Critics maintain that it is unreasonable to expect students to "discover" the standard methods through investigation, and that flexible thinking can only be developed after mastering foundational skills.
[7] Commentators have argued that there is philosophical support for the notion that "algorithmic fluency" requires the very types of cognitive activity whose promotion reform advocates often claim is their approaches' unique virtue.
Some curricula incorporate research by Constance Kamii and others that concluded that direct teaching of traditional algorithms is counterproductive to conceptual understanding of math.
Some parents have accused reform math advocates of deliberately slowing down students with greater ability in order to "paper-over" the inequalities of the American school system.
In fact students tend to achieve the same procedural skill level in both types of curricula as measured by traditional standardized tests.
In 2006, the NCTM released Curriculum Focal Points,[16] a report on the topics considered central for mathematics in pre-kindergarten through eighth grade.
Its inclusion of standard algorithms led editorials in newspapers like the Chicago Sun Times to state that the "NCTM council has admitted, more or less, that it goofed," and that the new report cited "inconsistency in the grade placement of mathematics topics as well as in how they are defined and what students are expected to learn.
"[17] NCTM responded by insisting that it considers "Focal Points" a step in the implementation of the Standards, not a reversal of its position on teaching students to learn foundational topics with conceptual understanding.
[16] Francis Fennell, president of the NCTM, stated that there had been no change of direction or policy in the new report and said that he resented talk of “math wars”.
The National Math Panel examined and summarized the scientific evidence related to the teaching and learning of mathematics,[19] concluding in their 2008 report, "All-encompassing recommendations that instruction should be entirely 'student centered' or 'teacher directed' are not supported by research.
"[20] The Panel effectively called for an end to the Math Wars, concluding that research showed "conceptual understanding, computational and procedural fluency, and problem-solving skills are equally important and mutually reinforce each other.
The Panel's final report met with significant criticism within the mathematics education community for, among other issues, the selection criteria used to determine "high-quality" research, their comparison of extreme forms of teaching, and the amount of focus placed on algebra.