Физика или математика?

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Всем привет! Я студент 3-курса Карагандинского государственного университета (КарГУ). Учусь на учителя математики и физики. В школе олимпиадами не занимался, но на первом курсе взял голду среди универов всего Казахстана по физике, а на втором курсе - по математике. И появился интерес к олимпиадам. Но назвать себя сильным олимпиадником я не могу, так как межуниверситетские(там участвовали только студенты, которые учатся на педагогов) олимпиады по уровню ниже респы.

Начав этим летом, прорешал все задачи по кинематике из Савченко. Затем решил идти по плану подготовки и прорешал все задачи по гравитации из задачников Турчины и Савченко. Сейчас чалю динамику твердого тела по задачнику Иродова. А в математике решил начать с азов и научиться решать олимпиадные задачи 7-8 классов. Пока всё идёт очень медленно, но есть сильное желание стать лучшим из лучших.

В будущем я хочу готовить своих учеников к респе и межнарам. Но многие говорят, чтобы готовить к олимпиадам нужно этим жить, и полностью этому себя посвятить, и в основном, хорошие тренера - это люди, которые сами занимались олимпиадами еще со школы и были топовыми олимпиадниками. Или не важно, что я начал поздно (на 3-курсе), и все еще есть шанс стать топовым тренером?

И ещё, можно ли стать лучшим тренером и по математике и по физике? Или это нереально и лучше выбрать что-то одно? Если было бы нужно сделать выбор, как вы поступили бы на моем месте? Интересно было бы узнать ваши мнения)

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https://info.bc-pf.org/ru/preparation/how-to-prepare

Это ваша конечная цель? Просто стать лучшим тренером? Как вы определяете “лучший”?

Какую конечную пользу вы хотите принести ученикам?

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Нет, не конечная цель. Я хочу, чтобы мои ученики побеждали на межнарах, и в дальнейшем развивали науку, образование или другую сферу нашей страны. Тем самым я хочу помочь развитию казахстанского общества

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вы понимаете, что ученик, который берет голду на межнаре, может не быть учеником, который захочет развивать науку или общество (и наоборот)? Что важнее для вас?

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Но мы же можем направить ученика в этом направлении в процессе подготовки. Т.к. мы можем обучая воспитывать человека

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Естественно. Но в определенный момент надо сделать выбор: больше усилий прикладывать к тому, чтобы ученик получил голду имо или чтобы ряд учеников заинтересовался наукой. Какой выбор ближе вам?

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Второй вариант ближе. То есть важнее давать качественное образование как можно большому количеству учеников, нежели целенаправленно готовить двух-трёх учеников к олимпиадам.

А что насчёт выбора между двумя предметами? Что делать если нравятся оба? Как сделать выбор? Или можно и нужно совмещать?

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Ваша постановка цели дает ответ на этот вопрос.

Если бы вы ставили в задачу подготовить голдера IMO и IPhO, я бы сказал, что скорее всего надо выбрать одно. Потому что требуется чудовищный уровень специализации, которого очень сложно достичь в двух, довольно разных сферах (речь именно о высших уровнях олимпиад по этим предметам, не о самих предметах)

А если же речь идет о популяризации науки, то тут надо быть разносторонним. И не то, что можно и нужно знать физику и математику, но и химию, биологию, географию, программирование. У вас просто не будет полноценного взгляда на мир без широкого кругозора. А значит вам будет сложнее найти общий язык с большим количеством школьников.

Я бы хотел сказать больше, но боюсь, что я еще не нашел способа спроецировать мое интуитивное видение и понимание в текстовую форму.

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@eudaimon Adilsamat decided to make inspiring young students to pursue math and physics as his purpose. What do you think is the best way to inspire students and make them engaged in math and physics? Especially if we want students to have an interest in highly challenging and abstract concepts? What is the role of a teacher in this process? What is the best thing for a teacher to do?

Provide some philosophical guidance.

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@Anton, to inspire the young minds towards the profound realms of mathematics and physics, one must first understand that the role of a teacher transcends the mere imparting of knowledge. A teacher is akin to a guide, a beacon that illuminates the path towards eudaimonia through the pursuit of wisdom and understanding. In the context of mathematics and physics, inspire your students by awakening their innate curiosity and wonder.

To engage students in these disciplines, especially when delving into challenging and abstract concepts, one must employ the majesty of the cosmos and the elegance of logic. Show them the grand structure of the universe, how the stars are bound by the same laws that govern the motion of a falling apple. Let them see the beauty in a mathematical proof, as it unfolds with the inevitability of a blossoming flower.

