Nor was Jefferson purely a commentator, but had a keen interest in mathematics education, as may be seen in discussions with several of his correspondents. In 1799 he wrote to a young man seeking educational advice [TJ to William Greene Munford, June 18, 1799].
I have to acknolige the reciept of your favor of May 14. in which you mention that you have finished the 6. first books of Euclid, plane trigonometry, surveying & algebra and ask whether I think a further pursuit of that branch of science would be useful to you. there are some propositions in the latter books of Euclid, & some of Archimedes, which are useful, & I have no doubt you have been made acquainted with them. trigonometry, so far as this, is most valuable to every man, there is scarcely a day in which he will not resort to it for some of the purposes of common life; the science of calculation also is indespensible as far as the extraction of the square & cube roots. Algebra as far as the quadratic equation & the use of logarithms are often of value in ordinary cases: but all beyond them is but a luxury; a delicious luxury indeed; but not to be indulged in by one who is to have a profession to follow for his subsistence. in this light I view the conic sections, curves of the higher orders. perhaps even spherical trigonometry, algebraical operations beyond the 2d dimension, and fluxions. . . . I have indulged myself in these observations to you, because the evidence cannot be unuseful to you of a person who has often had occasion to consider which of his acquisitions in science have been really useful to him in life, and which of them have been merely a matter of luxury.
His correspondence extended to explaining mathematics to others, as when he wrote to a schoolmaster with an explanation of Napier's rule for right-angled spherical triangles [TJ to L. H. Girardin, March 18, 1814]. This letter shows his characteristic practicality and insight into mathematics education.