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I have seen so many conflicting answers to this question in various places so I wanted to ask it again. IUPAC defines a transition element as

an element whose atom has a partially filled d sub-shell, or which can give rise to cations with an incomplete d sub-shell.

By this definition, scandium would be a transition element as its atom has an incomplete d shell.

However, I have seen many other definitions which require an incomplete d shell as a stable ion. This also adds confusion as the common scandium ion is $\ce{Sc^3+}$ which has no d electrons, so wouldn’t be a transition element, yet it’s my understanding scandium can display a +2 oxidation state also (albeit less commonly).

What’s the correct definition? Is scandium considered a transition metal or not?

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It may depend on who you ask, and maybe even when you ask. The tl, dr of what is below is that we are moving towards counting scandium as a transition metal.

Wikipedia follows the IUPAC definition and accepts the label for scandium because it forms atoms with partially filled $d$ orbitals, and also copper because it forms ions with partially filled $d$ orbitals in common settings. Either possibility is admitted by IUPAC and thus by Wikipedia.

On the other hand, Britannica does not use the label "transition metal" for Group 3 elements, because they do not retain $d$ electrons in their ions. Instead they render a separate classification, the "rare earth metals", in this group.

Britannica is based in the UK, of course, and we may be seeing a difference based on different countries. Let's look at a couple other sources:

https://chemed.chem.purdue.edu/genchem/topicreview/bp/ch12/trans.php, based in the United States, says yes, again following the IUPAC definition. https://www.chemguide.co.uk/inorganic/transition/features.html, based in the UK, reports that most UK syllabuses use a definition that excludes scandium from the transition metals. The latter source does state, however, that "the most recent IUPAC definition" would include scandium because of its neutral atom configuration.

The development of organometallic chemistry may have something to do with this evolution. Many elements, including magnesium and more recently calcium, show lower oxidation states in some organometallic environments. In the case of scandium this shows up as an atom retaining its $d$ electron while using the $s$ electrons and/or vacant $d$ orbitals for bonding to organic ligands. Going back to the Wikipedia article on scandium, this gives references to several organometallic examples in which scandium has reduced oxidation states, from +2 all the way down to 0. Looking at one such reference, it clearly shows a single scandium atom in a low oxidation state in a setting similar to how a later transition metal might appear. Such developments favor, and may have motivated, the broader, scandium (and yttrium) inclusive definition of a transition metal now used by IUPAC.

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