In secondary school (1953-60), some aids to calculation were needed. For physics and chemistry, a 10 inch slide rule was mostly adequate - I had an "Aristo Scholar" which served me well. For more accuracy, 4 figure log tables were used - I had "Knotts four-figure mathematical tables" - with the outside copiously decorated with useful formulae. These two pieces of equipment also served me well as a physics undergraduate (1960-3)
Slide Rule: Aristo Scholar
Log tables: Knotts Four Figure Mathematical Tables
Early calculators were mechanical: worked by turning a handle (crank).
Brunsviga
This is the classic: with iron work like a sewing machine. This model dates from 1934.
Brunsviga 15   Manual
Later electro-mechanical models used an electric motor to turn the crank. MADAS was the most sophisticated - the name stood for Multiplication, Addition, Division And Subtraction. The machinery required was very complicated - and expensive; new a MADAS cost about the same as a small car.
MADAS
Model 20 BTZG from circa 1950.     more infoAs soon as the first integrated circuits became available (chips), electronic calculators became feasible. Some of the early ones were made in Britain.
Anita 1011 LSI: Nixie tube display from circa 1971.
More details.   ManualAdvanced Electronics 16R Executive: LED display
This has a square root function as well as two memories: hence the R in the name. From circa 1973.
Info about Advanced Electronics Calculators.The first fully scientific calculator widely available was the HP35 - introduced in 1972: I first used one in the early 1970's while at CERN. It used "Reverse Polish Notation" which was tricky to get used to. It was very accurate but also very expensive. HP35 with attachments
Sinclair introduced a scientific calculator in 1974, it had many limitations, but at around £ 50 it was much cheaper than the HP35. I bought one but it was stolen. I was, at the time, not too unhappy since I was able to replace it with a scientific calculator (Sharp EL-531 with LCD display from 1984/5) that had no limitations and was not expensive. I have used this calculator ever since - I have no need of any more features than it has, since I write a program for anything more complex. This model number remains in production today (2012). Sharp introduced LCD displays in 1973. Vintage EL531A info: this is later but similar model.
Commodore Minuteman 6 : LED display. circa 1974
More infoCasio FX-31 from circa 1978. Vacuum Fluorescent display.
I still use this calculator. More info
.Citizen W8 solar cell calculator: LCD display
Bought in Japan around 1991
Solar powered credit card size calculator