In Ecclesiastes 7:27, there is a brief phrase, "says Qohelet" (ʾāmĕrâ qōhelet). In the rest of the book, it seems like masculine verbs are used with Qohelet, despite Qohelet itself having a feminine form. Yet in 7:27, the verb appears to be feminine in the MT. Was this a mistake? Does this somehow indicate that Qohelet might be female? Or does the author have a purpose in using a feminine verb here?
Ecclesiastes 7:27 unusually records: "says Qohelet" (אָמְרָה קֹהֶלֶת = ʾāmĕrâ qōhelet), notable for more than one reason. The problem here is the gender of the verb (which is, in the MT, 3rd feminine singular).
The title "Qohelet", usually translated (when it is translated) as "the Preacher" or the like, only occurs in Eccl. 1:1, 2, 12; 7:27; 12:8, 9, 10 - that is, 3x in the first and last chapters, and once (7:27) in between.
Although apparently a grammatically feminine noun (with the -et ending), qōhelet is regarded by grammarians as masculine. P. Joüon & T. Muraoka, A Grammar of Biblical Hebrew (Rome: Pontificio Istituto Biblico, 2006), §89b (p. 244) explain:1
A very small number [of singular masculine nouns] have a feminine ending, e.g. קֹהֶלֶת man of an assembly. Here the feminine ending has an intensive nuance, just as it has in [some] Arabic forms...
In 1:2 (with ʾāmar) and 12:8, 9, and 10 (ʾāmar, limmad, and biqqēš, respectively), the verb used with Qohelet is a masculine form. So OP is quite right to wonder what is going on in 7:27 which is the only time a feminine verb is used with it.
The long-suggested solution appears (for example) in Gesenius-Kautzsch-Cowley at the end of §122r. A similar phrase occurs in 12:8 as אָמַר הַקּוֹהֶלֶת = ʾāmar haqqōhelet, "says the Preacher" - with the same (almost) consonants but a different word division, attaching the h/ה as the definite article to "Qohelet" rather than as feminine suffix on the verb:
The suggestion is to "re-divide" the consonants in the same fashion as 12:8 in 7:27. This solution is followed more or less routinely -- see, for example, George Barton's ICC commentary from 1908, or Michael Fox's monograph on Qohelet from 1989.
(This verse is also significant as being the only overt expression of the "compiler"/editor's voice outside the prologue/epilogue, but that's a different matter...)
See also GKC §122r cited later in this answer. Note also the grammatical information for קֹהֶלֶת given in BDB, p. 875a:
The verse appears as follows in the Masoretic Text.
The word קֹהֶלֶת is the same grammatical form as the feminine singular qal active participle, which is based on the triliteral root קָהַל, which means to assemble or call together (people or sayings). Although the word is feminine in gender, the referent is to someone male.
Ecclesiastes 12:9 (MT)
9 ...וְיֹתֵר שֶׁהָיָה קֹהֶלֶת חָכָם
9 In addition, because the teacher was wise...
The subject of the clause (קֹהֶלֶת) is feminine, but the predicate adjective חָכָם -- meaning wise -- is not in the feminine, but the masculine. For example, the word for teacher (קֹהֶלֶת) occurs seven times, but only once with the "holem waw" in Ecc 12:8 (הַקֹּוהֶלֶת), which is consistent with the alternative grammatical form of the feminine qal active participle. So the narrator in the text is a male, and therefore this noun attracts the male gender of the verb. O'Connor and Waltke (1990) indicate that such absence of "concord" (as they cite the example of the feminine form of קֹהֶלֶת) is not uncommon in the Hebrew Bible. They cite several examples to show that the written practice appears throughout the Hebrew Scriptures. In fact, the nuance of the phenomenon exists in modern Spanish: la persona [feminine] es un hombre [masculine]; modern German, das Mädchen [neuter] ist eine Frau [feminine]; or modern English: she [feminine] is an actor [masculine], instead of actress [feminine]. So in human language the gender of the grammatical noun does not always "concord" with the verb and/or its predicate adjective. The same happens in Biblical Hebrew.
Thus in the Book of Ecclesiastes the reference to this word for "teacher" occurs seven times, and in all but one instance we see the grammatical discord:- that is, the feminine noun (grammatical feminine form of the qal active participle) appears with the masculine verb (because the "teacher" is actually a man). But in one instance (the fourth and only instance which happens not to part of the prologue/epilogue), the word appears in "concord" with its verb: that is, in Ecclesiastes 7:27 the feminine קֹהֶלֶת would therefore appear to correlate to the feminine form of the verb, which is אָמְרָה. In other words, the "concord" is not consistent with the other usages of this word in this text, since the reader understands the קֹהֶלֶת to be a male. In this light, we may formulate the hypothesis that this "concord" was not some accident (for example, scribal elision), but in fact was deliberate.
If we therefore test the hypothesis that the intent of the author was not in reference to himself as the subject of the sentence (male), but to the woman mentioned in the previous verse (female), then the "concord" of subject and verb makes more sense.
In other words, if we assume that the original pre-Masoretic text was received verbatim with no scribal errors before (or after); if we assume that there were no quotation marks in the original autograph or Masoretic Text to discriminate who is speaking; if we assume that the nominative and vocative case may appear the same in Biblical Hebrew; and, finally, when we consider that there is no explicit verb in this verse to qualify "one and one" (and therefore point to the subject of the sentence), then the following translation is plausible.
Ecclesiastes 7:26-29 26 And I discovered more bitter than death the woman whose heart is snares and nets, whose hands are chains. One who is pleasing to God will escape from her, but the sinner will be captured by her. 27 Behold, I discovered this: [this same woman] says, “Teacher, [add] one plus one to find the answer,” which was what my soul was seeking and had not found. I discovered one man among a thousand [was able to add it up], but I have not found a woman among all these. 28 Behold, I have found only this: God made mankind upright, but they [men and women] have sought out many ingenious ways of trying to figure things out.
If we assume this translation is accurate, then the picture emerges that men in right relationship with God are apt to be in right relationship with women. Most men are not, although the original divine intent was that men and women be "upright" (with one another). That is, most people cannot "add it up" (i.e., only 1 man of every 1,000 people appears to understand). Since so many have not figured this out, they invent various explanations ("λογισμοὺς πολλούς" or מְשָׁלִים הַרְבֵּֽה) of how the sexes interact, as if adding one plus one were that simple as the woman had suggested to the teacher.
O'Connor, M. and Bruce Waltke (1990). Biblical Hebrew Syntax. Winona Lake: Eisenbrauns, 109.