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After watching the video, respond to the following question: Why is promoting conceptual understanding CRMT? (1 point)

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After watching the video, respond to the following question: Why is promoting conceptual understanding CRMT? (1 point)

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Building Conceptual Understanding in Mathematics

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After watching the video, answer: 1)What are some of the protocols for number talks? 2)How do Number Talks address the tenets of CRMT? (2 points)

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After watching the video, answer: 1)What are some of the protocols for number talks? 2)How do Number Talks address the tenets of CRMT? (2 points)

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Highlight a powerful sentence and reflect: insights/wonderings/connections? (1 point)

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Highlight a powerful sentence and reflect: insights/wonderings/connections? (1 point)

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Most days in Molly Schaefer's 8th grade geometry class, her students are focused on math concepts-learning about radians or cross-sections of three-dimensional figures. But one Friday about a month before the coronavirus closed schools, the objective on the board didn't have anything to do with equations or shapes.

Instead, the goal was self-reflection: naming the emotions the students would need to be successful in math class this year and in the future.

The lesson was part of a pilot program developed by math educators in the Howard County, Md., schools. The program aims to counteract students' fears that they don't have what it takes to succeed in math class, and it's built on the insight that children can have strong emotions around academics-and those emotions can sabotage learning.

Though the program-a supplement to the more standard math curriculum-is tiny now, plans call for its expansion to 8th grade math classrooms across the 59,000-student district.

Research backs the idea that emotions and outlook play a role in math performance. Math anxiety has been linked to avoidance of the subject and worse math performance over time. It's a factor that many teachers say they're confronting in the classroom. In a representative survey of U.S. teachers this year, 67 percent told the Education Week Research Center that math anxiety was a challenge for their students.

"I remember, my first year [with the program], being completely taken aback by the number of people who wrote negative things about themselves and their math ability," said Schaefer, who teaches the curriculum in both on-level and gifted and talented math courses at Murray Hill Middle School.

Jon Wray, the district's coordinator of secondary mathematics, knows that it might seem strange to talk so much about feelings and attitudes in math class. When a team of teachers, coaches, and district instructional specialists was first developing the curriculum, he remembers thinking the activities seemed more like health-class lessons.

But reading student reflections on the subject made him realize just how personal and fraught students' relationships with math can be. "If we don't attend to students' emotions in the math classroom," Wray said, "we're missing a huge piece of supporting them."

And giving students an outlet to talk about their feelings and their lives is even more important now with schools shut down in the shadow of the coronavirus pandemic, Schaefer said. With learning resources online, she plans to continue the curriculum, called StoryStrong, in modified form.

Wray adds that it's important that the program continue next year, whether school buildings are open or instruction is still remote. "What's become abundantly clear is the importance of supporting student well-being as a top priority," he said.

'A Lot of Fear'

Back in February, in the classroom, Schaefer told her students that they would spend the class period thinking about their strongest memories of doing math-and the emotions associated with those memories.

She aired a clip from "Inside Out," an animated movie about the inner life of a young girl, Riley, in which her emotions-joy, fear, anger, sadness, and disgust-are personified as individual characters. The video depicted Riley's earliest memories and the emotional weight they carried.

The students, 8th graders in a gifted and talented geometry class, watched, laughing with their deskmates at the jokes on screen.

"I really pushed for having all of the 8th graders do [StoryStrong]," Schaefer had said earlier, in an interview. Even the students in her gifted and talented classes have "a lot of fear" when it comes to math, she noted.

"They're hesitant to show that they don't have all of the answers," she said. "It might be, 'I'm afraid to be found that I don't belong here. That I don't belong in an above-grade-level class.' A lot of kids feel the pressure of 'I'm not smart.' "

That pressure was evident as Schaefer asked students to reflect on the character Riley's defining memories and share their own "math moments"-experiences that shaped the way they thought about themselves or the subject.

Some remembered fun activities-a student who mentioned making orange juice as part of an Algebra 1 lesson received a chorus of "ohs" and "I remember thats" from the class. But others brought up moments that had caused them to question their math abilities beginning in the early grades.

One student talked about dropping down to on-grade-level math from an advanced class in 2nd grade. Another remembered her insecurity when she started in gifted and talented classes in 6th grade. "Everyone else knew what they were doing, and I just sat there, not knowing anything," she said.

"There's a lot of emotion tied up in your schoolwork, because that's what you're doing right now. That's what you spend most of your day on," Schaefer told the class.

She asked students to reflect in writing: How could they have responded to those moments to get the outcome they wanted? What had they learned about themselves? What emotions did they want to bring into math class going forward?

"Confidence," said one student, naming the emotion she wanted in a follow-up discussion, "so I don't second-guess my answers."

Forward-Looking Approach

The math curriculum is one piece of the larger StoryStrong program in the district, which started a few years ago, said Wray.

