Myths and Realities about Educational Acceleration

Acceleration does not lead to adverse psychological consequences in capable students; rather, whether a student is ready for advanced mathematics depends solely on whether they have mastered the prerequisites. Acceleration does not imply shallowness of learning; rather, students undergoing acceleration generally learn – in a shorter time – as much as they would otherwise in a non-accelerated environment over a proportionally longer period of time. Accelerated students do not run out of courses to take and are often able to place out of college math courses even beyond what is tested on placement exams. Lastly, for students who have the potential to capitalize on it, acceleration is the greatest educational life hack: the resulting skills and opportunities can rocket students into some of the most interesting, meaningful, and lucrative careers, and the early start can lead to greater career success.

This post is part of the book The Math Academy Way (Working Draft, Jan 2024). Suggested citation: Skycak, J., advised by Roberts, J. (2024). Myths and Realities about Educational Acceleration. In The Math Academy Way (Working Draft, Jan 2024). https://justinmath.com/myths-and-realities-about-educational-acceleration/

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The benefits of mathematical acceleration are as numerous as the misconceptions surrounding it. As lamented by researcher James Borland (1989, pp.185):

“Acceleration is one of the most curious phenomena in the field of education. I can think of no other issue in which there is such a gulf between what research has revealed and what most practitioners believe. The research on acceleration is so uniformly positive, the benefits of appropriate acceleration so unequivocal, that it is difficult to see how an educator could oppose it.”

The purpose of this post is to clear up misconceptions and, at the same time, communicate the benefits of mathematical acceleration.

Developmental Appropriateness: Advanced Study is Appropriate Once Prerequisites Have Been Mastered

A common myth goes like this: Learning math early is not appropriate for students’ social/emotional and cognitive/academic development.

In reality, educational acceleration does not lead to adverse psychological consequences in capable students. For instance, according to a study titled Academic Acceleration in Gifted Youth and Fruitless Concerns Regarding Psychological Well-Being: A 35-Year Longitudinal Study that followed thousands of accelerated students throughout their lives over the course of 35 years (Bernstein, Lubinski, & Benbow, 2021):

“The amount of educational acceleration did not covary with psychological well-being. Further, the psychological well-being of participants in both studies was above the average of national probability samples. Concerns about long-term social/emotional effects of acceleration for high-potential students appear to be unwarranted, as has been demonstrated for short-term effects.
…
These findings are consistent with research on the effects of academic acceleration on psychological well-being. That is, there is little evidence that academic acceleration has negative consequences on the psychological well-being of intellectually talented youth (Assouline et al., 2015; Benbow & Stanley, 1996; Colangelo et al., 2004; Gross, 2006; Robinson, 2004).
…
These findings do not support the frequently expressed concerns about the possible long-term social and emotional costs of acceleration by counselors, parents, and administrators… Those who were accelerated had few regrets for doing so. Indeed, if anything, they tended to wish that they had accelerated more.”

Whether a student is ready for advanced mathematics depends solely on whether they have mastered the prerequisites. If a student has mastered prerequisites, then it is appropriate for them to continue learning advanced math early, and not appropriate to stunt their development by holding them back. As the study authors note:

*“Many fear negative possibilities of moving a gifted child to a more advanced class. Yet it also is important to consider the negative possibilities of holding children back in classes aiming to teach subject matter that they have already mastered (Benbow & Stanley, 1996; Gross, 2006; Stanley, 2000). Choosing not to accelerate is as much of a decision as choosing to do so…

This is particularly important given the extensive empirical literature showing positive effects of acceleration on academic achievement (Kulik & Kulik, 1984, 1992; Lubinski, 2016; Rogers, 2004; Steenbergen-Hu et al., 2016) and creativity (Park et al., 2013; Wai et al., 2010)… Presenting students with an educational curriculum at the depth and pace with which they assimilate new knowledge is beneficial. Other studies have shown that academic acceleration tends to enhance professional and creative achievements before age 50 (Park et al., 2013; Wai et al., 2010).”*

Numerous other studies on the long-term effects of educational acceleration have drawn similar conclusions. As Wai (2015) summarizes:

”…[F]or many decades there has been a large body of empirical work supporting educational acceleration for talented youths (Colangelo & Davis, 2003; Lubinski & Benbow, 2000; VanTassel-Baska, 1998). Although neglecting this evidence seems increasingly harder to do (Ceci, 2000; Stanley, 2000), putting research into practice has been challenging due to social and political forces surrounding educational policy and implementation (Benbow & Stanley, 1996; Gallagher, 2004; Stanley, 2000).
…
The educational implications of these studies are quite clear. They collectively show that the various forms of educational acceleration have a positive impact. The key is appropriate developmental placement (Lubinski & Benbow, 2000) both academically and socially. … Educational acceleration is essentially appropriate pacing and placement that ensures advanced students are engaged in learning for life. Every student deserves to learn something new each day (Stanley, 2000). The evidence clearly supports allowing students who desire to be accelerated to do so, and does not support holding them back.
…
[T]he long-term studies reviewed here show that adults who had been accelerated in school achieved greater educational and occupational success and were satisfied with their choices and the impact of those choices in other areas of their lives.”

