essay about math teacher

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My Favorite Math Teacher by Brianna

Briannaof Miami's entry into Varsity Tutor's July 2014 scholarship contest

My Favorite Math Teacher by Brianna - July 2014 Scholarship Essay

A teacher who positively affected my attitude toward education was my middle school math teacher Ms. Ross. She made math easy by explaining the problems clearly as well as by giving shortcuts to solve problems. Additionally, she gave me confidence in my ability to do math as well as methods to use in the future. I believe she has positively affected my attitude towards education because she’s an example of a good teacher who has helped students improve their math skills.

Ms. Ross made math simple by giving her students quicker ways to do problems. She also worked out the problems on the board step by step which made it easier to learn. When it comes to math I’m a visual learner and I need a detailed explanation. In addition, she explained everything clearly and was always willing to help her students.

Furthermore, while I was in her class I felt more confident in my math abilities. Math is not a subject I’m strong in so I usually need a really good teacher in order for me to understand the lesson. She taught me skills that I currently use and she made it easy to remember by turning math rules into chants.

To conclude, Ms. Ross has positively impacted my opinion on education because she is one of the few exceptional math teachers I've had. Ms. Ross’ simple teaching method gave me the strategies to be successful in solving math problems. She also wouldn’t hesitate to help her students whenever they were confused. Overall she was a great teacher and pleasant person as well.

Home — Essay Samples — Education — Teacher — Why Be a Teacher: My Journey to Teaching Mathematics

Why Be a Teacher: My Journey to Teaching Mathematics

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Published: Apr 17, 2023

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Teaching Math: The Best Learning Practice Essay

Learning math is not an easy task for many students, especially if they are of a young age. It is not always interesting to deal with numbers and develop various calculating activities to meet educational standards and get high grades. However, students have to learn mathematics as an obligatory part of the elementary school system. Therefore, to facilitate a learning process and raise students’ interest, teachers offer various practices and improve their understanding of children’s needs, abilities, and expectations. The examples introduced on video lessons show that teachers may cooperate with children in a variety of ways. Still, the main task is to involve students in a learning process by giving vivid examples, clear instructions, and options to choose from. In this paper, the attention to three teaching strategies, which are explicit teaching, developmental activities to support a diversity of levels, and reflection, will be discussed and explained through the prism of mathematics classes and teachers’ intentions to improve their classroom work.

Motivation and interest are the two crucial aspects of student education. It does not matter what subject has to be learned or what activities must be developed, teachers have to make sure that their students are ready and eager to participate in classroom activities. In both videos, teachers make use of explicit teaching as the main learning practice for their students to be offered. This type of learning aims at directing student attention towards certain subjects and topics in the already established learning environment. In math classes, it is not enough for teachers to provide students with an opportunity to learn new material and follow the given instructions (Selling, 2016). Explicit learning is used to make mathematical practices interesting to students through real-life representations, generalizations, problem-solving, and justifying (Selling, 2016). When students can use their own examples and explanations of the theoretical material given, it is easy for them to realize why all these tasks cannot be ignored, and what the essence of all these tasks is.

Another significant step in classroom learning is the attention to developmental activities in terms of which a diversity of levels and group work can be taken into consideration. Student learning and achievements depend directly on the teachers’ level of professionalism (Bayar, 2014). On the one hand, following the instructions and recognizing standards cannot be ignored in the classroom. On the other hand, students may easily get bored with all those requirements being set. In both videos, teachers underline the necessity to promote development activities and observe what students can do, want to do, and try to avoid. Sometimes, it is better to observe the work of students in groups or make them work individually and investigate their strengths and weaknesses. In schools, children of different backgrounds should cooperate, demonstrating their ability to use knowledge and their tolerance for other students’ mistakes. Teachers have to underline the importance of development and create the required environment to support but never offense or reproach a child.

Finally, the teachers from both videos agree that reflection has to be one of the main learning activities in the classroom. It helps not only to clarify what students learn but also focuses on the gaps that still exist. The possibility to reflect on the already gained experience and personal progress is the skill that has to be developed through teachers’ and students’ cooperation (Kiemer, Grőschner, Pehmer, & Seidel, 2015). In addition, reflection as a learning activity has a number of crucial benefits for students. First, they learn how to use the classroom material in real life. Second, sharing their thoughts, doubts, and ideas, students are able to comprehend the true importance of mathematics. Finally, students who are able to reflect on their activities demonstrate intentions to learn new information and participate in classroom activities. Therefore, the choice of this practice is not only a sign of a high-level professionalism of an educator, but an example of how teachers should respect and support their students.

To conclude, it is necessary to say that the offered videos help to realize how to improve mathematics classes and how to choose appropriate learning activities. The justification of this choice is based not only on the benefits students may gain in the classroom. The recognition of explicit learning, developmental activities, and reflection as the best practices to study math is explained by the possibility to focus on the merits and demerits of the subject and underline the importance of student participation. Though rules and plans cannot be ignored in teaching, educators should never forget that student motivation, interest, and achievement are the core values. Students may vary in their backgrounds, personal experiences, and skills. The task of teachers is to promote development, organize group projects, and reflect on the achievement made. Math can be one of the greatest subjects for students to deal with in elementary school, and explicit learning alone with group activities and reflections can help to achieve the best results in teaching practice.

Bayar, A. (2014). The components of effective professional development activities in terms of teachers’ perspective. International Online Journal of Educational Sciences, 6 (2), 319-327.

Kiemer, K., Grőschner, A., Pehmer, A. K., & Seidel, T. (2015). Effects of a classroom discourse intervention on teachers’ practice and students’ motivation to learn mathematics and science. Learning and Instruction, 35 , 94-103.

Selling, S. K. (2016). Making mathematical practices explicit in urban middle and high school mathematics classrooms. Journal for Research in Mathematics Education, 47 (5), 505-551.

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Reflecting on My Own Math Experiences

Hi thank you so much for being here..

Welcome! I am so glad you have come across this post! My name is Julia Park and I am a senior at Millersville University! I am an Early Childhood Education major and I have learned so much so far! If you have a moment, feel free to check out my previous blog posts!

In my last post, I shared information about learning centers in math class! In this post, I will be reflecting on my mathematical journey. My experiences in math have really shaped the way I teach my students.

My Early Math Memories

I believe that early math experiences can really shape a child’s mindset towards mathematics. It has definitely shaped mine. Unfortunately, it has been a long journey of growing my interest in math, and I am still working on it! 

When I was in elementary school, even up until my time at Millersville, math has been a huge struggle for me. I have grown up with the incredibly damaging misconception that you have to be a “math person” to excel in math.  A lot of my peers had the same mindset, which made it even harder to let go of those limiting thoughts. 

I discussed this in my growth mindset blog post , but “math people” do not exist! I have my own reasons as to why I thought there were math people, but children’s experiences often vary. I think my fixed mindset was formed from experiences with not-so-nice teachers, the pressure of time limits and the need for accuracy in class, and a lack of hands-on learning. Those are just a few ideas of why I think I have had a tough time with math and I will be discussing more ideas later in this post!

Although it was hard to get through math class sometimes, I am really grateful that I have had these experiences because I can learn from them and relate to my own students. I want my students to feel comfortable with asking for help and to know that it is possible to learn and grow in many ways!