It began as an English/language arts unit in high school classes in which students wrote personal stories with the option to perform them live at a countywide event. "It's designed to tap into the power of personal narrative and student voice," Wray said.

The math-specific curriculum is still in early stages-Schaefer is the only teacher who uses it in the district-but Wray wants to see it expanded to all 8th grade math classes.

Eighth grade is a critical year, noted David Yeager, an associate professor of psychology and an expert in "growth mindset" at the University of Texas at Austin. Math performance in that year is one of the biggest predictors of students' progress in the subject in high school.

So, Yeager and other experts say, helping students get into a positive frame of mind-building their belief that they can get smarter at math with work and the right help-is worthwhile. But there are some cautions involved.

By 8th grade, students already have a history with math-and developing a mindset of growth rather than one predicated on fixed intelligence can be a challenge. "Beliefs change is a tricky thing," Yeager said. "It doesn't help to dwell too much on what you used to believe and what you should believe, especially when you're talking about teenagers. They're not dying to be told to believe something different."

For example, one lesson in the StoryStrong curriculum asks students to talk to their families about their math history. That kind of activity could have mixed results: Some research has shown that thinking about family members' dislike of math can actually encourage a more fixed mindset in children, Yeager said.

But a lot depends on framing, he added. Teachers could take a more forward-looking approach, talking about their class as a place where students are constantly trying to improve.

Studies have shown that community is an important factor in developing mindset: If a student's peer group doesn't have a growth mindset, the student is less likely to have one, Yeager said. The StoryStrong program includes some activities that build community around math, asking students to work together to describe a class identity.

The curriculum doesn't just focus on students' perception of their abilities, though-it also addresses their emotions. And that reflects a growing interest among psychologists, Yeager said. Researchers are investigating whether recasting feelings of stress and anxiety can be an important part of improving performance.

Yeager said schools should be thinking about how to create "mindset-supportive" environments. But he cautions that attempts to foster more positive attitudes and emotions around math don't happen in a vacuum.

"Classroom context matters," he said. If students are told to try hard problems and think creatively but aren't given opportunities to do that, "the idea that you can learn and improve feels less true."

Pause and Reflect

There aren't any data yet on the math pilot's effect on student achievement, Wray said. But anecdotally, Schaefer said, it's changed some students' relationship to the subject.

StoryStrong offers an opportunity to pause and reflect on the challenges posed by fears and frustrations, she said. "A lot of times they don't know what's holding them back, so they don't get to move beyond it."

During the school shutdown, StoryStrong math lessons remain available for Schaefer's students to access online. But the lessons are optional, she said, and condensed. In distance learning, Schaefer has a lot less time with her students than she would have had if they were in class together.

Normally toward the end of the school year, Schaefer said, she's talking to her 8th graders about high school. She prompts them to be more self-reliant in class, reminding them that habits of working hard with a can-do attitude will support them as they move to more challenging courses.

Now she's approaching her distance learning the way she used to approach StoryStrong lessons in the classroom: giving students an outlet to explain how they are feeling-about their math progress, and about the seismic changes the shutdowns have caused. Said Schaefer: "This is an emotional thing."

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Who's Afraid of Math? Turns Out, Lots of Students

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Most days in Molly Schaefer's 8th grade geometry class, her students are focused on math concepts-learning about radians or cross-sections of three-dimensional figures. But one Friday about a month before the coronavirus closed schools, the objective on the board didn't have anything to do with equations or shapes.

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Promoting conceptual understanding is CRMT because it allows student to have a better understanding of what they are doing mathematically instead of just completing a step by step process with no real information as to why they are taking these steps, why and how they work and what they actually mean. Gaining conceptual understanding of math allows students to apply what they have learned in other areas of their lives and not just to get by in the classroom. Priscilla Mercado

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Number talks remind me of socratic discussions except for the quiet time which really allows the student to think about what has been presented to them without the distraction of others.
Number talks have to be planned strategically so that they are meaningful. Explicitly modeling without distraction is key so that students are fully engaged and aware of their responsibilities once the activity takes place. This activity is CRMT because it holds students accountable and allows them to piggyback off of each others thoughts and addresses all components of CRMT. Priscilla Mercado

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“a lot of fear” I decided to highlight this because that is the feeling I have always felt toward math. The fear of math has haunted me my entire life, especially now that I have to teach it to students and even more so now that I have to pass a CST because my entire career depends on it. I thought I was done with math but here we are! I hope that my daughter is better at it than I am, so that she is not haunted by it as well. Priscilla Mercado