Why the Myth of Developmental Inappropriateness Persists

This myth of acceleration being developmentally inappropriate may be perpetuated in part by convenience. In schools, each grade typically progresses through the math curriculum in lockstep, which means that accelerated students would need to be placed in above-grade courses. This can lead to major logistical challenges.

For instance, if above-grade course is not offered by the school (which would certainly be the case for accelerated 5th graders in elementary schools, 8th graders in middle schools, and 12th graders in high schools), then either

the students would need to take the class at another school (which introduces transportation, scheduling, and administrative issues) or
the school would need to hire a teacher who is capable of teaching the higher-grade material (and it’s hard enough for schools to hire teachers who are capable of teaching grade-level mathematics).

And even if the above-grade course is offered by the school, there may be schedule conflicts with grade-level courses that mathematically accelerated students still need to take. (Course schedules are typically optimized to minimize conflicts within grade levels, but not across grade levels.)

Besides logistical issues, there are other factors that can disincentivize acceleration and lead the myth to be perpetuated out of convenience. As Steenbergen-Hu, Makel, & Olszewski-Kubilius (2016) describe:

*“[E]ducation administrators may have perverse incentives to avoid acceleration. For example, although acceleration can often actually save schools money because students spend fewer years in school, it can also ‘cost’ schools money. Because school funding is often allocated based on headcounts and accelerated students spend fewer years in school, schools receive fewer dollars overall, or in the case of dual enrollment, may have to spend some of those dollars outside the district.

Similarly, in states that offer open enrollment, students could leave a district for one where their needs are better met. Moreover, in the age of accountability via test score performance, keeping students who could be accelerated with their same-age peers can boost average test scores, regardless of whether the students are learning.”*

Even in schools that do offer acceleration, typically only a small portion of students per grade are accelerated. Given how many logistical challenges and other disincentivizing factors there are, how few students are typically accelerated, and how easy it is to imagine a young student struggling socially when they are placed in a class with older students away from age-level friends, it is not surprising that the myth persists.

Depth of Learning: Accelerated Students Learn More Material, Just as Deeply

A common myth goes like this: Mathematically accelerated students become accelerated by rushing through watered-down courses, leading to shallower learning.

In reality, it is well documented in the literature of academic acceleration studies that students undergoing acceleration generally learn – in a shorter time – as much as they would otherwise in a non-accelerated environment over a proportionally longer period of time.

For instance, Kulik & Kulik’s well-known review (1984) of 26 academic acceleration studies found that talented students who were accelerated by one year (i.e. they learned two years’ worth of material in one year) performed as well as students one year older who were equivalently talented but not accelerated:

“First, talented youngsters who were accelerated into higher grades performed as well as the talented, older pupils already in those grades. Second, in the subjects in which they were accelerated, talented accelerates showed almost a year’s advancement over talented same-age nonaccelerates.”

As Kulik & Kulik (1984) noted, “most [other] reviewers of the controlled studies have reached favorable conclusions about the effects of acceleration.” Furthermore, many of these conclusions were expressed with a level vehemence that is rare to find in academic literature, except out of frustration when a result so clearly supported by science is ignored by the education system for no reason other than the inertia of tradition:

“In her 1958 review, Goldberg pointed out that it was hard to find a single research study showing acceleration to be harmful and that many studies proved acceleration to be a satisfactory method of challenging able students.”
“A 1964 review by Gowan and Demos concluded simply that ‘accelerated students do better than non-accelerated students matched for ability’ (p. 194).”
“Gold (1965) echoed their [Gowan and Demos’s] sentiments and added, ‘No paradox is more striking than the inconsistency between research findings on acceleration and the failure of our society to reduce the time spent by superior students in formal education’ (p. 238).”
“Perhaps what is needed,” Gallagher suggested in 1969, “is some social psychologist to explore why this procedure [of academic acceleration] is generally ignored in the face of such overwhelmingly favorable results” (p. 541).
“Dillon in 1973 also lamented the lack of interest in acceleration and offered a social psychological explanation: ‘Apparently the cultural values favoring a standard period of dependency and formal education are stronger than the social or individual need for achievement and independence. This is an instance of the more general case one remarks throughout education: When research findings clash with cultural values, the values are more likely to prevail, (p. 717).’”
“In a review of research on acceleration in mathematics, Begle (1976) concluded that accelerated students scored higher than comparable controls in almost all comparisons and almost never scored lower. The accelerated students also did better than average, nonaccelerated, older students, and when they did not do as well as talented older students, they did not lag far behind.”

