2 Clarified somethings
source | link

For presenting proofs, I would only use terminology such as "obviously", "clearly", "routine", etc if it would be for a levelcourse just below the class had the student had 'perfect' recollection. For instance, in a introductory commutative algebra class, if the proof should be routine for the previous regular algebra class (i.e., something involving a course below algebra), then I would use such terminology. It should be used only as an indicator for how difficult the proof is relative to their expected skills. Another example, in Multivariate Calculus, I would say "obvious", "routine", or whatnot to Intro. Calculus concepts, but not necessarily to Calculus 2 concepts.

If it is not at this level, I would just present it without comment or just state the result without explanation. Many students at the level of proofs would question it if it wasn't obvious.

In general, I use such terminology to indicate what I expect my students to have as prior knowledge that they should recall pretty quickly. I do this even in the calculus sequence, quickly going through prior knowledge that should be clear quicker.

Using the measure of "material from two classes prior in a course series" as "obvious" has worked for me so far in indicating expectations to students while not perturbing them. Sometimes it takes a semester or two for things to "click."

For presenting proofs, I would only use terminology such as "obviously", "clearly", "routine", etc if it would be for a level just below the class. For instance, in a introductory commutative algebra class, if the proof should be routine for the previous regular algebra class, then I would use such terminology. It should be used only as an indicator for how difficult the proof is relative to their expected skills.

If it is not at this level, I would just present it without comment or just state the result without explanation. Many students at the level of proofs would question it if it wasn't obvious.

In general, I use such terminology to indicate what I expect my students to have as prior knowledge that they should recall pretty quickly. I do this even in the calculus sequence, quickly going through prior knowledge that should be clear quicker.

Using the measure of "material from two classes prior in a course series" as "obvious" has worked for me so far in indicating expectations to students while not perturbing them. Sometimes it takes a semester or two for things to "click."

For presenting proofs, I would only use terminology such as "obviously", "clearly", "routine", etc if it would be for a course just below the class had the student had 'perfect' recollection. For instance, in a introductory commutative algebra class, if the proof should be routine for the previous regular algebra class (i.e., something involving a course below algebra), then I would use such terminology. It should be used only as an indicator for how difficult the proof is relative to their expected skills. Another example, in Multivariate Calculus, I would say "obvious", "routine", or whatnot to Intro. Calculus concepts, but not necessarily to Calculus 2 concepts.

If it is not at this level, I would just present it without comment or just state the result without explanation. Many students at the level of proofs would question it if it wasn't obvious.

In general, I use such terminology to indicate what I expect my students to have as prior knowledge that they should recall pretty quickly. I do this even in the calculus sequence, quickly going through prior knowledge that should be clear quicker.

Using the measure of "material from two classes prior in a course series" as "obvious" has worked for me so far in indicating expectations to students while not perturbing them. Sometimes it takes a semester or two for things to "click."

1
source | link

For presenting proofs, I would only use terminology such as "obviously", "clearly", "routine", etc if it would be for a level just below the class. For instance, in a introductory commutative algebra class, if the proof should be routine for the previous regular algebra class, then I would use such terminology. It should be used only as an indicator for how difficult the proof is relative to their expected skills.

If it is not at this level, I would just present it without comment or just state the result without explanation. Many students at the level of proofs would question it if it wasn't obvious.

In general, I use such terminology to indicate what I expect my students to have as prior knowledge that they should recall pretty quickly. I do this even in the calculus sequence, quickly going through prior knowledge that should be clear quicker.

Using the measure of "material from two classes prior in a course series" as "obvious" has worked for me so far in indicating expectations to students while not perturbing them. Sometimes it takes a semester or two for things to "click."