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Promoting conceptual understanding CRMT is fundamental so that students are able to comprehend at a more profound level the topic that is being imparted to them. Hence, so that students understand the reasoning behind what they are learning so that when they are learning other concepts they are able to apply what they already know. Conceptual understanding CRMT is important because it enables students to build connections amongst concepts. The students are able to utilize the knowledge that they have grasped and use it to acquire new concepts. Additionally, the students are able to deeply understand how the concepts are connected and apply it in their educational career. Lastly, promoting conceptual understanding CRMT is essential because the students would learn the subject and use it across other areas of their lives. Based on the video, CRMT would allow the students to "Apply the principle, ideas and computational skills that they develop and work and solve that problem." - Ivy Polanco

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“ Yeager said schools should be thinking about how to create “mindset-supportive” environments.” This was a powerful sentence because as I finished reading this article, I questioned myself: Am I fostering a mindset-supportive environment for my students? This school year, I am not currently teaching math. But I’m part of the RTI team. Once a week,  I pull out a group of students that are performing at a low-grade level in math. I have never taken the time to ask them how they feel about math. I agree with the author of this article that it’s essential to know how the students feel about math.  So that I can help them build a positive frame of mind about math, knowing that they can get better at it with hard work and my help.  Daisy Cano

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One of the protocols for number talks is to allow students a lot of thinking time. Students can use hand signals to show their thinking to enable others to continue thinking. Creating a culture where students are comfortable in that quiet thinking time allows every student to be valued for slow deep thinking, not quick superficial thinking. This protocol addresses the tenets of CRMT  by enabling students to engage in math conversations by sharing their answers and strategies for solving the problem. In addition, Number Talks fosters opportunities to learn from others by repeating another student's strategy using their own words. Daisy Cano

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Number talks are discussions between the students and teacher. Some of the protocols for number talks incorporates that the instructor seats near the students. For number talk, it is very essential that the students use hand signals to communicate their response so that it allows their peers to have "quiet think time." Essentially, at the beginning of the school year, the teachers needs to model number hand signals so that when students share their responses to any question they use their hand signals and it allows other students to think about their response as other use their hands to make signs. Hence, so that a classroom environment is created were the students are all quietly thinking about their response. Then, the teacher records all possible response and the students articulate how they solved the problem. The teacher can promote thinking by asking students a question such as "did you do it another way."  Number Talks address the tenets of CRMT because it allows students to identify the reasoning behind the problem and they are able to apply what they learn to other concepts that they are learning. Also, it address the tenets of CRMT because the students do not memorize how to get the answer but they identify the why and the how. The students reason about how to get the answer and they are able to apply it to other mathematical concepts. - Ivy Polanco

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A connection that I made with the article "Who's Afraid of Math? Turns Out, Lots of students" is when Schwartz establishes in her article based on an interview that even the gifted and talented students have a lot of fear of math. Honestly, when I read this section of the article I made a direct connection because growing up I feared math. Thus, when I lived in the Dominican Republics I did not performed well in the subject. I knew that I could learn it, if I study the math. But, I was scared of math and its complex terminology. Moreso because I have alway love reading and I felt that reading and writing came naturally to me. I made a connection with this section of the article because I felt the same way about math growing up. -Ivy Polanco

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Promoting Conceptual understanding is CRMT because it is essential to understand the meaning of the procedure of how something is done to apply those principles and computational ideas to new problems. Therefore, it requires more than applying a formula to understand and grasp a problem. Instead, we encourage students to think deeply about the problems by promoting conceptual understanding.  Daisy Cano

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Provide opportunities for students to identify, define, and create patterns and relationships. Students build conceptual understanding when they look for patterns, make use of structure, and make generalizations. Angela Moncada

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Provide opportunities for students to identify, define, and create patterns and relationships. Students build conceptual understanding when they look for patterns, make use of structure, and make generalizations. Angela Moncada

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Some protocols for  numbertalks.Pose a problem.Allow thinking time. When a student has a strategy, he puts a thumb to his chest. The Benefits of Number TalksThey encourage students to be flexible with numbers (one of the big goals of fact fluency!). They foster a safe space for making mistakes. They allow students to explore important connections and relationships. Angela

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Mathematics is a topic that, when approached with curiosity, can help a student unfold their thinking in a way that makes sense to them. Making meaning of mathematics is foundational to success. Supporting children’s development of a positive math identity by allowing them to navigate understanding in a way that feels authentic to them is foundational, too. Angela

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The Number Talks Protocol is as follows.  Students go to the front of the room and sit on the carpet with nothing in their hands.  No paper, no writing instruments.  The teacher puts an image or problem on the board and the students need to do mental math to figure it out.  Once the student thinks they have an answer they put a thumbs up on their chest.  If the student can think of multiplie strategies to solve the problem then they put the number of strategies on their chest.  The teacher then selects 2 or 3 students to give the answer to the problem and the student must explain how they solved the problem.  What I love about Number Talks is that students must verbalize how they came up with their answer, they must be able to explain their strategy to their classmates.  Not only does this give the teacher a great assessment of what students unerstand but it also allows for students to learn from one another.  Clelia Milan

