I almost failed calculus. Today I'm a math prof.

Dr. Trefor Bazett
26 Jul 202212:07
EducationalLearning
32 Likes 10 Comments

TLDRIn this inspiring video, a math professor shares his personal journey of struggling with calculus as a student and how his mindset and approach to learning transformed his academic performance. He emphasizes the importance of a growth mindset, active learning, and the possibility of falling in love with mathematics later in one's academic journey. The professor also highlights the availability of online resources like Brilliant, an interactive learning platform, to support students in their mathematical endeavors.

Takeaways
  • 🎓 The speaker, a math professor, struggled with calculus as a student but has since improved and changed their perspective.
  • 📚 Calculus is a challenging course and a requirement for many STEM programs, often leading to a reality check for students who initially feel confident about math.
  • 🧠 The importance of a growth mindset is highlighted, suggesting that believing in one's ability to improve in mathematics leads to more effective learning behaviors.
  • 🔄 A fixed mindset can hinder progress; the speaker's belief in being naturally good at math led to passive learning behaviors and a lack of effort to truly understand the material.
  • 🚧 The speaker's passive learning approach and lack of engagement with the material were barriers to success in university-level calculus.
  • 💡 The realization that struggling with calculus does not mean one is not suited for mathematics is crucial; improvement is always possible with the right approach.
  • 🔄 Active learning is emphasized as a key to success in mathematics, contrasting with the speaker's initial passive approach.
  • 📈 The speaker's experience with abstract algebra sparked a love for mathematics that later enhanced their appreciation for calculus.
  • 🌐 Online resources like Brilliant.org can provide interactive and supportive learning environments for students struggling with subjects like calculus.
  • 💌 The speaker acknowledges their own privileges that may not be available to all students, such as time to focus on studies without the pressures of part-time jobs.
Q & A

  • What was the speaker's initial experience with calculus as a student?

    -The speaker initially struggled with calculus, barely passing the first year, and had a poor attitude towards mathematics, believing that they were naturally good at it without needing to work hard.

  • What is the significance of having a growth mindset in mathematics according to the speaker?

    -A growth mindset, as opposed to a fixed mindset, encourages students to believe they can improve in mathematics, leading to more effective learning behaviors and actual improvement.

  • Why did the speaker's fixed mindset hinder their progress in calculus?

    -The speaker's fixed mindset led them to believe they were inherently good at math and thus did not engage in behaviors that would allow them to improve, such as practicing problems and seeking deeper understanding.

  • What was the speaker's approach to learning in university, and how did it affect their performance?

    -The speaker adopted a passive approach to learning, merely copying notes without engaging with the material, which resulted in poor performance and a lack of understanding.

  • How did the speaker's perception of their mathematical abilities change over time?

    -The speaker transitioned from a fixed mindset to recognizing the importance of effort and active engagement in learning, which improved their performance and emotional relationship with mathematics.

  • What advice does the speaker give to students who are struggling with calculus?

    -The speaker advises students not to let fixed mindsets limit their potential for improvement, to be active learners, and to understand that struggling with calculus does not mean they cannot succeed in mathematics.

  • Why is being an active learner important in mathematics according to the speaker?

    -Being an active learner involves engaging with the material, asking questions, practicing problems, and seeking understanding, which leads to a deeper grasp of concepts and better performance.

  • How did the speaker's relationship with mathematics evolve after university?

    -The speaker fell in love with mathematics, particularly the definition, theorem, and proof style, which led to a deeper appreciation for calculus and a stronger connection with the subject.

  • What is the speaker's perspective on the role of teachers in students' learning experiences?

    -The speaker acknowledges that teachers play a significant role in inspiring a love for mathematics, but also notes that the way calculus is commonly taught may not always be inspiring.

  • What resources does the speaker mention as being beneficial for students learning calculus today?

    -The speaker mentions the internet as a valuable resource with an abundance of materials to support learning, including interactive platforms like Brilliant, which offer visual intuition and practice opportunities.

  • How does the speaker's personal journey with mathematics reflect on their teaching philosophy?

    -The speaker's journey informs their teaching philosophy by emphasizing the importance of a growth mindset, active learning, and the potential for all students to improve and enjoy mathematics.

Outlines
00:00
🎓 Struggling and Overcoming Challenges in Calculus

The speaker, a math professor, shares their personal journey with calculus as a student. Initially struggling and barely passing first-year calculus, they discuss the importance of mindset and learning behaviors. They highlight the common misconception that struggling with calculus means one is not suited for mathematics. The professor emphasizes the growth mindset, which encourages the belief in one's ability to improve in mathematics, as opposed to a fixed mindset that can lead to passive learning and avoidance of challenges. They also touch on the psychological aspects of learning, such as the fear of disproving one's self-perceived abilities, and how these can hinder progress.

05:02
🌱 Cultivating a Growth Mindset and Active Learning

The professor continues by sharing insights from their experience teaching thousands of students. They assert that no student is incapable of improving in mathematics and that prior learning experiences and habits can influence the difficulty one faces with calculus. The speaker advises against letting fixed mindsets dictate one's learning behaviors and suggests that taking time to adjust to university life can be beneficial. They stress the importance of being an active learner, engaging with the material, asking questions, and practicing problems authentically. The professor's own realization of the need for active participation in learning significantly improved their relationship with mathematics and their academic performance.

