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Something that really resonated with me was the idea of teachers messages being very powerful. I can see this in my own learning. In my highschool calc class I did not feel very confident in my ability to do this new math at the beginning of the year, but my teacher reminded us that he knew we were all capable and were meant to be there and that we could all do the math we were being tasked with. By the end of the year calc was my favorite class I had ever taken and it made me realize math was something I wanted to do for the rest of my life. 

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Something that really resonated with me was the idea of teachers messages being very powerful. I can see this in my own learning. In my highschool calc class I did not feel very confident in my ability to do this new math at the beginning of the year, but my teacher reminded us that he knew we were all capable and were meant to be there and that we could all do the math we were being tasked with. By the end of the year calc was my favorite class I had ever taken and it made me realize math was something I wanted to do for the rest of my life. 

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I would like to know how, as future educators, we should shift from making students do math quickly to allowing them to more deeply understand it in the classroom setting. I want to know what this might look like for us when we are teaching in the future. 

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I would like to know how, as future educators, we should shift from making students do math quickly to allowing them to more deeply understand it in the classroom setting. I want to know what this might look like for us when we are teaching in the future. 

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What are practical was that teachers can take emphasis off of speed in math when class periods are only so long? Students will still need to complete tests/quizzes in the allotted period of time and will still feel that time pressure.

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What are practical was that teachers can take emphasis off of speed in math when class periods are only so long? Students will still need to complete tests/quizzes in the allotted period of time and will still feel that time pressure.

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Something that resonated with me was the finding that one instance of a teacher telling a student they believe in them can have long-term results. As a teacher, I want to find those influential moments to voice that I believe in and value my students.

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Something that resonated with me was the finding that one instance of a teacher telling a student they believe in them can have long-term results. As a teacher, I want to find those influential moments to voice that I believe in and value my students.

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something that pushed my thinking is the difference between growth and fixed thinkers in math.  A growth learner is a fixed thinking with confidence. So many people just say I am not good at math and don't even attempt the problem. A big part of understanding math is having the confidence to do the problem. Im sure if people gave full effort into their math problems they would be surprised on how much they can do. And through all of this they will become growth learners.

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Something that really pushed my thinking from the reading was that we need to make mistakes and struggle in order to learn or to fully grasp a mathematical concept. The reason why this made me think is that personally I feel like math classes for me was relatively on the easy side for me all the way up to high school, but that might actually because the teacher's weren't presenting problems that are challenging. I remember just having to pay attention in class and remember how to do the examples that are demonstrated in class, and on the exam they would have pretty much the same structure as the examples expect that they change the numbers. I feel like this sort of examination is giving students a inaccurate reflection on how much they've learned because the exam questions does nothing to propose challenge to the students.

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I really enjoyed the discussion of how making mistakes and struggling is one of the best ways to learn. It actually reminded me of my computer science days - when I made a program with tons of bugs and went through resolving all of them, I had a really good understanding of why my final solution worked. But when my solution worked on the first or second try, I had a hard team fully comprehending what I had just done. I loved the idea that problem solving and hard work is such an effective way to learn and gain information.

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Something that really resonated with my own thinking about teaching and/or learning is the "fixed mindset." The truth of what Boaler says is evidenced by me. I'm a high-achieving girl with a "fixed mindset." I try to avoid challenging math and high-level courses. I beat myself up if I get anything but an A. I think this could also be connected with the idea that timed math assessments can cause anxiety. This is certainly true for me.

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I resonated with the section on speed. Whenever I would have to solve math expressions quickly I would experience stress blocking my working memory. After playing games like around the world where you would have to answer questions really fast, I would think I was bad at math because I could never answer the questions fast enough. I still get anxious about timed math tests.

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I really struggled with trying to accept the idea that separating children based on their academic performance could be a bad thing. I have never been in a public school that did not have merit, honors, accelerated, AP, etc. Every core subject in my schools had these type of class levels and I was always told by my parents and teachers that putting lower performing students with higher performing students was a bad for the higher performing students development. This is an example of how people do not put as much faith into teaching lower achieving students. The article presents the opposite view, saying that lower achieving students have the same potential as any other student and that under the right teachers, they can achieve as high as any other student. 