What I Have Learned From Past Teachers

Through my time as a student in math class, I have had many different experiences with a variety of teachers. I want to share the good and the bad of what I have gone through because I think it is beneficial for teachers to reflect on all experiences related to learning. We can take what we learn to inform our own teaching practices. 

Positive approaches I have learned from teachers:

• Providing assistance outside of class
• Using a hands-on learning approach
• Giving time to practice skills in class
• Utilizing interactive math games
• Facilitating class discussions 
• Being kind and encouraging when a student is struggling 

Approaches of teachers that were difficult for me: 

• Focusing on accuracy only and not effort
• Putting pressure on students to turn in extensive assignments with a limited amount of time
• Teaching new concepts too fast
• Using too many lectures and PowerPoint presentations
• Not having time to reflect on concepts in class
• Being intimidating when a student is struggling 

Every student learns differently. These experiences are unique to me and not everyone will be able to relate to what I have taken from my past math classes. However, I think it is important to recognize that although one strategy might work for one student, it might not work for another student.  This notion emphasizes the need for differentiation. I will be discussing differentiation more in the next section. 

Strategies I Want to Use to Teach Math

As I finish this semester at Millersville University, I am leaving with so many new ways of teaching math that I was not even aware of previously. I have a new passion for making math class fun and interesting for my students. The following are some examples of strategies I would love to incorporate in my future math class: 

• My math instruction will be differentiated based on my students’ needs. I will monitor their progress through various assessments and observations to modify or individualize my instruction when needed.
• Hands-on learning will be included to increase the engagement and participation of my students. I want to make math fun and exciting!!
• Class discussions will be a huge part of my mathematics instruction. Discussions in math class promote a deeper understanding of mathematical concepts in children.  
• I would love to try to use interactive notebooks to organize my students’ learning and create engaging experiences. I had not heard of these notebooks until this year and I love them!
• Technology , manipulatives , and children’s literature are just a few tools I plan on using to enhance mathematics instruction for my students. 
• Parent involvement is very important for a child’s education and I will consistently keep in contact with families to increase this involvement. 
• I am very passionate about modeling a growth mindset for my students. I want my students to believe in themselves and in their ability to grow.
• I will strive to create a safe and welcoming environment for my students. I want them to be comfortable with sharing their ideas and to not fear making mistakes. To do this, I will value effort just as much as accuracy. 

Mistakes Are Learning Opportunities!

One of the biggest lessons I have learned throughout my time at Millersville is that making mistakes is okay. I used to put so much pressure on myself to be perfect and know everything, but that is not healthy. Teachers are not robots made to feed information to students. Instead, we have a purpose to learn alongside our students and to welcome mistakes as learning opportunities.

I am much more comfortable now being honest with my students in moments of uncertainty. I would rather figure something out with them than provide them with the wrong information. It’s really fun to explore ideas with students and work together toward a common goal. These experiences with students are valuable and strengthen the student-teacher relationship. When children trust their teachers, they are more engaged, motivated, and feel an increased amount of comfort when reaching out for help and sharing their thoughts with others. 

Check out my blog post about growth mindset to learn more about the importance of making mistakes and the value of having a positive mindset in math class!

Thank you so much for reading!

I had a blast sharing my mathematical experiences with you all! I have grown so much through the years and I can’t wait to keep growing as I gain more experience. I hope you learned about some ways you can teach mathematics in your own classroom! Thank you for reading. I sincerely appreciate it!

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Hi! I am Julia Park and I'm a junior at Millersville University. I am currently studying Early Childhood Education. I am so excited to share my journey through my new blog! View all posts by Julia Park

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Qualities of a Good Math Teacher: The superpowers every math teacher needs!

Generally, mathematics is known to be a challenging subject for many students because it requires a significant amount of effort and a high level of understanding to solve complex problems. This is where a good math teacher comes in.

What are the qualities that make a great math teacher? According to research , the most common characteristics of a good math teacher include teacher behaviors, beliefs and practices, subject and pedagogical knowledge, and credentials. I also believe that a teacher who has the passion, knowledge, patience, and skills to teach mathematics can make a world of difference in a student’s life.

In this blog post, I will be discussing the qualities of a good math teacher. If you wonder whether teaching high school math is hard or not , I wrote a whole article that I encourage you to read.

Table of Contents

Qualities of a Good Math Teacher

I believe that every student deserves a math teacher who does their job with a purpose. Here are the qualities of a good math teacher; I believe that these qualities will help bring math to life, ignite curiosity, boost confidence, and deepen understanding.

Here are the fundamental qualities that make a good math teacher:

1- Passion for Teaching Mathematics

One of the most critical qualities of a good math teacher is a passion for the subject. A teacher who loves math will inspire their students to learn and engage with the material . In addition, passionate teachers usually have creative strategies and resources to make the subject exciting and enjoyable for their students.

Generally, passionate math teachers use their passion to motivate their students to work hard and never give up.

More importantly, a passionate math teacher wakes up in the morning thinking about how to make the class more engaging, how to explain a concept more simply, how to challenge students within their abilities, and how to make everyone feel successful .

2- Effective Communication Skills

The ability to communicate effectively is essential for any teacher, but I believe that it is even more critical for a math teacher. Since math can be seen as an abstract subject, a good math teacher must be able to explain complicated concepts in simple terms .

Good math teachers should also be able to break down problems and clearly explain how to solve them, which means they should also be able to listen to their students’ questions and concerns and address them.

3- Strong Knowledge of The Subject Matter

Another key quality is a sound knowledge of the subject matter. Math is not just a subject but a series of interrelated concepts and relationships that build upon themselves. A good math teacher must be a master of essential mathematical concepts .

A good math teacher should be able to explain a concept from different angles to cater to different learning styles, spot where students might face difficulty, and review what has already been learned before introducing something new.

4- Have Confidence And Show Humility

Confidence and humility are essential qualities to become a good math teacher. Generally, a confident math teacher is also willing to show humility. They are not afraid to say, “I don’t know,” or “I made a mistake.”

Knowing how to learn from mistakes is a skill that should be demonstrated to students. When a teacher acknowledges a mistake and then re-teaches and corrects it, they reinforce transparency, respect for the student, and a commitment to a culture of learning.

Being human in front of students is relatable and endearing.

5- An Effective Math Teacher is Also Patient

Patient math teachers understand that students come from different backgrounds, have different learning styles, and learn at different paces.

Patience means breaking a concept down into smaller and more manageable pieces and providing extra support for those who need it .

Patience also means waiting for those who need extra time to understand a concept. Patience fosters an atmosphere of comfort and helps to remove the stress and anxiety math can bring to even the brightest students.

6- A Successful Math Teacher Is Creative

Mathematics is a subject that can be approached through games, puzzles, and even art. I believe that infusing creativity makes math more fun and accessible to students who struggle with it .

A math teacher who can turn a class into a game show can write a riddle on the board and challenge students to solve it.

I believe that a math teacher who can tell an interesting story about the history of math, like discussing famous mathematicians and their contributions , is likely to be more effective than a teacher who only delivers from a textbook.

7- A Good Math Teacher Should Care

In addition to being patient, a good math teacher should possess a great deal of care for their students.

There will be times when some students may not grasp the material straight away and may need extra time to understand it. In these situations, it is helpful for the teacher to be caring, patient, understanding, and supportive.

A caring and patient math teacher can facilitate an environment where the student feels comfortable asking questions and sharing their ideas.

