Five Principles of Extraordinary Math Teaching | Dan Finkel | TEDxRainier

TEDx Talks
17 Feb 201614:42
EducationalLearning
32 Likes 10 Comments

TLDRThe speaker passionately advocates for a transformative approach to math education, emphasizing the importance of fostering a love for mathematical thinking. She shares her concern about the common miseducation in math that leads to aversion and lack of critical thinking. The speaker proposes five principles to reinvigorate math learning: starting with a question, allowing time for struggle, not being the answer key, saying 'yes' to ideas, and encouraging play. These principles aim to cultivate curiosity, resilience, and creativity, ultimately changing the perception of math from a tedious subject to an exhilarating journey of discovery.

Takeaways
  • 😢 Many people have a negative perception of math due to how it's taught, associating it with tedium and frustration.
  • 🔥 Mathematical thinking can profoundly impact lives, yet there's a widespread issue of mathematical miseducation.
  • 🚨 The traditional approach to math education focuses on memorization and repetition, leading to a lack of motivation and appreciation for the subject.
  • 📝 Starting with a question rather than an answer in math classes can spark curiosity and engagement.
  • ⚔️ Emphasizing struggle and perseverance in solving math problems helps develop critical thinking and problem-solving skills.
  • 📖 Teachers don't need to be the answer key; fostering a classroom environment where questioning and exploration are encouraged is more valuable.
  • ✔️ Encouraging students to propose and explore their ideas, even if incorrect, promotes a deeper understanding and respect for mathematical processes.
  • 💡 Playing with ideas and concepts in math, such as considering alternative outcomes or scenarios, can lead to new insights and discoveries.
  • ✏️ Engaging with math through play and exploration can make the subject feel more accessible and enjoyable, akin to a creative adventure.
  • 🏆 Embracing mathematical thinking prepares students for the future by fostering courage, curiosity, and creativity.
Q & A

  • Why did the speaker's friend's son express hatred for math?

    -The son likely developed a dislike for math due to the common miseducation practices in math classes that focus on rote memorization and repetition, rather than fostering a love for mathematical thinking.

  • What impact does mathematical miseducation have on students?

    -Mathematical miseducation can lead to students lacking motivation, disliking math, and even avoiding it for the rest of their lives. This can limit their career opportunities and make them vulnerable to manipulation by entities that use statistics to influence decisions.

  • How does the speaker suggest we should approach teaching math?

    -The speaker suggests that math education should start with a question, encourage struggle and perseverance, involve the students in genuine thinking and problem-solving, and allow for exploration and play within the subject.

  • What is the significance of René Descartes' quote, 'I think, therefore I am', in the context of math education?

    -Descartes' quote emphasizes the importance of thinking in existence and is used to illustrate that math classes should foster a similar kind of thinking, where students doubt, understand, conceive, and perceive, rather than just memorize facts.

  • What are the five principles the speaker offers for math education?

    -The five principles are: 1) Start with a question. 2) Allow time for struggle. 3) The teacher is not the answer key. 4) Say 'yes' to students' ideas, even wrong ones. 5) Encourage play and exploration in math.

  • How does the speaker describe the feeling of engaging in mathematical thinking?

    -The speaker describes it as an exhilarating journey of discovery, and even compares it to feeling 'like a God' when a participant in a workshop used that phrase to describe their experience with mathematical thinking.

  • What is the importance of allowing students to struggle with math problems?

    -Allowing students to struggle with math problems helps them develop tenacity, courage, and perseverance. It also fosters deeper curiosity, powers of observation, and the ability to take risks and engage in mathematical conversations and debates.

  • Why should teachers not act as the answer key in math classes?

    -When teachers are not the answer key, it creates space for students to engage in their own thinking and problem-solving. This encourages students to take ownership of their learning, argue their points, and learn from each other's insights and mistakes.

  • How does the speaker suggest handling incorrect ideas in a math classroom?

    -The speaker suggests accepting even incorrect ideas into the debate, allowing students to explore the consequences of those ideas, and learning from the process. This approach shows respect for students' right to participate in mathematical thinking and can lead to breakthroughs and a deeper understanding of concepts.

  • What role does play have in the learning of mathematics?

    -Play is crucial in mathematics as it allows students to own the subject, explore concepts freely, and develop a love for the subject. It is through play that students can exercise their creativity and curiosity, leading to a more profound understanding of mathematical concepts.

  • What is the ultimate goal of the speaker's approach to math education?

    -The ultimate goal is to help students experience the beauty and power of authentic mathematical thinking, fostering a generation that meets the future with courage, curiosity, and creativity, and potentially leading to a shift in perception where students can genuinely say they love math.

Outlines
00:00
🤔 The Impact of Mathematical Miseducation

The speaker discusses the negative impact of traditional math education, which often involves rote memorization and repetition rather than fostering a love for mathematics. They highlight the importance of mathematical literacy and how a lack of it can limit career opportunities and make individuals vulnerable to manipulation by statistics. The speaker emphasizes the need for a change in educational approach, advocating for a method that encourages questioning, doubting, and exploring the beauty of mathematical thinking.

05:05
🚀 Encouraging Perseverance and Curiosity in Math

The speaker argues that education should teach students to be persistent and courageous when facing mathematical challenges. They share an experience of engaging a classroom in a thought-provoking question about numbers and colors, which led to active participation and deeper curiosity. The speaker emphasizes that teachers should not be seen as the sole source of answers, but rather as facilitators of exploration and discovery, fostering an environment where students feel empowered to question and contribute their ideas.

