Is there research on effectiveness of teaching with high extraneous cognitive load?

Background

While researching a particular author's mathematical exposition, I found out (directly from a primary source) that the author was probably intentionally using overly complex syntax. Purportedly, the idea was that by producing a high extraneous cognitive load the student would be subject to more "mental exercise," deepening understanding and cementing concepts. This led me to the following line of inquiry.

Question

We all probably agree that cognitive load is the very nature of education, at least, intrinsic cognitive load is unavoidable. But does additional extrinsic cognitive load improve the learning outcomes for students? Doesn't it seem preferable to minimize extraneous cognitive load at all times, while ramping up the level of required intrinsic cognitive load?

However plausible the idea of "more mental work means more mental muscles" might be, I have to question its effectiveness. The success of students under these conditions might easily be explained by other traits such as grit.

Is there research that says high extraneous cognitive load (e.g. intentionally complex exposition) either improves or degrades learning outcomes (such as recall and retention) in some situations?

Examples

I have two minor expository examples, but I hope they don't limit what you, the reader, may also have encountered like this elsewhere.

For example, something might be defined with a "double negative" pattern where there was already a (seemingly) simpler positive pattern:

A set $X$ is called closed if there is no limit point of $X$ which is not in $X$

(Compare to: A set $X$ is called closed if every limit point of $X$ is in $X$.)

if there exists a number $x$ which is not less than any element of $X$, then there is a least number which is not less than any element of $X$.

(Compare to: if there is a number $x$ which is greater or equal to every element of $X$, there is a least number which is greater or equal to every element of $X$.)

Another example is that some things are stated two or three layers deep: having a list of hypotheses, of which one bullet point is another list of hypotheses. An example of that is a pattern of the form "element of the set $X$ such that for all elements $y$ of the set $Y$, $y$ has the property that for every element of the set $Z$..." (I still owe a better written example of this from what I was reading.) (I think something like that is usually simplified by modularizing definitions in a different way to bundle the layers separately before stacking.)

PS

I've just discovered the wiki on desirable difficulty which may also be helpful for me and for anyone offering a solution.

• You may be interested in "Processing Fluency/Ease". There is a large body of evidence that suggests that memory recall is significantly improved by making material hard-to-read (eg, using less readable fonts, poor choice of colours or contrast, or using other methods that make for difficult reading - example here: ncbi.nlm.nih.gov/pubmed/21626231). I'm not sure if this extends to complex writing, but might get you started. – Arnon Weinberg Apr 8 '17 at 17:40
• @ArnonWeinberg Yes! That is definitely a helpful lead. Thank you for your help. Things like this and their bibliographies will probably lead me to my answer. – rschwieb Apr 8 '17 at 17:46