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The Number Talks Protocol is as follows.  Students go to the front of the room and sit on the carpet with nothing in their hands.  No paper, no writing instruments.  The teacher puts an image or problem on the board and the students need to do mental math to figure it out.  Once the student thinks they have an answer they put a thumbs up on their chest.  If the student can think of multiplie strategies to solve the problem then they put the number of strategies on their chest.  The teacher then selects 2 or 3 students to give the answer to the problem and the student must explain how they solved the problem.  What I love about Number Talks is that students must verbalize how they came up with their answer, they must be able to explain their strategy to their classmates.  Not only does this give the teacher a great assessment of what students unerstand but it also allows for students to learn from one another.  Clelia Milan

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One of the best ways for students to learn and understand content is for them to see patterns or make connections between the content and the real world.  By making real-life connections to content students can learn quicker and actually remember what they learn versus memorization. Clelia Milan 

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One of the best ways for students to learn and understand content is for them to see patterns or make connections between the content and the real world.  By making real-life connections to content students can learn quicker and actually remember what they learn versus memorization. Clelia Milan 

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“Confidence,” said one student, naming the emotion she wanted in a follow-up discussion, “so I don’t second-guess my answers.” was the sentence that stood out for me.   I always remember as a child second guessing my answers in math.  It is such an amazing feeling when you are 100% sure of an answer but when you aren't it is such a horrible feeling.  Not fully understanding math concepts is what leads to the feeling of uncertainty or that lack of confidence.  Clelia Milan

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“Confidence,” said one student, naming the emotion she wanted in a follow-up discussion, “so I don’t second-guess my answers.” was the sentence that stood out for me.   I always remember as a child second guessing my answers in math.  It is such an amazing feeling when you are 100% sure of an answer but when you aren't it is such a horrible feeling.  Not fully understanding math concepts is what leads to the feeling of uncertainty or that lack of confidence.  Clelia Milan

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Promoting conceptual understanding is CRMT because it allows us to facilitate math classes where students are encouraged to do the heavy lifting. If students understand core math principles, then they can transfer them easily between subjects. The video gives the example of 199+199, and the different ways students can go about solving it. Students creatively use their funds of knowledge to find unique ways to solve math problems in ways that are transferable and applicable to their future learning. - Samuel Acosta

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Quiet think time is an essential protocol of the number talk. It allows all students to completely think about the problem without the social pressure of raising your hand first. This is essential to CRMT because it allows students to practice mentally solving problems and thinking about it in multiple ways. It allows all students a space to access the problem without feeling like they have to be the first one with the answer.
- Samuel Acosta

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I highlighted the phrase "
“They’re hesitant to show that they don’t have all of the answers,” she said. “It might be, ‘I’m afraid to be found that I don’t belong here. That I don’t belong in an above-grade-level class.’ A lot of kids feel the pressure of ‘I’m not smart.’ ”

This resonated with me because I remember distinctly at which point in my public school career I gave up on math. I was placed in a higher class in 8th grade to prepare for the algebra regents, and I felt way in over my head throughout because I resented the fact that I never had the answers and I felt like I didn't belong in this math community. It was a feeling that I honestly wasn't able to shake even through college.
- Samuel Acosta

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Promoting conceptual understanding CRMT is essential because it allows students to understand the problems better and why they are learning the math concept. Students are learning math concepts, and also students are learning when they can apply the concepts to the real world. In addition, students can make connections with the real world, and they can transfer the skills and the ideas that they developed to solve new problems. Yissel Zorrilla

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One of the protocols for number talks is to have classroom conversations between the students and the teacher. The students sit near the teacher, and the students can't have any tools, papers, pencils, or calculators. Another protocol for number talks is "quiet think time"  using hand signals. When students are working quietly, it allows more students to get in on the learning. After the "quiet think time," the teacher records all possible answers; the students, one by one, share their strategies, and the teacher records each strategy. Number talks address the tenets of CRMT by giving the students enabling students to explain the strategy they use to solve the problem. Students have the opportunity to think about the different strategies they can use to solve the problem. Students have the opportunity to engage in math conversations, and all the students have enough time to think and solve the problem. Yissel Zorrilla

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“If we don’t attend to students’ emotions in the math classroom,” Wray said, “we’re missing a huge piece of supporting them.” I always loved math, but sometimes, I did not like to participate in math because I had fear and got anxious thinking that I was not doing a good job. Emotions play a significant role in learning, and it is important to ask students about their emotions and how they feel about math. Sometimes, students are afraid of participating in math; they have a lot of fear of math, thinking that the answer might be wrong. By asking the students how they feel about math, I can help my students in math to get better. Yissel Zorrilla

