Developmental psychology
Chapter 12
Reading and mathematics in developmental psychology

Introduction

Cultural tools: any tools that help us to calculate, produce models, make predictions and understand the word more fully.

Reading and writing

One characteristic of cultural tools is that they can vary from culture to culture.

Orthography: a writing system. Orthography is used to describe any aspect of print, or, the spelling

Alphabetic script: a writing system in which written symbols (letters) correspond to spoken sounds. Individual phonemes represent the individual letters of an alphabetic script.
There are several different alphabetic scrips, and there are radical differences among orthographies that use exactly the same script.

Morpheme: a unit of meaning.
In some scripts, each character signals a morpheme.

Syllabary: the name given to a language that relies heavily on syllables for meaning.

Mora: a rhythmic unit in languages like Japanese that can be either a syllable or part of a syllable.

Syllable: the smallest unit of a word whose pronunciation forms a rhythmic break when spoken.

The difficulty of alphabetic scripts

Represents speech at the level of phonemes.
No language has many phonemes in it and thus one does not need many letters to represent them.

The problem

• Phonemes pose an enormous problem to young children. The is hard at first for children to realize that letters represent phonemes.
• We have to learn how individual words can be broken down into phonemes and assembled from them

Phonemic awareness and learning to read

Children get better with phonemes as they grow older.
This has to do with instruction.
Experience of learning to read an alphabetic script does make people aware of phonemes. Children need this form of awareness to become successful readers.

Rhymes and rimes

Some research suggests that children’s awareness of other phonological units, beside phoneme, plays a part in learning to read.
Between the levels of the syllable and the phoneme lies a set of phonological units which is called intrasyllabic. These are usually smaller in size than the syllable and larger than the phoneme. (like onset and rime).

Onset: of a syllable is the consonant, cluster of consonants, or vowel at the beginning of a syllable.

Rime: the vowel sound of a syllable plus any consonants that follow.

Monosyllabic words rhyme because they have a rime in common. (cat and hat).
Most children are aware of rimes from an early age and often actively and spontaneously create, and play with, rhymes.

Children’s scores in rhyme oddity tasks predicted their success in reading over the next few years. And so their ability to detect phonemes.
There is a good relationship between children’s sensitivity to rhyme and their success in reading.
Suggests that children’s awareness of phonemes is not just the product of reading instruction, but also stems form their earlier experiences with other easier phonological units.

Conditional spelling rules

Letter-sound associations: where one letter represents one sound or phoneme.

Conditional spelling rules: rules which determine that a letter, or a group of letters, represent one sound in one context and another sound in a different context.

Invented spelling

Children play little or no attention to conditional rules at first.
They stick a letter-sound associations in a most literal manner.

Inexperienced children use their knowledge of letter-sound relationships in original and ingenious ways. There are certain stubborn weaknesses in these spellings:

• A frequent confusion between letter names and letter sounds.

The split digraph (or the silent ‘e’)

The final ‘e’ rule is quite difficult for young children, despite the intensive instruction that they are given about it at school.
It usually takes several years for them to learn the rule when writing real words.

Pseudo-words: a non-existing but pronounceable non-word.

Children learn complex orthographic rules, largely by themselves, by reading text, and then use these rules in their spelling.

Morphemic spelling rules: the case of English

Morpho-phonemic: a description of orthographies in which there are regular relationships between letters or groups of letters and morphemes as well as sounds.

Derivational morphemes:; affixes that create new words which are called ‘derived’ words.

Genitive: a possessive word.

Morphemic spelling rules in Greek and French

Inflectional morphemes: affixes whose presence, and also whose absence. Provide essential information about words.

Morphemic spelling rules are difficult

Long after they have acquired a good working knowledge of letter-sound association, children continue to make errors with the conventional spelling of morphemes.
Reasons could be:

• Children are not at first aware of the morphemic structures of the words that they are trying to write.
• Children must go through a sequence of steps to learn morphemic spelling rules, like talking, they apply the new rule to often.

Three steps in learning morphemic spelling rules

1. Children start by spelling a particular sound
2. They learn another way of spelling this ending, and first begin to use it without understanding when it is right to do so.
3. As a result of the feedback they get when they use this new spelling, they learn the rule for its use.

Children’s word specific knowledge is the basis for their learning of morphemic spelling.

Number and counting

Logic and number

Logical principles:

• Cardinality: the numeral principle that states that any set of items with a particular number is equal in quantity to any other set with the same number of items in it.
• Ordinality: numbers come in an ordered scale of magnitude. (2 is more than 1)

Universal counting principles

• One-to-one principle: when counting a set of objects, each object must be counted once and once only and each must given a unique number tag.
• Stable order principle: number words must be produced in a set order.
• Last-number-counted principle: the last number counted represents the value for that set
• Abstraction principle: the number in a set is independent of any qualities of the members in that set
• Order irrelevance principle: the order in which members of a set are counted does not affect the number of items in the set.

Different counting systems

There is variation in counting systems

• In the words of numbers
• Counting systems (some are not 10-based).

Infants’ knowledge of number

There is not quite enough support for this claim.

Infant’s knowledge of addition and subtraction: Wynn’s work

Infants must have knowledge of addition and subtraction.

Criticisms of Wynn’s work

One cannot be sure that infants have a genuine understanding of subtraction (she did not include it).
Children can just respond on the base of numerosity.
Results failed to duplicate.

Principles before skills

Procedural skills.
Children’s mistakes with the larger sets might be due to difficulties in applying the right procedures in increasingly difficult circumstances.

Acquiring an understanding of number gradually: Carey’s individuation hypothesis

Theory:
Some innate knowledge but children acquire their understanding of number gradually and as a result of much experience.
Human infants are born with a ‘parallel individuation’ system, which makes it possible for them to recognize and represent very small numbers exactly.

Bootstrapping

The children lifting themselves up by their own intellectual bootstraps.
This takes place some time in children’s fourth or fifth year of age.
Two forms

• With the help of the constant order of number words in the count list, children begin to learn about the ordinal properties of numbers
• Because the count list which the children learn goes well beyond 3, they eventually infer that the number words represent a continuum of distinct quantities which also stretches beyond 3.

Number as a cultural tool

The decimal system

The decimal system is an obvious example of a cultural tool.
It does not come easily to young children.

Cross-cultural differences in the difficulty of the decimal system

In language.
In some languages they don’t have words as eleven, but one-ten.
These children are better at counting and at constructing numbers than European and American children.

Logic in the understanding of number

Logic and cardinality

Piaget’s work on conservation.
Children judge that spreading out a set of objects alters its quantity.

Young children sometimes do not realize that same number = same quantity

The importance of one-to-one correspondence

One-to-one correspondence: two sets are in one-to-one correspondence if each object in one set has a counterpart in the other set. They are equal in number.
Children’s difficulties with cardinality was the difficulties that they have with one-to-one correspondence.

But,
It seems that young children do grasp one-to-one correspondence and cardinality when sharing before they go to school, but not all of them apply this understanding to number words.