8- A Good Math Teacher Should be Adaptable

As educators, we must recognize that not every student learns in the same way. I believe that a good math teacher must be adaptable and recognize when one approach is not working .

As math teachers, we should be able to think of innovative ways to engage students who have difficulty understanding the material.

I also believe that a good teacher should present information in different formats, such as diagrams, videos, or interactive activities.

9- A Good Math Teacher Should Show Classroom Leadership

A good math teacher should be a great leader in their classroom, inspiring respect from all their students for their knowledge of mathematics and their overall actions, attitude, and actions.

A good math teacher must also respect all students regardless of their abilities, knowledge, and social backgrounds.

Moreover, good math teachers manage their classrooms well by establishing and following clear student rules and setting clear expectations.

10- A Good Math Teacher Should Be Motivating, Encouraging, and Supportive

A good math teacher should encourage and support their students continually and recognize each student’s progress and celebrate their achievements in and out of the classroom.

I strongly believe that good teacher will also mentor their students and help them develop the necessary skills to succeed in their academic and professional lives.

What to read next:

• Make Math Class Fun: 11 Tips for Teaching Math in an Interesting Way!
• 8 Key Components of a Successful Mathematics Curriculum .
• Reasons Why Teaching Middle School Math is a Challenging but Rewarding Job .
• A Step-by-Step Guide to Structuring a Math Lesson Plan .

Final Thoughts

I believe that becoming a good math teacher requires much more than just being knowledgeable in the subject matter.

Generally, the qualities of a good math teacher include building a passion for learning in their students, communicating effectively, and being caring, inspiring, patient, adaptable, and supportive. I believe that these traits can help students overcome the challenges of the subject while fostering a love for math.

As teachers, it is our responsibility to inspire and support the next generation of mathematicians, engineers, and scientists. What qualities would you like to see most in your math teacher? Share your thoughts below!

I am Altiné. I am the guy behind mathodics.com. When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting mathodics.com.

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High School Mathematics at Work

Essays and examples for the education of all students.

Traditionally, vocational mathematics and precollege mathematics have been separate in schools. But the technological world in which today's students will work and live calls for increasing connection between mathematics and its applications. Workplace-based mathematics may be good mathematics for everyone.

High School Mathematics at Work illuminates the interplay between technical and academic mathematics. This collection of thought-provoking essays—by mathematicians, educators, and other experts—is enhanced with illustrative tasks from workplace and everyday contexts that suggest ways to strengthen high school mathematical education.

This important book addresses how to make mathematical education of all students meaningful—how to meet the practical needs of students entering the work force after high school as well as the needs of students going on to postsecondary education.

The short readable essays frame basic issues, provide background, and suggest alternatives to the traditional separation between technical and academic mathematics. They are accompanied by intriguing multipart problems that illustrate how deep mathematics functions in everyday settings—from analysis of ambulance response times to energy utilization, from buying a used car to "rounding off" to simplify problems.

The book addresses the role of standards in mathematics education, discussing issues such as finding common ground between science and mathematics education standards, improving the articulation from school to work, and comparing SAT results across settings.

Experts discuss how to develop curricula so that students learn to solve problems they are likely to encounter in life—while also providing them with approaches to unfamiliar problems. The book also addresses how teachers can help prepare students for postsecondary education.

For teacher education the book explores the changing nature of pedagogy and new approaches to teacher development. What kind of teaching will allow mathematics to be a guide rather than a gatekeeper to many career paths? Essays discuss pedagogical implication in problem-centered teaching, the role of complex mathematical tasks in teacher education, and the idea of making open-ended tasks—and the student work they elicit—central to professional discourse.

High School Mathematics at Work presents thoughtful views from experts. It identifies rich possibilities for teaching mathematics and preparing students for the technological challenges of the future. This book will inform and inspire teachers, teacher educators, curriculum developers, and others involved in improving mathematics education and the capabilities of tomorrow's work force.

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Using Positive Feedback in Math Classrooms

Providing math students with positive feedback can help them clarify their thinking, take risks, and apply concepts in new contexts.

If you were a “good” math student, your teacher may have filled your papers with a checkmark next to each correct answer. But handing back “perfect work” with a slew of checkmarks is a missed opportunity for math teachers. Every time we provide a student with feedback, we have a chance to send a message. We can signal what we value and the strengths we see in the student’s work, providing insight into areas for growth and further learning. In math we value clarity and logic, creative solutions, perseverance, and curiosity. Used strategically, positive feedback can reinforce these cornerstones of the discipline. Although the examples I provide in this article are geared toward middle and high school math classes, positive feedback can be used at a variety of grade levels.

Reinforcing Effective Communication

Math teachers frequently ask students to show their work. When students give us insight into their thought processes by writing enough on the page, we can provide positive and specific comments in return. Our reinforcement helps students learn what specific aspects of their work were effective at clarifying their logic.

Here are some examples:

• Your explanation here helps me see how you got from one step to the next.
• The picture you drew helped me to understand how you’re thinking about this.
• When you defined the variable before using it, I was able to follow your reasoning.
• The sentence at the end helped me to see that this is your final answer.

All of these comments acknowledge the time that students put into explaining their reasoning. Providing positive reinforcement when students effectively convey their thought processes helps them develop into effective communicators of mathematics.

Recognizing a Mathematician’s Craft and Choices

Math teachers constantly remind their students that “there is more than one way to solve a problem.” This is true—the art of problem-solving allows students to discover elegant paths to a solution. Math talks have become popular because of their emphasis on multiple problem-solving techniques. The comments that we make on student work can reinforce the value of mathematical thinking.

You might write something like these:

• I didn’t think of this strategy!
• This is a clever implementation of factoring.
• This step reminds me of the example we looked at when _____.
• I like how you adapted the idea from _____ to this problem.

These comments will help students see their technique within the space of many pathways to a solution. When we reference the strategy that they used and contextualize it, we help them connect their problem-solving process to the content.

Celebrating Growth and Perseverance

Math is hard! Math teachers must find ways for students to grapple with the content and engage in productive struggle. If we give students credit for their progress and perseverance, we can encourage them to push through challenges the next time they arise.

Here are some examples of how you might emphasize growth and praise perseverance:

• Great job catching the mistake here.
• I can tell this was a long and messy computation. By keeping your work organized and sticking to your plan, you persevered.
• I noticed that you had trouble with this skill in the last unit, but you have mastered it now! Great job sticking with it.

Students don’t always notice their own growth. When we can point it out to them, they see that their hard work and struggle is worth it.

Encouraging Reflection

When students perform at a high level, positive comments can push their thinking beyond the standard content. With feedback, we can inspire their curiosity and encourage deeper thinking.

Here are some reflective comments you could make:

• What about this problem helped you realize that you needed this particular strategy?
• How did you check your work?
• What strategies did you use to keep track of all the steps needed to solve this problem?
• How will you remember the connection that you made here?
• What do you think would happen if the problem were slightly different? How would you have to adapt your approach?

All of these questions send the message that learning doesn’t stop at a perfect test score. We should continue to ask questions, pursue our curiosity, and find new and novel ways to apply what we’ve learned.

I hope that these ideas inspire you to provide comments beyond the simple check mark. We should be putting just as much care and attention into the feedback we provide to high-achieving students as what we give to students who need more practice.

