Readings

[Required] "Introduction to Connectionism" The Mind Project. This gives you a general idea about neural networks. Don't worry too much about the mathematics.
[Required] Garson, James, "Connectionism", The Stanford Encyclopedia of Philosophy.

What is connectionism?

It is a theoretical framework in cognitive science.
Connectionists explain mental processes as computations carried out by neurally-implemented connectionist networks.
Connectionist networks are networks of interconnected neuron-like computing units of a certain kind.
Key terms: units, activation function, weight, hidden units, layer, error, learning algorithm

Biological plausibility - Connectionist networks look like networks of neurons, and so they are more biological plausible.
Fast distributed processing - The 100-step argument. (See Feldman, J. A., & Ballard, D. H. (1982) "Connectionist models and their properties" Cognitive Science, 6, 205-254.)
Graceful degradation - A connectionist network does not completely fail to perform a task when dealing with noisy inputs, and when the network is partially damaged.
Learn from examples - Connectionist networks are very good at pattern recognition through learning from examples. E.g. Sejnowski, T. J. and Rosenberg, C. R. (1986) "NETtalk: a parallel network that learns to read aloud" Cognitive Science, 14, 179-211.