These reflections were developed during my teaching credential coursework. They capture how I engaged with complex topics and began forming my own perspective as an educator.
Each piece reflects my thinking at a specific point in time, and together they show how that thinking has evolved. I share them here as part of my ongoing development in education, grounded in critical analysis, reflection, and practice.
If these reflections resonate with you, please follow me on LinkedIn: Nadiya Mamalyga | LinkedIn
Encouraging Cultural Communication In My Classroom – September, 2025
Cultural communication is very important. It opens up the field, and learning and appreciating other cultures in addition to your own. It helps students feel accepted and also appreciate their cultural heritage.
I am also a former English Language Learner (ELL). I immigrated to the United States from Ukraine at age 13. I spent two years in an ESL classroom, and even now I sometimes find it hard to catch up to native English speakers, although I consider myself fluent. This experience makes me especially sensitive to students who come from other cultures and linguistic backgrounds. I know how it feels to arrive in a new country, navigate a language that is not your own, and adjust to unfamiliar customs and cultures.
I can share my experiences to build rapport with my students. By sharing aspects of my own culture as an act of vulnerability, I can encourage students to share elements of their cultures in ways that feel comfortable to them. The main goal is to provide a safe space where students can be themselves and where open minds listen as they share what matters to them.
Insensitive responses such as “We don’t do this here,” or “You are not there now,” or “You are wrong” can shut down a student’s identity by imposing another one on them. Historically, colonizers often imposed their own norms, making local people feel that their culture was inferior. We still have much to learn from these lessons. This dynamic of cultural oppression is unfortunately universal, regardless of who is the oppressor and who is oppressed.
The way forward is through extending an olive branch – a teacher’s act of openness, vulnerability, and reconciliation. This aligns with culturally empathetic teaching, which emphasizes relational trust. I need to show them they do not have to wear a mask of conformity. They are accepted as they are. Everyone can maintain their own customs, culture, views, and interests. Being sensitive to and appreciative of differences is part of growing into a well-rounded and curious young adult. Understanding that others may hold different views is part of becoming a more empathetic person, and this must be taught in the classroom. Therefore, I will begin by establishing classroom expectations for a safe space and facilitating a discussion of cultural appreciation that we will formalize into our classroom community norms.
Cultural Appreciation of Mathematics – September 2025
My content area is mathematics. As we explore culture and new ways of teaching mathematics, I will ask students to investigate how mathematics is practiced in their own cultures. Many problems can have more than one valid solution or method. Problems arise in different contexts and can be explained in other ways. What matters most is logical reasoning and critical thinking, alongside clarity and accuracy. Students commonly encounter Western mathematics traditions through rule-based problem sets. However, I can link grade-level standards to historical challenges, such as those faced by the Aztecs. This approach will keep students engaged, build cultural connections, and promote creativity. I will start by asking my students whether they know any mathematicians from their country or community, as well as any mathematical accomplishments of their ancestors. I can then prepare a standards-based lesson that incorporates these cultural contributions. The students might role-play as an engineering team building a Maya monument or solve a problem faced in another civilization. I would then ask them to reflect on how it connects to today’s world. I am not looking for a five-paragraph essay. Even a single sentence such as, “I did not realize that my ancestors contributed to mathematics,” would demonstrate appreciation of their culture and mathematical understanding. Another interesting activity would be to ask students what cultural impression they would want someone from another culture to take away from our classroom community. This would challenge students to pull everything together: their culture, the main lesson, and their role as part of a community, leaving an impact on someone else.
Reflection on the “Pedagogy of the Oppressed” article – September 2025
What stuck out to me when reading this article is the use of the banking system as a model for learning. Identifying teachers and students as bank accounts and describing learning as a transaction where information is transferred from the teacher’s account to the student’s account is unique but also illustrates its shortcomings. It is transactional and leaves little room for creativity. In this system, the transaction either succeeds, and students accomplish their academic goals, or it fails, and students disengage, often leaving with a dislike of mathematics. A teacher in the next class then has several jobs to do: rebuild the student’s confidence in mathematics, close learning gaps, and support mastery of new material.
