A working list of constrained and unconstrained skills that support reading and math achievement
Reading, math, and nonacademic skills identified by researchers. And knowledge, too.
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 about a working list I developed of constrained and unconstrained skills. It’s compiled from academic writing about 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
I compiled this working list of constrained and unconstrained skills from multiple research papers. There currently is no single authoritative list of constrained and unconstrained skills in the academic literature.
Knowledge is included in this working list as a “skill.” This is akin to the way that cognitive scientists describe skill building as constructing and generalizing new knowledge to different tasks and contexts.
Constrained and unconstrained is not just another way to say “basic” and “complex” skills (or “easier” and “harder”). This is most evident when we consider that executive skills—working memory, cognitive flexibility, inhibition control—and world knowledge are unconstrained skills.
A working list of constrained and unconstrained skills
Currently, there is no single authoritative list of constrained and unconstrained skills (Rosengarten et al., 2024). This working list is based upon research studies that explicitly focus on constrained skill theory. It’s also augmented by research studies that identify component skills of reading and math achievement (Lervag et al., 2018; Language and Reading Research Consortium & Chiu, 2018; Hjetland et al., 2019; Kim, 2020; LeFevre et al., 2010; Sowinski et al., 2015; Rittle-Johnson et al., 2017; Rittle-Johnson et al., 2020).
This working list is further supported by research on the role of “nonacademic” skills to reading and math achievement (Stafford-Brizard, 2016a; Dawson & Guare, 2018; Cartwright, 2023). These skills help children manage their thoughts, emotions, and behavior and take goal-oriented actions (Cantor et al., 2021). The group of eight core nonacademic skills are foundational for the more complex social and emotional and higher-order thinking skills that support success in school, the workplace, and in life (Stafford-Brizard, 2016b). Research studies find that these skills directly and indirectly support reading and mathematics.
The working list also includes knowledge as its own category. The definition of knowledge I use comes from Cantor et al. (2021):
The ability to use facts, principles, and ideas to decide and do complex tasks.
This pairs nicely with the definition of skill from Fischer and Biddell (2006):
The capacity to act in an organized way in a specific context.
Knowledge is essential to skill-building. Researchers often refer to different types of knowledge as a reading or math skill (Kim, 2023; Rittle-Johnson et al., 2001). Hattan and Lupo (2020) remind us that knowledge comes in many forms. I think there is a case to be made that knowledge is the ultimate unconstrained skill.
The organization of this table is precisely wrong
Not only is this is a working list. It is precisely wrong in conveying the dynamic and complicated nature of these skills. For example, working memory, attention control, vocabulary, and inference skills make important contributors to both reading and math achievement (Kim, 2021). Some skills belong in multiple categories. Social understanding in nonacademic skills overlaps with perspective taking under reading skills. Nonacademic skills support virtually everything.
Researchers behind large federal studies like the Early Childhood Longitudinal Study described reading and math skills as hierarchical. Mastery of lower level reading and math skills are required at each level before one can learn the material at the next higher level. Along the way there are likely cognitive differences in subsequent levels of skill mastery.
For example, research in math cognition finds qualitative differences in cognitive processing of addition and subtraction compared to multiplication and division. Our brains are demonstrably slower to produce the answer for 2x3 than for 2+3 (Dowker, 2019). The mathematical cognition involved in finding an solution for one side of an equal sign (arithmetic) is different than that involved in determining how to make both sides of an equal sign the same (algebra).
I look forward to future conversations to determine how to improve the visual representation of constrained and unconstrained skills in this list.
Is “unconstrained” a complicated way to describe “harder”?
Looking at this list, it’s reasonable to wonder whether “unconstrained” is an overly complicated way to say “harder”? Kim and Pilcher (2016) refer to skills such as vocabulary and listening comprehension as “large problem spaces” that are expansive and continue to grow through our lifetimes. They assert, “[t]his is in contrast to a confined or constrained skill (Paris, 2005) or mastery skill such as acquiring alphabet letters, which has a limited number of units to be learned, and can be taught to mastery in a relatively short time.”
