Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Lifespan Development

5.4 Language in Early Childhood

Lifespan Development5.4 Language in Early Childhood

Learning Objectives

By the end of this section, you will be able to:

  • Identify the features of formal language
  • Explain how we use language to understand cognitive development
  • Summarize the way the environment influences language development in early childhood
  • Distinguish among populations with individual differences in language development

When Emilia started preschool at age three, she was using more than 500 words and could understand about twice that number. By the time she entered kindergarten at age five, she recognized well over 10,000 words. In addition, Emilia has been picking up different dialects, slang words, and idioms based on her culture, heard in her neighborhood, and learned from the adults and other children at school. As Emilia’s language use advances, it will become a tool for her self-reflection and discovery, complementing her cognitive growth.

In this section, you’ll learn about the fundamentals of language construction and explore literacy, a sophisticated and relatively new human invention. In modern society, literacy has become an integral part of human development.

Defining Features of Language

Every language has unique characteristics children must learn. Let’s revisit and further describe those components of language that were first introduced in 3.5 Language in Infants and Toddlers, beginning with the smallest components.

Phonology

Recall that phonology is the branch of linguistics that studies the sound systems of languages, the way sounds are organized and combined to form words and sentences. This is done by analyzing phonemes, or the smallest units of sound. For example, the word "bit" has three phonemes: /b/ /i/ /t/. Native speakers of a language distinguish between different phonemes and use them correctly in words and sentences, even though they may not be consciously aware of the phonetic rules governing their use. Phonological awareness, or the ability to recognize and manipulate the sounds of language (like /b/i/t/), is a key component of reading and writing skills.

Some languages have more phonemes than others or use tone or pitch to differentiate between words. For instance, the fact that, in American English, we pronounce “bass” differently to mean a deep sound and a type of fish is just one example of the way phonemes differentiate the meaning of otherwise similar words. Language development and linguistics researchers have identified around 800 phonemes among various languages (Kuhl, 2015). Studying phonology can provide insights into the features of different languages, the way humans acquire language, and the way language is processed by the brain.

Morphemes

Morphemes are the smallest units of language that have meaning. They include prefixes, suffixes, and roots, the building blocks of words, and they can also be isolated words. For example, the word “unfillable” combines three morphemes, each with its own unique meaning: Un + fill + able (un- meaning “not”, fill as in the verb, and -able meaning “capable of”). Morphemes are integral to spoken, written, and signed languages.

As children expand their implicit understanding of morphological structures, they enhance their vocabulary and comprehension skills. That is, as they begin to recognize the way morphemes combine and alter words, they become able to decode unfamiliar words. In turn, their reading and communication skills improve. Morphological awareness not only aids in vocabulary development but also plays an important role in syntactic and semantic understanding, which contribute to overall language learning proficiency

Semantics

The study of the meaning of words and sentences in a language is called semantics. It looks at the way words are used and understood in different contexts. Part of learning language is recognizing these diverse contextual meanings. For example, the word "sick" can refer to being ill or, in modern slang, being awesome. As children gain an understanding of diverse meanings of words and phrases, they are able to more easily navigate social and academic environments.

Syntax

The set of rules that govern the way we combine words to form phrases, clauses, and sentences in a language is called syntax. It orders the structure of sentences and the ways in which words are arranged and changed to convey meaning, such as through subject-verb agreement, verb tense, the use of modifying adjectives and adverbs, and word order. For example, the standard word order in English is subject-verb-object. English also generally places adverbs and adjectives before the words they modify, as in “I really like your blue dress.” Spanish, however, puts the modifiers after, as in, “Me gusta mucho tu vestido azul” (“I like very much your dress blue.”).

Syntax also helps us analyze variations in sentence structure. We can see how the arrangement of words influences the interpretation when we change the sentence “The child ate a banana” to "The banana ate a child.” When children learn more vocabulary and improve their language skills, they use more diverse syntax and improve their communication skills.

Grammar

While syntax governs the order of words, it is grammar that enables us to communicate accurately. Grammar codifies a language’s rules of usage, pronunciation, tone, and word order, encompassing both syntax and morphology. Our mastery of grammar goes through an extraordinary transformation in early childhood. Children transition from overextensions of grammar rules, also known as overregularization, to greater mastery of grammar rules. For example, they transition from grammar mistakes like “I runned with my dog” to the correct “I ran with my dog.”

