I would like to ask the experts of this chemistry community their opinions on which balance is more accurate and effective to use in a high school chemistry lab- a triple beam balance or a digital balance. I would appreciate your rationales for your answers as well. Thanks!
Recall that Theodore W. Richards got a Nobel Prize on "in recognition of his accurate determinations of the atomic weight of a large number of chemical elements." Guess which year was that? 1914!! Digital balances did not exist then. All high accuracy balances were mechanical balances then.
The point is that you can have a very crappy digital balance or a triple beam balance (= low price, no certification). All the accuracy of balances depends on their calibration with known weights. The accuracy of those known weights, depends on how they were calibrated by national and international standardizing agencies.
It all depends on the purpose. For organic synthesis work, a triple beam balance would be fine where ultrahigh accuracy of measured weight is not a big deal. What is being weighed and what is the level of accuracy required? How many accurate digits are required?
In short, both digital and triple beam balances are fine for routine work. We cannot say one is more accurate than the other. After all, the digital balance is also requires mechanical movement (i.e., it also has moving parts which you cannot see).
A digital balance is much easier to use. I guarantee some of your HS students are going to have huge errors when using a triple beam because they don't know how to read it. That's not necessarily a downside—you might want to give them training in the skill of using and reading a mechanical balance. OTOH, if you want them to focus on other aspects of the lab, or are concerned about time constraints, then a digital balance (which can be used much more quickly) would be the way to go.
As far as accuracy goes, at the entry level for calibrated quality scales (~\$150), you can get a digital balance with NIST-traceable calibration and the following specs (Cole-Parmer Symmetry Compact Portable Toploading Balance, 300g x 0.01g):
Triple beam balances typically only have 0.1 g readability. To get 0.01 g readability in a beam balance, you'd need to add finer adjustment, with either a dial or an extra beam. These get pricer (~$250+). Here's a quadruple-beam balance with 0.1 g readability, though without specs for repeatability or linearity: Ohaus 311-00 Cent-O-Gram Overhead Mechanical Balance, 311g x 0.01g.
But for a HS lab, you'll probably want to spend more like $30/scale. There the only way to determine the relative accuracy of the triple beam and digital balances will be to buy a set of calibrated weights and check for yourself. [Regardless of what claim the vendors make.] [And note that there will probably be a lot of inter-unit variation at that cost level, where some will be much more linear than others.]