While some may think that math teachers have it easy when it comes to grading, we shouldn’t take the easy way out. Writing a few comments might add a minute or two to the time it takes to mark a paper, but I assure you that the gains you will see in student confidence, motivation, creativity, and understanding will be worth it. By taking the time to provide meaningful, detailed, specific, and positive feedback, we provide all of our students the opportunity to grow.

Note: I wrote this piece after reading Alex Shevrin Venet’s “ How to Give Positive Feedback on Student Writing ,” because I was struck by how many of the guidelines that she provides are applicable to the math classroom. I recommend taking a look if you haven’t already!

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Math Teacher, Essay Example

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At the beginning of the school year I received student achievement records. During the first, week faculty and administration met to detail our plans for the coming months. The plans are required to contain goals for the three month mark, the six month mark, and year-end goals. As a math teacher, I must understand how well my students can apply what we learn directly to assignments, quizzes and homework. What follows are some relevant questions and my answers to them.

What will you prepare for the meeting?

Goal Setting

• Sort students in order of high to low in terms of achievement.
• Quiz students to know what they remember from last year.
• Formulate methods for bringing the lowest performing students up to speed.
• Formulate methods to keep the best performing students engaged in learning.
• Interpolate methods to keep learning from becoming too boring for everyone.

To the principal, I would report my goal setting method as well as specific strategies. Having evaluated how well my students understand concepts from last year and judging from their previous performance, I formulate a system by which better students are challenged but those less so are not frightened off by failure. Futheremore, I plan to include ways of teaching math that will keep everyone engaged in learning. The most difficult challenge a math teacher must contend with is students becoming bored with the material.

What kinds of goals might you prepare for each timeframe regardless of the student data?

Here I specify goals according to timeframes. In the first 3 moths, I expect to bring all students up to speed from last year. By the 6 th month, I expect to have a significant portion of new material covered. By the end of the year, I expect all students to pass with a sufficient understanding of the new material. By this time, last year’s material will be less important because students must sufficiently understand the concepts in order to perform at the next level.

How will you measure your goals? I will measure my goals by quizzing students on a regular basis – say, once a week, on Friday. By 3 months, I expect 90% of the students to sufficiently understand the material from last year. By 6, I expect all of the students to sufficiently understand the material from last year and 80% the students to sufficiently understand at least 60% of the new material from this year. By year’s end, I expect all students to understand at least 60% of the new material.

Imagine a scenario where at the end of the three-month period, you have met less than 50% of the goals you have set for your students. What would your two immediate next steps be? Why? My plan includes a contignecny for this secenario. If it is shown that less than 50% of the goals I have set have not been accomplished. I will set aside time to work specifically with students who are missing the mark. My reasoning is that on average a majority of students will sufficiently achive the goals I have set. If we fall below the 50% mark, it will most likely be because there are a few students who are not effectively learning the concepts. Thus, to bring them up to speed will mean reaching our year-end goal. As a math teacher, I must understand how well my students can apply what we learn directly from assignments, quizzes and homework. At the beginning of the school year I received student achievement records. During the first, week faculty and administration met to detail our plans for the coming months. Here, I have iterated my plan as mandated by the administration

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Math Essay Ideas for Students: Exploring Mathematical Concepts

Are you a student who's been tasked with writing a math essay? Don't fret! While math may seem like an abstract and daunting subject, it's actually full of fascinating concepts waiting to be explored. In this article, we'll delve into some exciting math essay ideas that will not only pique your interest but also impress your teachers. So grab your pens and calculators, and let's dive into the world of mathematics!

• The Beauty of Fibonacci Sequence

Have you ever wondered why sunflowers, pinecones, and even galaxies exhibit a mesmerizing spiral pattern? It's all thanks to the Fibonacci sequence! Explore the origin, properties, and real-world applications of this remarkable mathematical sequence. Discuss how it manifests in nature, art, and even financial markets. Unveil the hidden beauty behind these numbers and show how they shape the world around us.

• The Mathematics of Music

Did you know that music and mathematics go hand in hand? Dive into the relationship between these two seemingly unrelated fields and develop your writing skills . Explore the connection between harmonics, frequencies, and mathematical ratios. Analyze how musical scales are constructed and why certain combinations of notes create pleasant melodies while others may sound dissonant. Explore the fascinating world where numbers and melodies intertwine.

• The Geometry of Architecture

Architects have been using mathematical principles for centuries to create awe-inspiring structures. Explore the geometric concepts that underpin iconic architectural designs. From the symmetry of the Parthenon to the intricate tessellations in Islamic art, mathematics plays a crucial role in creating visually stunning buildings. Discuss the mathematical principles architects employ and how they enhance the functionality and aesthetics of their designs.

• Fractals: Nature's Infinite Complexity

Step into the mesmerizing world of fractals, where infinite complexity arises from simple patterns. Did you know that the famous Mandelbrot set , a classic example of a fractal, has been studied extensively and generated using computers? In fact, it is estimated that the Mandelbrot set requires billions of calculations to generate just a single image! This showcases the computational power and mathematical precision involved in exploring the beauty of fractal geometry.

Explore the beauty and intricacy of fractal geometry, from the famous Mandelbrot set to the Sierpinski triangle. Discuss the self-similarity and infinite iteration that define fractals and how they can be found in natural phenomena such as coastlines, clouds, and even in the structure of our lungs. Examine how fractal mathematics is applied in computer graphics, art, and the study of chaotic systems. Let the captivating world of fractals unfold before your eyes.

• The Game Theory Revolution

Game theory isn't just about playing games; it's a powerful tool used in various fields, from economics to biology. Dive into the world of strategic decision-making and explore how game theory helps us understand human behavior and predict outcomes. Discuss in your essay classic games like The Prisoner's Dilemma and examine how mathematical models can shed light on complex social interactions. Explore the cutting-edge applications of game theory in diverse fields, such as cybersecurity and evolutionary biology. If you still have difficulties choosing an idea for a math essay, find a reliable expert online. Ask them to write me an essay or provide any other academic assistance with your math assignments.

• Chaos Theory and the Butterfly Effect

While writing an essay, explore the fascinating world of chaos theory and how small changes can lead to big consequences. Discuss the famous Butterfly Effect and how it exemplifies the sensitive dependence on initial conditions. Delve into the mathematical principles behind chaotic systems and their applications in weather forecasting, population dynamics, and cryptography. Unravel the hidden order within apparent randomness and showcase the far-reaching implications of chaos theory.

• The Mathematics Behind Cryptography

In an increasingly digital world, cryptography plays a vital role in ensuring secure communication and data protection. Did you know that the global cybersecurity market is projected to reach a staggering $248.26 billion by 2023? This statistic emphasizes the growing importance of cryptography in safeguarding sensitive information.

Explore the mathematical foundations of cryptography and how it allows for the creation of unbreakable codes and encryption algorithms. Discuss the concepts of prime numbers, modular arithmetic, and public-key cryptography. Delve into the fascinating history of cryptography, from ancient times to modern-day encryption methods. In your essay, highlight the importance of mathematics in safeguarding sensitive information and the ongoing challenges faced by cryptographers.

Writing a math essay doesn't have to be a daunting task. By choosing a captivating topic and exploring the various mathematical concepts, you can turn your essay into a fascinating journey of discovery. Whether you're uncovering the beauty of the Fibonacci sequence, exploring the mathematical underpinnings of music, or delving into the game theory revolution, there's a world of possibilities waiting to be explored. So embrace the power of mathematics and let your creativity shine through your words!

