What we’ve got wrong about learning mathematics | Alf Coles | TEDxBath

TEDx Talks
10 Dec 202115:26
EducationalLearning
32 Likes 10 Comments

TLDRIn this inspiring talk, the speaker reflects on 27 years of teaching mathematics and the challenge of making it relevant to students' lives. They share their journey from a disillusioned first-year teacher to embracing Caleb Goto's教育理念, which emphasizes understanding how students learn. The speaker argues against the traditional belief in a linear progression of learning, instead advocating for an interconnected approach that leverages the innate problem-solving abilities of students. Through examples like negative numbers and algebra, they illustrate how complexity can clarify concepts and unlock potential in all learners.

Takeaways
  • 🌟 The speaker has been dedicated to finding ways to make mathematics relevant and connected to students' lives for 27 years.
  • 📚 The speaker's initial teaching experience in South London revealed the challenge of engaging students and the need for a different approach.
  • 💡 The influence of Caleb Goteño's ideas on the speaker's teaching philosophy highlighted the importance of understanding how students learn.
  • 📈 The traditional belief in learning as a vertical construction, especially in math, was questioned for its effectiveness in engaging all students.
  • 🚫 The speaker argues against the common practice of separating students based on their academic progress and limiting their access to more advanced math concepts.
  • 🔄 The issue of students revisiting the same concepts without progress is highlighted, emphasizing the need for a more dynamic learning approach.
  • 🏃‍♂️ Learning is often non-linear, as exemplified by children learning to run before they walk, suggesting that foundational skills can be acquired through complex, immersive experiences.
  • 🌐 The speaker's research with Professor Natalie Sinclair suggests that certain beliefs about learning can hinder our ability to improve our skills daily.
  • 🔢 The concept of negative numbers and algebra, typically challenging topics, are used to illustrate how a more complex approach can lead to better understanding.
  • 📚 A case study of a low-attaining student who grasped the concept of square roots after engaging with more complex material supports the speaker's argument.
  • 🎓 The speaker encourages teachers and parents to consider offering more complex, rather than simpler, concepts to those who struggle, to unlock their potential.
Q & A
  • What is the main challenge the speaker has been grappling with for the last 27 years?

    -The speaker has been trying to understand how to make learning mathematics relevant to students' lives, connected to their interests, and significant for the world we live in.

  • How did the speaker's initial teaching approach affect students?

    -The speaker's initial approach, which emphasized student autonomy, inadvertently led to many students losing interest in mathematics, as it did not account for the fact that autonomy could be expressed by ignoring the teacher.

  • Who has significantly influenced the speaker's journey towards becoming a better teacher?

    -The speaker was greatly influenced by the writings and ideas of Caleb Gotoño, an educator born in Africa.

  • What is the main message in Caleb Gotoño's 45-second clip?

    -Caleb Gotoño emphasizes the need to stop teaching in ways that do not engage or reach students, and instead focus on becoming more skilled in helping them learn by understanding their needs.

  • How did the speaker change their teaching approach after the first year of teaching?

    -The speaker began collaborating with others, particularly Lorinda Brown, and started focusing on students asking questions and writing down their ideas about mathematics, moving towards a more engaging and inquiry-based curriculum.

  • What is the 'belief' that the speaker and Professor Natalie Sinclair believe hinders continuous skill development in learning?

    -They believe that the belief that learning is a vertical construction, where one must understand the basics before moving on to more complex concepts, can inhibit people from reaching their potential.

  • How does the speaker challenge the traditional view of learning as a building block process?

    -The speaker challenges this view by providing examples of learning in real-life situations, such as children learning to walk by running and school-age children achieving functional fluency in a new language in a short time, which do not follow a step-by-step, building block approach.

  • What alternative image of learning does the speaker propose?

    -The speaker proposes an image of learning as a meshwork or network, where learning involves piecing together small, relevant knots of practice and understanding, rather than a linear, vertical construction.

  • How does the speaker use the concept of negative numbers to illustrate the need for a more complex approach in teaching?

    -The speaker uses the concept of negative numbers to show that by presenting a more complex situation that includes negative numbers and their patterns, students can better understand and engage with the concept, rather than being limited by the simpler, concrete representations.

  • What example does the speaker provide to demonstrate that struggling learners might benefit from more complex, not simpler, content?

    -The speaker shares a story of a low-attaining student who, after working on the Pythagorean theorem, which was more complex than her current curriculum level, was able to understand and retain the concept of square roots, which she had struggled with for years.

  • What advice does the speaker give to teachers and parents regarding students who find certain subjects difficult?

    -The speaker advises teachers and parents to consider providing more complex content rather than simpler material when students struggle, as it may offer a more meaningful context and help the students engage with the subject more effectively.

Outlines
00:00
🤔 The Journey of Relevance in Mathematics Education

The speaker reflects on their 27-year quest to make mathematics education relevant to students' lives and the world. Initially a new teacher with high ideals, they learned that their first year's approach did not engage all students. Influenced by Caleb Goteño's ideas, they shifted their teaching to foster creativity and autonomy. The speaker emphasizes the importance of understanding how students learn and the need to move away from traditional beliefs that hinder effective teaching and learning.

