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Zoie, the information Plumbata has provided is correct. I would venture that Plumbata is either a Geologist or someone with a strong interest in mineralogy.
Your area is a prime hunting ground for ammonites. Have you found any of those around? My father found one a few years ago that he said was 3-feet in diameter in Whitney. Unfortunately, he just left it and did not bother to bring it back.
The pieces are most likely Gypsum, or possibly Calcite, as DanKnug suggested. Considering how you can scratch it with your fingernail, it is almost certainly Gypsum. It occurs in several forms with different names, but the clear/translucent masses like the ones your son discovered, or clear slender needle-like crystals of hydrated calcium sulfate (Gypsum), are often referred to as "Selenite". If you scrape an example and collect a bit of powder to mix with vinegar, not much should happen if it is Gypsum, though if it is Calcite it will react and visibly bubble.
Crystalline gypsum can form in many sedimentary environments in a "geologically" short period of time. I've collected rosettes in Miocene deposits of compressed sand and clay, with fossilized shark teeth coming from the same area. Since the material you have came from a sand mine (sedimentary deposit) it is highly unlikely that it is quartz or another silicate mineral, as it would be very unlikely that a layer of quartz/glass/fused silica could form between undisturbed layers of "loose" sand, as far as I understand. If one is not too familiar with minerals though, it would certainly make sense that a similar-looking rock is made of the same stuff as the sand above and below.
The core fact here is that a fingernail can scratch the mineral, implying that it has a Moh's hardness of less than 3/10. The hardness of a fingernail is around 2.5-3/10, Gypsum is 2/10, Calcite is 3/10, Iron is around 5/10 I think, and Quartz/SiO2 has a Moh's hardness of 7/10, which clearly rules it out.
Anyway, those are nice specimens, it is great that your son thought they were interesting and saved them!