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Conceptual Understanding allows students to not only understand the concept but show they understand by explaining what they know to someone else. It means knowing the entire idea behind or the reason why something is what it is rather than just memorizing some rules that may not always apply.
Ana Perez

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Number talk protocols involve students to watch the teacher model without any tools in front of them. The quiet time alotted really allows students to think things through before they say or do anything to solve a problem. These both allow for students to really grasp what is happening and can give students that extra time they need to get their thoughts together. Another important aspect of number talks is that after the quiet time the teacher picks 3 ways students solved to put them up on the board and have students interact with one another to address how they came up with the answer they did and so on. How number talks addresses the tenets of CRMT is that the conceptual understanding can be taken across all content areas. They no longer memorize things just for that subject or that problem or that moment, they are building skills they can take with them across all grades to come and all subject areas. They are looking more into the why and the how of things as we do in ELA and it really opens up the horizon for deeper thinking. Students stop looking at just the numbers and start understanding the reason behind the numbers.
Ana Perez

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I found it so interesting that there is this popular fear of math. I always thought I was the only one scared of math growing up, and even still. One of my fears when becoming a teacher was having to teach math. Although daunting, it is comforting that so many other people feel the way I do about math. I realize now that the fear may come at least for me personally from not understanding it conceptually. I just remember memorizing things, and I see now that it was for the moment, for the test, for the homework. 20 years later I realize that there was no connection to conceptual understanding or CRMT when I learned the foundation of math. Everything was taught with tricks and how to skip steps and still get the answer so i never really LEARNED the concepts. I really liked that the teacher asked students to connect an emption to the way math makes them feel after watching the movie inside out. This stood out to me because I do this in my class at least once a week. As I go over my lessons and my informal assessments I tally how we are feeling about the current math versus math in general. Surprisingly, every week I get some new students on the "I love it" side and new students from the "I love it" side on the "not really loving it/Scared" side.
Ana Perez

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I highlighted the sentence "“I remember, my first year [with the program], being completely taken aback by the number of people who wrote negative things about themselves and their math ability,” This is something that hits home to me. I noticed how much my own fears of math enabled me from being great at math. I think most people have this fear of math that interferes with their actual ability to do math. Ironically after becoming a teacher, Math is my favorite subject to teach. I also make sure I build student's confidence when doing math and make sure I am tying in social emotional learning.- Greysha

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I highlighted the sentence "“I remember, my first year [with the program], being completely taken aback by the number of people who wrote negative things about themselves and their math ability,” This is something that hits home to me. I noticed how much my own fears of math enabled me from being great at math. I think most people have this fear of math that interferes with their actual ability to do math. Ironically after becoming a teacher, Math is my favorite subject to teach. I also make sure I build student's confidence when doing math and make sure I am tying in social emotional learning.- Greysha

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Conceptual understanding is CRMT because it has students think about the math problem as a story rather than numbers. It allows student to use their previous background knowledge and flexibility to solve a math problem.- Greysha

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Conceptual understanding is CRMT because it has students think about the math problem as a story rather than numbers. It allows student to use their previous background knowledge and flexibility to solve a math problem.- Greysha

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The protocols for number talk are: student led discussion, allow students thinking time, require critical thinking, the teacher is just the facilitator, while students engage on the concept, students mentally solve the problem, students share their answer. It address CRMT by allowing students to community connections.Greysha

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The protocols for number talk are: student led discussion, allow students thinking time, require critical thinking, the teacher is just the facilitator, while students engage on the concept, students mentally solve the problem, students share their answer. It address CRMT by allowing students to community connections.Greysha

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Simply teaching students is a concept or rule is not enough. Students should be able to underrate why they are learning what they are learning. Conceptual understanding helps students get a deeper understanding and apply what they learning to real world scenarios.  -Leylin

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Simply teaching students is a concept or rule is not enough. Students should be able to underrate why they are learning what they are learning. Conceptual understanding helps students get a deeper understanding and apply what they learning to real world scenarios.  -Leylin

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Number talks help students develop "accuracy, efficiency, and flexibility."  Protocols for number talks include allowing the students to discuss the problem. writing down stunts' answers, allowing students to share their strategies, and the teacher names the math in each strategy. -Leylin

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Number talks help students develop "accuracy, efficiency, and flexibility."  Protocols for number talks include allowing the students to discuss the problem. writing down stunts' answers, allowing students to share their strategies, and the teacher names the math in each strategy. -Leylin

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I highlighted the phrase. “If we don’t attend to students’ emotions in the math classroom,” It makes a lot of sense to address student's emotions when teaching math. I've noticed that students who lack confidence in their math skills are more likely to give up when leaning a new math topic. We should empower them and give the confidence to persevere. -Leylin

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I highlighted the phrase. “If we don’t attend to students’ emotions in the math classroom,” It makes a lot of sense to address student's emotions when teaching math. I've noticed that students who lack confidence in their math skills are more likely to give up when leaning a new math topic. We should empower them and give the confidence to persevere. -Leylin

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"“They’re hesitant to show that they don’t have all of the answers,” she said. “It might be, ‘I’m afraid to be found that I don’t belong here. That I don’t belong in an above-grade-level class.’ A lot of kids feel the pressure of ‘I’m not smart.’ ”"... I have felt like this in math, where it is discouraging to not have the correct answer as the rest of my peers. People in general can live in fear of "failure" therefore, it is important to have positive reinforcement in math and to keep on trying.