05:02
🏗️ Challenging the Building Block Approach to Learning

The speaker critiques the common belief in education that learning, especially in math, is a vertical construction requiring solid foundations. They argue against the practice of segregating students based on their progress and offer examples of how learning often occurs in more complex and holistic ways. The speaker suggests that teaching should respect the innate problem-solving abilities of students and focus on a more interconnected approach to learning.

10:04
🔄 Understanding Negative Numbers and Algebra Through Complexity

The speaker discusses the challenges students face with concepts like negative numbers and algebra. They propose that instead of simplifying these topics, introducing more complex ideas can help students grasp these concepts better. By using complex situations that allow students to spot patterns and make predictions, learning becomes more meaningful and effective.

15:07
🌟 Success Stories in Overcoming Traditional Learning Barriers

The speaker shares a story of a student who, despite years of struggle with math, was able to understand and apply the concept of square roots after being exposed to more complex material. The speaker emphasizes that students should not be limited by the belief that they have reached their 'mathematical ceiling.' Instead, educators and parents should consider offering more complex, rather than simpler, content to help students overcome learning barriers.

🙏 Final Thoughts on the Meshwork of Learning

In conclusion, the speaker encourages teachers, parents, and learners to rethink the traditional vertical construction of learning and embrace a more interconnected, mesh-like approach. They suggest that by providing students with complex, meaningful contexts and opportunities to use their innate problem-solving skills, educators can help students reach their full potential in mathematics and beyond.

Mindmap
Keywords
💡Learning Relevance
The concept of making learning, specifically mathematics, meaningful and connected to students' lives and the world around them. This is central to the speaker's mission as an educator, aiming to engage students by linking mathematical concepts to real-world relevance and their personal interests.
💡Teaching Philosophy
The speaker's personal beliefs and ideals about education, which emphasize creativity, independence, and the potential for teaching to drive social change. This philosophy is shaped by the speaker's experiences and influences, such as Caleb Goteño's ideas, and is applied in the classroom to foster a more equitable and sustainable society.
💡Caleb Goteño
An influential educator from Africa whose writings and ideas significantly impacted the speaker's approach to teaching. Goteño's emphasis on understanding how students learn and the importance of teaching in a way that reaches them is a cornerstone of the speaker's educational philosophy.
💡Student Engagement
The active involvement and interest of students in the learning process. The speaker's goal is to create an environment where students are not just passive recipients of knowledge but are actively participating and asking questions about the subject matter.
💡Vertical Construction
A metaphor for the traditional belief that learning, especially in mathematics, occurs in a sequential and hierarchical manner, building upon a solid foundation of basics before moving on to more complex concepts. This approach can lead to students being separated and limited in their learning based on their perceived level of understanding.
💡Meshwork of Learning
A concept that represents learning as a network of interconnected ideas and skills, rather than a linear progression. This perspective encourages viewing learning as a complex, holistic process where understanding emerges from the interplay of various elements rather than a step-by-step buildup.
💡Negative Numbers
A mathematical concept that introduces numbers less than zero, often causing difficulty for learners due to its abstract nature and the challenge of visualizing or conceptualizing these values in the context of traditional number systems.
💡Algebra
A branch of mathematics that uses symbols and rules to manipulate these symbols to solve equations. It is often perceived as a challenging subject, especially when introduced through abstract and arbitrary symbols.
💡Pythagorean Theorem
A fundamental principle in geometry that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The speaker uses this theorem to illustrate how engaging with complex ideas can lead to better understanding and retention of mathematical concepts.
💡Educational Beliefs
The underlying assumptions and convictions that educators hold about the process of learning and teaching. These beliefs shape the strategies and methods used in the classroom and can either empower or limit students' potential for understanding and growth.
💡Social Change
The transformation of social structures, institutions, and cultural patterns within a society. The speaker views teaching as a potential driver of social change, aiming to foster a fairer, more equitable, and sustainable world through education.
Highlights

The speaker has spent 27 years pondering how to make mathematics relevant to students' lives and the world.

The speaker's journey began as a newly qualified teacher in South London with aspirations for a creative and independent classroom.

The realization that the speaker's initial teaching approach was alienating some students from mathematics.

Influence from Caleb Goteño, an educator who emphasized understanding how to teach in a way that reaches people to learn.

The importance of students asking questions and writing down their ideas about mathematics.

The concept of teaching as a driver of social change towards a fairer, more equitable, and sustainable society.

The existence of a set of beliefs that hinder educators from becoming more skilled every day.

The belief that learning is a vertical construction, particularly in math, with a focus on solid foundations.

The practice of separating children in schools based on their progress in this vertical construction.

The idea that children learn by running, not walking, challenging the traditional step-by-step learning approach.

The example of Caroline Herschel, who despite not knowing her times tables, became a renowned astronomer.

The notion that learning is more like a meshwork or network rather than a vertical construction.

The difficulty of teaching negative numbers when only focusing on simple addition.

The suggestion that struggling students may need something more complex, not simpler.

The story of a low-attaining student who grasped the concept of square roots after engaging with more complex ideas.

The encouragement for teachers and learners to consider a more complex approach to overcoming difficulties in learning.

The final message to rethink learning as a network of messy knots of relevance rather than a vertical construction.

Transcripts
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