The connectionist approach is well described in Effective Teachers of Numeracy in Primary Schools: Teachers' Beliefs, Practices and Pupils' Learning.
In essence, connectionist teachers:
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have a conscious awareness of connections and relationships, and use mental mathematics to develop agility with this
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believe that students of all levels of attainment need to be challenged in mathematics, and have high levels of expectation for all students
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maintain a high degree of teacher–class, teacher–group, teacher–individual and student–student focussed discussion
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believe students learn computational skills through modelling, problem-solving and investigations
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plan their teaching around connections between ideas.
There are different levels of connectedness, which are explained in the article Connected Understanding on the AAMT website.