The method/apparatus does not have to be very accurate. The more simple, the better. I have looked into ELISA and it is not feasible with the environment that I am working in (high school lab).
To test the concentration of any specific protein, you have to perform molecularbiological methods, e.g. Western blottin or ELISA. Maybe, you can determine indirctly other parameter, e.g. general protein concentration (photometrically).
To calculate the concentration of a unknown protein you can perform the BCA assay using various concentration of BSA and two specific reagent (A&B) from Pierce. It's a standard protocol easily accessible in internet.
You can also go with congo red staining if you are interested in aggregatory forms of the amyloids, not the monomeric ones. Antibodies too have different specificities with different forms, like monomeric, oligomeric, fibrillar and plaques. So, the quantification in ELISA would also be not very accurate. Thanks
It is not a trivial problem. I suggest you to read this paper:
Article Quantification of Intrinsically Disordered Proteins: A Probl...
From my experience a very reliable technique (but not for everyday use) is 1D proton solution NMR by using references such as known amounts of DSS. However also spectrophotometry (NanoDrop) provides reliable measurments.
It is not trivial since Abeta is very hydrophobic. Unfortunately it seems you might have to take the students on a field trip to the lab. ELISAs can take 2-3 days so the alternatives would be 1) Western blot densitometry with known amounts of Abeta for a standard curve or at least a reference or 2) use the extinction co-efficient for tyrosine (i.e., HPLC or FPLC w/ UV detector).