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The nominal entry level into university-level mathematics is first-semester freshman calculus. The way that class is customarily taught, it makes only extremely modest demands on students' high-level reasoning skills, such as reading comprehension, creativity, and sense-making. There are almost no "word problems," and the class consists almost entirely of differential calculus, at which students can succeed simply by mastering rules.

Students need skills like the following in order to succeed in such a class:

  • ability to manipulate fractions
  • order of operations
  • ability to solve an equation for an unknown
  • knowledge of some very basic trigonometry, such as being able to tell what is the sine of 90 degrees and explain why without recourse to rote memorization
  • knowledge of exponents and logarithms and basic properties such as $\log(ab)=\log a+\log b$

Many students at this level have only been exposed to solving multiple equations in multiple unknowns in the case where the equations are linear. That is probably sufficient in most cases for success in such a class.

The classes that will more stringently test their preparation are second-semester calculus (because integration is not algorithmic) and first-semester physics (because it's all word problems and interpretation, and one often has to solve multiple nonlinear equations in multiple unknowns).

The nominal entry level into university-level mathematics is first-semester freshman calculus. The way that class is customarily taught, it makes only extremely modest demands on students' high-level reasoning skills, such as reading comprehension, creativity, and sense-making. There are almost no "word problems," and the class consists almost entirely of differential calculus, at which students can succeed simply by mastering rules.

Students need skills like the following in order to succeed in such a class:

  • ability to manipulate fractions
  • order of operations
  • ability to solve an equation for an unknown
  • knowledge of some very basic trigonometry, such as being able to tell what is the sine of 90 degrees and explain why without recourse to rote memorization
  • knowledge of exponents and logarithms and basic properties such as $\log(ab)=\log a+\log b$

Many students at this level have only been exposed to solving multiple equations in multiple unknowns in the case where the equations are linear. That is probably sufficient in most cases.

The classes that will more stringently test their preparation are second-semester calculus (because integration is not algorithmic) and first-semester physics (because it's all word problems and interpretation).

The nominal entry level into university-level mathematics is first-semester freshman calculus. The way that class is customarily taught, it makes only extremely modest demands on students' high-level reasoning skills, such as reading comprehension, creativity, and sense-making. There are almost no "word problems," and the class consists almost entirely of differential calculus, at which students can succeed simply by mastering rules.

Students need skills like the following in order to succeed in such a class:

  • ability to manipulate fractions
  • order of operations
  • ability to solve an equation for an unknown
  • knowledge of some very basic trigonometry, such as being able to tell what is the sine of 90 degrees and explain why without recourse to rote memorization
  • knowledge of exponents and logarithms and basic properties such as $\log(ab)=\log a+\log b$

Many students at this level have only been exposed to solving multiple equations in multiple unknowns in the case where the equations are linear. That is probably sufficient in most cases for success in such a class.

The classes that will more stringently test their preparation are second-semester calculus (because integration is not algorithmic) and first-semester physics (because it's all word problems and interpretation, and one often has to solve multiple nonlinear equations in multiple unknowns).

Source Link
X Y
X Y
  • 59
  • 2

The nominal entry level into university-level mathematics is first-semester freshman calculus. The way that class is customarily taught, it makes only extremely modest demands on students' high-level reasoning skills, such as reading comprehension, creativity, and sense-making. There are almost no "word problems," and the class consists almost entirely of differential calculus, at which students can succeed simply by mastering rules.

Students need skills like the following in order to succeed in such a class:

  • ability to manipulate fractions
  • order of operations
  • ability to solve an equation for an unknown
  • knowledge of some very basic trigonometry, such as being able to tell what is the sine of 90 degrees and explain why without recourse to rote memorization
  • knowledge of exponents and logarithms and basic properties such as $\log(ab)=\log a+\log b$

Many students at this level have only been exposed to solving multiple equations in multiple unknowns in the case where the equations are linear. That is probably sufficient in most cases.

The classes that will more stringently test their preparation are second-semester calculus (because integration is not algorithmic) and first-semester physics (because it's all word problems and interpretation).