This seems to indicate to me I am right?

Indicate what? The BEd at the UofA has always required course work in the major and minor area of teaching.

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Perhaps I am wrong, but generally speaking professors seem to give the Education students down here a lot of slack since they are doing so much work, and often say in classes that these students are essentially doing the work of a master's.

They can tell you that all they want. If you are applying for a job that requires a graduate degree the BEd won't be enough.

I'm not sure by what measure they say the degree in education is not considered an undergraduate degree. Maybe that is specific to Lethbridge? Maybe the professors who say students doing a BEd are 'essentially' doing the work of a master's are trying to build the confidence of their students?

tbh I don't think those professors are doing their students any favours. I don't think it would help students in an interview to state that their BEd is essentially a graduate degree.