What are constrained and unconstrained skills?

A powerful insight on what drives reading and math achievement.

Mar 07, 2025

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 provides an overview of characteristics of constrained and unconstrained skills. 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

Constrained skills such as word reading and numerical operations involve limited amounts of information. Kids typically build constrained reading and math skills in the classroom. Despite early gaps in elementary school, all student groups achieve high proficiency in constrained skills between elementary and middle school.
Unconstrained skills such as vocabulary, relational thinking, cognitive flexibility, and world knowledge involve broad amounts of information. Unconstrained skills grow slowly over time in the schoolhouse, at home, and in the community. Proficiency gaps in unconstrained skills emerge between student groups in elementary school and persist through high school.
The opportunities kids have to develop constrained skills are likely more similar than not. Opportunities to develop unconstrained skills are more likely to vary across kids.

Skill is essential for goal-oriented behavior

Skill is the capacity to act in an organized way in a specific context (Fischer & Bidell, 2006). Highly developed skills are automatic actions used to achieve objectives without the conscious awareness of the substeps or control involved (Afferblach et al., 2008). Skills are built up gradually through the practice of real activities in specific contexts. They are gradually extended (transferred) to new contexts through this same constructive process. “Skills beget skills” (Cunha & Heckman, 2007; Heckman, 2008). Simpler skills support the learning of more sophisticated (and complex) ones (Bailey et al., 2017). Skills are hierarchical, interactive, and dynamic (Fischer & Bidell, 2006; Kim, 2020).

Skill development occurs as a function of support and environment (among other factors). There are two basic preconditions for acquiring a skill: 1) an environment that is sufficiently regular to be predictable; and 2) an opportunity to learn these regularities through prolonged practice (Khaneman, 2011). Children’s skill development is a product of reciprocal interactions between their personal characteristics (skills, interests, motivation, etc.), their environment, and the people and organizations they interact with (Bronfenbrenner & Morris, 2006). Academic achievement in part is a function of the opportunities kids have to develop skills within their personal systems of support (Byrnes & Miller, 2007).

Constrained skill theory

In 2005, Scott Paris, a former University of Michigan professor, published the first of a series of academic papers describing differences in relationships over time between various reading skills (Paris, 2005). He divided reading skills into two categories based largely upon features related to their mastery: constrained and unconstrained. Over the next 20 years, other researchers built upon this Constrained Skill Theory. Initial contributions continued to focus on early literacy, adding implications for instruction and policy. Later researchers added math skills and nonacademic (executive) skills.

Today, researchers suggest skills differ in four fundamental ways:

The amount of knowledge or information associated with learning a particular skill.
The definition of mastery of a skill and whether it’s the same for everyone.
The amount of time typically needed to reach mastery of a skill.
The manner in which a skill is learned or acquired.

Constrained skills

Constrained skills involve relatively limited amounts of knowledge. Everyone has access to and learns the same information. Skills like the alphabet, word reading, counting, addition, and subtraction. Mastery is clearly defined and is the same for everyone. Typically developing kids generally master constrained skills within relatively limited periods of time.

Constrained skills are relatively straightforward to teach and assess. They are mostly learned in the classroom. Explicit and systematic instruction is needed in order for children to successfully learn these skills. Some children of course have learning challenges with constrained reading skills (dyslexia) and constrained math skills (dyscalculia). Good systematic instruction can help children develop these skills, particularly if challenges are diagnosed and addressed early.

Unconstrained skills

Unconstrained skills involve much broader amounts of information. Everyone doesn’t have access to the same information. Skills like vocabulary, comprehension, relational thinking, word problem solving, and knowledge. There is no universal finish line for mastery – and always the opportunity to learn more. Kids acquire these skills at different rates and to different levels of ability. It is not as straightforward to teach and assess unconstrained skills. There are greater sustained gaps in unconstrained reading and math skills. Unconstrained skills tend to develop more slowly over time compared to constrained skills.

Knowledge is the ability to use facts, principles, and ideas to decide and do complex tasks (Cantor et al., 2021). Knowledge is essential to skill building and sometimes is referred to as a skill. There are many types of knowledge which affect reading and math achievement (Hattan & Lupo, 2020). Like other unconstrained skills, its development depends upon instruction, experiences, and practice both inside and outside of the classroom. These different opportunities appear to explain gaps in kids’ world knowledge.