This review (Kulik & Kulik, 1984), considered together with about a dozen more recent others, gave rise to the following conclusion in the second-order review titled What one hundred years of research says about the effects of ability grouping and acceleration on K–12 students’ academic achievement (Steenbergen-Hu, Makel, & Olszewski-Kubilius, 2016):

”…[T]he conversation needs to evolve beyond whether such interventions [of academic acceleration] can ever work. There is not an absence of evidence, nor is there evidence of absence of benefit. The preponderance of existing evidence accumulated over the past century suggests that academic acceleration … can greatly improve K–12 students’ academic achievement.”

Continuity of Courses: Accelerated Students Don’t Run out of Math Courses

A common myth goes like this: If a student takes math classes early, they will run out of math classes to take.

In reality, while many people think calculus is the “end of the road” for math, it is but an entry-level requirement for university-level math courses. There are even more university-level math courses above calculus than there are high school courses below calculus.

After a single-variable calculus course (like AP Calculus BC), most serious students who study quantitative majors like math, physics, engineering, and economics have to take core “engineering math” courses including Linear Algebra, Multivariable Calculus, Differential Equations, and Probability & Statistics (the advanced calculus-based version, not the simpler algebra-based version like AP Statistics). Beyond those core “engineering math” courses, different majors include plenty of specialized courses that branch off in various ways.

There are so many university-level math courses that a student could not fit them all into a standard 4-year undergraduate course load even if they overloaded their schedule every year – however, the more of these courses a student is able to take, the more academic opportunities and career doors are open to them in the future.

Credit: Advanced Students Can Place Out of College Courses Beyond Placement Tests

A common myth goes like this: There’s no use in learning math past calculus in high school because you’ll have to take it again in college (since advanced placement courses and college math placement tests only go up through calculus).

In reality, when the most advanced students place out of classes, it is not through transfer credit or placement exams. Generally, they are placing out of courses that are beyond what’s tested on the placement exam.

They do this by not only learning the material beforehand, but also taking the initiative to schedule a meeting with an undergraduate advisor or coordinator for the math department. Some schools have a policy of arranging undergraduate for-credit exams, while others may have a less formal process, such as arranging a meeting with a professor who will determine the student’s placement by discussing mathematics with them, getting a sense of their background and knowledge, and maybe having them solve some problems at the board.

If you want to learn math ahead of time and place into more advanced courses, there are a couple pitfalls to watch out for:

If you learn material ahead of time, but not comprehensively, then you might not be able to evidence enough knowledge to place out of it. Or, if you manage to place out of a course without having learned the material comprehensively, you might end up way out of your depth in the more advanced course that you end up taking.
If you learn material ahead of time, but do not continually review that material, then you will likely become rusty and unable to evidence enough knowledge to place out of it.

In order to avoid these pitfalls, you need to learn material comprehensively and continually review it after learning it.

Relevance to Students’ Futures: Learning Math Early Reduces Risk and Opens Doors to Opportunities

A common myth goes like this: Learning math early can be impressive, but it’s just a party trick. It doesn’t have much real impact on a student’s future, especially if they’re going into something other than engineering.

In reality: You know how, when you take a language class, there’s often a couple kids who speak the language at home and think the class is super easy? You can do that with math. Learning math ahead of time basically guarantees an A and guards against all sorts of risks such as the teacher not knowing the content very well or otherwise not being able to explain it well. This is especially helpful at university, when lectures are often unsuitable for a first introduction to a topic.

Of course, the natural objection is “won’t you be bored in class?” – but if you do super well in advanced classes, especially at university, then that opens all kinds of doors to recommendations for internships, research projects with professors, etc. Even if you aren’t a genius, you appear to be one in everyone else’s eyes, and consequently you get a ticket to those opportunities reserved for top students. Students who receive and capitalize on these opportunities can launch themselves into some of the most interesting, meaningful, and lucrative careers that are notoriously difficult to break into.