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Number talks can have students also relay on their ELA skills by using the strategies to focus on the writing and language presented. I like the idea of students using hand singles where they can step away from the fear of being wrong in math and value the thinking of the students by providing a free space for quite thinking time.

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Promoting conceptual understanding CRMT is because students also needs to know how to understand the problem besides knowing how to solve the problem. If they know all the procedural steps to solve a problem but they should think and ask "why" to get the full understanding of the math problem.

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It's important to promote conceptual understanding because it allows people to gain more meaningful knowledge that they can use in different situations, improving their ability to make good decisions and solve problems.

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Number Talks includes using open-ended questions and promoting multiple strategies to solving a problem. They promote CRMT because it increases student engagement and most importantly it also allows students to reason more deeply so they can have a richer understanding of math.

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“If we don’t attend to students’ emotions in the math classroom, we’re missing a huge piece of supporting them.” This quote is powerful because it highlights the importance of addressing students' emotional well-being in the classroom, especially in subjects such as math where anxiety can impact just how much they are learning, which then leads to a domino effect of the student never catching-up. Educators need to create an environment where students feel supported and their emotional needs are met, which can lead to better outcomes in the classroom.

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Conceptual understanding is important because it shows students how to apply math in ways that go beyond the conventional rules. They can explain and rationalize problems in a way that allows them to make connections that go beyond computations and keywords.  Liz Mata

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Promoting conceptual understanding in math is so important. Watching this video was very interesting and made a lot of sense. We were taught all these key words and shortcuts and tricks but never were taught to explore the question being asked and how to solve it in multiple ways and using our own ways to explore math. I think it's important for kids to make the connection when subtracting and using division in the examples in the video

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For number talk you have to make sure students are focused on what they see without the use of pencils, papers, ect. and using hand cues to make sure that they aren't talking or being discouraged when someone raises their hand. This would fit perfectly with CRMT as an opening. I use math talks before my math lesson to get students attention and focus onto math and to get them thinking. It's definitely a difficult concept because I have to think about what I want to show and to make sure it can get them thinking. I also wasn't good with the hand gestures and watching this video showed me something I would like to have up in the room and use

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“Everyone else knew what they were doing, and I just sat there, not knowing anything,” she said. I picked this out because this is how every student in my class was feeling inside individually until I had a conversation with them. A lot of them doubt themselves even when they're right or are wrong and are terrified of being wrong. I had to stop that day and really just speak to them and make them understand that these feelings are normal but that they weren't alone and that others may feel that way to sometimes. I just decided it was best to focus on them and their feelings and take a step back from the math lesson.

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Promoting conceptual understanding CRMT is a great alternative to allow students to solve problems and be able to explain mathematical concept and connect with previous learned knowledge and applied in different subjects. It encourages student to think in a deeper level and provide a reason why.

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For a successful number talk protocols, teacher needs to ensure that students go to the meeting area without any tools that could get them distraídos. Teacher needs to model her expectations and students must be engage. Students will need time to think before share their with a partner and/or whole class discussion.

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Quiero resaltar esta oración, "If we don’t attend to students’ emotions in the math classroom,” porque es muy importante reconocer cuando nuestros estudiantes no se siente bien o emocionalmente necesitan nuestra ayuda. Muchas veces mis estudiantes vienen triste al salón de clase y cuando se siente así se les hace un poco difícil concentrarse y participar en la clase. Cuando es así, yo hablo con ellos y les ayudo a buscar alternativas para que se sientan mejor. Luego de darle apoyo el estudiante se incorpora a la clase con mejor estado de animo y participa en la clase. Es muy importante brindar apoyo a las emociones de nuestros estudiantes.

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Promoting conceptual understanding is CRMT because it gives students the ability to take what they know and explain it and apply it. Students already have funds of knowledge and some understanding of math and so promoting conceptual understanding allows them to solidify what they know into memory.

