National Survey of Algebra Teachers

How have we missed this?

Research Question #2: To the degree that the teachers believe students need to be better prepared, what are the major shortcomings?

The teachers were asked to rate the importance of a “solid foundation” in the each the 15 skill/knowledge areas asked about with respect to their target class students’ background preparation. Since the same background skills and knowledge for which the teachers rated student background as inadequate were also rated as important, the following areas emerge as the major shortcomings: rational numbers, word problems, and study habits.

Final Report on the National Survey of Algebra Teachers for the National Math Panel (pdf file)
National Mathematics Advisory Panel

They're not too keen on parents:

Research Question #12: Do they find more parents helpful in encouraging students in their mathematics studies, or do too many parents make excuses for their children’s lack of accomplishment?

Questionnaire item II.1i asked teachers to rate the extent to which they see “too little parent/family support” as a problem in their school. The responses indicate that about 28% of the algebra teachers feel family participation is a serious problem and another 32% believe lack of family participation is a moderate problem (Figure 13).

It's a bit difficult to cess out what this means exactly. The question itself seems off-base; the handful of direct quotations from teachers have nothing to do with parents "encouraging" their kids versus "making excuses" when their kids do badly:

The written-in “verbatim” responses most often mentioned included handling different skill levels in a single classroom, motivation issues, and student study skills. Some notable responses were:

Walking into a class of 30 students in which 1/3 of them don't have the prerequisite skills necessary to be in the class. Many of whom don't know their basic arithmetic facts and know they aren't going to be successful from day one no matter how hard they try.

Students come to me without a basic understanding of math. I am constantly re-teaching concepts that should have been mastered in the earlier grades.

Parents not letting me do my job as I see fit. (Autonomy in the classroom.)

Getting students and parents to believe that education is important. Students don't do their homework...you call the parents...they say that the student will start doing the work (and coming to tutorials). The students still don't do the h.w. -and still don't come to tutorials.

Engaging students who have come to believe that they are stupid because they are struggling with my state's cognitively inappropriate standards.

Report's conclusions:

The Algebra I teachers generally reported that students were not adequately prepared for their courses. The teachers rated as especially problematic students’ preparation in rational numbers, solving word problems, and basic study skills. A lack of student motivation was by far the most commonly-cited biggest challenge reported by the teachers. The problems the teachers identified with the pre-Algebra I mathematics curriculum and instruction and with the lack of parental support for mathematics were likely to be contributing factors to the lack of adequate student preparation and motivation.

[snip]

In light of the generally favorable views the teachers report with respect to curriculum and instruction, the issue of unmotivated students implicitly is something the teachers view as more of an “algebra-student problem” than an “algebra-teacher problem”. The generally-negative views expressed by the teachers of parental support for mathematics reinforce that attribution. Taken together with the generally negative ratings of background preparation, the lack of student motivation suggests that careful attention to pre-algebra curriculum and instruction in the elementary grades is needed, both to remedy the specific skill deficiencies as well as to identify ways in which negative attitudes toward mathematics are developed.

Our schools need a paradigm shift. If you've got an "algebra-student problem" then you also have an "algebra-teacher problem" by definition and you need to take action. Institute supervised homework study halls, formal reteaching of foundational skills, whatever.

Motivation as the Magic Key to All Learning is overrated in any case, I think. How motivated were Siegfried Engelmann's students in Project Follow-through? How motivated are the KIPP kids?

My own 8th grade child is not exactly gripped by a coursing desire to learn algebra. However, he is learning algebra, and he's learning it pretty well. That has to do with the teacher.

And, yes, it has to do with "parental support for mathematics," which in our case means that I do every homework assignment so I can check C's work and have him re-do the problems he missed.

You can't leave algebra up to student motivation.