A history of the academic research behind constrained skill theory
An annotated summary of 20 years of academic writing on constrained skill theory.
Note: Unconstrained Kids unpacks, translates, and integrates academic research and data about constrained and unconstrained skills for people that run, fund, and assist organizations that teach and serve kids. This post is for research nerds. It provides an annotated summary of the academic research (“the canon”) that developed constrained skill theory. Like everything on this Substack, this post is a work-in-progress. I will make updates as needed. Citations are included at the end. Questions, comments, and suggestions are welcome.
Last updated: March 15, 2025
Three big ideas
Scott Paris, a former University of Michigan professor, first proposed Constrained Skill Theory in a peer-reviewed article published in 2005. He wrote a total of seven articles and edited book chapters on this topic. His primary focus was the challenge posed by constrained reading skills to statistical analyses of reading.
Two articles were published by other researchers in 2011 and 2016 that expanded upon the constrained skill framework for early literacy. Writing directly to educators and policymakers, they sought to expand the audience beyond academic researchers.
Between 2020 and 2023, multiple groups of researchers published articles and research briefs expanding the constrained skill framework to include mathematics and nonacademic (executive) skills. The intended audience appears to be largely policymakers and academic researchers.
Literacy skills
Scott Paris, a former University of Michigan professor, in 2005 published the first academic paper to describe two types of reading skills—constrained and unconstrained.
Paris, S. G. (2005). Reinterpreting the development of reading skills. Reading Research Quarterly, 40(2), 184-202.
This paper largely focused on statistical methods. Paris argued that constrained reading skills go from no ability to proficiency in a relatively brief period of time. Unconstrained skills develop slowly over longer periods of time. Paris argued that these characteristics and differences affect statistical analyses and interpretation. When researchers cite Paris, this is typically the paper they refer to. According to Google Scholar, this paper has been cited over 1,200 times. You can find this paper online.
The same year, Paris and three co-authors published a chapter in an edited book.
Paris, S. G., Carpenter, R. D., Paris, A. H., & Hamilton, E. E. (2005). Spurious and genuine correlates of children’s reading comprehension. In S. Paris & S. Stahl (Eds.), Children's Reading Comprehension and Assessment (pp. 149-178). New York: Routledge.
This chapter also had a heavy statistical methods focus. Interestingly, it included a vignette on the origin story for the discovery of constrained skill theory. The paper analyzed the relationships between oral reading fluency and print knowledge (both constrained skills) and reading comprehension (unconstrained). The paper discussed temporary relationships (correlations) between constrained and unconstrained reading skills. It described challenges with aggregated data and sampling related to interpreting results involving constrained and unconstrained skills. The paper concluded with a discussion of long-run relationships (correlations) between reading comprehension and (individually) language skills, vocabulary, and narrative reasoning skills. These four literacy skills are all unconstrained.
Two years later, Paris co-authored another chapter on constrained skill theory in an edited book.
Paris, S. G., & Paris, A. H. (2007). Assessments of early reading. In Damon, W., Lerner, R. M., Renninger, K. A., & Sigel, I. E. (Eds.). Handbook of Child Psychology, Volume Four: Child Psychology in Practice. (pp. 48-74) Hoboken, NJ: John Wiley & Sons.
This chapter focused on assessments of early reading skills. There was more limited statistical methods discussion in this chapter. It featured a notable shift toward implications of constrained skill theory for application, practice, and policy compared to the two previous papers. The chapter discussed reading assessments, the five parts of reading, and reading interventions. It also mentioned that constrained skill theory might also be applied to mathematics and other skills. In my opinion, this is one of the better — if not the best — papers authored by Paris on constrained skill theory.
Two years later, Paris authored a chapter in an edited book on constrained skill theory.
Paris, S. G. (2009). Constrained skills–So what? In K. M. Leander, D. W. Rowe, D. K. Dickinson, M. K. Hundley, R. T. Jimenez, & V. J. Risko (Eds.), 58th Yearbook of the National Reading Conference (pp. 34-44). Oak Creek, WI: National Reading Conference.
This chapter revisited the methodological argument behind constrained skill theory. It explained the nature of constrained and unconstrained skills. It discussed how the “shape of skill development” challenged prevailing theories of reading development. The chapter concluded with a discussion about the challenges that constrained skills in particular pose to common statistical analyses of reading development.