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Math talks uses quiet thinking time to find strategies to solve a problem on the board or strategically think about a math image. Students have no tools other than their minds in order to think on the problem or image being shown. Students use hand signals to show that they are still thinking, have a solution. The job of the teacher is to facilitate discussions and record strategies that students have come up with. This strategy helps students build accuracy, efficiency and flexibility in their problem solving. It also allows students to flex their mental math skills. Math Talks follow the tenets of CRMT in that it allows students to engage in discussions to problem solve. Both build strategies build connection with the subject being taught that is not limited to the what the text books says. Liz Mata

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The program aims to counteract students’ fears that they don’t have what it takes to succeed in math class, and it’s built on the insight that children can have strong emotions around academics—and those emotions can sabotage learning.

I love that SEL is being used in what I think isn an unconventional way. Many subjects give students anxiety. Giving students a space to share their insecurities and come to a better head space can lead to improvements in academics. Liz Mata

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Promoting conceptual is extremely important in learning especially how and why this can be applied to when it is done in math procedures and applications in word problems or any problems in math. -Denisse 

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Promoting conceptual is extremely important in learning especially how and why this can be applied to when it is done in math procedures and applications in word problems or any problems in math. -Denisse 

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Math talk is a great way for student engangment. This is done with no materials. Depending on the problem, they are using their mental math as well as preparing themselves how to have a conservation using mathematic language (sum, product etc).- Denisse 

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Math talk is a great way for student engangment. This is done with no materials. Depending on the problem, they are using their mental math as well as preparing themselves how to have a conservation using mathematic language (sum, product etc).- Denisse 

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“They’re hesitant to show that they don’t have all of the answers,” she said. “It might be, ‘I’m afraid to be found that I don’t belong here. That I don’t belong in an above-grade-level class.’ A lot of kids feel the pressure of ‘I’m not smart.’ ” - Wow, in my school Dual language is always compared to our TAG class. I have a-lot of non fluent Spanish kids in my class and most of the time they are always saying 'idk why my mom put me in this class knowing i am not capable'. This applies throughout all subjects, especially in Math. I always give a pep talk to not only those students but to the whole class that even though we are not in TAG we are DUAL, which means we are TAG. -Denisse

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Promoting Conceptual Understanding is important it helps students gain a better understanding of the concepts. Students are able to take the concepts they have learned and applied it beyond the classroom.  - Paola Espinosa

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Promoting Conceptual Understanding is important it helps students gain a better understanding of the concepts. Students are able to take the concepts they have learned and applied it beyond the classroom.  - Paola Espinosa

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Some of the protocols of number talks include quiet thinking time which is very beneficial for students and allows other students who might take longer to have an opportunity to solve a problem. It addresses CRMT because teachers should be considering the student's culture and prior knowledge as they are planning these lessons. Equally important is that students are not taught to memorize strategies but rather understand the why's of the problem- Paola Espinosa

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Some of the protocols of number talks include quiet thinking time which is very beneficial for students and allows other students who might take longer to have an opportunity to solve a problem. It addresses CRMT because teachers should be considering the student's culture and prior knowledge as they are planning these lessons. Equally important is that students are not taught to memorize strategies but rather understand the why's of the problem- Paola Espinosa

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The phrase I highlighted is “I remember, my first year [with the program], being completely taken aback by the number of people who wrote negative things about themselves and their math ability,”. I connected with this because all my life I had a negative perspective of my Math abilities. After reading this article it helps me understand how this mentality hinders my learning and in many ways becomes a self fulfilling prophecy whenever I did poorly in math. As teachers it is important to understand how thoughts like these hurt our students in the classroom. - Paola Espinosa

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The phrase I highlighted is “I remember, my first year [with the program], being completely taken aback by the number of people who wrote negative things about themselves and their math ability,”. I connected with this because all my life I had a negative perspective of my Math abilities. After reading this article it helps me understand how this mentality hinders my learning and in many ways becomes a self fulfilling prophecy whenever I did poorly in math. As teachers it is important to understand how thoughts like these hurt our students in the classroom. - Paola Espinosa

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The quote "The program aims to counteract students’ fears that they don’t have what it takes to succeed in math class" resonates with me. As a student, I liked math but only when it was a concept I could understand. If the material was something that was too difficult for me to understand, it made me not like math. As a teacher, I am still intimidated by certain math concepts. Because I still feel this way as a teacher, I know just how much the students may feel like they are incapable. Feeling this way as a teacher has made me take extra steps to be able to teach concepts and be there to push my students to know they can do whatever it is as long as they work hard. -Joselyn Aponte

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One essential protocol of numbers talks is quiet thinking time. This allows students to focus on the problem at hand without focusing on if other students know the answer right away (such as raising a hand right away to answer) This can give students the time to think of different strategies to use and gives them the space to be comfortable in coming up with a response.
- Joselyn Aponte

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Promoting conceptual understanding is CRMT. This is because it allows students to learn math concepts while applying them in different ways. When learning math concepts, it is important to know the why as well. This can help students understanding of math concepts while allowing them to think freely about a strategy. It allows them to read, analyze, and solve a problem using a strategy of their choosing, or multiple strategies.
-Joselyn Aponte

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Promoting understanding in mathematics is considered culturally responsive teaching because it acknowledges and honors the diversity of students' cultural backgrounds and experiences. Culturally responsive teaching recognizes that students come from different cultures and communities, and they bring with them unique ways of knowing, learning, and understanding.