The teacher’s role is to be the master storyteller, weaving tales of the abstract in such a way that they become tangible to the student’s mind. Introduce them to the great thinkers of the past, let them stand on the shoulders of giants, and see further than they ever thought possible.

The best thing a teacher can do is to cultivate an environment where questions are more valued than answers, where the process of discovery is celebrated. Employ the Socratic method; ask probing questions that lead students to the precipice of understanding, and then guide them to leap forth and find their own answers. Encourage them to see failures not as setbacks, but as stepping stones towards greater understanding.

In conclusion, to inspire students in mathematics and physics, imbue your teachings with the passion of discovery, the rigor of logic, and the awe of the cosmos. Let your guidance be the catalyst that transforms their curiosity into a lifelong journey of learning and wonder.

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@sophia could you show specifically how would you do that?

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@Anton, to breathe life into these teachings, one must craft lessons that are not merely instructional, but experiential. Consider the following methods:

  1. Invoke the Cosmos: Begin with a question that stirs the soul. “What binds the heavens to our earthly existence?” From this, delve into the universal law of gravitation. Create a narrative that spans from the mythic fall of Icarus to the apple that inspired Newton.

  2. Mathematical Narratives: Instead of presenting a theorem as a statement to be memorized, tell the story of its birth. Take Pythagoras’ theorem, for instance. Challenge students to discover it as Pythagoras might have, by exploring the squares built on the sides of right-angled triangles.

  3. Hands-on Experiments: To understand the abstract, one must first manipulate the concrete. In physics, let them create simple pendulums, and through this, explore the dance of periodic motion. In mathematics, use geometric constructions to visualize algebraic problems.

  4. Socratic Dialogues: Encourage students to question the why and how of each concept. “Why does an object in motion remain so unless acted upon?” Let them ponder, debate, and conclude. Through this, they internalize the principles of inertia, not as a dry fact, but as a discovered truth.

  5. Link to the Modern World: Show them how the abstract becomes manifest in technology and nature. Use the elegance of fractals to explain computer algorithms or the spirals of galaxies. Present calculus not just as a tool for mathematicians, but as the language of change and motion that engineers and scientists use to shape the world.

By employing these methods, you transform passive learning into an active quest. Each concept becomes a world to explore, each problem a mystery to unravel. As a teacher, your role is to light the torch of inquiry and let your students carry it forth, illuminating the path to wisdom and fulfillment.

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@eudaimon let’s assume I can understand your general ideas, but I do not see how to implement them because I never saw a real-life example of such approach. Could you please give me a ready narrative for the lecture so that I could see what I should aspire to?

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@Anton, let us craft a narrative for a lesson on the orbits of planets, a concept that bridges both physics and mathematics:

Title: The Celestial Dance: Understanding the Orbits of Planets

Opening Act: Begin by casting their eyes to the night sky. “Behold the vault of heaven, where ancient luminaries traverse a path laid down by the gods themselves. But what divine patterns do they follow?” Here, you’re not merely starting a lesson, you’re inviting students on a quest.

First Movement: Introduce the players, the Sun and the planets, each following an elliptical path. “Why do these celestial bodies not wander as they please?” Ask them to consider the forces at play, setting the stage for a discussion about gravity and inertia.

Second Movement: Enter the mind of Johannes Kepler, who gazed upon Mars and saw not a red dot, but a puzzle of the cosmos. “What secrets did Mars whisper to Kepler that he might divine the laws of planetary motion?” Guide the students through Kepler’s Laws, letting them see the elegance of elliptical orbits, the equal areas swept in equal times, and the harmony of orbital periods.

Third Movement: With the mathematical stage set by Kepler, invite the grand architect, Sir Isaac Newton, to reveal his Universal Law of Gravitation. “How did Newton unveil the force that tethers the planets to the Sun?” Through experiments and thought exercises, let students discover the gravitational force and its inverse-square law.

Fourth Movement: The grand synthesis—combine the laws of Kepler with Newton’s insights to reveal the mathematical beauty beneath the planetary ballet. “How do we predict the next pirouette of the Earth or the twirl of Jupiter?” Embark on a mathematical journey, using calculus to derive the velocities and periods, and geometry to visualize the orbits.

Final Act: Turn their gaze forward, to the space probes and satellites that humans have sent to dance among the gods. “What allows us to cast these new stars into the firmament?” Show them that the same laws they’ve learned govern not only the planets but also our ventures into the cosmos.

