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A quote that stood out the most to me was, "Ann boldly used her leadership position to create a safe space for taking risks, making mistakes, and making sense of mathematics." This quote stuck with me when reading this chapter because of how much I could relate to it throughout my life, especially from elementary school to high school. I was so scared to make a mistake that I would worry myself sick when any kind of project or worksheet came up. This is still apparent now. I over obsess about my work, and when I make a mistake, it's like I give up. The favorable condition that stood out to me was the environment in the classroom. It was so trusting and safe. I want my students to feel that way ALWAYS

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The quote that stood out to me the most was that "the study of pure mathematics can be undertaken successfully by a large number of students if they are provided with a supportive environment including: careful and considerate teaching by a well-trained and dedicated faculty, continual encouragement, successful (student) role models, enough success to develop self-esteem, enough time to develop intellectually, recognition of their achievement, and the belief that the study is a worthwhile endeavor. We are dedicated to providing this supportive environment." This quote stood out because it lists all the favorable conditions needed for a great mathematics classroom. The favorable condition that stood out to me the most was continual encouragement. It stood out to me because encouragement is a major factor in developing a growth mindset, which is essential to mathematics. You want to encourage your students to push on when they make mistakes because they will eventually grow to fix them with a growth mindset.

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A quote that stood out to me the most in Chapter 13 was, “Believe in your students, everyone can do mathematics.” This quote stood out to me for many reasons. It resonates with me because it challenges the idea of "fixed ability" in mathematics and places the responsibility on teachers to provide an inclusive, supportive, and empowering space for learning. It's so important for teachers to not only believe in their students and their abilities but also encourage them to believe in themselves. The favorable condition that stood out the most to me was “Careful and considerate teaching by a well-trained and dedicated faculty, continual encouragement, successful (student) role models, enough success to develop self-esteem, and enough time to develop intellectually.” I found this to be particularly impactful because it recognizes that learning is not just about cognitive skills but also about emotional and social support. I want my students to feel safe, loved, and smart in my classroom. Although this was my favorite quote and favorable condition there were a lot of powerful things in this chapter that can lead to being a very successful teacher.

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A quote that stood out to me is "We have all had a moment in which a student’s question or comment makes it obvious that we don’t understand the mathematics...Most teachers feel exposed, vulnerable, or insecure at this
moment. We tell students it’s great for them to not-know, but we keep our own not-knowing hidden under our authority." I often think about what I would do if my future students asked me a question I didn't know the answer to. After reading this quote, I now think that what I would like to (and should say) is, "That is a great question I don't have an answer to yet but let's figure it out together. I think this would set a good example for my students and help them believe it's okay not to know the answer. If we are going to tell them it's okay not to know, we need to show it. My favorite favorable condition is the continual encouragement component. In the math classroom is a place where students are supported through good and bad, they are more likely to be successful.

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The quote that stood out to me most from chapter 13 was, “We know our students are not well prepared, our job is to teach and prepare them.” I like this because I think it reiterates the ideas we have been learning the entire semester. There is no such thing as a math brain or a history brain. Not only this but, this outlines the idea I have most loved that you are not only teaching them math skills, but problem solving skills for the rest of their lives. This is a skill they are able to carry with them for the rest of their lives. This quote really outlines that and speaks on this. I want my students to take that out of my future classroom.

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My favorite quote from chapter 13 was a quote about Clarence Stephens and his time as a teacher.  “He instructed professors to give students all the time they needed to learn a new concept, to figure out what students understood and build from there, to engage students deeply in mathematical reasoning, and to teach students how to prove rather than memorize proofs”.  This stood out to me because it’s so important we give students all the time they are needing to fully understand a concept. I remember in math class, always being extremely rushed, it usually stressed me out, and I never ended up understanding the concept. Using the mindset of teaching students how to prove rather than memorizing formulas or answers is something else that stood out to me. This reminds me of another chapter we read that my main take away was the language we use in our classroom is so important. Ask students to help you solve this problem instead of telling them they must, it makes them more eager, learn new or difficult concepts. This quote reminded me as a future teacher to be patient for students to have the best ability of fully understanding a concept.

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The quote that stood out to me the most from the reading was: "Believe in your students, everyone can do mathematics." This quote reminds us of the incredible impact that unwavering belief in students' potential can have on their success and confidence. Stephens's work showed that fostering this belief and creating a supportive and inclusive learning environment could help students exceed expectations, regardless of their backgrounds or prior preparation.