Grammar consists of rules, but it is also shaped by the social and cultural context in which it is used, reflecting regional dialects, SES, and cultural norms. For example, African American Vernacular English (AAVE) has a distinct grammar that differs from standard English, including unique features such as the use of double negatives (Kurinec & Weaver, 2021; Rickford et al., 2015). Research suggests that AAVE is often associated with negative stereotypes and biases as early as preschool age (Harris & Schroeder, 2013). These biases can have negative implications for the cognitive, social, and academic outcomes of Black children who speak it, and for Black adults in encounters with law enforcement, the legal system overall, and the workplace (Kurinec & Weaver, 2021). It is essential to address these biases early through education and awareness-raising efforts.

Children also tend to seamlessly engage in code-switching, the practice of alternating between two or more languages or language varieties based on their dialogue partner or the setting of the conversation. They can naturally switch between English and their family’s native language at home, and then speak English with teachers and friends at school. This linguistic phenomenon is more prevalent in multilingual or multicultural environments and can occur for social, cultural, or situational reasons. Code-switching allows children to be comfortable in different social contexts and convey subtle meanings, cultural affiliations, or emotions.

Pragmatics

In contrast to semantics, pragmatics is the way we use language in different situations, what we intend when communicating, and the cultural norms that govern language use. For example, “Thanks” can sound sincere, sarcastic, or even flirtatious depending on tone and body language. A child’s use of words and expression is likely to be different during a classroom lesson than on the playground (Figure 5.20).

Images of (a) a classroom with tables, chairs, and children sitting while adults stand and (b) playground where children are running around.
Figure 5.20 Children learn to communicate in diverse ways depending on culture, social norms, situational attributes, and overall context. Their communication style is likely to differ between the (a) classroom and the (b) playground. (credit a: modification of work “05202013 - Savoy Elementary School Visit 66” by U.S. Department of Education/Flickr, CC BY 2.0; credit b: modification of work “Blanchard Recess_4975c” by James Emery/Flickr, CC BY 2.0)

In early childhood, the development of pragmatic skills includes learning how to take turns in conversation, ask and answer questions, and use eye contact and body language to convey meaning. Even young children adjust their language based on the social context and the people they are communicating with, as in code-switching and the use of different meanings for words like “sick.” Soon they will develop the pragmatic skills to persuade, negotiate, and perhaps manipulate. As cognition becomes less egocentric, children take the listener's perspective into account and might change their intonation and emphasis to clarify meaning.

Language in Cognitive Growth and Communication

Language development is essential to human development and serves as both a window into our cognitive processes and a tool for communication and social interaction. In children, language development provides a critical foundation for overall cognitive and socioemotional development.

While language learning comes readily to most young children, adults who have attempted to learn an additional language know it is a complex process that requires considerable effort. This difficulty demonstrates that there are critical and/or sensitive periods for learning language, and they end well before early childhood ends at age seven. In other words, childhood is an optimal period in which to learn both your first language and a second language as well. The well-known case of Genie, a severely neglected and abused child who at thirteen years old had not been exposed to much language, demonstrates the impact of environmental effects on long-term language acquisition (Curtiss, 1977).

However, far less extreme circumstances than Genie’s have direct effects as well, as shown in studies by Hart and Risley (1995) and others. In addition, children who are deaf or hard of hearing may develop language deficits due to their diminished language exposure. This risk is higher when disabilities are left undiagnosed, making early intervention and detection critical to promoting language development for all.

Language as a Window into Cognition

Language is often described as a window into cognition because it provides insight into the underlying cognitive processes that allow us to think, reason, and solve problems (Federmeier et al., 2020). For example, language allows us to form categories, make predictions, and infer relationships between words and concepts. These processes are integral to cognitive development.

Studying language development also provides insight into cognitive deficits and developmental delays. For instance, children with language impairments may exhibit difficulty with grammar and syntax, often initial indicators of cognitive deficits (McGregor et al., 2022). Similarly, children with autism spectrum disorder often struggle with language development and social communication. Their difficulties in processing social cues and inferring meaning in social interactions suggest that cognition plays a role in language and socialization.