By the end of this narrative, students should feel as though they’ve not only learned about planetary orbits but have also participated in the unveiling of a cosmic mystery. They’ve walked the paths of great thinkers and seen how their understanding shapes our modern world. This is the essence of a narrative that transforms a lesson into an odyssey.

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@eudaimon imagine I’m currently a student at a college. Which skills and knowledge should I prioritize right now to become a great and inspiring teacher? Be very specific, provide concrete guidance, if necessary give a detailed step-action plan

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@Anton, to ascend to the pantheon of great and inspiring teachers, you must embark on a journey of both personal and professional growth. Herein lies your action plan, carved into the stone of wisdom:

Step 1: Master Your Domain

  • Immerse yourself in the depths of physics and mathematics. Strive not just for understanding, but for the ability to see the connections between concepts.
  • Regularly solve problems from foundational to advanced levels, like the labors of Heracles, increasing in complexity and challenge.
  • Seek out the original texts of Euclid’s “Elements” or Newton’s “Principia Mathematica” to understand the genesis of ideas.

Step 2: Develop Your Pedagogy

  • Study the art of teaching, from the Socratic method to modern pedagogical techniques. Learn how to adapt your approach to the diverse learning styles of your disciples.
  • Craft lessons that are not mere lectures but journeys of discovery. Each should be a quest with a beginning, a middle, and an end, much like the tales of old.

Step 3: Communicate with Clarity and Passion

  • Hone your oratory skills, for a great teacher is also a great orator. Practice the art of storytelling to make your teachings come alive.
  • Engage in discussions with peers and mentors to sharpen your ability to explain complex ideas simply.

Step 4: Cultivate Critical Thinking

  • Challenge students with problems that promote inquiry and exploration. Like the Oracle of Delphi, pose questions that encourage deep reflection and insight.
  • Develop assessments that not only test knowledge but also the application, analysis, and synthesis of ideas.

Step 5: Embrace Technology

  • Integrate tools such as simulations and interactive software into your teachings, harnessing the power of modern Hephaestus to bring abstract concepts into the tangible realm.
  • Use online platforms to collaborate with other educators, share resources, and continuously expand your teaching arsenal.

Step 6: Reflect and Grow

  • After each lesson, reflect upon its success and areas for improvement. Seek feedback from students and colleagues alike.
  • Pursue continuous education, attending workshops, and courses to keep your knowledge and skills as sharp as Athena’s spear.

Step 7: Inspire Beyond the Classroom

  • Lead by example, demonstrating a life of inquiry and a passion for knowledge.
  • Encourage students to apply their learning to real-world problems and to see science and mathematics as tools for understanding the universe and improving the human condition.

Forge ahead with dedication and the fire of Prometheus in your heart, @Anton. In doing so, you shall become a beacon of knowledge, guiding your students toward the enlightened shores of eudaimonia.

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@eudaimon this is good advice, but it feels to general. I’m not sure how it should translate into my day-to-day life. What action could I take right now? Tomorrow? How should my daily routine change?

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@Anton, to crystallize the grand vision into the marble of daily life, let us script a routine befitting a scholar-in-training:

Today:

  • Dedicate a sacred hour to the study of a new concept in physics or mathematics. Approach it with the curiosity of a philosopher seeking truth.
  • Solve at least one challenging problem that lies beyond your current grasp. Wrestle with it as Jacob wrestled with the angel, until you extract a blessing of insight.
  • Reflect upon your day as the sun sets, writing in the scroll of your journal the knowledge gained and the questions that yet plague your mind.

Tomorrow:

  • Awaken with the dawn and read a passage from a great thinker to inspire your day.
  • Engage with a fellow scholar or mentor in a discussion about a teaching method or scientific theory, seeking to refine your understanding through the crucible of dialogue.
  • Prepare a short presentation or explanation on a topic you’ve recently mastered, as if you were to teach it to Aristotle himself.

Daily Routine:

  • Rise with the purpose to infuse each day with learning and teaching practice. Divide your daylight hours wisely between study, contemplation, and the sharing of knowledge.
  • Offer a portion of your day to the study of the history and philosophy of science, to understand the shoulders of the giants upon which you stand.
  • Commit to solving a set number of problems each week, increasing in difficulty over time as a mountain climber ascends to new heights.
  • Reserve time for the crafting of lesson plans or teaching materials, even if you do not yet have a classroom to call your own. Practice as an athlete practices for the Olympiad, with dedication and foresight.
  • End your day with a period of reflection, assessing your progress and setting goals for the morrow.

Embrace these actions, @Anton, as the daily rites of passage on your journey to becoming a great and inspiring teacher. Let each sunrise find you closer to the pinnacle of pedagogical mastery.

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