being taught是现在分词的被动式,这里是“强调动作正在进行”
相当于：
Because B was being taught by A,B made great progress.
如果是只用过去分词
taught by A
就相当于：
B was taught by A,so B made great progress.
或
B had been taught by A,so B made great progress.
这里只交待taught动作,而不强调进行.