Remember, these are just a few math essay ideas to get you started. Feel free to explore other mathematical concepts that ignite your curiosity. The world of mathematics is vast, and each concept has its own unique story to tell. So go ahead, unleash your inner mathematician, and embark on an exciting journey through the captivating realm of mathematical ideas!

Tobi Columb, a math expert, is a dedicated educator and explorer. He is deeply fascinated by the infinite possibilities of mathematics. Tobi's mission is to equip his students with the tools needed to excel in the realm of numbers. He also advocates for the benefits of a gluten-free lifestyle for students and people of all ages. Join Tobi on his transformative journey of mathematical mastery and holistic well-being.

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What Teachers Really Want for Teacher Appreciation Week

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It’s that time of year again for social media posts, emails, and gifts thanking teachers for their hard work —and legions of teachers who still report feeling unappreciated. For years, writers have taken to Education Week’s opinion pages to mark the week with both heartfelt thanks and searching reflections on how to make that appreciation last far longer than five days.

In 2021, teachers of the year from seven states came together to write “ It’s Teacher Appreciation Week. Flowers? Mugs? We’re Looking for Something More ,” expressing their hopes for appreciative gestures that won’t wilt by the end of the week.

Their No. 1 ask? “Include teachers in education decisions.”

Another former state teacher of the year came to a similar conclusion several years earlier, when 2014 Texas Teacher of the Year Monica Washington argued that messages of appreciation ring hollow when they aren’t accompanied by a seat at the decisionmaking table: “We are often told that we are ‘valued professionals’ who ‘change the lives of our students every day.’ But we are also micromanaged to immobility, not trusted to make the simplest decisions that affect students’ learning and well-being.”

Sharif El-Mekki has taken on a principal eye view of this conundrum in several recent essays. “What if we made Teacher Appreciation Week last all year?” he asked school leaders last spring , before laying out five actionable recommendations.

Several months later, the former principal kept the theme of teacher appreciation alive into the fall by offering “ The 4 Gifts Principals Should Give Teachers This Year (Hint: Not Another School Mug) .”

That’s not the only call to action opinion writers had for principals. Explaining her own approach in “ Why One Principal Is Asking Her Staff to Do Less ,” Indiana Principal Crystal Thorpe dialed in on the ABCs of school—academics, behavior, and culture—to slow down the runaway snowball of demands on teachers.

For some quick-hit ideas of how school leaders can back up those “thank you” emails with action, look no further than teacher and blogger Larry Ferlazzo’s three roundups of educators sharing the one thing principals can do to support their teachers:

• 7 Ways Principals Can Support Teachers
• Principals: Supporting Your Teachers Doesn’t Have to Be Such Hard Work
• Advice for Principals: Empower Your Teachers

Part of appreciating teachers starts with respecting their profession as more than just a steppingstone to administration or some other career changes. That’s the message of “ Why I’m Happy Being ‘Just a Teacher,’ ” in which Amanda Myers works through her response to a recent dinner party guest who pushed for answers on her “next step” after teaching. The widespread assumption that every teacher is an administrator-in-waiting undermines the valuable types of leadership that teachers bring to the job they already have, she writes.

Gratitude doesn’t just come from outside the profession: Teachers are ready to appreciate each other as well. Just look at what these teachers and student-teachers had to say about the educators who inspired them:

Those words of affirmation are just in line with instructional coach Lisa Westman’s prescriptions in the 2017 opinion essay “ Teachers, Do We Appreciate One Another? ” To help her fellow educators join the mutual-appreciation party, Westman translates the popular love languages—gift giving, words of affirmation, quality time, acts of service, and physical connection—into work-appropriate gestures to make colleagues feel valued.

“Teachers most frequently say they feel unappreciated by society and administration,” she wrote. “And it is easy to look outward at factors we cannot control, we can’t make society appreciate us. But, when we look inward, we must ask, what part do we, teachers, play in creating a culture of appreciation?”

A decade into retirement, former English teacher Laurie Barnoski was still feeling the appreciation when she sat down to write a love letter to teaching back in 2018. After reconnecting with four former students—two of whom had gone on to become English teachers themselves—she was reminded of the long-tail influence of her job.

“By taking time to say thank you,” she wrote, “my students were telling me that my 32 years in the classroom meant something; my goal to have a positive impact on my students was complete. They gave me the greatest gift human beings can give one another: They told me that I mattered.”

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Essay on My Teacher

List of essays on my teacher in english, essay on my teacher – essay 1 (300 words), essay on my teacher – essay 2 (400 words), essay on my teacher – essay 3 (500 words), essay on my teacher – essay 4 (750 words), essay on my teacher – essay 5 (1000 words).

Introduction:

Teachers are the ones who play a very vital role in shaping our future. From the Pre-Kinder Garden to your Post-Doctoral fellowships, they teach, impart knowledge, share ethical values, and imbibe morality, thereby shaping our personality as a strong one.

My Teacher:

Throughout our lives, we will be having many kith and kins who will hold a special place in our hearts. For me, one such person is my teacher. All of us, for sure, will definitely agree to the fact that the kinship between us and our kinder garden teachers could not be well-defined. I like my nursery teacher, so much. There is something very magical about her. Maybe, she was the first teacher in my life or maybe, she was very sweet in talking to all of us, I am unable to portray why she is always my favourite. I relied on her blindly.

Unforgettable Memories:

I have some cherished memories with my teacher. Whenever I think of those memories, it makes me blissful. On the last day of my nursery school, I started crying at the very thought of leaving her and having a new teacher. I had fallen sick due to crying for hours together. I skipped my food. My parents were not able to do anything. They called for her to make me feel better. My teacher travelled a few miles across the city and reached the hospital. She, then, said that she would never forget any of her students and asked me to write to her. I started writing to her every week from then on and she replied to every letter of mine. Till date, I look at my teacher as my second mother and she guides me in all my difficult situations.

Conclusion:

Having a good teacher who can share an amalgamated relationship with the students is a boon. A good teacher should be a good mentor, a philosopher, a guide, a friend and above all a surrogate parent to the children. I am lucky that I had gotten one in my lifetime.

My favorite subject is English and my most favorite teacher is Chitra Ma’am. She teaches us English. She likes me a lot and appreciates my hard work. She joined our school one year ago. Before that, I was not so good at English. But after attending her classes, we have all become much better at this subject.

I like her for many reasons. First of all, she teaches the lessons in a very interesting way. Even when we have doubts or questions, she never gets upset with us. Her best quality is her loving nature. She would come to school daily without missing a day.

Her dressing sense is nice. She wears simple salwar suits. She always speaks to her students softly and respectfully. I eagerly wait for her class and do my English homework on time. Chitra Ma’am puts a lot of effort in explaining every chapter.

There are many activities given at the end of every lesson and she makes us participate in all of them. Not only that, but she also encourages us to take part in drama and poem competitions. Since her first day, she made a rule for us.

All of us has to speak in English during the English period. Every student tries to talk in English even if the sentence sounds improper. She has taught us to never laugh at each other’s mistakes. This has improved our spoken English in a great way. Now, we are able to talk in English with more confidence.