How would this affect my teaching? I am a mathematics teacher. In the traditional sense, the easiest way for me to teach would be to stand at the whiteboard and have students copy notes and solve problems. In this situation, I would risk acting as an oppressor, forcing information onto students who would have little choice in the matter.
The question is whether the goal of this process is to use the most straightforward method or the most engaging method. Is the point to transfer information, or to inspire students to learn? Should students be made to sit and absorb information without any choice in the matter, or become co-creators of this process through guided exploration?
Are students required to memorize solutions and regurgitate them on homework and tests, or encouraged to find their own creative solutions and support them with critical reasoning? Students can interpret problems in various ways and apply different models to develop a more comprehensive understanding of the problem. Whether through a data set, algebraic equations, a number line, or a graph visualization, the problem can come to life, resisting the banking model, rather than remaining just numbers and formulas on a page.
Making more textured mathematics lessons – September, 2025
I can make the lesson more engaging by using mathematics to bring students’ everyday experiences to life. For example, if they live in an area that experienced a weather disaster, I might use this context to solve problems. I might discuss how we calculate the total damage, how housing prices might have been affected, how interest rates changed, how much more debt the average person might carry, and how much effort it would take to recover from such an event.
I suggest having students work in groups and write a letter from the perspective of a local community leader to Washington, reporting on a particular problem they are analyzing and proposing a solution. This would encourage critical thinking, mathematical reasoning, and citizenship.
By taking ownership of a problem and proposing a solution, students can prepare to take these reins when the time comes. It is excellent practice for them, since our subconscious minds respond similarly to imagined experiences as to real ones.
In addition to these scenarios, I encourage students to approach the problem through modeling in various ways. They may look at the problem as a set of data points and analyze it statistically. Students may generate diagrams and graphs. They may draw a picture or write an equation. Asking students to show all work will promote logical reasoning, even if there is no time to go in depth on proofs.
My thoughts about strategically pushing the status quo – September, 2025
I personally define pushing the status quo as noticing if the current standards and practices do not work and then thinking creatively about solutions and alternatives. My subject is math. Specifically, if teaching in the prescribed way does not produce results on tests, I cannot wait for the system to catch up. I need to make changes in my classroom today. What is more important is that my students truly understand math, which means I need to take action rather than sit on the sidelines.
I am constantly curious and a lifelong learner – this is what I expect from my students, too. I value giving it your all and going all in. Giving up is not an option, even when it gets hard. I would rather investigate solutions that might take longer but still lead to success than give up upfront. I analyze my choices at every step; if a choice I made yesterday is not optimal, I change it. That’s exactly how solving math problems works – many problems have multiple ways to solve them, but some of them are better than others.
I do not have a “my way or the highway” mindset, and I want to encourage my students to have an open mind. I don’t yet have enough experience to question the curriculum, but as I get it, I will. I intend to choose materials that are more inclusive of my students, such as learning about math contributions from their cultures. When addressing outdated lessons, I would brainstorm an alternate method of teaching that learning objective. I plan to try out different methods and then let students co-create with me for future classes by sharing their feedback on their experiences.
Students can question assumptions by learning logical and mathematical arguments – these are called proofs in math and can be used even in a non-standard way. Once I build up my own problem library, we won’t have to rely only on the standard textbook. A teacher I am observing in early fieldwork is doing exactly this.
I will offer extra help to everyone. For students who are doing well and want to help others, I will encourage this. Even though I only have two hands, if high-performing students help, we can make a bigger difference.
I am learning about high-level cognitive tasks and would like to use them as much as possible. I plan to have smaller, more frequent assignments and multiple paths for success. Of course, it will take me some time to build up to that, so I may need to start with more traditional methods. I am going to be fair by using rubrics – these will become more detailed as I gain experience.
Solving real-world problems is central in math, whether it is calculating how long it will take a local community to recover from a weather disaster or evaluating business opportunities. Mathematics is a delicate balance of independent mastery, building, and collaboration. I will work on both. I want to help students look at any situation critically and not just accept what society gives them.
