In reply to cap'nChino:
My guess would be it's not a "winter climbing teacher", rather a Design&Technology (or whatever it's now called) teacher, who may or may not climb, who was looking for something that would involve different types of metal-working techniques (do you forge, cast, &c, how do you connect the bits together, what material would you use...) to suggest for GCSE coursework.
And while you could ask exactly the same questions about e.g. carabiners, ice axes probably have a little more recognition/"coolness factor" amongst schoolkids.
My advice for all these pupils would be threefold:
Firstly - Google is your friend; companies like DMM and Black Diamond have loads of videos/articles promoting their snazzy manufacturing techniques...
Secondly - if you're making these things, don't actually use them for a strength-critical application such as a belay unless you make loads and test them to destruction (and, related, if you research and mention the legal standards and testing; e.g. T-rated vs B-rated it will probably help your grade)
Thirdly - go and try ice-climbing if there's any indoor ice wall near you (or if you can convince the parents to shell out for a taster day in the mountains... (if Plas-y-Brenin or similar do such a thing)); it'll give you a much greater appreciation of how the axes are used than you could ever get from a theoretical study. It's also great fun!