Indeed, the unconstrained skills in the table appear less complicated than the unconstrained skills. Many unconstrained skills are clearly more complex. There is more information to be acquired, consolidated, and integrated to (eventually) use automatically. Proficiency in unconstrained skills often requires mastery of a mix of other constrained and unconstrained skills. In this sense, it is accurate to describe more complex unconstrained skills as “harder” to develop.
But unconstrained skills also are distinguished from constrained skills in other ways:
Constrained skills involve information that everyone has virtually equal access to—letters, numbers, high frequency words, numerical operations, etc.
Not everyone has equal access to the information involved with unconstrained skills—vocabulary, comprehension, background knowledge, etc.
Unconstrained skills tend to be “caught and taught,” developing in informal learning environments (e.g. home, community) as well as formal learning environments (e.g. the classroom).
Unconstrained skills such as working memory, cognitive flexibility, and background knowledge develop from learning experiences in and outside of the classroom. Not all kids enjoy the same opportunities for these experiences.
Differences in proficiency of unconstrained skills is as much about the available of opportunity and a supportive environment for skill development as it is about the nature of the skills themselves. This appears to potentially align with the “Opportunity-Propensity Framework” proposed by Byrnes and Miller (2007). The O-P Framework asserts that academic achievement in school is a shaped by factors that occur before students start school (e.g., demographics that predict opportunities and propensities occurring before formal schooling), opportunities (exposure to experiences afforded in the home, community, and school), and propensities (pre-existing skills that help children take advantage of opportunities).
But wait, there’s more
If you’d like to learn more about constrained and unconstrained skills, check out these other posts:
Constrained and unconstrained skills drive achievement in reading and math
An annotated summary of the major research papers behind constrained skill theory
Works cited and consulted
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Byrnes, J. P., & Miller, D. C. (2007). The relative importance of predictors of math and science achievement: An opportunity–propensity analysis. Contemporary Educational Psychology, 32(4), 599-629.
Cantor, P., Osher, D., Berg, J., Steyer, L., & Rose, T. (2021). Malleability, plasticity, and individuality: How children learn and develop in context. In P. Cantor & D. Osher (Eds.), The Science of Learning and Development: Enhancing the Lives of All Young People (pp. 3-54). New York: Routledge.
Cartwright, K. B. (2023). Executive skills and reading comprehension: A guide for educators. New York: The Guilford Press.
Dawson, P., & Guare, R. (2018). Executive skills in children and adolescents: A practical guide to assessment and intervention. New York: The Guilford Press.
Dowker, A. (2019). Individual differences in arithmetic: Implications for psychology, neuroscience and education. Oxford: Routledge.
Fischer, K. W., & Bidell, T. R. (2006). Dynamic development of action and thought. In R. M. Lerner & W. Damon (Eds.), Handbook of child psychology: Theoretical models of human development (6th ed., pp. 313–399). New York: John Wiley & Sons, Inc.
Hattan, C., & Lupo, S. M. (2020). Rethinking the role of knowledge in the literacy classroom. Reading Research Quarterly, 55, S283-S298.
Hjetland, H. N., Lervåg, A., Lyster, S. A. H., Hagtvet, B. E., Hulme, C., & Melby-Lervåg, M. (2019). Pathways to reading comprehension: A longitudinal study from 4 to 9 years of age. Journal of Educational Psychology, 111(5), 751.
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Kim, Y. S. G. (2021). Inferencing skill and attentional control account for the connection between reading comprehension and mathematics. Frontiers in Psychology, 12, 709944.
Kim, Y. S. G. (2023). Simplicity meets complexity: Expanding the simple view of reading with the direct and indirect effects model of reading. In Cabell, S. Q., Neuman, S. B. & Patton Terry, N. (Eds.), Handbook on the Science of Early Literacy, New York: The Guilford Press, pp. 9-22.
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