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I really struggled with trying to accept the idea that separating children based on their academic performance could be a bad thing. I have never been in a public school that did not have merit, honors, accelerated, AP, etc. Every core subject in my schools had these type of class levels and I was always told by my parents and teachers that putting lower performing students with higher performing students was a bad for the higher performing students development. This is an example of how people do not put as much faith into teaching lower achieving students. The article presents the opposite view, saying that lower achieving students have the same potential as any other student and that under the right teachers, they can achieve as high as any other student. 

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Something that pushed my thinking was the main idea of the article that there is a myth that some students are 'naturally' bad at math, and others will just simply never be good at it. This is the way I thought growing up, and I had always just assumed that I was just good at math. But after reading that students who grasp math faster than others is not because of genetics, but because of chances to make brain connections earlier in their life makes much more sense than a natural ability. I hope as a teacher I can continue to break this myth and keep this in mind after now thinking about it deeper.

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Many parts of this article resonate with me, and this "resonance" is probably the reason I'm walking on this pathway. The support of a growing mindset, the clear opportunity to let everybody be confident with the mathematical principles and the importance of the personal timing to manage these principles, are all extremely important things in my idea of teaching...and learning.

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The concept that all students can achieve at high levels and learn new concepts in very short amounts of time is something that pushed my thinking. I had always believed that anyone could do math, but I assumed that there were some people who would always struggle with it or be behind other students. However, the research showed that when given effective instruction, students who had been diagnosed with math learning disabilities could achieve at just as high a level as all other students. I think this emphasizes just how important quality teaching is. 

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The concept that all students can achieve at high levels and learn new concepts in very short amounts of time is something that pushed my thinking. I had always believed that anyone could do math, but I assumed that there were some people who would always struggle with it or be behind other students. However, the research showed that when given effective instruction, students who had been diagnosed with math learning disabilities could achieve at just as high a level as all other students. I think this emphasizes just how important quality teaching is. 

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Something that really resonated with me is idea that students' perception of their own abilities in math impacts their achievement and lifelong learning. This is part of the reason why I want to teach math specifically. I have known so many peers who have deemed themselves "bad at math" and even teachers who have marked students as bad at math. I know that students' self-confidence is important, and so many people give up on math or dread it because they think they are bad at it. So as a future math teacher I want to show students that they are all capable of doing math, and I want to help them build their confidence in their math abilities. 

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Something that really resonated with me is idea that students' perception of their own abilities in math impacts their achievement and lifelong learning. This is part of the reason why I want to teach math specifically. I have known so many peers who have deemed themselves "bad at math" and even teachers who have marked students as bad at math. I know that students' self-confidence is important, and so many people give up on math or dread it because they think they are bad at it. So as a future math teacher I want to show students that they are all capable of doing math, and I want to help them build their confidence in their math abilities. 

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How are some ways that teachers can ensure that all students are getting the instruction and support they need in classrooms where there are many students with different needs, and only one teacher?

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How are some ways that teachers can ensure that all students are getting the instruction and support they need in classrooms where there are many students with different needs, and only one teacher?

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How can we move towards detracking without boring the students that are advanced or leaving the students that are performing "below average" behind? I understand the importance of not grouping students into categories, but I think there needs to be an appropriate cognitive challenge for all students, which can be difficult to meet in a subject like Math.

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Something that resonated with my thinking was the fact that math is a gift to some is a myth. A while ago, I used to think that math was one of those subjects where you would get it or you didn't. But with more learning and having hands on experience with teaching, it opened my eyes that anyone can have the "gift" of math when given proper teaching and resources that work for them. I have been good at math for most of my time in school, so I have had many chances to connect with math throughout life. According to the article, this is why I am good at math. I found that fact interesting and haven't really thought about it before, but it makes sense logically.