Math educators separate themselves into camps as to the value and emphasis to be placed on students performing algorithms, with or without meaning.
Now, the word algorithm did not appear in Webster's dictionary until after 1957.
It was predated by the word Algorism, which means "the proces of doing arithmetic using Arabic numerals.
The OED claims the word algorithm was a "corruption," being algorism "erroneously refashioned" by "learned confusion" with the word arithmetic.
Currently, math historians disagree with this claim, suggesting rather that it comes from the name Abu Ja'far Mohammed ibn Musa Mūsā al-Khwārizmī. A Persian author (ca. 825), he wrote the text Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala, from which we gain the term algebra.
Oddly, the text's name means "Rules of Restoration and Reduction," which befits how some view algebra. That is, 3x +2 = x +2 + 5 becomes 2x = 5.
Also, the title is connected to the practice of bloodletting, which many also associate with algebra!
Source: D. Knuth's The Art of Computer Programming (V 1), 1973.