I'm an engineer and this is a history of science question at its core, with no regards to the education of the mason, because... the math did not exist in 1150.

Newton's Laws of Motion were described by Newton in 1687. This is the basis of classical mechanics which is required for the absolute simplest of structural analysis, truss analysis.

Calculus was required for more advanced versions and was developed around the same time but the application of calculus to structures was later.

To analyze a beam element, Euler-Bernoulli beam bending theory is used which was developed in the mid 18th century. Column buckling was analyzed around the same time, again by Euler. Between beams and columns you have pretty much all structures, so this is what's used to build buildings.

So, it was a good 500-600 years between your mason and the development of the knowledge required to understand the physics of buildings.

It really depends what you mean by understand. Could they use rigorous quantitative methods? No. Can you catch a ball without performing detailed calculations? Quite likely, and so much in the same way they developed an intuitive understanding of the materials they worked with.

Inherent in the question is an anachronistic understanding of mathematics. This is a high resolution scan of Newton's own 1687 copy of his Philosophiæ Naturalis Principia Mathematica, the most important work on mathematics since Euclid's Elements written circa 300BC (note most of the Elements likely isn't his own work). Flicking through you'll notice it doesn't really resemble today's mathematical notation: it's word and geometry heavy, with few equations. The adoption of Arabic numerals and equations was largely a development of the Italian Renaissance. This tells you something about the way people thought about mathematics until really surprisingly recently.

Mathematics in Europe had its first resurgence since the Greeks in the 12th century with the translation into Latin of works preserved or developed in the Arabic world. The word algebra itself was introduced to Europe in 1145, the period of your question, when Robert of Chester translated Muḥammad ibn Mūsā al-Khwārizmī's 820 work The Compendious Book on Calculation by Completion and Balancing. The book was a compilation of known methods for solving quadratic equations and finding areas and volumes. It essentially founded algebra as a discipline and like the work of the Greeks has a very heavy geometric focus.

Even if this translation had made its way to your mason, and he was literate enough to read it, it doesn't contain the kind of mathematics needed by an architect or engineer. Nor does Euclid's Elements, or indeed any other book of the time. Mathematics was until much later a fundamentally geometric discipline. This is apparent even in the musings of Descartes in The Meditations in the early 1600s where his objects of mathematics are all figures. Your mason would have had to wait another 500 years before mechanics had developed to the stage where it could answer questions about structural integrity, stress and strain as opposed simply to shape.

An add-on question, were large stone medieval buildings of this time like castles and churches well-constructed and that's why we see many of them standing today, or were they generally poorly constructed and the ones we see today are the few that were solidly built?