One way I do this is by giving my students real-world problems. For example, I can give my students a real-world problem, such as the sandals purchase with sales tax and a gift card, and have them form groups to explore as many different solution methods as they can before adapting the problem to their own situations. The added bonus is having a set of problems that the class is encouraged to solve independently or together for more practice. This way, students are not just following a textbook procedure but creating and solving problems that connect to their lives, which is how I push against the status quo in my classroom.
Reflection on “Teaching being rachetdemic” – October, 2025
I found that at the beginning of the TED Talk, Emdin highlights the misconception that students from lower-performing schools or from not-so-good neighborhoods may have lower abilities (Emdin, 2021). When he mentioned that he was discouraged from hanging out with kids from those schools, it suggests that, by not being from those schools, the system implied he was better. I picked up that this is not a “fault” of the students, but because they have much more to deal with; what else can you expect? Thus, having different expectations and metrics for students of different backgrounds suggests that students come from either bright or boxed-in environments. Emdin challenges this by arguing that adults need to ensure that students in more challenging environments also have the same opportunities. When I came to the United States, I was in an ESL class for two years. I did not really feel out of place, but the teacher used me as an example to encourage other students to speak English. I did not have another student to speak Ukrainian with, so the teacher said, “Look at Nadiya; she does not have anyone to speak her language with. She must speak English. Can you try to do the same?” The expectation was that, since I did not have the guardrails of speaking my language, others in the class should not have used them either. My adaptation was simple: I had to speak English, and over time I felt more comfortable. This aligns with Emdin’s message: students will come from different backgrounds, and just as my ESL teacher helped me get more comfortable, I should do the same. The rainbow part implies that we should bring hope even in the most challenging spaces. We should be the rainbows in our students’ lives. We should prioritize safety and let them be themselves in a world that forces them to conform. In this way, the students will develop their own rainbows as well.
References (APA 7th edition):
1. Emdin, C. (2021, July). Teaching & being ratchetdemic[Video]. TED Conferences. https://www.ted.com/talks/christopher_emdin_teaching_being_rachetdemic
Resilience to challenges reflection – October, 2025
“Life is not what you alone make it. Life is the input of everyone who touched your life and every experience that entered it. We are all part of one another.” Yuri Kochiyama
When I think about this quote, I am amazed at both the people whom I have worked with and the challenges that have arisen on my path. Overcoming the challenges in some way has propelled me more than working with and learning from people who have helped me. I say this because overcoming what has seemed a roadblock and a dead end at the time challenged me to think creatively and dig deeper in myself than I have before. I think of a story about a tortoise and the hare frequently. And I frequently align myself more with the tortoise. This is because while it sometimes seems that my achievements and rewards are not coming to the surface, I persevere and not give up. I constantly revise and optimize my course and am not afraid to try something new. And as I say that I realize the ironic theme…tortoise really? Right now, I am taking 5 classes? I am planning to apply for an internship track. These two concepts seem contradictory. I think the truth in this is that we all have both elements of the tortoise and the hare in us. We need to persevere when things get tough and be grateful when we are “cruising”. We need to recognize everyone that challenges us and molds us into a diamond under high pressure just as much as those who are our cheerleader and coaches. As a future teacher this shows me that I can be both caring and there for my students and at the same time challenge them to be their best.
What safe space looks like in my classroom. – October, 2025
For me safe space means that everyone is respected and everyone’s point of view is considered. A student can make mistakes and learn from them. A student does not have to “get it” from the first try. A student can come to class with a learning debt, and I will do my best to catch that student up. That person does not need to feel embarrassed for not knowing or not understanding something or getting it wrong. The same goes for needing material to be presented in a different way or adjusted for ELL. What a student cannot do is anything that will make the learning environment not safe for other students. It is ok to disagree if it is respectful.