Learning math early also gives students the opportunity to delve into a wide variety of specialized fields that are usually reserved for graduates with strong mathematical foundations. This fast-tracks students towards discovering their passions, developing valuable skills in those domains, and making professional contributions early in their careers, which ultimately leads to higher levels of career accomplishment. As described by the authors of a 40-year longitudinal study of thousands of mathematically precocious students (Park, Lubinski, & Benbow, 2013):

“The relationship between age at career onset and adult productivity, particularly in science, technology, engineering, and mathematics (STEM) fields, has been the focus of several researchers throughout the last century (Dennis, 1956; Lehman, 1946, 1953; Simonton, 1988, 1997; Zuckerman, 1977), and a consistent finding is that earlier career onset is related to greater productivity and accomplishments over the course of a career. All other things being equal, an earlier career start from acceleration will allow an individual to devote more time in early adulthood to creative production, and this will result in an increased level of accomplishment over the course of one’s career.
…
[In this study] Mathematically precocious students who grade skipped were more likely to pursue advanced degrees and secure STEM accomplishments, reached these outcomes earlier, and accrued more citations and highly cited publications in STEM fields than their matched and retained intellectual peers.”

And while it’s true that students don’t need to know much beyond algebra to get a job in fields like computer science, medicine, etc. – the people in such fields who do also know advanced math are extra valuable and in demand because they can work on projects that combine domain expertise and math.

Higher-Grade Math is Typically More Productive than Grade-Level Competition Problems

Another common myth goes like this: If a student learns their grade-level math and wants to do more math, it is more productive to have them work on extremely challenging competition math problems at their current grade level than to continue learning more advanced math that they would normally learn in higher grade levels.

But in reality, when a middle or high school teacher has a bright math student, and the teacher directs them towards competition math, it’s usually not because that’s the best option for the student. Rather, it’s the best option for the teacher. It gives the student something to do while creating minimal additional work for the teacher.

Competition math problems generally don’t require students to learn new fields of math. Rather, the difficulty comes from students needing to find clever tricks and insights to arrive at solutions using the mathematical tools that they have already learned. A student can wrestle with a competition problem for long periods of time, and all the teacher needs to do is give a hint once in a while and check the student’s work once they claim to have solved the problem.

But if you look at the kinds of math that most quantitative professionals (like rocket scientists and AI developers) use on a daily basis, those competition math tricks show up rarely, if ever. What does show up everywhere is university-level math subjects like linear algebra, multivariable calculus, differential equations, and (calculus-based) probability and statistics. Given that most students who enjoy math end up applying math in some other field (as opposed to becoming pure mathematicians), it would be more productive for them to get a broad view of math as early as possible so that they can sooner apply it to projects in their field(s) of interest.

Of course, the countering view is that “students should go ‘deep’ with the math that they’ve already learned – they’ll learn the other math subjects when they’re ready.” But, in practice, the second part of that claim is not true. There are so many other math subjects that even most math majors only learn a tiny slice of all the math that’s out there.

Students generally can’t learn other math subjects “on the job” after graduation, either – if you’re trying to solve cutting-edge problems that nobody has solved before, then there is no “known path” that can tell you what additional math you need. And to even realize that a field of math can help you solve your problem, you generally need to have learned a substantial amount of that field in the first place.

In practice, the only way for students to “learn the other math subjects when they’re ready” is to learn as much math as possible during school.

References

Bernstein, B. O., Lubinski, D., & Benbow, C. P. (2021). Academic acceleration in gifted youth and fruitless concerns regarding psychological well-being: A 35-year longitudinal study. Journal of Educational Psychology, 113 (4), 830.

Borland, J. H. (1989). Planning and Implementing Programs for the Gifted. New York: Teachers College Press.

Kulik, J. A., & Kulik, C. L. C. (1984). Effects of accelerated instruction on students. Review of educational research, 54 (3), 409-425.

Park, G., Lubinski, D., & Benbow, C. P. (2013). When less is more: Effects of grade skipping on adult STEM productivity among mathematically precocious adolescents. Journal of Educational Psychology, 105 (1), 176.

Steenbergen-Hu, S., Makel, M. C., & Olszewski-Kubilius, P. (2016). What one hundred years of research says about the effects of ability grouping and acceleration on K–12 students’ academic achievement: Findings of two second-order meta-analyses. Review of Educational Research, 86 (4), 849-899.

Wai, J. (2015). Long-term effects of educational acceleration. A nation empowered: Evidence trumps the excuses holding back America’s brightest students, 2, 73-83.

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