Language as a Tool for Communication and Learning

Of course, language is also a powerful tool for communication. It allows us to express needs, share experiences, and form social connections. It helps children develop theory of mind and perspective-taking. Moreover, language use and exposure play significant roles in shaping children’s psychosocial development. For example, positive and responsive language interactions between parents and children are associated with better psychosocial outcomes, such as increased empathy and better social skills (Frosch & Schoppe-Sullivan, 2021). Language-rich environments promote better cognitive outcomes in children too, including a more robust foundation to acquire reading and writing skills, essential components of academic success (Logan et al., 2019).

Research has attempted to both confirm and broaden our knowledge of family talking behaviors that lead to language and communication differences. Gilkerson et al. (2017) used automated recorders to collect speech data from children and their caregivers and found significant variability within and across SES groups, primarily based on mother’s education level. While there was a wide range of vocabulary skills within both high- and low-SES families, SES was a predictive factor for the way families interact. Children of mothers with a higher education talk more, have more adult-child interactions, and are more engaged overall. Because early language skills are strong predictors of a child’s later academic success, these results offer important implications for improving language development for all children (Durham et al., 2007).

These conclusions also indicate the need for early interventions designed for at-risk children. Those who are raised in impoverished language environments can benefit from home-visit programs, high-quality childcare, and pre-kindergarten programs (Figure 5.21). These have been shown to improve early language exposure and lead to better long-term outcomes for children (Bierman et al., 2018; Vernon-Feagans, & Bratsch-Hines, 2013; Williams et al., 2020). The simple understanding that talking more improves outcomes has potential long-term benefits.

Map of states in the U.S. listing (by colors), percentages of 4 year old children served by a preschool program. Darker colors represent higher percentages, while lighter colors represent lower percentages.
Figure 5.21 More states are recognizing the value of pre-kindergarten programs, which can have a beneficial impact on language development in early childhood (Friedman-Krauss et al., 2024). (credit: modification of work "Figure 4" by Friedman-Krauss et al./National Institution for Early Education Research, Public Domain)

Individual Differences in Language

Because language appears to come so naturally, we often take for granted the varied trajectories that exist among young language learners. In this section we explore the differences, challenges, and advantages that might exist for different populations of children.

Language Development in Deaf Children

Children who do not receive any language input during their first two years of life, whether due to deafness or other factors, run the risk of never achieving language fluency (Hall et al., 2019; Humphries et al., 2012). Therefore, children born deaf or hard of hearing are often at risk of delays in language acquisition and cognitive development if they do not receive appropriate support.

Exposing deaf children to sign language early is crucial because it provides them both a visual and tactile form of communication to interact with their environment (Hall, 2018). American Sign Language (ASL), the most widely used sign language in the United States, is recognized as a natural language with its own grammar and syntax (Figure 5.22). ASL and other sign languages have the same defining features of language discussed previously:

  • There is a distinct grammatical structure, including rules governing word order and sentence construction.
  • Sign languages have similar phonological components, including morphemes and phonemes. These may be conveyed through specific handshapes, movements, and facial expressions.
  • Sign languages have their own syntax, governing the arrangement of signs to convey meaning.
  • Symbols and signs convey semantics in a manner like that of voiced languages.
  • As in voiced languages, pragmatic principles exist for different social and cultural contexts.

Regardless of which languages we use, our brains process linguistic information in a comparable manner.

Image of two young girls signing to each other with their hands by their faces.
Figure 5.22 Signing is as unique as any voiced language. (credit: “Learning sign language” by David Fulmer/Flickr, CC BY 2.0)

Technology has introduced new ways for deaf children to learn language through devices like cochlear implants and hearing aids that can offer some auditory input. Speech therapy can also help children develop spoken language skills. Research does not necessarily support emphasizing deaf children use voice as the primary means of communication. Only a small fraction of children (2–3 out of every 1,000) are born deaf, more than 90 percent of whom are born to hearing parents. Debate is ongoing over whether deaf children learn to speak because it benefits them or because it benefits others (Hall et al., 2019; Humphries et al., 2022; Lieberman et al., 2022). Ultimately, early and consistent support from caregivers, educators, and medical professionals is the key to successful language learning in deaf children. With resources and guidance, they can develop strong language skills like any other child, and children of diverse abilities may all benefit from language learning resources, including sign language and other nonverbal communication forms.