The same year, Paris and Hamilton published a chapter in an edited book.
Paris, S. G., & Hamilton, E. E. (2009). The development of children’s reading comprehension. In S. E. Israel & G. G. Duffy (Eds.), Handbook of Research on Reading Comprehension (pp. 56-77). New York: Routledge.
The first part of the chapter reviewed major models of reading comprehension. It highlighted three key research issues regarding the relationship between working memory, self-regulation, and oral reading fluency with reading comprehension. The chapter focused heavily on one methodological aspect of constrained skill theory: proficiency thresholds. The core idea was that the mastery level of different component skills required to support reading comprehension varied by skill type.
The following year, Paris and Luo published an article critiquing statistical analyses in the National Early Literacy Panel report.
Paris, S. G., & Luo, S. W. (2010). Confounded statistical analyses hinder interpretation of the NELP report. Educational Researcher, 39(4), 316-322.
NELP was convened in 2002. Its charge was to produce a synthesis of scientific research on the development of early literacy skills in children birth to five. This article applied the arguments developed in the previous three papers to the NELP report. Paris and Luo argued that the combination of constrained and unconstrained skills challenged the statistical analyses, interpretations, and recommendations in the report. (The report’s authors responded: they disagreed. Interestingly, one of authors of this response would later co-author a paper that expanded constrained skill theory beyond literacy.) In this paper, Paris and Luo suggested that longitudinal studies were better than cross-sectional studies for understanding the developmental dynamics of constrained and unconstrained skills from low to high mastery. You can read this paper online.
A year later, Paris published a chapter on constrained skill theory in an edited book. As far as I can tell, this appears to be Paris’s seventh and final publication on constrained skill theory.
Paris, S. G. (2011). Developmental differences in early reading skills. In S. Neuman & D. Dickinson (Eds.), Handbook of early literacy research (Vol. 3, pp. 228-241). New York: Guilford Press.
This chapter focused on differences in developmental trajectories of early reading skills. It made three claims: 1) some skills are mastered universally to the same end point; 2) some skills do not exhibit regular and steady growth; and 3) some skills are temporarily co-dependent on other skills. The chapter highlighted developmental trajectories of a set of reading skills to argue its case: alphabetic principle, concepts of print, phonological awareness, phonemic awareness, and oral reading fluency. The chapter concluded with two suggestions for the field. First, it proposed that new theories of reading development be generated that take these constraints into account. Second, it suggested reanalyses of data derived from constrained skills in previous studies. Next to the 2007 paper, I think this is arguably the second best in the Paris canon.
Up to this point, the arguments posed by Paris for constrained skill theory were largely centered on statistical analyses of differences in skill trajectories. Moreover, only two of the seven publications appeared in academic journals that offered greater potential visibility than edited books. In 2011, Katherine A. Dougherty Stahl published the first paper on constrained skill theory written for classroom educators.
Stahl, K. A. D. (2011). Applying new visions of reading development in today's classrooms. The Reading Teacher, 65(1), 52-56.
Stahl described constrained skill theory as “a reconceptualization of reading development that has important implications for classroom practice, curricula, and assessment.” This paper emphasized the varying levels of constraint across skills (“a continuum of constraint”). It defined highly constrained skills (name writing, alphabet knowledge, concepts of print, high-frequency words, phonics), moderately constrained skills (phonological awareness and reading fluency), and unconstrained skills (vocabulary and comprehension). This paper emphasized implications for classroom instruction and assessment. It acknowledged that unconstrained skills were more complex and time consuming to teach and assess than constrained skills. The paper discussed limits of assessments and classroom practices that support the development of unconstrained literacy skills. At the conclusion, Stahl thanked Scott Paris for providing feedback on the development of this paper. You can read this paper online.
Five years later, Catherine Snow and Timothy Matthews co-authored a paper on constrained skill theory targeted at policymakers.
Snow, C. E., & Matthews, T. J. (2016). Reading and language in the early grades. The Future of Children, 57-74.
