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High school mathematics

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This page includes a brief overview of the high school mathematics curriculum, with a focus on college preparatory tracks in United States schools. Some of the remarks may not apply to homeschoolers and to high school students outside the United States.

The information on this page is useful.

Tracks

Quick summary

Track names are not standard and grade subdivisions are approximate, intended to provide a quick idea. Some schools cover a mix of topics.

Track name Courses, roughly in sequence (grades 9-12)
Comprehensive college preparatory track Prealgebra (quick review of algebraic ideas), Algebra 1, Geometry, Algebra 2, Precalculus/Trigonometry and Statistics (basic, not calculus-based), Calculus (basic, not at AP level)
Advanced Placement or equivalent Honors track Algebra 1, Geometry, Algebra 2, Precalculus/Trigonometry, AP Calculus (AB or BC)
Accelerated Advanced Placement track Algebra 2, Geometry, Precalculus/Trigonometry, AP Calculus BC (finish junior year), use senior year to do AP Statistics, multivariable calculus, linear algebra, or other subjects

Comprehensive college preparatory track

Starting point (beginning grade 9): Student comes in somewhat familiar with but not proficient in the language of algebra.

Ending point (end of grade 12): Student has the requisite foundation in algebra, trigonometry, and functions to begin the study of calculus in college. Some students on this track take a calculus course in high school that is targeted at a level below the Advanced Placement students.

Advanced Placement or equivalent Honors track

Starting point (beginning grade 9): Student comes in proficient with basic algebra (equivalent to US course label prealgebra in most schools)

Ending point (end of grade 12): Student completes an Advanced Placement Calculus class, either AB or BC.

Sub-tracks:

  • Advanced Placement AB track: Ends with completion of Advanced Placement Calculus AB.
  • Advanced Placement BC track: Ends with completion of Advanced Placement Calculus BC.

Of the people we have interviewed for case studies, all reported having an Advanced Placement Calculus track in their school. However, not all students have such tracks available in their school. Students interested in their intellectual development who find themselves in a school that does not offer Advanced Placement tracks should probably consider either switching schools or finding out ways to take Advanced Placement courses through other means.

However, some of our interviewees have reported that their school either did not have an Advanced Placement Calculus BC track, or had very few students enrolled in the track and/or very strict criteria for entry into that track. The differences between the AB and BC curricula are not significant, and students generally do not master the additional material in the BC curriculum well in any case. So, this should not be a cause for big concern, though it is still preferable to take the BC course in order to learn more and improve one's prospects for admissions as well as transfer credit.

Accelerated Advanced Placement track

Starting point (beginning grade 9): Student comes in proficient with basic algebra and possibly Algebra I (the first high school algebra course in the Advanced Placement track).

Early ending point (end of grade 11): Student completes Advanced Placement Calculus BC.

Senior year (grade 12): Student may take multivariable calculus and linear algebra courses, either at the school or at an online high school or local university. Some students may not exercise this option.

Sub-tracks:

  • Accelerated Advanced Placement track without additional courses in senior year.
  • Accelerated Advanced Placement track with additional courses (typically, multivariable calculus and linear algebra) in senior year.

Some schools, including elite private schools and science/technology magnet schools, have a highly populated accelerated Advanced Placement track. However, many schools attended by people we have talked to do not offer such a track explicitly. Keep in mind, however, that:

  • If a parent or other mentor of the student advocates well for the student, and the student meets the academic prerequisites, it may be possible for the student to take AP Calculus BC in junior year (grade 11) along with senior year students.
  • Even if the school does not offer multivariable calculus or linear algebra classes, the student may be able to attend such classes through an online high school or local university.

Staying on the right track

Better to stay ahead than fall behind

Many schools are inflexible about accelerating students. Therefore, it is important for students to stay on, or ahead of, their desired track. It may be necessary to start paying attention to this starting from middle school. Also, Students transferring from one school to another may face the problem that their credits or courses are not recognized.

What track is recommended?

  • For the majority of students who are very keen on intellectual development and want to stay open to many career options, we would recommend the Advanced Placement Calculus BC track (or the AB track if the BC track is unavailable).
  • We generally recommend an accelerated track in any of the following circumstances:
    • The student has a significant degree of passion or interest in mathematics.
    • The student shows significant potential or skill in mathematics.
    • The student is interested in pursuing mathematics or a mathematically based discipline (such as physics, chemistry, or economics) as a career.
    • The student's school recommends this track to the student.