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As educators, it is our job to facilitate and guide the creation of positive mathematical identities for our students. Students deserve a teacher who is knowledgeable and curious, one that fosters a consistently positive outlook on the subject of math. If our students do not sense importance, they will not pay attention. However if we utilize instruction that helps our students see themselves as mathematicians, we are instilling further engagement and importance.

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When assessing a student's performance in math, there are so many structural barriers that prevent accurate perceptions - this is especially true for our marginalized students.

Segregating structures like tracking leaves our students without opportunities for growth. High stakes assessments are often biased and leave POC students in a box of "lower" achievement. Curriculum is often unrelatable or relevant to student lives and communities leaving students unengaged and disinterested.

When assessing our students, we need to use as many forms and varieties of data as possible to gain an accurate understanding of their knowledge. Students should additionally be given consistent opportunities to work with different peers who have different levels of understanding to allow for growth. Finally, instruction needs to obtain relatable and relevant content.

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A key component in learning is having some sort of personal relevance or connection to the material. Far too often, math is taught without making connections to the world or communities students live in. It is important to show students the purposes of math, and how it can be used to solve real world problems. It is vital to relate the math content to things students can conceptualize, things they see in daily life. Without these connections, it becomes easy for students to believe math isn't important or relevant to them. When we show students that math is indeed for them, they can see/feel the purposes and uses.

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Students need conceptual understandings in mathematics in order to truly gain knowledge. If students don't conceptualize the "why" of what they are doing in a mathematical problem, then authentic understanding is not being reached.

Catalyzing change emphasizes that memorization is not enough in math education, and that it is far too often the focus in the elementary level. Instead, students should be focused on the "how" and "why."

I made a connection with a division lesson I witnessed in a previous practicum; students were being told to memorize the procedures - additionally, language like "carry over" and "drop down" was being used. Students had no conceptual understanding of how place value of was being impacted when they moved these digits - it was just a memorized procedure.

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After watching the video, I reflected on my own attitudes toward math. Sometimes math could be frustrating for me. I had a teacher that turned that around for me when I wasn't in the advanced math class and he was able to push me up the next year. I think that some of my negative feelings about math stem from that experience of not being in the advanced class. I was in advanced English and it made me feel insufficient in math and I started to see math as my weak point. I feel that the labels on classes makes it inequitable.

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Continuous checks for understanding during lessons are important to ensure that they are learning. We should also be collecting different forms of evidence to check understanding so that we are not assessing in one way. The complication with developing meaning is that high-stakes testing is prioritized in school. However, these assessments are rooted in privilege and result in segregating students.

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In implementing equitable mathematics instruction it is also helpful to include the student's grownups. If sending home a letter to parents there should be translated versions as needed and the language in the notes should not be full of jargon. We want their families to feel included in their child's education. The idea of including their family was something that was discussed in the presentation. It is our responsibility to make our math accessible to our students and also to their grownups if they are working on it with them at home. We can further develop our practices as well and learn about research-informed practices through professional development opportunities.

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It is important to not label students as "slow" or "behind," but it is also equally important not to label other students as "high achievers" or "gifted." Students notice what label they are pinned with. It is especially noticeable when you do grouping. To create equitable structures in mathematics I feel it is important to encourage all students in math and not to set them up on a deficit track. A useful tool for this is collaborating with other educators and continuing to learn more about new practices.

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Students need to know the importance of math. A great book that I own is "What's the point of math?" This book helps students see how math is used daily and how significant it is. I think this book is a great tool to broaden the purposes of learning mathematics. It is helpful to remind them that math can become a career, but when you neglect the everyday purposes you lose the children who may not want a career in math. Therefore, providing the significance of math day-to-day is vital.

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For the best success in a math classroom, it is important that the students are understanding the concepts they are being taught. Teachers should make sure to do check-ins and assessments regularly to monitor how well the students are processing the information they are learning. By doing this, each student will have a better chance to be able to succeed so that they are not  behind and are able to go further with a positive education in mathematics.

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For equitable mathematics instruction to be implemented, teachers should display passion and a positive attitude towards what they are teaching to their students. It is really easy to tell when a teacher does not care about what they are teaching, and that will reflect onto the student. If a teacher shows excitement for the students to learn a new material, the students will have a much more beneficial experience. It is also important to have the right knowledge of the material that is being taught so the students are getting the proper information.

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Creating equitable structures in mathematics should be done so all students can learn together and no one feels like they are not as smart as their peers. This feeling can cause a student to give up and not care to learn.

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In order to broaden the purpose of learning mathematics, I think it is important to have math incorporated in life daily by families. Getting children involved and curious about math will cause them to start to gain an understanding and want to learn. Students will begin to see the importance of math and how math is not only used in a classroom, but in the real world.

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After watching the video I realized that you want to be passionate when teaching math. You want to build the learned as confident and capable, you want to really dig deep in mathematics, they want to think of "themselves as a doer in mathematics". This should be "fostered" in early childhood.

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When developing deep mathematical understanding is strong support for teachers, as well as administrative support. You always want to support your teacher. The importance of getting everyone on the same page on what deep mathematics looks like. You want to provide materials for the teachers to be able to teach well. You want to make sure to stay positive. I also read that you want to make sure you have a pathway for the students, allowing them to advance each year and take different math courses.

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When teaching the information, you want to make sure that you are well informed about the information you are giving to the children. You also want to make sure you want to work with collaborative partners, that will help students essentially better understand more about mathematics. You also always want to make sure you are consistent with your teaching strategies, so you don't confuse the students.

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To create an equitable structure in mathematics you don't want to group the students together based on the ability of the child as well as challenging spaces with privilege. You don't want to do this because students are smart, they will notice if you put them in a certain grouping, this could make the student try less.

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In my opinion, broadening the purposes of learning mathematics is to have more focus on key content areas as well as implementing instructional practices that can help students have high-quality learning opportunities. You can broaden the purposes of learning mathematics also by seeing in what ways you can work with children, educators, and families. If you engage more with the students, that will bring the students more joy and make students want to learn more.

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A strategy to build equitable structures in mathematics is to stop using labels such as 'gifted'. Labels have an impact on how children see themselves and could be the reason as to why a child is not able to thrive in math.

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Based on the video, there are many things that overlap. The one major idea across all four categories is to collaborate with not just the students but with other educators, administrators, and parents.

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A teacher should believe they are a doer of mathematics and portray math in a positive way because this will allow the students to be more confident in their own math skills and be able to identify as a doer of mathematics.

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If a math lesson does not incorporate students learning needs then are they actually deeply understanding the material? I believe teachers need to incorporate a variety of things within a lesson such as observation, conversations, and written work. Doing this can satisfy students learning needs while also allowing the students to become doers of mathematics.

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I believe a good way to broaden the purposes of learning mathematics is to invite families into the classrooms. This can allow the parents to work with their kids and get a better understanding of how math is different from when they took math in school. In addition, this can help the student build a positive mathematical attitude.