Believe your 2nd grade teacher

Actually the story is more complicated:
Steel and Aluminum are a straightforward example of efficient recycling because you don't get any energy from burning them and it takes a lot of energy to get those out of the earth and into usable form. So they easily top the list of energy efficient recycling.
Paper is a fuel and as such you can get energy from burning it - and since it is a "biofuel" this energy is even carbon dioxide neutral, but you have spent lots of energy in producing paper from wood and it costs less energy to produce (lower quality) paper from paper so this is efficient as well.
Glass is better reused then recycled and here transport is usually the restricting factor when determining efficiency - producing glass from glass costs less energy then producing glass from sand, but this difference is often dwarved by the energy costs of collecting and transporting the glass to and from recycling facilities - so this is border line
Plastic is a fossil fuel so you get energy from burning it, you also preserve some fossil fuel by not burning but rather recycling it - in theory, however in order to efficiently recycle most plastics you need to sort them really pure and this is difficult from "household" wastes where a lot of different plastics are included, today it is usually more energy efficient to burn the plastic and make new ones from oil then to burn the oil and make new plastic from old plastic
Landfills are a waste of energy, pollute the environment and are a health hazard to humans and all other living things around them. There is no reason for them today
Source for energy savings:
NRDC Note: they do not take into account energy costs of sorting the plastics and they don't show energy savings for many common plastics, like PVC, Polystyrene, Teflon, Polyamides, Polyacrylamide etc. thats for the reason that those plastics never are energy efficiently recycled, but when you collect them with the household waste to recycle PE, PET and PP which themselves might merit recycling you loose the energysavings by collecting and transporting those other products usually.
Bottom line: Metals and paper are good for recycling (paper looses quality in each cycle so this is no closed cycle), glass can be good - but you don't want to ship the glass bottle from Texas to Maine, the broken glass back to Texas and the new glass back to Maine if you want to save energy

Plastics are better burned for electricity then recycled unless you have a source of almost pure type of plastics - which can be the case in industry and building waste...