When I was in late primary and middle school (east coast US, early 1990's), we were assigned a lot of word problems of the following general form:
Mary has eight self-sealing stem bolts. She sells half to John and then finds an additional self-sealing stem bolt on the playground. How many self-sealing stem bolts does she now have?
The obvious way to solve this is to show:
8 - (8/2) + 1 = 5
My teachers expressed to me in no uncertain terms that this was absolutely wrong. The correct answer was:
8 self-sealing stem bolts - ( 8 self-sealing stem bolts / 2 ) + 1 self-sealing stem bolt = 5 self-sealing stem bolts
Sometimes, if we failed to fully clarify the units of the answer, the teacher would mock us by saying things like, "Five? Five what? Five elephants? You need to be more specific."
This always struck me as redundant and pedantic. The wording of the question indicates that any response must be addressed in terms of self-sealing stem bolts and not any other unit (e.g. elephants, crystals, spiral notebooks, or planet-killing photon cannons) to qualify as a reasonable answer, so an answer of "5" is in fact perfectly clear and unambiguous when taken in context with the question asked and not as a lone number floating out their in the void of context-free and content-free nothingness.
Certainly, if I was asked today on the job, "Hey, how many vials of delta-omega varuonic acid do we have left on the shelf?", I would give an answer like, "Hey, yeah, looks like five.", rather than pedantically wasting everyone's time by saying, "The answer to your question is that there are five vials of delta-omega varuonic acid on the shelf."
I am aware that tracking units throughout is useful when doing dimensional analysis, but the vast majority of problems that we were assigned involved only one dimension or unit.
A small number of teachers went even beyond this and required all answers to word problems to be expressed in complete sentences. For them, an answer of "5 self-sealing stem bolts" wasn't good enough, the correct answer was "Mary has 5 self-sealing stem bolts.", but discussing that is a question for another day.
So, I can come up with the following cases in which requiring students to disclose, declare, or identify the units of their steps or answer might be considered pedagogically relevant:
- The problem inherently requires dimensional analysis/unit conversion in such a way as to require the student to track and record the units in order to identify the correct mathematical operations to perform.
- Identifying the units of the answer is part of the problem itself rather than stated within the question. For example, asking students "What is Ann's speed?" may require them to recognize the difference between units of speed, time, and distance, and so having the student identify which unit is the speed unit demonstrates learning.
- The problem is worded in such a way as to give the student choice over which units to give the answer in. For example, a question requiring the student to "Provide the length" might allow the student to choose whether to express the length in terms of meters, centimeters, inches, furlongs, or FIFA-regulation soccer field lengths, and thus the grader must know which units the student chose in order to grade their answer.
Other than the cases above, is there pedagogical value in requiring students to explicitly state the units of answers when the appropriate units are already clear from context?