The National Mathematics Advisory Panel final report states that algebra is the gateway to higher math, to a college degree, and higher earnings from employment. It also states that success in algebra is dependent on understanding multiplicative reasoning, including proficiency with rational numbers and proportional relationships. Furthermore, there is ample evidence that difficulty with multiplicative reasoning is pervasive and failure rates in algebra classes are unacceptably high. One of the report's recommendation is:
The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percent, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected. (p. 18)
If improvement in the teaching of fractions is necessary for improvement in student achievement in algebra, then isn’t multiplicative reasoning the gatekeeper to higher math rather than algebra?
Does anyone know of any research that sheds light on this question? For example, math placements exams for entering college students could be analyzed for proficiency with multiplicative reasoning and with algebra, and related to math courses taken in college. The same could be done for 8th grade and 12th grade standardized math tests or other tests like the PISA, and related to college attendance as well as math courses taken. The difficulty, I expect, would be access to all the necessary the data for individual students.
In a blog post, krikii says “Research has shown that the extent to which elementary school students master rational numbers is a strong predictor of future success in mathematics.” There is ample research showing poor performance on rational number tasks, but what research is there that uses rational number knowledge to predict future success in math?
Another way to research this is to ask, "When do students start to dislike math and not want to take any more math courses?"
UPDATE: littleO’s comment and Tom Au’s answer got me thinking about defining more clearly what I mean by “gatekeeper to higher math.” Students are having difficulty in making the change from additive reasoning to multiplicative reasoning, and in making the change from working with numbers to working with variables. Which adjustment in thinking is a greater separator between those who continue on to higher math and those who don’t? An important research question would be, “What percent of those who are not proficient in algebra are proficient in multiplicative reasoning?”