I am sorry if the question is not quite related to post in this forum. There is a distinction between substantive and syntactic knowledge particularly in mathematics. There are several definitions for both knowledge. However, what are the indicators and the examples of substantive knowledge and syntactic knowledge such that we can explain the constructs operationally?
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1I have seen the distinction drawn between knowing a fact (substantive) and being able to work out a fact (syntactic). This compares a primary teacher knowing that a diagonal cuts a rectangle into two equal parts and being able to work out that $\frac{a+b}{c+d}$ is between $\frac ac$ and $\frac bd$, not having seen mediants before – Henry Dec 01 '21 at 09:47
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Just in case one is not aware, there's a StackExchange Math Educators site. It is one of those site forever stuck in Beta despite some good content and good user base. There's a real possibility it will "graduate" along with others in the near future. – Lee David Chung Lin Dec 01 '21 at 10:45