Zhiqiang Cai, Jan Mandel, Steve McCormick, Multigrid Methods for Nearly Singular Linear Equations and Eigenvalue Problems, SIAM Journal on Numerical Analysis, Vol. 34, No. 1 (Feb., 1997), pp. 178-200 ...

The aim was to teach the formal solving method, which involved performing the same operations on both sides of the equation using, notably, the balance model. Analysis of students' reasoning showed ...