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The first two chapters of Mathematical Mindsets set the foundation for the book's content. Chapter 1 emphasized that all students are capable of learning; we just have to take the time to figure out what works best for different students. Chapter 2 stands out the most with its emphasis on mistakes. Making mistakes is the biggest part of our learning process. We must view mistakes as progress and a positive thing versus a negative outcome. This will help to boost the students confidence in themselves while learning.

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Chapter 3 of Mathematical Mindsets focuses on the importance of thinking of mathematics as something that can be creative and beautiful. She encourages students to explore and discover rather than having them memorize rules. Visualization is one of the most important strategies that should be implemented in every math class. Visualization can help students tremendously. It gives them concrete examples of concepts that can be hard to understand.

Chapter 4 talks more about the power of mistakes and struggles on a neurological level. it emphasizes that mistakes grow the brain and can contribute to creating new neural pathways. One thing that stands out to me the most is I never realized how much traditional learning can negatively impact our students. It has been taught for many years that mistakes are bad and you would get points taken away. Boaler's focus on the importance of mistakes has helped me to realize that it is crucial to our learning that students make mistakes and are not penalized for it but rather they are praised for realizing the mistakes and being able to fix them.

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Reflection #3: 5 Principals of Extraordinary Math Teaching & Number Sense

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Reflection #3: 5 Principals of Extraordinary Math Teaching & Number Sense

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These two videos both emphasize the importance of making math fun. They focus on the importance of making mistakes and critical thinking. Number sense helps students to develop good intuition about numbers and their relationships. Students have a different experience with their numbers because we come from other environments. What stood out most to me was the video on the 5 principles of extraordinary math teaching. In this video, he mentioned, "When we are not comfortable with math, we do not question the authority of numbers". This quote struck a nerve in me and gave me the biggest ah-ha moment I have had in my teaching journey so far. It is so clear that the less we know about numbers the more we automatically accept them as correct. We could have no idea what a statistic means if we are not comfortable with math and understand the weight that numbers have on our lives.

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Reflection #4: The beauty of mathematics

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Reflection #4: The beauty of mathematics

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This week's readings and video show how math is used daily. We emphasize the importance of play and how it encourages the brain to think critically and encourages exploration and discovery. The article "Mathematics for Human Flourishing" gives us five important reasons for mathematics: play, beauty, truth, justice, and love. Of these five concepts, play is what stands out to me the most. Growing up, I always loved math, but not because I thought it was fun. I loved it because it was easy and was a subject that made the most sense to me. But, looking at math now from a teacher's perspective, I can see all the ways and benefits of making math fun. We encourage play because it can foster perseverance and hopefulness. it gives students the ability to make mistakes without them feeling like they are. Play can be used to help with so many different areas of math such as patterns, place value and so many more. This can deepen their understanding and reasoning skills.

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Reflection #5: Chapter 5 and Math needs a makeover video

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Reflection #5: Chapter 5 and Math needs a makeover video

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Both of these resources show the importance of number sense and developing a strong mathematical foundation. Chapter 5 of Mathematical Mindsets stood out most to me because of its emphasis on fluency through understanding. It is SO important that our students are confident in their mathematical foundation. Yes, there is a need for memorization of certain basic facts, but memorization is not the foundation of mathematics. Decomposing and using visuals are just two examples of ways we can enhance learning math in a way that engages students. She also starts to mention the dangers of timed tests. This relates also to the video on the 5 principles of extraordinary math when he says students need time to struggle for thinking to occur. when we take away time for struggle, we force students to memorize instead of critically thinking and coming up with the right answer on their own.

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Reflection #6: Chapter 6, Podcast and TODOS

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Reflection #6: Chapter 6, Podcast and TODOS

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All three of these resources cover equity and cultural inclusion in the classroom but in their unique ways. A lot of these methods have been introduced because of our current learning environment as well as the COVID-19 pandemic. Going through this pandemic has caused a tremendous amount of social and emotional obstacles that children have had to face at home and school. One thing that stands out to me the most is the conversation between Dr.Seda and Dr.Brown. They discussed different techniques to incorporate into the classroom that make abstract concepts more tangible. A few of their ideas were collaborative learning, real-world problem-solving examples, and manipulatives. My personal favorite is the use of manipulatives in a classroom. I have seen firsthand how impactful physical elements can be in a classroom. More often than not, a majority of students in a classroom are visual or tactile learners, so having these manipulatives helps them to understand important foundational concepts. Chapter 6 in Mathematical Mindsets also covers the same information but with more emphasis on girls and students of color being the two groups that are affected the most. The label "not math people' has been attached to these groups for years giving them the mindset that they cannot achieve what they are supposed. We also read about ability grouping and how it can be detrimental to growth. Instead, we should be grouping various learning levels together to help all students.

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Reflection #7: Mathematical Mindsets Ch. 8 & 9

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Reflection #7: Mathematical Mindsets Ch. 8 & 9

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Both chapters this week focus on growth mindset and the importance of making mistakes and struggling. One thing that stood out to me most in Ch. 8 is the mention of fixed mindsets. We often learn too late that students have a fixed mindset about their understanding of math due to early struggles and challenges. These mindsets can lead to a lot of anxiety and avoidance for math. It is so important that we establish a comforting and enjoyable learning environment at a young age so that students can foster that positive experience for future learning. We know that math has so many building blocks that are used to grow and expand. But, if you have a student who has a weak or cracked step, then the rest are bound to fall at any minute. We need to have those foundational pieces solid and firm and we as teachers are able to help establish that foundation. Tying into chapter 9, it gives us the perfect way to help build those foundational steps. We need to let students know that it is okay to struggle and make mistakes in math. without mistakes, there is no room for a growth mindset to occur. We need to give students the time and opportunities to struggle and grow.

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Reading Reflection #8: What Grandma and James Meredith Knew

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Reading Reflection #8: What Grandma and James Meredith Knew

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"Schools are a reflection of the society that designs them." pg. 18

"We operate based on our assumptions of the world." pg 21

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"How could some be so inspired and others be so disparaging of the same words?" pg 29

"The default mode of communication is the classroom lecture." pg 35

"Linguistic relativity allows us to examine how ideas can have multiple representations that may be culturally different but conceptually similar." pg 45

"Highlights how our conceptions of language, race, and cognition hinder our ability to hear what students know." pg 56

Language

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"Our knowledge is deeply connected to the situations and meaningful contexts where people learn." pg 60

"We just need the ears to hear it." pg 85

" When we fail to respect the cultural diversity that people bring to conversations, we fail to understand the intelligence of those who have incredible ideas." pg 86

Meaning

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FINAL Reading Reflection #10: Chapters 6-7

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FINAL Reading Reflection #10: Chapters 6-7

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"The goal of instructional design is to select activities that produce opportunities to generate learning." pg 105

Empower