I would build trust by modeling how to be vulnerable to my students. I would model making mistakes and sincerely apologize to my students and thank them for helping me get better. On the first day, I would co-create a set of norms with the whole class. We would also define how we expect to treat each other in class and during group work. If a student crosses a boundary, I will work this out in restorative circles. I would state that everyone is valued in the classroom, and if a student cannot communicate because of a language barrier, everyone needs to try harder to make that student welcome. I would encourage students to feel safe emotionally. I would also use reflection exercises and gratitude practices. In the math context, something like “I am grateful that I understand percentages now” or “I am grateful that I am working on understanding percentages now. I am not there yet, but I am getting closer.” In doing this, I would also promote the growth mindset and being a lifelong scholar.
I would have posters that encourage logical reasoning and problem-solving. As a math class, I would need it quiet but not dead quiet. Of course, I would welcome collaboration. I would greet students by saying that I am happy that they are here in class. If someone is disengaged, I would not draw attention to it. At the end of the class, I would ask that student to stay and just say that I am here for that student…Or perhaps say to everyone that I am here for anyone who needs to talk in hopes that that person will take this on. Instead of asking directly, “Are you safe?” I would ask them what they would need to see in a classroom that is safe. I would implement a restorative and mindfulness circle. I would have team and community-building activities there so that the class can work through their issues and become more comfortable working together. I would say that mistakes are a part of learning and that by trying hard to solve problems, we challenge ourselves to be better. I would ask the class what kinds of problems they would like to solve in the context of the class material. I would address all issues in a restorative circle rather than punishment. I would provide an anonymous feedback mechanism. For parents I would try to put everything in perspective, if it is another child getting in trouble, I would ask them how they would feel if this would be their child and then I would explain the method of restorative circles to them.
Using senses to plan lessons – November, 2025
I have a lesson in mind that I have seen on several platforms. I would ask students for their favorite entrée, dessert, or drink. Then I would ask them to describe it, providing us with all the details. For my ELL students, I would give sentence frames to guide them. After we know what it is, what it tastes like, what it smells like, what it looks like, and if it makes any sound, as in the example of a drink, we can then incorporate math. We can make a recipe. Is it fruit punch, or pizza, or a turnover, or pie, or banana bread? How much of each ingredient is required? What if we double or halve the amount needed? What if the price for each ingredient is different? Now, let’s introduce sales tax. Would it impact the end price? In what way? In Chapter 4, German encourages us to allow students to experience the material with multiple senses. This works well when learning and analyzing math concepts. Students are encouraged to examine data points, graph the data set, experiment with the manipulatives, and explain in plain language why specific observations are accurate. This works well, as we would teach students visualization and mindfulness skills simultaneously. This would also enable students to be exposed to different cultures, as the example from a student from an Indian family would be different from that of a student from a Mexican family. It would enable students to learn math while at the same time appreciating their own cultures and the cultures of their classmates.
Reflections on Mindfulness – November, 2025
The interview of Mel Robins and Dr. James Doty was very inspiring. Actually I found two more interviews with Dr. Doty and listened to the summary of Mind Magic as well. This was partly because I believe in and was inspired by his message and partly because I am still sick and while I am coughing out of my lungs it helped me be more mindful. I can certainly say that I wish every 12 year old has someone who can teach them mindfulness and visualization. I would even say that this has to start even earlier. Yesterday I noticed my daughter start building these blocks. I heard her say “I am stupid”, she is 6. While I already started working on mindfulness techniques with my 8 year old son, I did not realize that I need to work on this with my daughter as well. I am saying this because In my case I am interested in the subject and I can look for mindful intervention strategies. Many kids do not have this. In fact many families think that mindfulness and manifestation are a form of excuse seeking and wu wu. This makes it increasingly necessary for teachers to be equipped to provide such support. Children as early as kindergarten need to be gently pattern interrupted. They need to be told that they are seen. They need help reframing their little bricks once they come up with them. It is easy to say “Toughen up and just do what you need to do!” It is like throwing them off the deep end and say “Just swim”. It is all good but you need to first teach them how to swim. I would like to provide a safe space for my students to open up to me if they want to and I want to be that woman in their lives.
