As others have noted, there are two distinct hypotheses being presented. The first is that younger students are developmentally incapable of learning algebra. This is generally not supported by education research.
You may be interested in the research summarized in this chapter from Algebra in the Early Grades titled "Early Algebra Is Not The Same As Algebra Early." The authors worked with students in an ethnically diverse school in Greater Boston. They conducted weekly early algebra activities, following the students from second grade to fourth grade. Here's an excerpt that I think is relevant:
We witnessed a dramatic shift in students’ thinking over one and one-half years. At the beginning of grade three, students interpreted a story with indeterminate quantities as a single tale about particular people and amounts. By the middle of grade four most students construed this sort of situation as entailing many possible stories involving variable quantities in an invariant functional relationship. A good many of the students made use of algebraic notation to convey the variations and invariance across the stories.
The decisive changes in their thinking surprised us. Several years ago, when invited to assess the evidence regarding whether young students could ‘do algebra’, we downplayed the discontinuity between arithmetic (as generally taught in K-8) and algebra. Our initial findings showed that young students could make mathematical generalizations and express them in algebraic notation...
Our present findings have convinced us that there is indeed a large leap from thinking in terms of particular numbers and instances to thinking about functional relations. But the fact that most students throughout the United States do not make this transition easily, nor early, may well say more about our failure to offer suitable conditions for them to learn algebra as an integral part of elementary mathematics than it does about the limitations of their mental structures.
Of course, the success of early algebra programs depends on a variety of factors, and it's not a given that earlier is always better. But according to the authors of this RAND working paper who studied the effects of California's push for early algebra:
Our analyses indicate that 8th grade Algebra enrollment has a substantial and lasting positive effect on students’ advanced math course enrollment, and more modest positive effects on students’ mathematics and ELA test scores. Importantly, however, we find evidence to suggest that the effects of 8th grade Algebra vary substantially across schools and placement strategies. In some settings, early Algebra has large and statistically significant positive effects on student achievement and attainment; in other settings, these effects are negative. Descriptive analyses suggest that the effects of early Algebra placement are more positive in schools with larger shares of relatively high-achieving and socioeconomically advantaged students, as well as schools that set high test score thresholds for enrolling in 8th grade Algebra.
The second hypothesis is that students are not adequately prepared for algebra in eighth grade due to bad curriculum design choices. This is significantly harder to address and research, because students' algebra readiness depends on a host of factors besides the design of the intended curriculum. Additionally, there are very few opportunities for comparative longitudinal studies on curriculum.
Since quantitative studies are hard to come by, another way to gain insight on this question is to study the history of the Common Core State Standards for Mathematics (CCSSM.) The new standards were motivated in part by the perception that existing U.S. mathematics curricula were inadequate, especially when viewed in international comparison. R. James Milgram and Hung-Hsi Wu, both mathematicians who have had a strong presence in curriculum reform efforts, wrote this in the introduction to a proposed K-7 mathematics intervention program, prior to the release of the CCSSM:
Analysis of the results from TIMSS suggests that the U.S. school mathematics curriculum is a mile wide and an inch deep. It covers too many topics and each topic is treated superficially. By contrast, the structure of mathematics instruction in countries which outperformed the U.S. follows a strikingly different pattern. In all cases, only a few carefully selected focus topics are taught and learned to mastery by students in the early grades. At the fourth grade level, since the students in these countries have not been exposed to as broad a curriculum as U.S. students, it sometimes appears on standardized tests such as TIMSS that they perform at a comparable level to U.S. students, but by grade eight the students in the leading countries are far outperforming our students. In fact, key test items already show serious weaknesses in our fourth grade student performances. This difference becomes even greater by the end of high school, where even our top students do not match up well with the average achievement levels of students in these countries.
Wu would go on to become a staunch proponent of the CCSSM. This is what he said in a piece for the AFT journal American Educator:
the very purpose of mathematics standards (prior to the CCSMS) seems to be to establish in which grade topics are to be taught. Often, standards are then judged by how early topics are introduced; thus, getting addition and subtraction of fractions done in the fifth grade is taken as a good sign. By the same ridiculous token, if a set of standards asks that the multiplication table be memorized at the beginning of the third grade or that Algebra I be taught in the eighth grade, then it is considered to be rigorous.
The CCSMS challenge this dogma. Importantly, the CCSMS do not engage in the senseless game of acceleration—to teach every topic as early as possible—even though refusing to do so has been a source of consternation in some quarters. For example, the CCSMS do not complete all the topics of Algebra I in grade 8 because much of the time in that grade is devoted to the geometry that is needed for understanding the algebra of linear equations.
There is general support among mathematicians and mathematics educators for the idea that, in the past several decades, U.S. mathematics curriculum standards have been unfocused and shallow. In my estimation, the predominant attitude towards the CCSSM is that the K-8 standards have improved in this regard, though there have been problems with uptake and implementation. However, a group of prominent mathematics educators called for the high school standards to be revised in an open letter last year, stating:
Over the past ten years, mathematics educators have recognized that the K-8 Common Core State Standards, while not perfect and certainly in need of tweaking, are internationally benchmarked, coherently based on research-affirmed learning progressions, fewer and deeper by design, and, most importantly, achievable. In stark contrast, the high school standards are cluttered, outdated, and, because of their scope, unteachable and unachievable for many. They are not based on coherent progressions, they do not accommodate the impact of widely available technology (including computer algebra systems), nor do they articulate equally rigorous differentiated pathways that reflect the broad range of post-secondary mathematical needs. By clinging to increasingly obsolete content, they leave little room for statistics and modeling, and most problematically, they reinforce serious inequities and limit opportunities.
Based on my personal experience teaching the high school standards, I agree.
