How do children process language as they get older? Is there continuity in the functions assigned to specific structures? And what changes in their processing and their representations as they acquire more language? They appear to use bracketing (finding boundaries), reference (linking to meanings), and clustering (grouping units that belong together) as they analyze the speech stream and extract recurring units, word classes, and larger constructions. Comprehension precedes production. This allows children to monitor and repair production that doesn’t match the adult forms they have represented in memory. Children also track the frequency of types and tokens; they use types in setting up paradigms and identifying regular versus irregular forms. Amount of experience with language, (the diversity of settings) plus feedback and practice, also accounts for individual differences in the paths followed during acquisition. Ultimately, models of the process of acquisition need to incorporate all this to account for how acquisition takes place.

Children’s first words are remarkably consistent over languages and over time: They first talk about people (dada, mama), food (juice), body-parts (eye), clothing (sock), animals (dog), vehicles (car), toys (ball), household objects (key), routines (bye), and activities (uhoh, up). Their first productions emerge between 12 months and 24 months, and they attain some 50 words in production about 6 months later. Earlier claims about a vocabulary spurt may rather reflect increased motor skill that aids production. Do children learn to produce nouns before verbs? The proportions of nouns and verbs differ by context, e.g., toy play versus book reading. Spontaneous speech samples and parental checklists of vocabulary often differ. Overall, production lags behind comprehension. This leads to communicatively driven overextensions in production until 2;6 or so, as well as reliance on general purpose terms (do, go, that). As children add more words, they stop using earlier overextensions. Early word meanings are based on children’s existing conceptual and perceptual categories, based on their experience of the world so far. And as they take different perspectives, they begin to use of different words for the same referent (animal, dog, pug; do, mend).

Children add more information to their utterances by packing more material into a single clause. They can specify roles, modify nouns with adjectives and verbs with added locatives and adverbs. They can add demonstratives (those) and quantifiers (many) to nouns, and make clearer what they are referring to. Young children’s early constructions tend to mirror parental usage, just as their lexical choices do. They follow preferred argument structure and place given information in the Agent slot of transitive verbs, and keep the Object slot of transitives and the Subject slot of intransitives for new information. They may omit given information at this stage and only later add the relevant pronoun subjects. In both questions and negations, they take time to master the use of auxiliary verbs and rely on fixed “frames” for some time as they learn the meaning of each wh- question word. Children also take time in learning how different perspectives can be marked within the clause, with choices of causative, location, or voice alternations. Here children must learn the options verb by verb.

Young children often lack words for what they want to talk about. To fill the gaps in their lexicon, they coin new words. They rely on compounding and derivation to do this. This means identifying and analyzing parts of words – roots or stems, and affixes – and learning their meanings, as well as which combinations are possible. Some languages favor compounding and some derivation in word formation. Children are sensitive to which options are the most productive and adopt those first. Two-year-olds offer analyses of word meanings, as in running-stick (I run with it) or high-chair (it is high), and provide analyses of novel compounds where they take account of language structure (head noun first in Hebrew, second in English). They also analyze derived forms with agentive endings. They start to produce novel words from as young as age two, whether compounds in Germanic languages, or derived forms in Romance and Semitic. They begin with simple forms (minimal or no change to the root), advance to compound or derived word forms that are transparent in meaning, and opt for the most productive options in the adult language, with the goal of finding the right words to convey the child-speaker’s meaning.

Infants attend to speech, even before birth, preferring what they heard in utero over another language. In the first months, they can identify certain sounds as the same. (Other species also display categorical perception of sounds.) By 7 to 8 months, infants can identify recurring sequencies of both nonsense syllables and real words. Measures used include high-amplitude sucking, head-turn preferences, and visual fixation. In segmenting speech, infants face two problems: variation in speakers’ word uses, and which sounds to group as the same. They can also recognize a few words. By 9 to 10 months, infants attend more to distinctions in the ambient language than distinctions outside that language, and appear sensitive to legal clusters of sounds that begin and end syllables. They also prefer the prosodic stress patterns of the ambient language and so can use multiple cues to possible word-boundaries. By age three and later, children manage to recognize words even when spoken in another dialect or with a foreign accent. Their recognition of words at age three shows their representations in memory are adultlike, and not based on their own productions. They store representations of words in memory for recognizing words from other speakers, and as targets for their own production.

This concise and rigorous textbook introduces students to the subject of continuum thermodynamics, providing a complete treatment of the subject with practical applications to material modelling.

• Presents mathematical prerequisites and the foundations of continuum mechanics, taking the student step-by-step through the subject to allow full understanding of the theory.

• Introduces more advanced topics such as theories for the investigation of material models, showing how they relate to real-world practical applications.

• Numerous examples and illustrations, alongside end-of-chapter problems with helpful hints, help describe complex concepts and mathematical derivations.

Hanoi entered into negotiations with Washington and Saigon in 1968–9, Chapter 4 explains, but merely to probe and sow division among its enemies. But then unsettling circumstances intervened, including the Sino-Soviet Border War of early 1969; the death a few months later of Ho Chi Minh, who, despite his lack of influence over communist decision-making, remained the venerable face of the Vietnamese struggle for reunification and independence and thus an important public relations tool; and, finally, Nixon’s decisions to “Vietnamize” the anticommunist war effort in the South and then to authorize incursions into Cambodia and Laos. The period 1969–71 was marked by uncertainty and indecisiveness as communist decision-makers reassessed their strategic priorities and placed greater emphasis on alternative modes of struggle. Concerned about potential diplomatic isolation and the loss of Soviet and Chinese support, Le Duan decided to go-for-broke once more. The 1972 Easter Offensive was an abject disaster. Hanoi then tried its luck at the bargaining table, resulting in the Paris peace agreement of 1973 and the suspension of the Fourth Civil War for Vietnam.

This chapter introduces recursive difference equations where the initial conditions are nonzero. The output of such a system is studied in detail. One application is in the design of digital waveform generators such as oscillators, and this is explained in considerable detail. The coupled-form oscillator, which simultaneously generates synchronized sine and cosine waveforms at a given frequency, is presented. The chapter also introduces another application of recursive difference equations, namely the computation of mortgages. It is shown that the monthly payment on a loan can be computed using a first-order recursive difference equation. The equation also allows one to calculate the interest and principal parts of the payment every month, as shown. Poles play a crucial role in the behavior of recursive difference equations with zero or nonzero initial conditions. Many different manifestations of the effect of a pole are also summarized, including some time-domain dynamical meanings of poles.

This concise and rigorous textbook introduces students to the subject of continuum thermodynamics, providing a complete treatment of the subject with practical applications to material modelling.

• Presents mathematical prerequisites and the foundations of continuum mechanics, taking the student step-by-step through the subject to allow full understanding of the theory.

• Introduces more advanced topics such as theories for the investigation of material models, showing how they relate to real-world practical applications.

• Numerous examples and illustrations, alongside end-of-chapter problems with helpful hints, help describe complex concepts and mathematical derivations.

In Chapter 9 we considered how to support student wellbeing in the digital space, and how to develop eSafety and digital citizenship. In this chapter, we will consider the implications of your professional digital image or identity and how it impacts upon your role as an educator who actively uses digital technologies. We will also discuss your responsibilities as an educator in developing student digital literacy skills, even if access to technology is limited. Additionally, we will explore strategies to overcome these limitations as well as considering educators’ responsibilities to communicate with students’ parents or carers, and how digital tools can help facilitate this communication.