Table 2b speaks for itself. Comparison with the course category subtable in Table 2a is interesting also. The Algebra Project is (comparatively) very successful in having students learn how to solve equations. This has to do with a more logical ordering of the material. We handle all linear equations in one chapter instead of having them scattered throughout the book. But before students get to this chapter they learn sequential thinking through extensive work with the step- by-step approach we use for the simplification of complex fractions.
As a review of the New Jersey Algebra Project has shown, the problem is not one of discrete skills that an individual student may lack and can be "remediated" for. This is patchwork and will not be effective in the long term. The real problem is with quantitative reasoning.
Too often people think of basic skills as low-level skills or minimum skills--they are not. We should think of basic skills as essential skills. What then are the basic skills needed for quantitative work in college and elsewhere? What proficiencies in math do we really want students to have?
There are three major skills, really abilities, involved. The first is the ability to analyze a situation or a problem and decide what needs to be found, then to verbalize an approach, which very often will be an equality, and finally, to translate from verbal form to symbolic form--that is, to set up an equation or equations. The second is the ability to solve the equation or equations--this involves various algorithmic skills, and these depend primarily on the capability for doing sequential thinking. And the final one is the ability to interpret and assess the solution to the equation--to determine whether the result answers the original question and is indeed a reasonable answer.