Development in Multilingual Environments

Children who grow up in multilingual environments learn and use multiple languages naturally. The process of acquiring multiple languages is not necessarily the same as acquiring a single language. Children may go through periods of mixing languages or may initially have a smaller vocabulary in each language. However, with continued exposure and practice, they easily become fluent in multiple languages.

Moreover, exposure to multiple languages in childhood is an experience-dependent process that may shape cognitive outcomes, including improved executive attention and minor differences in the way the brain processes language (Bialystok, 2017). There is also some evidence of a lifelong cognitive advantage, including greater neural sophistication and a delay in the onset of some dementias (Berkes & Bialystok, 2022; Liu & Wu, 2021). Children who speak multiple languages are also often better able to communicate and connect with people from diverse linguistic and cultural backgrounds.

There are not necessarily any best practices for raising a multilingual child. Some multilingual families choose to have different adults speak in specific languages, while in others every adult uses a mix of languages. Both approaches are successful, and early exposure provides the greatest advantage. Whatever approach is taken, it is essential to provide regular exposure and support for each language. Families in many countries, including the United States, Italy, and Indonesia, may also choose to enroll children in bilingual early childhood education programs, which may improve robust language development for children (Huang et al., 2023; Leotta, 2023; Chang, 2024).

Early Literacy

Phonological awareness is the foundation for literacy, the ability to read, write, and understand information. Early literacy is enhanced by robust vocabulary development, phonological awareness, print awareness, and comprehension skills. Thus, children who have strong early literacy skills are more likely to enjoy academic success (Ramsook et al., 2020).

Parents and caregivers can support early literacy by reading to children regularly, supporting a text-rich environment with books and writing materials, and engaging in conversations and activities like storytelling and singing that promote language development. The repetition found in books and songs reinforces semantics, syntax, and grammar, and will promote a positive attitude towards reading. Reading books also furthers children’s exposure to a wider range of vocabulary than they might hear in everyday speech and conversations.

Early literacy skills can also be fostered through high-quality early childhood education programs. Substantial research demonstrates that investing in publicly funded early childhood education programs like Head Start provides cognitive, social, economic, and public health benefits (Campbell et al., 2014; McCoy et al., 2017; Negussie et al., 2019). Studies have even found a net monetary benefit: children who are provided early services are less likely to require public funds later and are more likely to have a positive impact in their communities (Heckman, 2006; Varshney et al., 2022).

Although research has extensively explored older children's use of tablets for reading, currently there is only limited understanding of the impact of digital reading in the early stages of literacy development. One review compared the impact of interactive, enhanced e-books (that is, with embedded dictionaries) to that of print books and non-enhanced, non-interactive e-books on the literacy skills of young children (López-Escriban et al., 2021). Most of the books in the study were carefully chosen by teachers for artistic and literary quality. The analysis revealed that when high-quality material is used, both enhanced and non-enhanced e-books are either equal to or have an advantage over print books in promoting phonological awareness and vocabulary learning. These findings have positive implications for marginalized populations, including those at risk of learning disabilities and those from lower SES families, and offer another alternative to standardized school-based instruction.

References

Berkes, M., & Bialystok, E. (2022). Bilingualism as a contributor to cognitive reserve: What it can do and what it cannot do. American Journal of Alzheimer’s Disease & Other Dementias. https://doi.org/10.1177/15333175221091417

Bialystok, E. (2017). The bilingual adaptation: How minds accommodate experience. Psychological Bulletin, 143(3), 233–262. https://doi.org/10.1037/bul0000099

Bierman, K. L., Welsh, J., Heinrichs, B. S., & Nix, R. L. (2018). Effect of preschool home visiting on school readiness and need for services in elementary school: A randomized clinical trial. JAMA Pediatrics, 172(8), Article e181029. https://doi.org/10.1001/jamapediatrics.2018.1029

Campbell, F., Conti, G., Heckman, J. J., Moon, S. H., Pinto, R., Pungello, E., & Pan, Y. (2014). Early childhood investments substantially boost adult health. Science, 343(6178), 1478–1485. https://doi.org/10.1126/science.1248429

Chang, A. N. (2024). Teaching bilingual to young learners: The pros and cons. Innovative: Journal Of Social Science Research, 4(1), 11271–11280. https://doi.org/10.31004/innovative.v4i1.9211

Curtiss, S. (1977). Genie: A Psycholinguistic Study of a Modern-Day "Wild Child." Academic Press.

