Suppose you have 10 minutes left in a session with an ACT student. The student is currently getting every percent and punctuation question wrong (barring a lucky guess). You can only spend these 10 minutes on one topic. Which topic wins?
I think the ideal topic is one that 1) shows up a lot, 2) is currently missed by the student 100% of the time, and 3) is easy to teach. With that in mind…
1. How often do they show up?
On a sample of 7 recent ACTs, semicolons appeared 23 times, while percentages appeared 18 times. Because there are 75 English questions per test, but only 60 Math questions, that means that they were each present in a little more than 4% of the questions. However, in most cases, the answer choice with the semicolon is incorrect. So while knowing how to use semicolons improves a student’s chances of getting that question right (by eliminating one answer choice), it doesn’t guarantee a correct answer. In contrast, a student who fully understands percents will get most, if not all, percent questions correct. Advantage: Percents.
2. Do they already know it?
If a student is already getting every semicolon and percent question correct, neither is worth covering. In my scenario1, the student was missing every question related to either topic, so both are worth considering. Advantage: Equal.
3. How long is this going to take?
Do I have to change a lightbulb, or install a new appliance…or renovate a kitchen?
I would argue that teaching a semicolon is like changing a lightbulb for most students. If a student understands independent clauses (he can tell if something is a complete sentence or not), then I just have to tell him the rule: a semicolon separates two independent clauses. After a few examples, it should make sense, and very little follow-up is generally required. Worst case, I have to reinforce the rule, which takes less than a minute.
But if a student is getting every percent question wrong, I’m probably going to have to install a new appliance at best, and renovate a kitchen at worst. My student may not have ever heard the semicolon rule, but he has certainly been exposed to percents many times over the past 5+ years. If that concept still isn’t making sense, he probably does not feel comfortable with the concept of a proportion. He may be relying on all kinds of ‘shortcuts’ that I need to rip out so that I can rebuild everything from the ground up, starting with similar fractions. Ten minutes won’t be enough time, and whatever I do teach will need to be revisited over and over again in future sessions and homework assignments.
Advantage: Semicolons
3b. How much variety is there in this topic?
There are so many ways to ask a percent question. Here’s a small sample:
All of these questions will seem quite different to a student who has just been introduced to the topic.
On the other hand, while a semicolon can appear in an infinite variety of sentences, the task of determining whether a clause is independent or not does not vary too much in difficulty:
Advantage: Semicolons
Winner: Semicolons!
Okay, I cheated a little by counting that last category twice…but semicolons are the clear winner here for me. In practice, a similar number of points are most likely at stake, and it’s going to be so much easier to teach and maintain semicolons.
In a way, I’ve made this scenario unrealistically simple. Students would usually understand a little bit about percents, but it would take some time for you to figure out exactly how much they know.
I was thinking semicolons from the beginning, and, as it turned out, my reasoning was similar to yours. The only real background knowledge required is whether or not a student can identify a complete sentence. Percentages have numerous usage types, and the connection between types is not immediately apparent. Your point, however, about semicolons being used incorrectly most of the time was not something I had previously noticed, so nice work there. I liked your algorithm/thought process here!
Interesting and helpful. I have a few comments.
The serial semicolon is now tested on the SAT, and I've seen students confused by that on the practice adaptive test (the first time it showed up) since we hadn't emphasized it.
I think of percentages as part of a group of math concepts --- percentages, proportions, and probabilities/stats -- that all share some characteristics, other than starting with "p." They are mostly middle school subjects and thus are forgotten math, and also, easy to learn . But, they also are all concepts that are readily embedded in question frameworks that make easy math hard to figure out. So, there may be two levels of teaching these things.