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Daniel R. Collins
Daniel R. Collins
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Reasons for having automaticity with single-digit times tables (from the perspective of a community college lecturer with many remedial courses):

  • Long multiplication algorithm
  • Long division algorithm, and thus:
  • Convert fractions to decimals
  • Understand why rational numbers have repeating decimal expansions
  • Understand the proof why $\sqrt{2}$ is irrational
  • Factor integers, and thus:
  • Understand the Fundamental Theorem of Arithmetic
  • Reduce fractions by finding the LCD, and thus:
  • Add, subtract, multiply, divide, and compare fractions
  • Factor polynomials, and thus:
  • Reduce rational expressions
  • Solve higher-degree equations
  • Understand the Fundamental Theorem of Algebra
  • Estimations to double-check technology output

Perhaps on a deeper level I'd say that the base-10 place value writing system was architected specifically to easily support these operations, assuming that single-digit elementary operations were memorized (like phonemes) -- so if someone hasn't done that, they're really not using the language correctly.

Students should certainly know how to multiply any arbitrary number by 10. For products of two numbers above 10, I would agree that it's not really critical -- although the 11-table is trivial and knowing the 12-table may be handy when dealing with clocks, inches, and units in dozens (and $12^2$, one gross, does pop up a lot).

Reasons for having automaticity with single-digit times tables (from the perspective of a community college lecturer with many remedial courses):

  • Long multiplication algorithm
  • Long division algorithm, and thus:
  • Convert fractions to decimals
  • Understand why rational numbers have repeating decimal expansions
  • Understand the proof why $\sqrt{2}$ is irrational
  • Factor integers, and thus:
  • Understand the Fundamental Theorem of Arithmetic
  • Reduce fractions by finding the LCD, and thus:
  • Add, subtract, multiply, divide, and compare fractions
  • Factor polynomials, and thus:
  • Reduce rational expressions
  • Solve higher-degree equations
  • Understand the Fundamental Theorem of Algebra

Perhaps on a deeper level I'd say that the base-10 place value writing system was architected specifically to easily support these operations, assuming that single-digit elementary operations were memorized (like phonemes) -- so if someone hasn't done that, they're really not using the language correctly.

Students should certainly know how to multiply any arbitrary number by 10. For products of two numbers above 10, I would agree that it's not really critical -- although the 11-table is trivial and knowing the 12-table may be handy when dealing with clocks, inches, and units in dozens (and $12^2$, one gross, does pop up a lot).

Reasons for having automaticity with single-digit times tables (from the perspective of a community college lecturer with many remedial courses):

  • Long multiplication algorithm
  • Long division algorithm, and thus:
  • Convert fractions to decimals
  • Understand why rational numbers have repeating decimal expansions
  • Understand the proof why $\sqrt{2}$ is irrational
  • Factor integers, and thus:
  • Understand the Fundamental Theorem of Arithmetic
  • Reduce fractions by finding the LCD, and thus:
  • Add, subtract, multiply, divide, and compare fractions
  • Factor polynomials, and thus:
  • Reduce rational expressions
  • Solve higher-degree equations
  • Understand the Fundamental Theorem of Algebra
  • Estimations to double-check technology output

Perhaps on a deeper level I'd say that the base-10 place value writing system was architected specifically to easily support these operations, assuming that single-digit elementary operations were memorized (like phonemes) -- so if someone hasn't done that, they're really not using the language correctly.

Students should certainly know how to multiply any arbitrary number by 10. For products of two numbers above 10, I would agree that it's not really critical -- although the 11-table is trivial and knowing the 12-table may be handy when dealing with clocks, inches, and units in dozens (and $12^2$, one gross, does pop up a lot).

Source Link
Daniel R. Collins
Daniel R. Collins
  • 28.4k
  • 81
  • 132

Reasons for having automaticity with single-digit times tables (from the perspective of a community college lecturer with many remedial courses):

  • Long multiplication algorithm
  • Long division algorithm, and thus:
  • Convert fractions to decimals
  • Understand why rational numbers have repeating decimal expansions
  • Understand the proof why $\sqrt{2}$ is irrational
  • Factor integers, and thus:
  • Understand the Fundamental Theorem of Arithmetic
  • Reduce fractions by finding the LCD, and thus:
  • Add, subtract, multiply, divide, and compare fractions
  • Factor polynomials, and thus:
  • Reduce rational expressions
  • Solve higher-degree equations
  • Understand the Fundamental Theorem of Algebra

Perhaps on a deeper level I'd say that the base-10 place value writing system was architected specifically to easily support these operations, assuming that single-digit elementary operations were memorized (like phonemes) -- so if someone hasn't done that, they're really not using the language correctly.

Students should certainly know how to multiply any arbitrary number by 10. For products of two numbers above 10, I would agree that it's not really critical -- although the 11-table is trivial and knowing the 12-table may be handy when dealing with clocks, inches, and units in dozens (and $12^2$, one gross, does pop up a lot).