10:05
🤯 Embracing the 'What If?' Approach in Mathematics

The speaker illustrates the power of asking 'what if?' in mathematics, using the hypothetical scenario of 2 plus 2 equaling 12 as an example. They explain how exploring this idea can lead to a better understanding of mathematical concepts and even the invention of new mathematical fields, such as modular arithmetic. The speaker advocates for a playful and open-minded approach to math education, encouraging students to embrace their curiosity and the spirit of exploration.

Mindmap
Keywords
💡Mathematical thinking
Mathematical thinking refers to the process of using mathematical concepts, patterns, and logic to understand and solve problems. In the video, the speaker emphasizes the importance of this type of thinking, arguing that it can transform lives and should be fostered in education to encourage curiosity, creativity, and problem-solving skills. The speaker shares a personal story about a child who dislikes math, highlighting the need to change the traditional approach to teaching math that focuses on memorization and repetition, and instead promote a more engaging and thought-provoking method.
💡Miseducation
Miseducation in the context of the video refers to the ineffective teaching methods that lead to a lack of understanding and appreciation for mathematics. The speaker argues that the common practice of teaching math through rote memorization and disjointed facts without fostering a deeper understanding or critical thinking skills results in students disliking math and missing out on its beauty and power. This miseducation also has practical consequences, such as limited career opportunities and susceptibility to misleading statistics.
💡Literacy
In the video, mathematical literacy is described as the ability to understand and apply mathematical concepts in various contexts. It is portrayed as a critical skill that expands career opportunities and enables individuals to make informed decisions, especially in the face of persuasive statistics. The speaker emphasizes that without this literacy, people are more vulnerable to manipulation by entities like credit card companies and lottery systems.
💡Authentic questions
Authentic questions are those that are genuine, compelling, and arise from curiosity or a desire to understand something better. In the context of the video, the speaker advocates for starting math classes with such questions to engage students in real thinking, as opposed to beginning with predetermined answers that require memorization. This approach is meant to stimulate students' innate curiosity and encourage them to explore mathematical concepts more deeply.
💡Tenacity
Tenacity in the video refers to the quality of being persistent and determined, especially in the face of challenges or difficulties. The speaker argues that education should teach students to be tenacious, to persevere with math problems rather than giving up quickly. This principle is about fostering resilience and a growth mindset, where students learn that struggle is a natural part of the learning process and that taking risks and making mistakes are valuable for understanding and mastery.
💡Teacher's role
The teacher's role, as discussed in the video, is not to be the answer key but to facilitate learning by encouraging exploration, questioning, and critical thinking. Teachers should embrace moments when students ask questions they cannot answer, using them as opportunities to embark on a learning journey together. This approach shifts the focus from the teacher as the sole source of knowledge to a collaborative exploration of mathematical concepts.
💡Participation
Participation in the video signifies the active involvement of students in the learning process, particularly in the context of mathematical thinking. The speaker argues that by accepting even incorrect ideas into the debate and saying 'yes' to students' right to engage in mathematical thinking, educators empower students and respect their contributions. This inclusive approach validates students' efforts and encourages them to take ownership of their learning.
💡Play
In the video, play is described as a crucial element in learning mathematics. It is about engaging with math in a way that is exploratory, imaginative, and rule-breaking, which fosters a deeper understanding and appreciation for the subject. The speaker argues that play is not just for fun but is the highest form of research, as it allows for the exploration of new ideas and the potential for groundbreaking discoveries.
💡Courage
Courage, as discussed in the video, is the willingness to ask bold, potentially颠覆性的问题 and to explore the consequences of those questions. It is about challenging established norms and being open to new possibilities, even when they seem impossible or absurd at first. The speaker highlights that this courage is essential for innovation and breakthroughs in mathematics and should be encouraged in students to foster a mindset of inquiry and resilience.
💡Modular arithmetic
Modular arithmetic is a system of arithmetic for integers, where numbers 'wrap around' upon reaching a certain value, called the modulus. It is a fundamental concept in number theory and has applications in various fields, including cryptography and computer science. In the video, the speaker mentions modular arithmetic as an example of how play and exploration in math can lead to significant and practical discoveries, such as ensuring the security of credit card numbers online.
💡Number line vs. number circle
The number line is a straight, one-dimensional representation of numbers in sequential order, while the number circle is a conceptual model where numbers wrap around in a circular formation. In the video, the speaker uses the number circle as a metaphor for modular arithmetic, illustrating how thinking beyond conventional models can lead to innovative mathematical ideas. This concept challenges students to consider alternative ways of representing and understanding numbers, fostering creativity and deeper comprehension.
Highlights

The importance of mathematical thinking in personal and professional life.

Mathematics can be a source of joy or frustration, depending on one's educational experience.

The prevalence of mathematical miseducation leading to a lack of motivation and lifelong dislike for math.

The impact of mathematical literacy on career opportunities and susceptibility to misleading statistics.

The anecdote about a child disliking math despite the speaker's love for it.

The five principles proposed to improve mathematical education and promote thinking.

Starting with a question rather than answers to foster real thinking in math classes.

The necessity of allowing time for students to struggle with problems to develop perseverance and critical thinking.

Teachers not being the answer key, but rather facilitators of exploration and learning.

The importance of saying 'yes' to students' ideas, even incorrect ones, to encourage participation and respect their thinking process.

The concept of 'number circles' or modular arithmetic as an example of how playful exploration can lead to significant mathematical discoveries.

The role of play in mathematics, comparing it to the freedom and ownership felt in childhood play.

The potential of mathematics to teach courage, curiosity, and creativity to the next generation.

The transformative experience of a math workshop where a participant felt 'like a God'.

The philosophical exploration of thinking by René Descartes and its relevance to mathematical thinking.

The example of colors and numbers that provoke curiosity and authentic mathematical questions.

The empowerment of students through mathematical conversations and debates, rather than passive learning.

Transcripts

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