Reflection on learning environment in education – January 2026
This week I learned that the school campus is a unique environment where freedom of speech, religion, and expression must be handled differently due to the developmental stage of students. Younger audiences may form their views based on what they observe from authority figures. Because of this, both students and teachers are permitted to express themselves only to the extent that such expression does not interfere with the learning process, student safety, or equity. Teachers, in particular, are held to higher standards because of their role in shaping young minds.
Teachers are protected under freedom of speech; however, that protection is limited by professional responsibility. Teachers are expected to exercise sound judgment in areas such as student expression, religion, and safety, ensuring that their actions do not influence, persuade, or harm students. This can be especially challenging when navigating religion and other sensitive or controversial topics. While these beliefs may feel personal or harmless, they can be interpreted differently by students and families. Unlike universities, where debate is encouraged, K–12 settings must prioritize protecting students and maintaining objectivity.
Equity plays a critical role in these decisions. Both teachers and students are free to practice their religion, but they are not free to impose or promote those beliefs. This distinction reinforces the idea that teachers function more as public servants than private individuals. As a result, a teacher’s personal identity and public presence must be managed with care and respect.
Cell phone use, social media, and technology further emphasize the importance of intentional decision-making. Technology can support learning when used purposefully and monitored appropriately, but it can also distract from instruction or cause harm if misused. School policies and legal guidelines exist to ensure that these tools are used in ways that support a safe and effective learning environment.
In summary, learning about these legal and ethical boundaries has increased my awareness of the responsibility that comes with being a future educator. Understanding these limitations helps me recognize the importance of holding myself to high professional standards and making intentional choices that protect students while respecting individual expression.
Union Representation and “Right-to-work” – February 2026
My three main takeaways from this class were understanding the role of union representation, learning what “right-to-work” means, and engaging in the case study discussions.
I had not previously understood the structure of union representation and found it especially interesting how union representatives support and protect teachers. I also learned about the importance of communicating bargained agreements and, when necessary, bringing in an independent mediator to resolve disputes.
The concept of “right-to-work” was new to me. I learned that in cases of a reduction in force, such as those occurring around March 16, a teacher’s contract may still be maintained for an additional year. This helped me better understand the protections and procedures that exist within the system.
During the case study portion, I looked for the corresponding agreement in my local district and found it somewhat difficult to locate. That experience highlighted how important it is for educators to be familiar with where to find and interpret these agreements.
It was also eye-opening to examine Education Code 48910 and Article XXXIII, Section 3, related to student behavior and suspension. As a group, we discussed several key questions: What is the appropriate response? Does the situation constitute a grievance? Should the student have been sent to another classroom? Why did the teacher follow the principal’s direction? Why did the student remain in the class? These questions led to a thoughtful and engaging discussion.
Finally, reviewing the eight different case scenarios was valuable. It allowed the class to explore a range of situations and consider how policy and professional judgment apply in real contexts.
Overall, this class deepened my understanding of the legal and procedural framework that supports teachers, and it reinforced the importance of being informed, prepared, and intentional in professional decision-making.
State Assessment Data vs. Street Data – February 2026
State assessment data refers to standardized metrics used to measure student performance against established academic standards. These assessments allow states to compare schools and districts and identify patterns in student learning. Because test questions are aligned to specific standards, missed items can reveal achievement gaps. Schools are then held accountable and required to develop plans to address those gaps.
While this data provides structure and comparability, it can also have unintended effects. Students may experience anxiety tied to performance outcomes or internalize lower scores as indicators of failure. This is particularly important in California, which serves the largest population of English Learners (ELs) in the nation. The ELPAC system categorizes students by proficiency levels and supports their progression toward fluency, but it also highlights the complexity of measuring learning for students developing language skills alongside academic content.
Street data, by contrast, refers to qualitative and contextual information that is not captured by standardized assessments. This includes student voice, lived experiences, cultural and linguistic background, classroom observations, restorative practices, and whether students feel safe, seen, and supported in their learning environment.
Street data provides a more comprehensive understanding of student learning by placing performance within context. For example, an English Learner may score lower on a standardized assessment while simultaneously working harder than a peer who is not learning a new language. The same may be true for a student with an Individualized Education Program (IEP). I have experienced this firsthand during my own journey as an English Learner.
