Comfort with Numbers: Math
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Main Notes
- Classical education considers competency in higher-level math skills and comfort with mathematical thinking as part of basic literacy
- Students should complete courses in geometry, first-year algebra, and second-year algebra
- At least one year of advanced mathematics is recommended: trigonometry, pre-calculus and calculus, statistics and probability
- STEM-focused students should aim for a more advanced sequence
- All students should aim to complete at least one advanced mathematics course in twelfth grade
- Understanding of statistics and probability is vital for interpreting data and making informed decisions
- Trigonometry applies geometry to solve real-world problems
- Humanities-focused students often struggle to see the purpose of mathematics
- Online learning can be valuable for upper-level math
- Reading books about math can help build general math literacy
- Students struggling with algebra should change their approach rather than pushing forward
- High-school math requires at least an hour per day, four or five times per week
- A minimum of 3 high-school credits in mathematics is required; four is ideal
Cue Column
- What constitutes basic mathematical literacy in classical education?
- Why is advanced mathematics important for all students?
- How does the math sequence differ for STEM-focused students?
- What is the significance of statistics and probability in everyday life?
- How can trigonometry be applied to real-world problems?
- What challenges do humanities-focused students often face with math?
- How can online learning benefit upper-level math students?
- Why is reading about math important in addition to solving problems?
- What should be done if a student is struggling with algebra?
- How much time should be dedicated to high-school math study?
- What is the minimum number of math credits required for high school?
- How can math education be tailored for students with different career goals?
- What role does conceptual understanding play in math education?
- How can parents support their children's math education at home?
- What are the benefits of integrating math history and literature into the curriculum?
Summary
This chapter emphasizes the importance of higher mathematics in a classical education, considering it an essential part of basic literacy. The curriculum outline suggests that all students should complete courses in geometry, algebra I, and algebra II, with at least one year of advanced mathematics such as trigonometry, pre-calculus, calculus, or statistics and probability.
For STEM-focused students, a more rigorous sequence is recommended, potentially starting as early as seventh grade. The chapter stresses the practical applications of mathematical thinking, particularly in areas like statistics and trigonometry, which have real-world relevance.
The text acknowledges the challenges faced by humanities-focused students in seeing the purpose of abstract mathematical concepts. It suggests that this is often a teaching problem rather than a learning problem, emphasizing the importance of finding good teaching methods or resources.
Online learning is highlighted as a valuable tool for upper-level math education. The chapter also recommends supplementing technical math work with reading books about mathematics to maintain perspective on the broader significance of the subject.
For struggling students, the advice is to change approach rather than pushing forward unproductively. The chapter suggests a 'math reading' program as an alternative for students who find advanced math particularly challenging.
Overall, the chapter presents a balanced view of mathematics education, emphasizing both technical skills and conceptual understanding, while acknowledging the diverse needs and abilities of different students.
Action Items
- Complete Algebra I by 9th grade
- Complete Geometry by 10th grade
- Complete Algebra II by 11th grade
- Complete at least one advanced math course (Trigonometry, Pre-calculus, Calculus, or Statistics) by 12th grade
- Start Algebra I in 7th or 8th grade
- Complete Calculus by 12th grade
- Choose at least one book per year from the recommended reading list
- Focus on books that explain the purpose and real-world applications of math
- Change math program if a student is struggling with algebra
- Consider a 'math reading' program for students who struggle to reach Algebra II
- Allocate at least one hour per day, 4-5 times per week for math study
- Use the fifth day for general math reading if not used for regular study
- Explore options such as Art of Problem Solving, Math-U-See, Saxon, or VideoText
- Consider supplementary resources like Khan Academy or Life of Fred
- List each completed math course as 1 credit
- Aim for a minimum of 3 (ideally 4) high school math credits