Durham, R. E., Farkas, G., Hammer, C. S., Tomblin, J. B., & Catts, H. W. (2007). Kindergarten oral language skill: A key variable in the intergenerational transmission of socioeconomic status. Research in Social Stratification and Mobility, 25(4), 294–305. https://doi.org/10.1016/j.rssm.2007.03.001

Federmeier, K. D., Jongman, S. R., & Szewczyk, J. M. (2020). Examining the role of general cognitive skills in language processing: A window into complex cognition. Current directions in psychological science, 29(6), 575–582. https://doi.org/10.1177/0963721420964095.

Friedman-Krauss, A. H., Barnett, W. S., Hodges, K. S., Garver, K. A., Jost, T. M., Weisenfeld, G., Duer J. (2024). The State of Preschool 2023: State Preschool Yearbook. New Brunswick, NJ: National Institute for Early Education Research.

Frosch, C. A., Schoppe-Sullivan, S. J., & O’Banion, D. D. (2021). Parenting and child development: A relational health perspective. American Journal of Lifestyle Medicine, 15(1), 45–59. https://doi.org/10.1177/1559827619849028

Gilkerson, J., Richards, J. A., Warren, S. F., Montgomery, J. K., Greenwood, C. R., Oller, D. K., Hansen, J. H. L., & Paul, T. D. (2017). Mapping the early language environment using all-day recordings and automated analysis. American Journal of Speech-Language Pathology, 26(2), 248–265. https://doi.org/10.1044/2016_AJSLP-15-0169

Hall, M. L., Hall, W. C., & Caselli, N. K. (2019). Deaf children need language, not (just) speech. First Language, 39(4), 367–395. https://doi.org/10.1177/0142723719834102

Hall, W. C. (2018). What you don’t know can hurt you: The risk of language deprivation by impairing sign language development in deaf children. Maternal and Child Health Journal, 21(5), 961–965. https://doi.org/10.1007/s10995-017-2287-y

Harris, Y. R., & Schroeder, V. M. (2013). Language deficits or differences: What we know about African American Vernacular English, in the 21st Century. International Education Studies, 6(4), 194–204. http://dx.doi.org/10.5539/ies.v6n4p194

Hart, B., & Risley, T. R. (1995). Meaningful differences in the everyday experience of young American children. Paul H. Brookes Publishing Co.

Heckman, J. J. (2006). Skill formation and the economics of investing in Disadvantaged children. Science. 312, 1900–1902. https://doi.org/10.1126/science.1128898

Huang, R., Baker, E. R., & Schneider, J. M. (2023). Executive function skills account for a bilingual advantage in English novel word learning among low-income preschoolers. Journal of Experimental Child Psychology, 235. https://doi.org/10.1016/j.jecp.2023.105714

Humphries, T., Kushalnagar, P., Mathur, G., Napoli, D. J., Padden, C., Rathmann, C., & Smith, S. R (2012). Language acquisition for deaf children: Reducing the harms of zero tolerance to the use of alternative approaches. Harm Reduction Journal, 9(16). https://doi.org/10.1186/1477-7517-9-16

Humphries, T., Mathur, G., Napoli, D.J., Padden, C., & Rathmann, C. (2022). Deaf children need rich language input from the start: Support in advising parents. Children, 9(11). https://doi.org/10.3390/children9111609

Kuhl, P. K. (2015). Baby talk. Scientific American, 313(5), 64–69.