Students often do not need more checklists or additional assignments. Many are already motivated to improve. What they need are appropriate scaffolding, clarity, and support as they develop both academic understanding and language proficiency.
Both state assessment data and street data aim to improve student outcomes and inform instructional decisions, but they approach equity differently. State assessment data measures equity through subgroup performance and standardized benchmarks. Street data examines equity through lived experience, identity, and access to meaningful participation in learning.
As an educator, integrating both forms of data allows for more effective support. Quantitative measures provide structure and accountability, while qualitative insight ensures that instruction remains responsive, humane, and grounded in the realities of students’ experiences.
Integrating Technology and AI in the Mathematics Classroom – February 2026
There are many ways to integrate technology into a mathematics classroom. I currently use tools such as Google Classroom for communication and assignment organization. While I am still using a personal account for practice, this will transition to a district account once it becomes available. I also incorporate tools like Desmos to make mathematical concepts more interactive and engaging.
When it comes to artificial intelligence, the conversation often falls into two extremes: using AI as a “homework robot” or not using it at all. In practice, neither approach is effective. Today’s learning environment requires a structured middle ground.
Students are at a disadvantage if they are not exposed to safe and responsible AI use. With clearly defined expectations, AI can provide individualized support that would be difficult to replicate in a full classroom setting. As a teacher, it is my responsibility to establish those norms and monitor how these tools are used, intervening when necessary.
The goal is not to replace teacher–student interaction, but to extend it. AI should function as a student coach, not an answer key. For example, students can complete their work independently and then use AI to analyze patterns in their mistakes, identify misconceptions, and receive guided hints. The AI can prompt students to justify each step, explain their reasoning, and gradually reduce scaffolding rather than provide final answers.
This type of support mirrors what a teacher might do in one-on-one instruction, but at a scale that becomes possible with technology. It creates a different kind of interactivity, where students engage in structured problem-solving while receiving immediate, responsive feedback.
Because AI operates within the norms I define, it allows me to provide feedback to all students simultaneously while also identifying patterns across the class. Students benefit from individualized guidance, and I can use broader insights to adjust instruction and improve lesson design.
In this model, both students and teacher maintain independence and agency, while technology extends what is possible within the classroom. AI becomes a facilitator of learning, supporting clarity, reflection, and steady progress rather than replacing the work of thinking.
Standard of Care in the Mathematics Classroom – March 2026
The concept of standard of care has several important implications for me as a future single-subject mathematics teacher. Because my credential allows me to teach students from sixth through twelfth grade, it is my responsibility to understand what level of supervision is appropriate across this range and how it differs from younger age groups.
Educators are expected to exercise reasonable prudence and act with the same level of responsibility as other professionals in similar circumstances (Essex, pp. 168–183). This includes anticipating foreseeable risks and providing appropriate supervision, including monitoring student behavior and decision-making. Failure to meet this standard may result in legal consequences for both the teacher and the district.
In a middle- or high-school math classroom, the types of risks differ from those found in early childhood settings. While constant physical vigilance is not required in the same way as in TK or kindergarten, students between the ages of eleven and eighteen may still make unsafe or impulsive decisions. These can include rough play, misuse of materials, poor judgment during transitions, or bullying. Such behaviors create foreseeable risks that require active supervision and timely intervention. This reinforces the need to remain attentive to students’ developmental maturity and adjust supervision accordingly (Essex, p. 170).
At the high school level, particularly among juniors and seniors, students are often given greater independence. However, unless they are legally adults, they remain minors, and the responsibility for supervision still rests with the teacher. Even for students who are eighteen, the professional duty of care continues. Maintaining a safe classroom environment, monitoring peer interactions, and preventing foreseeable harm remain essential responsibilities.
The key implication for me is that teaching extends beyond delivering mathematical content. It requires the consistent exercise of legally informed professional judgment to ensure that students’ safety and developmental needs are met. Understanding the standard of care reinforces that I serve not only as an instructional leader, but also as a responsible steward of the classroom environment.
