, but students didn’t get exposed to the PowerPoint that contains lots of words, so they can easily concentrate on listening to the teacher. This is one of my favorite ways of having class online or in-person because as a learner, it is difficult to simultaneously listen to the teacher talking and watching what the PowerPoint shows. I think this way of teaching is very useful for elementary students as well because I believe they also don’t like to be watching an “essay” on a PowerPoint and they might prefer to have more conversations either with the teachers or their classmates. Now in the day, students and teachers are forced to adapt to online teaching and learning, which limits a lot of outside activities that are related to the learning material as well as the face-to-face interaction. So, I think it is very important to give students a chance to have a little breakout room with random classmates that can be discussed and interact with each other. Also, the part of student-centered learning during the class is very helpful for students, because students can show their works, discuss and learn any possible mistakes they have.

17. I enjoyed how the class was structure it made the class go by faster and I enjoyed the lesson much more. I think it was a great thing to go over the task and have each group explain a specific part of the task. This way we could see how the problems were solved in different ways and also it would help those who were confused. I personally think that a lecture is not helpful to students so shifting to other things is better. For instance, spending more time understand a concept or problem is more beneficial than just going over it and moving on to the next topic. Also getting different perspectives on how to solve a problem like how we did in class with the dots question. Things like this can help people learn more efficiently.

18. I thought the way class was structured on Thursday was great. I was grateful that we were able to get together with classmates and talk about the task that was due. When I was working on the task independently, I was second guessing myself and I was not sure if I was doing it correct. Talking about it in class helped me to understand the parts I did wrong. Furthermore, I thought the breakdown of the three-phase lesson plan was very useful. I can use the chart that explains all three sections of the plan as a guide when I am writing my math lesson plans. When going over the content and methods, especially practicing with “number talks,” I enjoyed gathering all the different strategies to solving the math problems. Having a variety of strategies to solve a problem is so useful, and as a future educator I can understand how allowing your students to discuss the different strategies they use is so important in your classroom. One change that I think would be helpful for me is maybe focusing in on the specific topic a little more directly. All in all, I really appreciate this class and I can’t wait to continue learning about all the different content areas and how to go about teaching an elementary level math class.

19. The way that the class is structured today is very common core standards-based. When I was in elementary school, it wasn’t as common core-based as now. When I did tutoring back then, there were new terms that my students had that I had never heard of. For example, one term was called regrouping instead of borrowing when subtracting in math. For math, doing more problems related to the topic will help me learn the content and the methods of how to solve the problem.

20. I liked the way class was structured today. I am a learner that likes to review what was done last class with classmates and then we moved onto a new topic which connected well with the last topic. I also liked that we were able to share out strategies of how we figured out the answer freely. I like when the class is very interactive because then the class doesn’t drag out for too long. I liked the little break in the middle too because it gave me some time to quickly go over new information we just learned and a chance to catch a break. Overall, class went pretty smoothly in my opinion and I liked that we got to make it around our needs and not just the professor talking about the material.

21. I believe a common obstacles to creating change in the math classroom today is first by how the teacher was taught math when he/she were in school, versus how math is being taught now. For example, when I was in school, there was no common core standards to follow which now changes how math is taught and learned completely. Therefore, teaching my students a math concept the way i taught it, will most probably not be beneficial to them as common core is completely different. In this case, i would need to see what the common core standards are for the math part of my teaching and update myself on it so i can efficiently teach the material to my students the correct way.
    Another common obstacle to creating change, is that there is more than one way to answer a question and just because it was taught one way, doesn’t mean that is the only way. For example, i had a teacher in junior high school that marked me wrong on a question on an exam that i got correct just because the work i showed wasn’t the way she taught it. My answer was correct, but because the work i showed wasn’t the work that my teacher taught me, the answer was marked wrong. From this, i can easily overcome this obstacle by realizing that i can have many students in my classroom who can come up with many different ways of getting the correct answer, and i shouldnt mark them wrong just because it wasnt the way i taught it to them.

22. The preconceived notions that you have about what a high-quality mathematics classroom looks like is that the lesson should follow a three phase lesson plan. One where there is a content and task decision part, lesson plan part, and reflecting on the design. Another notion that you have is that the lesson should mostly be student-centered where students are allowed to explore instead of given the solution strategy every time. The teacher should provide relevant information, allow multiple ways to solve problems- where an exploration of different strategies are allowed. On top of this another notion is that a visual representation should be available for the students. Another things is that when students are working on a problem they should be provided with vertical nonpermanent surfaces because it promotes students’ discussion and helps them visualize more clearly a problem or solution. Lastly, allowing students to communicate during the discussion at the end of the lesson where teachers actively listen to a student’s comment instead of evaluating every single time. This will allow the classroom to be a high-quality mathematics classroom by allowing students to reflect deeper into their findings and notice new strategies that can help them in the future. Students can use these discussion times to view how a strategy successfully works or perhaps notice when the appropriate time for a specific strategy to be used might be. These notions come from the fact that students should be allowed to explore new strategies instead of absorbing every strategy given to them like robots and these notions would help and serve the students better.

23. I believe that a high-quality mathematics classroom looks similar to Montessori education. This education allows for hands-on and creative play that is age-appropriate. It can be collaborative and but requires the students’ individual thinking and participation. This form of education promotes independence and is helpful since students may understand some mathematical methods and strategies quicker than others. It encourages students to be engaged and curious. Also, it’s important to learn how to think about math strategies rather than what to think for each problem specifically. I feel this way because I am frustrated as a learner when I would forget strategies taught by my teacher. I didn’t have my own thinking strategies to help me solve. I do believe it’s important to assist students when they need guidance to develop strategies. Especially with physical things like manipulatives, both lower and upper grades can use tangible methods to provide logical explanations. I think that incorporating technology may benefit students when they can play an online game that they can “play” and be creative while learning how to independently think about connections between curriculum and specific problems. During this class, I was part of the student side of a lesson. My classmates and I were able to collaborate and share various strategies to solve multiplication problems. I also was introduced to using collaborative lesson planning that encourages student engagement. It drives learning away from teacher-oriented lessons to student-oriented ones. This can be utilized in many classes where the teacher can see the student’s prior knowledge on a given topic. I wouldn’t want a student to be in the wrong direction or completely lost when learning a specific skill set etc. I believe that a lot of students are visual learners and this method could serve most students that can benefit from an individualized visual experience.

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