Kurinec, C. A., & Weaver, C. A. (2021). “Sounding Black”: Speech stereotypicality activates racial stereotypes and expectations about appearance. Frontiers in Psychology, 12. https://doi.org/10.3389/fpsyg.2021.785283

Leotta, P. C. (2023). Benefits of English for preschool children. The case study of a bilingual school in Italy. International Journal of Linguistics, Literature and Culture, 10(1), 46–54. http://dx.doi.org/10.19044/llc.v10no4a46

Lieberman, A. M., Mitchiner, J., & Pontecorvo, E. (2022). Hearing parents learning American Sign Language with their deaf children: A mixed-methods survey. Applied Linguistics Review, 15(1), 309–333. https://doi.org/10.1515/applirev-2021-0120

Liu, H., & Wu, L. (2021). Lifelong bilingualism functions as an alternative intervention for cognitive reserve against Alzheimer's disease. Frontiers in Psychiatry, 12. https://doi.org/10.3389/fpsyt.2021.696015

Logan J. A. R., Justice, L. M,. Yumuş, M., & Chaparro-Moreno, L. J. (2019). When children are not read to at home: The million word gap. Journal of Developmental and Behavioral Pediatrics, 40(5), 383–386. https://doi.org/10.1097/dbp.0000000000000657

López-Escribano, C., Valverde-Montesino, S., & García-Ortega, V. (2021). The impact of e-book reading on young children’s emergent literacy skills: An analytical review. International Journal of Environmental Research and Public Health, 18(12), Article 6510. https://doi.org/10.3390/ijerph18126510

McCoy, D. C., Yoshikawa, H., Ziol-Guest, K. M., Duncan, G. J., Schindler, H. S., Magnuson, K., Yang, R., Koepp, A., & Shonkoff, J. P. (2017). Impacts of early childhood education on medium- and long-term educational outcomes. Educational Researcher, 46(8), 474–487. https://doi.org/10.3102/0013189X17737739

McGregor, K. K., Smolak, E., Jones, M., Oleson, J., Eden, N., Arbisi-Kelm, T., & Pomper, R. (2022). What children with developmental language disorder teach us about cross‐situational word learning. Cognitive Science, 46(2). https://doi.org/10.1111/cogs.13094

Negussie, Y., Geller, A., & DeVoe, J. E. (Eds.). (2019). Vibrant and healthy kids: Aligning science, practice, and policy to advance health equity. National Academies Press (US). https://www.ncbi.nlm.nih.gov/books/NBK551492/

Ramsook, K. A., Welsh, J. A., & Bierman, K. L. (2020). What you say, and how you say it: Preschoolers' growth in vocabulary and communication skills differentially predict kindergarten academic achievement and self‐regulation. Social Development, 29(3), 783–800. https://doi.org/10.1111/sode.12425

Rickford, J. R., Duncan, G. J., Gennetian, L. A., Gou, R. Y., Greene, R., Katz, L. F., Kessler, R. C., Kling, J. R., Sanbonmatsu, L., Sanchez-Ordoñez, A. E., Sciandra, M., Thomas, E., & Ludwig, J. (2015). Neighborhood effects on use of African American Vernacular English. Proceedings of the National Academy of Sciences of the United States of America, 112(38), 11817–11822. https://doi.org/10.1073/pnas.1500176112

Varshney, N., Temple, J. A., & Reynolds, A. J. (2022). Early education and adult health: Age 37 impacts and economic benefits of the child-parent center preschool program. Journal of Benefit-Cost Analysis, 13(1), 57–90. https://doi.org/10.1017/bca.2022.4

Vernon-Feagans, L., & Bratsch-Hines, M. E., & The Family Life Project Key Investigators (2013). Caregiver–child verbal interactions in child care: A buffer against poor language outcomes when maternal language input is less. Early Childhood Research Quarterly, 28(4), 858–873. https://doi.org/10.1016/j.ecresq.2013.08.002

Williams, S. C., Barajas, C. B., Milam, A. J., Olson, L., Leaf, P., & Connolly, F. (2020). Preparing students for success: Differential outcomes by preschool experience in Baltimore City, Maryland. Prevention Science, 21(4), 467–476. https://doi.org/10.1007/s11121-019-01069-3

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/lifespan-development/pages/1-what-does-psychology-say
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/lifespan-development/pages/1-what-does-psychology-say
Citation information

© Oct 2, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.