This Math is SO HARD For People
TLDRThe video script discusses the challenges of learning trigonometry, a subject often found difficult due to its requirement for memorization of various functions and identities. The speaker, who has taught trigonometry, empathizes with students' struggles and shares personal experiences. They suggest that memorizing the unit circle and using reference angles can simplify the process. The script also reviews a comprehensive trigonometry textbook by Charles McKeague and Mark D Turner, highlighting its clarity and thoroughness, and recommends it for those looking to master the subject.
Takeaways
- 😌 Trigonometry is often considered a challenging subject for many students, including the speaker, who has struggled with it and observed others struggle as well.
- 📚 The speaker has taught trigonometry in college and found that students tend to struggle more with it compared to other math classes.
- 🤔 The difficulty in learning trigonometry might be due to the need to memorize a lot of information, which many people find hard to do.
- 📈 Trigonometry is typically taken after a course in college algebra, which covers topics like polynomial functions, rational functions, and graphing.
- 📘 The speaker introduces a specific trigonometry textbook by Charles McKeague and Mark D. Turner, which is comprehensive and dedicated solely to the subject.
- 📝 Memorization is a significant part of learning trigonometry, including memorizing values of trigonometric functions for various angles.
- 🧠 The speaker suggests that the best approach to learning trigonometric function values is to memorize the unit circle for quadrant one and use reference angles for the rest.
- 📉 The speaker empathizes with students who find trigonometry difficult and discourages the attitude of looking down on those who struggle with it.
- 🔢 Trigonometry involves learning new functions like sine, cosine, and tangent, as well as their reciprocals, which can be overwhelming for students.
- 👨🏫 The speaker advises teachers to go slow when teaching trigonometry, acknowledging its difficulty and the common struggle students face.
- 🔗 The speaker provides resources for learning mathematics, including trigonometry, through courses available on their website, mathsorcerer.com.
Q & A
What is the subject that the speaker finds many students struggle with?
-The subject that the speaker finds many students struggle with is trigonometry.
What is the usual prerequisite for taking a trigonometry course in the U.S.?
-The usual prerequisite for taking a trigonometry course in the U.S. is having some algebra skills, typically acquired through a course called college algebra.
What is the primary reason the speaker believes students struggle with trigonometry?
-The primary reason the speaker believes students struggle with trigonometry is the requirement to memorize a lot of information.
What is the speaker's opinion on the best way to learn trigonometric function values?
-The speaker's opinion on the best way to learn trigonometric function values is to memorize quadrant one of the unit circle and then apply the knowledge of trig functions and reference angles to find the rest of them.
What does the speaker suggest about the attitude towards students who struggle with trigonometry?
-The speaker suggests that it's not good to look down on students who struggle with trigonometry, as it takes a special kind of effort to get good at it.
What is the speaker's experience with teaching trigonometry?
-The speaker has taught trigonometry in college in the past and found that students really struggle with it compared to other math classes.
What is the speaker's strategy for making the trigonometry class easier for students?
-The speaker's strategy includes going slower, not assigning really hard homework questions, and making the tests fairly easy.
What is the name of the textbook the speaker is reviewing in the script?
-The textbook the speaker is reviewing is 'Trigonometry' by Charles McKeague and Mark D. Turner.
What edition of the 'Trigonometry' textbook is the speaker reviewing?
-The speaker is reviewing the sixth edition of the 'Trigonometry' textbook.
What are some of the topics covered in the 'Trigonometry' textbook by McKeague and Turner?
-Some of the topics covered in the textbook include the six trig functions, right angle trigonometry, radian measure, graphing and inverse functions, identities and formulas, equations, triangles, complex numbers, polar coordinates, review of functions, and exponential and logarithmic functions.
What advice does the speaker give to teachers who are teaching trigonometry?
-The speaker advises teachers to go slow when teaching trigonometry because it is a difficult subject for many students.
Outlines
📚 The Challenge of Learning Trigonometry
The speaker discusses the difficulty many students face when learning trigonometry, a subject that typically follows college algebra. They share personal experiences as a teacher and a student, noting the struggle to memorize trigonometric values and functions. The speaker empathizes with students, acknowledging the effort required to learn trigonometry and suggesting that memorization is a significant part of the challenge. They also hint at a preferred method of learning trigonometric values using the unit circle and reference angles, which minimizes the amount of memorization needed.
🔍 Comparing Memorization in Trigonometry and Algebra
This paragraph delves into the comparison between the memorization required in trigonometry versus algebra. The speaker points out that while algebra has a few key formulas that are relatively easy to remember and apply, trigonometry introduces a multitude of new functions, their reciprocals, and the need to graph them with consideration for asymptotes. The complexity of trigonometric equations adds to the challenge. The speaker also shares advice for teachers on how to approach teaching trigonometry, emphasizing the importance of going slow and being understanding of the difficulties students face.
📘 Reviewing 'Trigonometry' by Charles McKeague and Mark D Turner
The speaker presents a detailed look at a trigonometry textbook by Charles McKeague and Mark D Turner, discussing its comprehensive nature and the thorough coverage it provides on trigonometric topics. They highlight the book's clear explanations, such as the definition and importance of reference angles, and the 'reference angle theorem,' which is crucial for determining trigonometric function values. The speaker appreciates the book's depth, including sections on arc length, area of a sector, and velocities, which are not commonly found in pre-calculus textbooks. They recommend this book for those learning trigonometry and provide a link to their website for further math courses.
Mindmap
Keywords
💡Trigonometry
💡Memorization
💡Unit Circle
💡Reference Angle
💡Algebra
💡Polynomial Functions
💡Graphing
💡Mnemonic
💡Calculus
💡Charles McKeague and Mark D Turner
💡Mathsourcer.com
Highlights
Trigonometry is a challenging subject for many students, often more so than other areas of mathematics.
The instructor's personal experience indicates that students tend to struggle more with trigonometry compared to other math classes.
Efforts have been made by the instructor to simplify the teaching of trigonometry, such as slowing down the pace and assigning easier homework and tests.
Trigonometry requires a significant amount of memorization, which is a common challenge for students.
Memorization involves retaining mathematical values and formulas for extended periods, which can be difficult for many learners.
The sine and cosine values for specific angles, such as pi/3, must be memorized and recalled accurately throughout the course.
Some students in calculus may not have a strong grasp of trigonometry, which can hinder their progress.
The instructor emphasizes the importance of not underestimating the difficulty of trigonometry and the effort required to master it.
The method of memorizing only quadrant one of the unit circle and using reference angles is recommended for simplifying trigonometry.
Trigonometry's difficulty is partly due to the variety of functions and their properties, such as asymptotes and graphing.
Teaching trigonometry is considered particularly challenging due to the subject's complexity and the common struggles students face.
The book 'Trigonometry' by Charles McKeague and Mark D. Turner is highlighted for its comprehensive coverage of trigonometry topics.
The book provides clear definitions and examples, such as the concept of reference angles and their importance in trigonometry.
The reference angle theorem is a key concept that helps in finding the trigonometric function values of any angle.
The book includes a dedicated section on arc length and area of a sector, which is more in-depth than what is typically found in pre-calculus books.
The instructor offers courses on various mathematical topics, including trigonometry, through their website MathSourcerer.com.
The video concludes with encouragement for students taking trigonometry, acknowledging the subject's difficulty and the value of persistence.
Transcripts
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