This article used constrained skill theory to explain trends in early literacy development among American children. It expanded the framework to print-related and sound-related skills (constrained) and language- and knowledge-related skills (unconstrained). The article described unconstrained skills as key predictors of long-term literacy outcomes, i.e. “outcomes measured after third grade.” It drew a direct line between proficiency in unconstrained skills and socioeconomic status. The paper also directly addressed the key challenges of shifting educational practice: “[Constrained skills] are easy to teach and easy to test. Ensuring that teachers pay appropriate attention to unconstrained skills in early childhood and primary classrooms is a serious challenge.” The article discussed practices, programs, and interventions that support both constrained and unconstrained skill development. You can read this paper online.
Whenever constrained skill theory is cited in academic research, it most often includes one or more of three articles: Paris (2005), Stahl (2011), and/or Snow and Matthews (2016).
Mathematics and Non-academic skills
Researchers built upon this foundation over the last decade to go beyond literacy skills. The first paper to add mathematics to the constrained skills framework was published in 2020 by Meghan McCormick and colleagues. One of the co-authors was Catherine Snow.
McCormick, M. P., Weissman, A. K., Weiland, C., Hsueh, J., Sachs, J., & Snow, C. (2020). Time well spent: Home learning activities and gains in children’s academic skills in the prekindergarten year. Developmental Psychology, 56(4), 710.
This article examined the impact of constrained and unconstrained learning activities at home on Pre-K children’s academic skills in the classroom. The paper explicitly defined constrained and unconstrained math skills along with literacy skills. It also developed a list of constrained and unconstrained activities that support reading and math development.
The following year, Robert Pianta and colleagues from the Early Learning Network published a research brief that added math and executive skills to the constrained skills framework.
Pianta, R., Purtell, K., McCormick, M., Knoche, L., Burchinal, M., Ludvik, D. & Peisner-Feinberg, E. “Sustaining the pre-k boost: Skills type matters,” Spring (Lincoln, NE: Early Learning Network, 2021).
This research brief described constrained skills as “rote” or “basic” and unconstrained skills as “abstract.” It listed math and literacy skills in both categories, which it described as a continuum of skills. It also explicitly named executive functioning as an unconstrained skill. You can read this research brief online.
That same year, Jamie Spiegel and colleagues published an meta-analysis on the relationship between executive skills and reading, math, and oral language academic achievement.
Spiegel, J. A., Goodrich, J. M., Morris, B. M., Osborne, C. M., & Lonigan, C. J. (2021). Relations between executive functions and academic outcomes in elementary school children: A meta-analysis. Psychological Bulletin, 147(4), 329.
This meta-study examined the relationship between executive function skills — working memory, attention shifting, and inhibition control — and reading, math, and oral language achievement. The paper explicitly defined various reading, math, and oral language component skills as constrained or unconstrained. Unlike Pianta et al. (2021), the authors did not apply the framework to executive skills themselves.
The following year, Meghan McCormick and Shira Mattera published a research brief calling for assessment of both constrained and unconstrained skills in Pre-K programs.
McCormick, M., & Mattera, S. (2022). Learning more by measuring more: Building better evidence on pre-k programs by assessing the full range of children's skills. MDRC: New York, NY.
This research brief included a table that listed “more constrained” and “more unconstrained” language/literacy and math skills. Like Pianta et al. (2021), the research brief referenced executive function as an unconstrained skill. With echoes of Paris & Paris (2007), the research brief called for Pre-K assessments to include both constrained and unconstrained skills. You can read this paper online.
Finally, in 2023 Arya Ansari and colleagues published an article that used constrained skill theory to analyze the relationship between participation in Pre-K programs and academic achievement in first grade.
Ansari, A., Zimmermann, K., Pianta, R. C., Whittaker, J. V., Vitiello, V. E., Yang, Q., & Ruzek, E. A. (2023). The first-grade outcomes of pre-k attendees: Examining benefits as a function of skill type, environments, and subgroups. American Educational Research Journal, 60(6), 1139-1173.
This article explicitly used the constrained skill framework to analyze the convergence in early elementary school in ability between students who did and did not attend Pre-K programs. The study included four types of skills: reading, math, executive function, and socioemotional. It divided reading and math skills that were assessed into constrained (rote) and unconstrained (abstract) skills. It described both executive function and socioemotional skills as unconstrained. You can read this paper online.
Collectively, these research papers provide the research framework for constrained and unconstrained skills applied to reading and math achievement.
But wait, there’s more
If you’d like to learn more about constrained and unconstrained skills, check out these other posts: