0

When I studied physics (both in high-school and university), in all of the worked examples, variables would be used to denote physical quantities, and thus include dimensional units.

For example, with $F$ being a physical variable denoting force, the variable itself could be calculated in units of Newtons: $$ F=2\,\text{kg} * 5\,\text{m/s${}^2$}=10\,\text{N} $$ But I've recently started tutoring an engineering student, and saw in the worked examples from his lectures the use of variables as plain numbers, with the unit being outside the variable.

So modifying the same example, $F$ would now be a pure number that is multiplied by Newtons: $$ F\,\text{N} = 2\,\text{kg} * 5\,\text{m/s${}^2$} =10\,\text{N} \Rightarrow F=10 $$

Is there an educational benefit to one notational approach vs. the other? Has there been research done on this? Is this more relevant to particular levels of education or particular fields?

innisfree
  • 15,425
yoniLavi
  • 111

1 Answers1

1

Mathematicians just know pure numbers (or non-scalar entities, besides operators themselves) and don't like physical units, so I guess a math teacher designing an exercise involving a physical example might be tempted by anything that through units away so as to play with plain number.

While physicists consider than plain numbers mean nothing, excepted in the case of dimensionless quantities such as proportions. What has a unit is not only the final result but really each term in an equation. And since you cannot add inhomogeneous units (different unit or different power), this constrains the small subset of physically consistent equations among all the possible math equation (e.g. exp(x), log(x), sin(x) is physically consistent only if x is a dimensionless expression ). This allows physicists to immediately detect many errors. But it can also help even young math students to simplify fractions ( (m/s) / (m/s) = (m/m).(s/s) but can't be (m/s)*(m/s) ), and to understand why perimeter corresponds to + and area correspond to * (since unit is L+L=m vs L*L=m²).

So like colleagues, I just can be horrified by this new notation, and see mostly problems with using it. ( Contrarily, I urge math teachers to use more units in their examples and exercises. )

Fabrice NEYRET
  • 3,890