10:02
💡 Discovering Passion and Resources for Learning

In the final paragraph, the professor reflects on their journey to falling in love with mathematics, which happened unexpectedly through an abstract algebra course. They emphasize that everyone's path to appreciating mathematics is unique and that not finding immediate love for calculus does not preclude one from enjoying mathematics in the future. The speaker acknowledges their own privileges during their learning process, such as not having to work part-time, which might not be the case for many students. They also mention the abundance of online resources available today to support learning, including their own channel and Brilliant, an interactive online learning platform that offers STEM topics and encourages active engagement with the material.

Mindmap
Keywords
💡Calculus
Calculus is a branch of mathematics that deals with the study of change and motion, encompassing the concepts of limits, derivatives, integrals, and infinite series. In the video, calculus is depicted as a challenging subject that is often a requirement for STEM programs. The speaker's struggle with calculus during their first year and eventual improvement highlights the theme of overcoming academic challenges and the importance of a growth mindset.
💡Growth Mindset
A growth mindset is a psychological concept introduced by Carol Dweck, which posits that an individual's abilities can be developed through dedication and hard work. The video emphasizes the importance of having a growth mindset in mathematics, suggesting that believing in one's ability to improve can lead to more effective learning behaviors and better performance in calculus.
💡Fixed Mindset
A fixed mindset is the opposite of a growth mindset; it is the belief that one's abilities are static and cannot be changed. The speaker discusses how having a fixed mindset in mathematics led to a lack of effort and poor learning strategies, which contributed to their initial struggles with calculus.
💡STEM Programs
STEM stands for Science, Technology, Engineering, and Mathematics. These interdisciplinary programs are often emphasized in the video as fields where calculus is considered a fundamental requirement. The speaker's initial motivation for taking calculus was due to their interest in pursuing a career in either physics or computer science, both of which are part of STEM.
💡Struggle
Struggle in the context of the video refers to the difficulties and challenges the speaker faced while learning calculus. It is a central theme that illustrates the journey from being a student who barely passed to becoming a professor who teaches the subject. The speaker's personal story of struggle serves to inspire and reassure viewers that initial difficulties do not define one's potential for growth and success in mathematics.
💡Passive Learning
Passive learning is a learning approach where students are not actively engaged in the learning process but rather passively absorb information. The speaker describes their initial approach to learning calculus as passive, such as copying notes without understanding or reviewing them, which did not support deep understanding or improvement.
💡Active Learning
Active learning is a teaching and learning strategy where students are directly involved in the learning process, such as asking questions, participating in discussions, and solving problems. The video emphasizes the importance of transitioning from passive to active learning as a key to the speaker's improvement in mathematics and their eventual success.
💡Self-Perception
Self-perception refers to how an individual views themselves, particularly in terms of their abilities and characteristics. In the video, the speaker's self-perception as being 'good at math' initially led to a fixed mindset and poor learning behaviors. The realization and change in self-perception were crucial in the speaker's journey to becoming a proficient mathematician.
💡Abstract Algebra
Abstract algebra is a branch of mathematics that studies algebraic structures, such as groups, rings, and fields. The speaker mentions falling in love with mathematics through an abstract algebra course, which introduced them to a different, more rigorous and logical style of mathematics compared to the computational focus often found in calculus.
💡Resources
Resources in the context of the video refer to the various study materials and platforms available to support learning, such as online courses, interactive platforms, and educational channels. The speaker mentions the abundance of internet resources as a modern advantage for students struggling with calculus, which was not available during their own learning experience.
Highlights

The speaker initially struggled with calculus and barely passed first year, despite later becoming a math professor.

Calculus is a requirement for many STEM programs, leading to a wide range of students with varying levels of preparedness.

Research supports the idea that a growth mindset can lead to more effective learning behaviors in mathematics.

Fixed mindsets can lead to passive learning behaviors and a lack of deep understanding.

The speaker's self-perception as being 'good at math' led to a delusional belief that they could succeed with minimal effort.

University calculus exposed the limitations of the speaker's high school learning strategies.

Developing anxiety about mathematics can lead to avoidance and a reluctance to engage with the subject.

Passive learning, such as copying notes without understanding, was a common behavior for the speaker as a student.

The speaker emphasizes that struggling with calculus does not mean one is not suited for mathematics.

Students who withdraw or fail calculus and then retry often have a decent success ratio.

Active learning, engaging with the material, and practicing problems authentically are key to understanding and success in mathematics.

The speaker's approach to learning changed significantly in the second half of their second year at university, leading to improved grades and a better relationship with mathematics.

Falling in love with abstract algebra helped the speaker appreciate the beauty of calculus and other areas of mathematics.

Everyone's journey to loving or appreciating mathematics is different, and it's okay if calculus isn't the spark for everyone.

The speaker acknowledges the privileges they had while learning calculus, such as not having to work part-time jobs, which many students do.

There are now many online resources available to support learning in mathematics, including the speaker's channel and the sponsored platform Brilliant.

Brilliant is an interactive online learning platform that allows students to learn STEM topics at their own pace with visual aids and feedback.

Transcripts

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