Nonacademic skills (also known as executive skills) like working memory, cognitive flexibility, and inhibition control are also unconstrained skills. These skills support goal-oriented behavior. They help kids control and shift their attention, manage distractions, and use and organize information (Dawson and Guare, 2018). Although kids engage these skills when doing reading- and math-related tasks, they are sometimes referred to as “nonacademic” because they help support a range of goal-oriented activities (Stafford-Brizard, 2016). Research shows these skills directly and indirectly contribute to children’s reading and math achievement (Sowinski et al., 2015; Cragg et al., 2017; Kim, 2020). Early gaps in nonacademic skills persist through elementary school.

Characteristics of constrained and unconstrained skills

If there is one word that summarizes the primary difference between constrained and unconstrained skills, it’s opportunity. For multiple reasons, the opportunities kids have to develop constrained skills are likely to be more similar compared to unconstrained skills. This table offers a summary of the characteristics of constrained and unconstrained skills. It is derived from descriptions in research papers about constrained skill theory. It is inspired by similar summaries in Kuhn and Levy (2015) and Stahl and Garcia (2022).

Kids need to develop constrained and unconstrained skills together

Both constrained and unconstrained skills are important to success in reading and math achievement. Constrained and unconstrained skills complement and reinforce each other. Despite skill gaps early in school, most kids master constrained reading and math skills by late elementary or middle school. The greater challenge is unconstrained skills. These gaps close slowly, if at all.

But wait, there’s more

If you’d like to learn more about constrained and unconstrained skills, check out these other posts:

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Works cited

Afflerbach, P., Pearson, P. D., & Paris, S. G. (2008). Clarifying differences between reading skills and reading strategies. The Reading Teacher, 61(5), 364-373.

Bailey, D., Duncan, G. J., Odgers, C. L., & Yu, W. (2017). Persistence and fadeout in the impacts of child and adolescent interventions. Journal of Research on Educational Effectiveness, 10(1), 7-39.

Bronfenbrenner, U., & Morris, P. A. (2006). The bioecological model of human development. In R. M. Lerner & W. Damon (Eds.), Handbook of child psychology: Theoretical models of human development (6th ed., pp. 793–828). Hoboken, NJ: John Wiley & Sons, Inc.

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.

Cragg, L., Keeble, S., Richardson, S., Roome, H. E., & Gilmore, C. (2017). Direct and indirect influences of executive functions on mathematics achievement. Cognition, 162, 12-26.

Cunha, F., & Heckman, J. (2007). The technology of skill formation. American Economic Review, 97(2), 31-47.

Dawson, P., & Guare, R. (2018). Executive skills in children and adolescents: A practical guide to assessment and intervention. New York: The Guilford Press.

Fischer, K. W. (2008). Dynamic cycles of cognitive and brain development: Measuring growth in mind, brain, and education. In A.M. Battro, K.W. Fischer & P. Léna (Eds.), The educated brain, (pp. 127-150). Cambridge: Cambridge University Press.

Hattan, C., & Lupo, S. M. (2020). Rethinking the role of knowledge in the literacy classroom. Reading Research Quarterly, 55, S283-S298.

Heckman, J. J. (2008). Schools, skills, and synapses. Economic Inquiry, 46(3), 289-324.

Khaneman, D. (2011). Thinking, fast and slow. New York: Farrar, Straus and Giroux.

Kim, Y. S. G. (2020). Hierarchical and dynamic relations of language and cognitive skills to reading comprehension: Testing the direct and indirect effects model of reading (DIER). Journal of Educational Psychology, 112(4), 667.

Kuhn, M. R., & Levy, L. (2015). Developing fluent readers: Teaching fluency as a foundational skill. New York: The Guilford Press

Paris, S. G. (2005). Reinterpreting the development of reading skills. Reading Research Quarterly, 40(2), 184-202.

Sowinski, C., LeFevre, J. A., Skwarchuk, S. L., Kamawar, D., Bisanz, J., & Smith-Chant, B. (2015). Refining the quantitative pathway of the Pathways to Mathematics model. Journal of Experimental Child Psychology, 131, 73-93.

Stafford-Brizard, K. B. (2016). Nonacademic skills are the necessary foundation for learning. Education Week. Retrieved from http://www.edweek.org/ew/articles/2016/07/21/nonacademic-skills-are-the-necessary-foundation-for.html.

Stahl, K. A. D., & García, G. E. (2022). Expanding reading comprehension in grades 3–6: Effective instruction for all students. New York: The Guilford Press.