Another great quality of hers is that she treats every child equally. After explaining the lesson to us, she asks each one of us different questions about the chapter. Sometimes, we also love to talk about our personal lives, like what do we like about our lives, how our parents work hard for us, and things like that.

When we get confused or need an emotional support, she is the best person to talk to. Her advice and suggestions are always positive. Last month, on teacher’s day, all the students wished her and brought presents for her. We also sang a song to her.

I made a beautiful greeting card for her and a red rose with it. She accepted it with a smile and thanked us for everything. I feel grateful to have such a gentle and great teacher in my life who supports me in every way.

In school, you tend to interact with a lot of people who can either impact your life positively or negatively. A teacher is one neutral person who will manage to strike a balance between the positive and the negative. Teachers have a huge responsibility that we students may not understand. All in all our teachers try their best to provide an education, guidance and discipline despite the challenges we might impose on them. The life of a student is entirely dependent on a teacher because most of their time is spent in school rather than with parents that is why teachers play a major role in shaping the lives of young children through school.

Who Is my favourite Teacher?

I have several teachers now that I am in high school but there is only one whom I can relate to as “the teacher” because of the impact he has made in my life. The teacher is male, of Indian origin and has a funny accent when he speaks. He is married and has three children. Actually, one of his children is my age and I know him through tennis practice because he comes to train with us sometimes. I like him because his sense of humor gives a good learning experience for the students. He is a math teacher and he is very good at what he does. Students tend to make fun of him because of his accent but he make fun of it himself, which gets even funnier. This teacher has been a great mentor to me and other student ever since we joined high school. I met him on a personal level one day after class when I needed clarification on a topic I had not quite understood. The teacher was kind to me and guided me through it. Since then, he took his own initiative to do follow-ups on me and I became really good in math due to his efforts.

Coincidentally, he also coaches my tennis team and we meet out on the field. We have won several awards as a tennis team under him. I feel connected to the teacher through his mentorship and he has become like a school parent to me because whenever I have an issue, he is free to help me out.

How the teacher has impacted my life in school .

Mentorship goes along way depending on the approach used. When I first joined high school, I did not have much confidence in myself. This teacher mentored me and made me believe in myself. The good thing is the attention he gives t is students because most of the times, he follows up on the performances and ensures that he does everything he can to help students improve academically. He has also been a role model to me through his way of doing things. He is dedicated to his work and he is an achiever. Through following his footsteps, I have been able to dedicate myself into studies and sports, which has helped me to achieve my goals.

In conclusion, good teachers are hard to find but when you find one, make the most out of them.

The word “teacher” depicts a person that teaches. English dictionary defines teacher as “a person who teaches, especially one employed in a school”. A more recent definition of teacher in the linguistics field is “a tutor that interacts with the learners in order to facilitate good learning”.

Types of Teachers

Old method teachers: the teachers found under this method adopt the rigid mode of impartation of knowledge. They control the class the way a king would rule over his subjects. Old method teachers are less concerned about the welfare of their learners, they are syllabus-oriented.

New method teachers: the tutors under this model are student-oriented. They are more concerned about their learners and their various levels of understanding. They accept and promote contributions in class unlike the old method teachers. New method teachers encourage the inquisitiveness of their students.

Attributes of a Teacher:

A standard teacher has all or most of the various characters imbedded in them:

• Compassionate
• Open-minded
• A good counselor
• Friendly and most importantly
• Approachable.

Attributes of My Favorite Teacher:

Personally, I see my teacher as a mini-god because he leaves his mark on me. He influences my life in ways that enables me affect changes wherever I find myself.

He is a perfect example of the new model teachers. Basically, he is student-oriented. In the classroom, he employs the Eclectic mode of teaching (this is the combination of all the modes of teaching “discussion mode, play way mode, role play mode, question mode” so as to facilitate standard learning).

He comes into the classroom; starts the lecture with a recap of what was discussed in the previous class, gives room for the students to ask questions that arose from the last class, answers them and then starts a new topic.

To start a new topic, he starts with a mind-capturing introduction that attracts the attention of all students. Once he is through with introducing the topic, he gauges our reaction in order for him to know if his students are on the same page with him or left behind.

Then, he moves on to the discussion mode of teaching, whereby he throws questions to his students and accommodates both relevant and irrelevant answers, at the end of this model, he sieves through the answers provided, pick the relevant ones and add his own iota to it, he also always applaud the courage of all who answers his questions.

He moves either into the role play method or the play way method, here he selects students to either act out the lessons from the day’s topic or summarizes what he has taught for the day. The use of this particular mode enlightens the students more on the topic being discussed.

Finally, he moves over to the questions and revision mode, where he personally go through all he has taught over the course of the period. During this mode, he entertains questions from students on their personal areas of difficulties. Occasionally, he gives assignments to back up his teachings.

During his teachings, he pays close attention to the expression, mood, sitting posture and carriage of his students. This tells him when his students are lost, sad, worried, hungry, sick, away in dream land or simply tired.

Once he is done processing the information gotten from our faces, he either finds a way of brightening the mood of his students, bringing them back from the dream world, or ending his class without breaking his stride or alerting the whole population of students to what is currently going on.

It is only normal for a human being to reflect his mood whenever he is talking or interacting, but my teacher hardly ever allow his bad, horrible moods interfere with his teachings.

Outside the classroom, my teacher is approachable, fatherly, and jovial. He entertains all and no one is excluded from his open arms, smiles and affections.

He is a good counselor who is always ready to help me out of my tight corners. He gives twenty first century advises in a fatherly way.

Although, due to my teachers lenient ways with students, some students tend to be lazy, disrespectful, stubborn or rude. He has a way of being firm, maintaining class control while teaching.

In conclusion, my teacher has all the attributes and more of a new method teachers. He is capable of combining all modes of teaching, he is compassionate, passionate, and friendly. From my interactions with him, I can confidently say that he is one of the best teachers around.

A teacher plays a very important life in shaping your life as well as career. A good teacher is a blessing for the students in their early years and helps them understand the world; learn moral values along with education. Most importantly, a teacher helps you the art of survival and brings out the best of you.

Why a teacher is so important in a student’s life?

Teachers assume the essential job in our life to end up fruitful invocation and business. A decent teacher encourages us to end up great individual in the general public and great nation of the nation.

Teachers realize that students are the eventual fate of any country. So the future advancement of any country is in the hands of teachers. What we move toward becoming in life is relies upon teachers. Teachers confer the information and data in the mind of understudies to dissect. Investigating in the circumstance what is conceivable is the most essential thing that we gain from teachers. Energy about teachers is imperative since they are the most essential individuals in the nation. What we’re seeing today in business, legislative issues, and society all influenced by teachers. In this way, in India, we commend teacher’s day consistently on 5 September on the event of the birth Dr Sarvepalli Radhakrishnan.

My Teachers, My Role Models

During my formative years, I have come across many teachers who have influenced my life for the better. Having being studies in a convent school, I got to face a much-disciplined environment during my school years. The teachers, although were very polite in their behaviour, at the same time ensuring that we all followed a disciplined life. We were taught how to inculcate these values in our daily life so as to be better human beings when we grow up and face the world. Although all the teachers were good, there is one teacher whose teachings I just cannot forget. She is Ms Kirti Bhushan. Her teachings have been so powerful and impactful that I can still feel them during my day to day decisions even today.

