The National Math Panel has scrutinized only the most rigorous studies to draw its conclusions. Not surprisingly, some of the panel’s findings cast doubt on techniques recently in use–even in the best school districts.
Below are some interesting points extracted directly from the panel’s final report. Administrators and teachers should take note of these, and consider them in light of current practices and future professional development. Schools of Education should also take a hard look.
The first list consists of direct quotes from the panel. The second list is a summary of this blogger’s views and opinions, mapped to the first list. The final list highlights a few points of interest.
National Math Panel statements about Instructional Practices
(these are direct quotes)
1.Claims based on Piaget’s highly influential theory, and related theories of “developmental appropriateness” that children of particular ages cannot learn certain content because they are “too young,” “not in the appropriate stage,” or “not ready” have consistently been shown to be wrong. Nor are claims justified that children cannot learn particular ideas because their brains are insufficiently developed, even if they possess the prerequisite knowledge for learning the ideas.
2.The sociocultural perspective of Vygotsky has also been influential in education. It characterizes learning as a social induction process through which learners become increasingly independent through the tutelage of more knowledgeable peers and adults. However, its utility in mathematics classrooms and mathematics curricula remains to be scientifically tested.
3.The Panel recommends the scaling-up and experimental evaluation of support-focused interventions that have been shown to improve the mathematics outcomes of African-American and Hispanic students. [However,] average gender differences are small or nonexistent, and our society’s focus on them has diverted attention from the essential task of raising the scores of both boys and girls.
4.All-encompassing recommendations that instruction should be entirely “student centered” or “teacher directed” are not supported by research. If such recommendations exist, they should be rescinded. If they are being considered, they should be avoided. High-quality research does not support the exclusive use of either approach.
5.The Panel’s review of the literature addressed the question of whether using “real-world” contexts to introduce and teach mathematical topics and procedures is preferable to using more typical instructional approaches. For certain populations (upper elementary and middle grade students, and remedial ninth-graders) and for specific domains of mathematics (fraction computation, basic equation solving, and function representation), instruction that features the use of “real-world” contexts has a positive impact on certain types of problem solving. However, these results are not sufficient as a basis for widespread policy recommendations. Additional research is needed to explore the use of “real-world” problems in other mathematical domains, at other grade levels, and with varied definitions of “real-world” problems.
6.The Panel’s survey of the nation’s algebra teachers indicated that the use of calculators in prior grades was one of their concerns (National Mathematics Advisory Panel, 2008). The Panel cautions that to the degree that calculators impede the development of automaticity, fluency in computation will be adversely affected. The Panel recommends that high-quality research on particular uses of calculators be pursued, including both their short- and long-term effects on computation, problem solving, and conceptual understanding.
7.Research has been conducted on a variety of cooperative learning approaches. One such approach, Team Assisted Individualization (TAI), has been shown to improve students’ computation skills. This highly structured instructional approach involves heterogeneous groups of students helping each other, individualized problems based on student performance on a diagnostic test, specific teacher guidance, and rewards based on both group and individual performance. Effects of TAI on conceptual understanding and problem solving were not significant. There is suggestive evidence that peer tutoring improves computation skills in the elementary grades. However, additional research is needed.
8.Use of formative assessments in mathematics can lead to increased precision in how instructional time is used in class and can assist teachers in identifying specific instructional needs. Formative measures provide guidance as to the specific topics needed for assistance. Results [of studies] suggest that use of formative assessments benefited students at all ability levels. More studies are needed. Formative assessment should be an integral component of instructional practice in mathematics.
1.Piaget’s theories are not reliable for mathematics education. Interestingly, the constructivist approach to teaching is based on Piaget’s theories. This finding of the panel casts grave doubt on the validity of a constructivist model for the teaching of mathematics.
2.The use of peer groups for the purpose of students teaching other students has never been tested, and therefore should be used sparingly and with caution.
3.Teaching methods specifically intended to reach girls should be dropped.
4.”Discovery” has always been a useful teaching approach and continues to be. The “discovery” approach can once again take its rightful place as one of many teaching techniques, rather than the dominant or only one, as it has in constructivist schools and classrooms.
5.The broad policy of using real-world problems to introduce and teach mathematical concepts has not been sufficiently tested, and should be restricted to upper grades, and then only to certain domains of mathematics.
6.The use of calculators before ninth grade has not only not been tested, the panel cautions that their use before grade nine interferes with the development of automaticity and fluency. Therefore, their use should be dropped until studies can be done.
7.Cooperative learning helps develop computation skills but not necessarily conceptual understanding or problem solving. Until further testing is done, cooperative learning should be limited to use for developing computation skills.
8.The increasing use of “formative assessment,” also known as “authentic assessment” (assessment which is ongoing as opposed to traditional tests)is a good idea, and should continue.
A Few Points of Interest:
1.It is noteworthy that while the panel was quite negative about early use of calculators, they were much more positive about the use of computer-assisted instruction. So much for educators lauding use of all technology. They need to think a little more critically about which technology.
2.The practice of “formative assessment,” a method used increasingly in some schools and often referred to as “authentic assessment,” while understandably questioned by parents, has been tested and shows good results in the teaching of mathematics.
3.Teachers and administrators should pursue practices that have been well-tested, and must exercise restraint with regard to practices that are not sufficiently tested. Parents, taxpayers, administrators, and teachers need to place their trust in science and an eclectic approach, rather than any one “ism.”
4.With regard to the evidence that cooperative learning can help develop computation skills, so can computer assistance. Either way, the student is prompted to focus on drill, and the teacher is freed up to work with other students. However, gifted literature is rife with anecdotes of negative impact on the student who is leaned on too much. It is wise to exercise caution, therefore, until studies of gifted students can be scrutinized more closely to determine the extent of negative impact.