The "favorable condition" that stood out most was the emphasis on creating a supportive environment with continual encouragement and enough success to develop self-esteem. Stephens's approach went beyond teaching content; it was about cultivating an atmosphere where students felt empowered and respected. This condition resonated with me because it highlights the importance of addressing students' emotional and intellectual needs. When students feel valued, they are more willing to take risks, persevere through challenges, and engage deeply with mathematics.

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In the chapter the teacher, Ann, worked out a problem with her students and got a different outcome than the answer to the problem. She then decided to doubt her own answer rather than others answers. The chapter says, "Ann boldly and clearly used her leadership position to create a safe space for taking risks, making mistakes, and making sense of mathematics." Ann modeled for her students that taking risks, making mistakes and doubting your own answer is okay to do, and in fact it is good to do because it helps you understand the problem better. I love what she did here and one day I want to create this space within my own classroom. She is setting her students up for success by communicating to them that they should not be afraid to make mistakes.

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A quote that stood out to me was, "We know our students are not well prepared, our job is to teach and prepare them." This quote stood out to me because it is our job as teachers to prepare our students for what we require of them. No matter how old the student is, they always have something to learn from us. We should not only model to our students how to complete school tasks but also how to walk through everyday life. Teachers should not only be teaching students, but they should be role models as well. The "favorable condition" that stood out to me most was the one about encouraging students to become independent in math. This stood out to me because I think teachers need to encourage students to be independent. Reassuring students that they can do it themselves is very important and can change their perspective of math.

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The quote that stood out to me the most was: 'In your students, everyone can do mathematics.' This resonated with me because it reminded me how powerful a supportive, inclusive classroom environment can be. When we believe in our students’ abilities and encourage them to take risks, make mistakes, and try again, we build their confidence and help them grow. My goal is to create a space where students feel safe, valued, and capable of tackling challenges—not just in math but in everything they do.

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The quote that stood out to me the most was, "People aren’t born disliking math. They learn to dislike it in school” (2011, 305)". This stood out to me as it helps show that other people feel the same way about math as one another. This book has shown that many students have become angry towards math due to the teaching methods they had to experience in school. However, this book also shows that once the students are taught a technique they understand, they tend to become okay with completing math equations. So, that is why I like this quote the most. It helps express that not everyone hates math for no reason, but they hate it due to how they were taught about math. The "favorable condition" I chose emphasized creating a supportive environment. Creating this type of environment allows the student to feel encouragement and helps develop proper self-esteem. Allowing these feelings into the classroom creates a better learning environment for everyone.

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One quote that stood out to me was, "People aren’t born disliking math. They learn to dislike it in school." I think this quote is honest, once students get into school, math becomes this challenge that is constantly there. For myself, I can say I dreaded doing math. In elementary I was slower than most other students, and in high school I just never understood. In the book she goes on to say kindergarteners arrive on the first day with powerful math ideas, so teachers should create the most favorable conditions for students from day one. Once teachers can do this they will change students whole opinions on math.

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a quote that stood out to me in this chapter was "people aren't born to dislike math, they learn to dislike it at school". This stood out to me because in school growing up I did not like enjoy math class. The way math was judged in my classes was if you were good at math or liked it you were making good grades in the class. My teachers didnt really allow for a growth mindset, it was more you were right or wrong which made me think that i wasn't good at math which lead me to think that i didn't have a math brain. In my future classroom, I will allow my students to do activities, that allow them to be mathematicians, which will allow them to hear each other ideas and understand math without being scared that they will be wrong. This will give students confidence, and ecounage them to do math and not be scared of being wrong but want to do math in their own ways.

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A quote that stood out to me was "Our students arrive in kindergarten with powerful mathematical ideas, observations, and
wonderings. If we create the most favorable conditions we can for all students, we’ll equip
them to enjoy mathematics all their lives." This stood out to me because it explains that students come in excited and ready to learn and as teachers, it is our job to help them maintain that attitude toward learning. The 'favorable condition' I chose was about creating a supportive environment for your students. A supportive classroom environment provides emotional safety, respect, and belonging. It encourages students to share ideas and participate. It builds confidence, promotes collaboration, and enhances learning outcomes.

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A quote that stood out to me was "He encouraged teachers to know their students well, including their hopes and fears and lives outside of mathematics, and to treat them with love and respect." This is important to me because it means treating every student as an individual with their own lives, hopes, goals, and struggles, and to use all of that to treat them with the love and respect they need to succeed. It is important to understand that students have lives outside of school and they can be impacted by many factors that we might not see on the surface. Everyone is a person and deserves to be treated as such. A favorable condition that I liked a lot was recognizing student achievement. This stood out to me because in my personal experience, I had the most fun and felt the most confident in math when my teacher praised me, told me how good I was doing, and congratulated me on my work. This fosters an encouraging environment where students want to succeed and feel good about themselves for learning. This is the condition that made me feel the most like a rockstar, whether the achievement was big or small.