My Best Teacher

Ms Kirti was my class educator as well and took participation in the daily activities with us as well. She was a strict instructor anyway extremely amusing and mind in nature. At the same time, she was extremely restrained and dependable. She did her work perfectly with the class at a perfect time without getting late. I liked her, particularly as she attempted simple approaches to show us beneficial things. We made the most of her class. She taught us English subject as well. She even made us giggle by telling heaps of jokes in the middle of when she taught. She likewise managed us exceptionally well amid any school or between school rivalry of the move, sports, scholastic, and so on. She instructed us to share things in class among our associates, for example, lunch or other required things.

Her Background

She was from Varanasi and completed her initial studies there itself. She took her higher education degrees from the Banaras Hindu University. She was extremely friendly and kind in nature. She realized well about how to deal with little youngsters in the class. Her one of a kind style of educating is perhaps what I mostly recall her for. I even meet her at times at whatever point I have to explain some intense inquiries of my day to day issues, she advises me so easily and comfortably. She looks extremely savvy with shimmer eyes and fair hair.

Her Smiling Attitude

She generally smiled when she entered the classroom and first got some information about our prosperity. She additionally helped us in the games at whatever point our games instructor was missing. She had a smiling face even during the strict environment during the examination times. She constantly rebuffed to the students who were with fragmented home works. She was acclaimed for making loads of fun amid the class time and ensure there was a positive ambience all around.

She was an instructor with great aptitudes of educating, well-disposed nature, great comical inclination, understanding and nice. I am proud to be one of her favourite students, as she always said good things about me to other teachers. At times she gave us chocolates on doing great in the class tests and exams. She never gave us heaps of assignments at home. She was exceptionally eager and constantly spurred us for doing our best in the examination.

Teacher’s In Today’s Scenario

Today the general population are changing and their reasoning and advancement thoughts are more against nature. Presently for the world, a teacher is only a teacher. Various offices and departments only tend to remember them on teachers day during various events and usually do not remember them otherwise. Individuals also share few posts via web-based networking media with respect to teachers and after that just forget them. Individuals overlook a bigger number of things that they are gaining from teachers. Schools and students also praise the teacher’s day event and value the endeavours teachers are doing. This is incredible if individuals ought to pursue the exercises of teachers also.

The genuine present for teachers is when students turn into a decent individual, effective in their vocation and business. Not all teacher are great in instructing and comparatively, not all students resemble “Shishya and Guru” particularly in the advanced period. A few teachers are incredible and they are dependable in heart of students all life along.

Students admire teachers for counsel and direction. Students are inspired by scholastic exercises as well as they are intrigued to pursue their life exercises. That is the reason it’s exceedingly essential for teachers to motivate students to pursue great propensities not terrible by their own precedent. An instruction is critical in everybody’s life and assumes different jobs in various phases of life. It’s imperative that individuals understand the significance of teachers and pursue their teachers in the right spirit.

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Objects of study in research on mathematics teacher education

• Published: 06 May 2024

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• Takeshi Miyakawa 1  

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It has been more than a quarter century since the Journal of Mathematics Teacher Education (JMTE) first appeared in 1998. Unlike the broader field of mathematics education research, studies focusing on mathematics teacher education are somewhat circumscribed due to their primary emphasis on mathematics teachers. Despite the passage of time, the scope of research themes appears not to be diminishing but rather expanding.

Confronted with the nine papers included in this current issue and reflecting on the historical trajectory of this journal, I am compelled to revisit the diversity of research on mathematics teacher education (Miyakawa, 2022 ), particularly in terms of the objects of study. The research showcased in JMTE is dedicated to enhancing our understanding of various aspects related to mathematics teacher education, such as teacher knowledge, professional development, and university training courses. This leads me to ponder the various objects of study within our field and whether it is feasible to encapsulate the diversity of our research by explicitly delineating them.

An insight that emerged from reviewing the papers in this issue is the relevance of the concept of relation proposed within the Anthropological Theory of the Didactic (ATD) (Chevallard, 2019 ; Chevallard & Bosch, 2020 ). The concept of relation serves as a modeling tool for analyzing individual or societal knowledge, cognitions, attitudes, etc., toward various objects. I observed that each paper, to some degree, investigates a relation that can be found in the context of mathematics teacher education. In this editorial, I briefly examine the objects of study in our field with these papers.

Let us first describe the concept of relation (for the details, see Chevallard & Bosch, 2020 , p. 54). This concept involves several interconnected notions: person , institution , position , and object. A person is defined as any human being, and an institution is anything instituted. The notion of institution should be understood in a broader sense. It may be a class, a family, a government, a school, and so forth. The relationship between a person and an institution is characterized by the notion of position . A person occupies a position (e.g., student, teacher) in an institution (e.g., classroom) . An object is anything that is recognized as existing. Footnote 1 Therefore, “[g]iven an object o and a person x , the relation of x to o , denoted by R ( x , o ), is all that x can do with and about o ” (ibid., p. 54). R ( x , o ) is “the set of links of any kind between x and o ” (Chevallard & Bosch, 2019 , p. xix). This formalization also applies to the position when replacing person x with an institutional position. The relation of p to o is denoted by R I ( p , o ).

In the realm of research on mathematics teacher education, the object of study is often the relation R between an institutional position p (e.g., teacher, teacher educator) occupied by a person or some persons (of collected data) and an object o (e.g., mathematical concepts, tasks, students’ thinking) in an institution I (e.g., primary school, secondary school, university course). This relation could be thinking and feeling about o , envisioning o , using o , handling o , etc. These four elements— R , I , p , and o —thus define the object of study in our scientific field.

I have identified these four elements in each paper of this issue. For instance, Jacobs et al. (this issue) explored the professional noticing of children’s mathematical thinking. The position p under discussion is that of practicing elementary school teachers, and the object o is children’s mathematical thinking about fractions. The primary object of study in this paper is the relation R between p and o in terms of noticing within a specific institution I of professional development in the US. Accordingly, these four elements identified across the nine papers are compiled in Table  1 , which contrasts the differences and commonalities of the objects of study among them. One may find some positions that vary from preservice to inservice teachers, from elementary to secondary, and from teacher to teacher educator, and their various ways of relating to different objects in mathematics education.

One interesting characteristic is the nested nature that can be found in the formalization of relations. In the case of Jacobs et al. (this issue), children’s mathematical thinking can be modeled as a relation R ( X , fractions) modeling how children X handle the fractions. Therefore, the object of the study investigated in this paper can be described as R I ( p , R ( X , fractions)). This nested nature is also evident in other contributions. Lai & Ahrens (this issue) and Hoffmann & Even (this issue) investigate how mathematicians—teacher educators of mathematical content—in the university ( p ) perceive ( R ) secondary teachers’ content knowledge ( o ) in two distinct institutions ( I )—university in the US for the former and university in Germany in the latter. This object o is often investigated as an object of study in our field, as in the study by Yudt et al. (this issue). It can be described as the relation R I’ ( p’ , math) modeling how the secondary teacher p’ knows or perceives mathematics in the institution I’ of secondary school in the US or Germany. Therefore, the object of study for these papers can be described as R I ( p , R I’ ( p’ , math)).