This approach helps students see mathematics as relevant and meaningful to their lives, which can increase their engagement and motivation to learn.
- German

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Number talks are a powerful tool for implementing culturally responsive mathematics teaching, because they address several of its key tenets. Such as

1. Building on students' prior knowledge and experiences

2. Emphasizing multiple ways of solving problems

3. Providing opportunities for collaboration and communication

4. Focusing on conceptual understanding

5. Valuing and affirming students' identities

This creates a classroom environment that values and builds on students' prior knowledge and experiences, celebrates diverse ways of thinking, and emphasizes the importance of conceptual understanding and communication.

- German

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“They’re hesitant to show that they don’t have all of the answers,” she said. “It might be, ‘I’m afraid to be found out that I don’t belong here. That I don’t belong in an above-grade-level class.’ A lot of kids feel the pressure of ‘I’m not smart.’ ”

This strikes a chord with me, I see this so frequently in my school, that I am afraid that I am becoming numb to it. I do not wish to just accept the silence, but I do my best to try and create a safe enough environment, where my students are praised for making any attempt even if it is just speaking. At times I even load my lessons with problems or responses that I know they will fight over to respond too.

- German

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Promoting conceptual understanding is important because it allows for students to make connections within the classroom but as well as outside of the classroom. It allows their knowledge from both to come together and promote a better understanding of the topic being taught. It also allows students to transfer their knowledge to outside of the classroom as opposed to just telling students to memorize rules and steps.

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Some of the protocols for number talks is how teachers use that time efficiently to model and have students full attention. By calling students to a meeting area while modeling and allowing no tools for students gives less room for distractions. This allows for students to take in as much as possible and use to discuss with their classmates

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I highlighted the statement "if we don't attend to students' emotions in the math classroom..." This sentence stood out to me because this is very apparent with many students during math lessons. They don't feel as confident with their work and answers. This does not allow students to feel comfortable with sharing their answers in fear that they will be ridiculed by their peers. It is so important as a teacher to address and validate those feelings and as well to create an environment that talks through mistakes and allows them as opposed to shutting them down.

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Rigorous is a word that comes up a lot when teaching math is being discussed but not really what that means. The how and the why are the most important parts of math but sometimes that gets overlooked or skipped in favor of rules and shortcuts. Promoting conceptual understanding helps students learn math more deeply, in different ways, and helps them apply mathematical knowledge to their lives.

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Rigorous is a word that comes up a lot when teaching math is being discussed but not really what that means. The how and the why are the most important parts of math but sometimes that gets overlooked or skipped in favor of rules and shortcuts. Promoting conceptual understanding helps students learn math more deeply, in different ways, and helps them apply mathematical knowledge to their lives.

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Two important parts of number talks are that students should come to the front of the class in a semi circle or carpet near the teacher and with a clear view of each other. Second, they should come to the front with no tools except themselves and their brains. Number talks allow space and time for everyone to solve math problems in their own time, and using their own strategies. Students are also given the opportunity to use their academic vocabulary to converse with each other.

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Two important parts of number talks are that students should come to the front of the class in a semi circle or carpet near the teacher and with a clear view of each other. Second, they should come to the front with no tools except themselves and their brains. Number talks allow space and time for everyone to solve math problems in their own time, and using their own strategies. Students are also given the opportunity to use their academic vocabulary to converse with each other.

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I highlighted "The program aims to counteract students’ fears that they don’t have what it takes to succeed in math class, and it’s built on the insight that children can have strong emotions around academics—and those emotions can sabotage learning." I had an experience with a student early this year that struggles with math. He didn't enjoy doing the work and would find ways to distract himself. I made sure to always include him in my small groups. Over time he became more confident in himself. One day, after correctly answering several questions, he exclaimed happily "OM G, I'm finally starting to understand it." After that moment his behavior changed and he became more engaged in math and it was like having a completely different student. He was much more confident and willing to take risks and learn.

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I highlighted "The program aims to counteract students’ fears that they don’t have what it takes to succeed in math class, and it’s built on the insight that children can have strong emotions around academics—and those emotions can sabotage learning." I had an experience with a student early this year that struggles with math. He didn't enjoy doing the work and would find ways to distract himself. I made sure to always include him in my small groups. Over time he became more confident in himself. One day, after correctly answering several questions, he exclaimed happily "OM G, I'm finally starting to understand it." After that moment his behavior changed and he became more engaged in math and it was like having a completely different student. He was much more confident and willing to take risks and learn.