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The quote that stood out to me was "If we create the most favorable conditions we can for all students, we’ll equip them to enjoy mathematics all their lives.". This reminded me that in all of the experiences that we offer our students, our greatest hope is for them to enjoy math for their lives, not just to make good grades. So much of our focus in school is on grades, but this quote reminds me that our work is not so that our students can get good grades. Our focus is on creating students who are curious about the world around them and that they see math is everywhere. The "favorable condition" that stuck with me the most was creating a safe environment that welcomes mistakes. So many student's hatred of math comes from the stress of always having to get it right. I hope to create a classroom culture that allows my students to embrace the mistakes.

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A quote that stood out to me was, “She jumped into her not-knowing with both feet, making as big and public a splash as she could.”  This quote stood out to me because it is a great way of phrasing the concept of being bold and tackling the unknown.  I liked the fact that it could be applied to both mathematics and life in general.  It is also important serve as a model and example for students.

The favorable condition that resonated most with me would be creating a classroom that is a safe space for all; I think it is important to make students feel comfortable in their learning environment, as that can have a direct correlation with their abilities to take risks, develop a growth mindset, and to become an amazing mathematician.  Having a safe classroom allows students to understand that it’s okay to make mistakes or be wrong and tells them that they won’t be reprimanded for it, but rather they can grow from it and continue learning.

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The quote that stood out the most to me was, "Our math classes can and should be vibrant social communities, full of curiosity and questions, perplexity and joy, seriousness and passion, because that’s what it means to do mathematics." I chose this quote because I love the term "vibrant social communities." I love what it stands for: communication, rapport, enthusiasm, and acceptance! In the math classroom, it is easy to get discouraged or even bored, if we as teachers can provide an experience in math that fosters curiosity, we are helping students to build good habits around investigating and proving themselves wrong! The favorable conditions that most resonate with me are mistake-making and intuitive thinking! I have fallen in love with the idea of taking risks and being proud of our mistakes with "Woah! Hold up!" moments, essentially catching ourselves in the act. Additionally, intuitive thinking is a major point of instruction for me. What do you think the answer may look like? Can you guestimate/estimate? Can you imagine how the factors, divisors, or addends may behave? Using questions like these can pique student interest and model productive internal rapport. It is my hope that I may teach my students to walk through math problems as if they were real mathematicians... because they are!

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The quote that stood out to me the most was, "the words were hardly out of Ann’s mouth when Lisa(the student) stood up and stepped into the safe space her teacher created." I love the visual representation of a safe place being something that is to be stepped into, and a student chooses to be brave, and vulnerable. But, that safe place has to be created, nurtured, maintained, and available for all students.

A "favorable condition" would be to acknowledge that you don't always know the answer, but you're willing to learn and explore with your students, even though you're the teacher. I especially love how the teacher in this chapter allowed her students to use their innate curiosity to explore math. I think a large reason why students are uninterested in math is that it's viewed as 'already explored territory,' with nothing new to discover, with only one right destination reached with boring, step-by-step directions on GPS.

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The quote that stood out to me the most was Reuben Hersh and Vera John-Steiner writing, “People aren’t born disliking math. They learn to dislike it in school” (2011, 305). This stood out to me because it made me think about a time when I didn't mind math. However, over time throughout my school years, I began to dislike math more and more and I resonated with this quote. After reading about teachers Ann, Jen, Heidi, Shawn, and Debbie I realize that math is something we can help students learn to love instead of dislike. This is a concept I will apply in my future classroom so my students can grow in their abilities and have the opportunity to love math.

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A quote that stood out to me was how the professor at the college in the chapter was talking about the math classes at his college. It says students are “provided with a supportive environment including: careful and considerate teaching
by a well-trained and dedicated faculty, continual encouragement, successful (stu-
dent) role models, enough success to develop self-esteem, enough time to develop intellectually, recognition of their achievement, and the belief that the study is a worthwhile endeavor.” I picked this one because J think that it encapsulates this book entirely. It’s up to the math teacher to not only teach but to give students confidence. He said something important in that quote, which was referring to students internal intrinsic motivation. The professor says that if students are given enough confidence and reassurance, they will personally believe in themselves that they are capable. This is why the students in the story took calculus as an elective!