As such, the concept of relation in the ATD allows us to delineate our object of study. This is especially useful in the case of the nine papers in this issue, because they focus on the aspect of knowledge, cognition, or attitude of a person/position in mathematics teacher education. However, the object of study in our field may be the systems of professional development or classroom teaching in their own right without focusing much on the specific relation of a person toward a specific object. In such a case, it would require other perspectives for a comprehensive characterization of the object of study and the diversity of research in our field.

The use of the term “object” as an element related to the notion of relation is confusing because it is also used for the expression “the object of study” in this editorial. The former “object” should be understood as a theoretical contract, while the latter is a general term denoting the system the researchers are trying to understand.

Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: an attempt at a principled approach. Hiroshima Journal of Mathematics Education, 12 , 71–114. https://doi.org/10.24529/hjme.1205

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Chevallard, Y., & Bosch, M. (2019). A short (and somewhat subjective) glossary of the ATD. In M. Bosch, Y. Chevallard, F. J. García, & J. Monaghan (Eds.), Working with the anthropological theory of the didactic in mathematics education. A comprehensive casebook (pp. xviii–xxx). Routledge.

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Chevallard, Y., & Bosch, M. (2020). Anthropological Theory of the Didactic (ATD). In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 53–61). Springer. https://doi.org/10.1007/978-3-030-15789-0_100034

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Miyakawa, T. (2022). Handling the diversity of research on mathematics teacher education. Journal of Mathematics Teacher Education, 25 (6), 633–636. https://doi.org/10.1007/s10857-022-09559-y

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Former Worthington teacher hosts PBS show teaching kids math using central Ohio locations

A former Worthington City Schools teacher is making a national splash on PBS with her new educational television show that teaches children about math in the real world using central Ohio businesses and other places.

"How It's Math" is a new show airing for children on PBS created by Caroline Farkas, a former Worthington City Schools teacher and educational video producer, through her educational company Doodles & Digits, according to a release.

The PBS show follows Farkas and her animated "math chicken" as they explore how various real-world careers and industries use math, according to the release. Geared toward upper elementary students, the show covers learning standards for grades 3, 4 and 5.

Farkas said she hopes to change people's perceptions of math with the show.

"Math is everywhere, and I aim to highlight its relevance in our daily lives," Farkas said.

The program also features interviews with local places like Westerville's Asterik Supper Club, Bake Me Happy on Columbus' South Side and the Worthington Public Library — all to highlight how math is used every day for things from baking to pricing to organizing.

Farkas attended undergraduate school at Miami University and graduate school at Clemson University, and was a Worthington City Schools teacher for more than seven years until 2021, when she decided to start Doodles & Digits during the pandemic after seeing the challenges of distance learning.

"I struggled to find resources that my students enjoyed and could comprehend during distance learning," Farkas said. "I realized there weren't many resources available to assist parents with math education, especially for upper elementary grades. So, I decided to create them myself."

Three episodes of the show have already aired and are available for viewing on the PBS app, PBS.org , the Doodles & Digits' YouTube channel or on broadcast slots on PBS channels nationwide. The show is sponsored in part by Scotts’ Miracle-Gro Foundation.

Filming for season two of "How It's Math" is scheduled for the summer, according to the release.

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Teacher Salary Stories: A South Carolina High School Math Teacher Earning $49,500 in 2024

“I am thankful I am able to provide for my family.”

In our series  Teacher Salary Stories,  We Are Teachers readers share how they’re making it work—or not—on a teacher’s salary. The goal is to take an honest look at teacher pay in the United States and around the world—what’s working, what’s not, and what needs to change if we want to stem the flow of educators leaving the profession and recruit new teachers to the field.

In today’s Teacher Salary Story, we hear from a South Carolina high school math teacher who has been teaching for seven years, marking his second career. He started at a salary of $32,000 and currently earns $49,500. He is now working toward additional qualifications to further increase his salary. Living with a family of four with a baby on the way, he is the sole earner, managing a $750 mortgage while his wife homeschools their children. His net worth is approximately $100,000, including savings and investments, with a monthly take-home pay of $3,500. Despite financial constraints, he finds satisfaction in his ability to support his family, rating his contentment with his salary at 8 out of 10. His story reflects the broader issues facing many teachers who strive to balance professional dedication and financial realities, underscoring the ongoing conversation about teacher pay and the importance of supportive measures to retain dedicated educators.

Where do you live?

Greenville, South Carolina.

What is your job title?

High school math teacher.

What is your annual salary?

What is your highest level of education.

Bachelor’s degree.

How did you pay for your education?

Scholarships, work, and help from family.

How long have you been teaching? Is this your first career?

7 years, and no, this is not my first career.

What was your starting salary as a teacher?

$32,000. I took a break, and then it was $40,000 when I came back.

Tell us about your income progression (e.g., have you received standard step increases, taken on extra duties, gotten an advanced degree, or switched roles?).

Standard step and our state has been working to increase teacher pay for the past decade. Working on my plus-18 (hours of graduate credit) now.

How much is one paycheck, after taxes, and how often are you paid?

$1,750 twice a month. I exempt myself from federal and state income taxes.

What is your approximate net worth including savings, investments, retirement, and other assets?

Who lives with you in your household are you the only earner.

Four people and one more on the way. Yes, I am the only earner. My wife stays home and homeschools our kids.

What are your approximate monthly expenses (e.g., rent/mortgage, car payment or other loans, childcare, food, entertainment, phone/Internet/utilities, other subscriptions)? 

$750 mortgage

$200 car payment

$1,700 (food, gas, misc, family fun, homeschooling, household needs)

$120 utilities

$500 giving

Do you receive a school- or PTA-provided budget for classroom supplies? If so, how much?

How much of your own money do you spend on your classroom every year, what kinds of things do you buy when you treat yourself.

Vacations with family, out to eat with wife, music, garden stuff.

What expense would you take on if you suddenly got an extra $1,000 per paycheck?

Save or invest.

How does your district handle retirement? Will you receive a pension?

I am at a charter school. They have a 401k program. I put in 6% and they put in 8%.

Do you have any secondary sources of income, like a side hustle or another job?

Not currently, but I did in the past.

How satisfied are you with your teaching salary on a scale of 1 to 10, 10 being very satisfied and 1 being not at all satisfied? Please explain.

8. I am thankful I am able to provide for my family, and when I learned I was able to exempt myself from income taxes with no penalty to me, it really opened up my finances. Right now I’m not able to set too much aside for savings, but it has always worked out.

Has your current and/or future salary impacted your decision-making around other major life choices (e.g., where you live, whether you rent/own, whether or not to have kids, etc.)? Please explain.

No. My wife and I learned early on not to allow money to be something that guides our major life decisions. We are about to have at 3 kids and have no doubt they will have a safe and loving home provided for them.

Do you plan to stay in education?

Do you have any other thoughts about teacher pay that you’d like to share.

I am appreciative of the awareness around raising teacher pay.

Are you interested in participating in our Teacher Salary Stories project?  Fill out the Google Form here.  If we choose your story for publication, we will notify you and send you a $150 gift card. All responses will be published anonymously.

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Watch CBS News

Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries

By Bill Whitaker

May 5, 2024 / 7:00 PM EDT / CBS News

As the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years. 

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything. 

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students. 

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told  them  was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it." 

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson:   So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash. 

Bill Whitaker: Did you look at the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter) 

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics. 

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch. 

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh) 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans. 

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates. 

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in. 

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.  

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven. 

Bill Whitaker: What do you mean by that?

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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