...to our request to give direction on how to think of Śāstra-aviruddha-Vidyā (learning that is not violative of the infinitely vast beginning-less, author-less Veda) in our current worldly education:

Let us take the example of Gaṇita Śāstra. The origins of the same come from our ancestors and later, it may be the case that it has been expanded on by others. To teach students from these origins and how it evolved into what we get to see the expanse today can be said to be  Śāstra-aviruddha. Efforts definitely ought to be made to educate the students about the foundations and their strength. This is a minimum thing that must necessarily happen instead of the manner in which the foundations are being attributed to others as is being done in formal education today.
On further being asked about the absence of adhi-daivata* dhāraṇa (~sense of the sacred in every animate and inanimate aspects of the world) in modern day learning, Svāmī-ji said that we have come to accept many things which cannot be found to have the adhi-daivata dhāraṇa, but in all such instances where we are aware of the same, they must be brought to the attention of the students and in such instances where it is not known, if students are provided with the imagination about what alters when one looks at the world with a sense of the sacred and how it differs in its absence, such an education can also be stated to Śāstra-aviruddha.
* adhyātma -- adhi-daiva -- adhi-bhūta -- these are the three planes put together that capture reality in its whole. This will be elaborated elsewhere.