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CMG Glossary

Children's Mathematical Graphics

These are children's own graphical signs or symbolic tools that

they use freely and by choice, to communicate their personal, mathematical thinking. In the literature they are sometimes referred to as inscriptions, or notations.     

 

'Funds of knowledge'

 As active participants of family cultural practices children draw on their personal knowledge in their play, enabling their previously acquired body of cultural knowledge, their “funds of knowledge” to come to the fore (Moll et al., 1992, p. 133-4). Children’s funds of knowledge also provide valuable information for teachers, informing them “what children know and are capable of doing” (Riojas-Cortez, 2001, p. 39), [and] supplying indications that may guide teachers in supporting children’s interests (Worthington, 2021, p. 108).

     

    Lexicon                                                           

    A lexicon is a collection of 'all the words used in a particular language or subject' (Cambridge dictionary).

         In the context of Children’s Mathematical Graphics, we use this term to refer to the collection of graphical signs that young children intuitively (and mentally) build from adults' modelling and from peers' graphics. This can be likened to a mental 'toolbox' that they can unconsciously dip into to locate a sign appropriate to their needs, in order to communicate their mathematical meaning.    

         Since children's graphical sign-use is enveloped in their personal meanings, their signs make very real sense to them, and understanding is likely to be deep and lasting.

     

    Mathematical literacy                                                                      

    From the perspective of Children’s Mathematical Graphics, we relate the term 'mathematical literacy' to being literate in mathematics they exploring ways of representing their mathematical thinking, and gain confidence in 'reading' and interpreting others' Mathematical Graphics, (especially in relation to children from approximately 2 - 8 years). Mathematical literacy is a 'key step for all students, beyond language literacy; the ability to use numbers to help solve real-world problems [and] also the ability to understand the “language” of math’ (Oxford Learning).

     

    Multimodality

    Children make meanings with "lots of different stuff" (Kress, 1997, p. 7). Research by Kress and others (e.g., Jewitt & Kress, 2003; Pahl, 1999) encourages us to “re-think children’s paths into writing” (Kress, 1997, p. xviii) and challenges conventional conceptions of literacy*. Kress emphasises that whereas literacy as a social practice focuses on collaborative acts, multimodality attempts to understand the tools people use as they engage in joint social actions (2006). He proposes that “we cannot understand how children find their way into print unless we understand the principles of their meaning making” (p. xvii). (Worthington, 2021).

    * And in relation to Children's Mathematical Graphics - to mathematical literacy.

     

    Pretend play

    Pretend play - also called imaginary play and symbolic play - offers potentially rich contexts for children, and. is of particular value for young children, especially when it is child-initiated, free and spontaneous (Worthington, 2021): such play allows children to connect their personal, cultural knowledge (i.e.,  their 'funds of knowledge' (Moll et al., 1992) with their new understandings. It  can be rich in talk and provides opportunity for children to communicate through Mathematical Graphics.

         In their pretend play, children make and represent meanings through substitution, use gestures, actions and objects to symbolise something else (such as wearing a plastic bowl to represent a hat, or holding a brick to their ear as a phone).

         The social aspect of collaborative play (sometimes with an adult participating) means that pretend play provides a rich context for turn-taking dialogue, collaborative talk constituting a 'zone of proximal development' (Creaghe & Kidd, 2020, p. 1138). Not only is pretend play symbolic, but language and graphical marks, signs and symbols are also symbolic. 

     

    Semiotics (meaning-making)

    Semiotics is the study of symbolic communication; the study or theory of signs and  the communication  of meaning.  It can include signs, logos, gestures and other linguistic and non-linguistic communication methods. In the context of Children's Mathematical Graphics, semiotics is concerned with children making and communicating personal mathematical meanings, through choosing to use their own graphical marks, signs and symbols.

     

    Sign

    Anything that communicates a meaning. Signs are found in the physical form of words, images, sounds, acts or objects. In the context of graphical communication, we use the word 'sign' to refer to all graphical signs, whether graphical marks, signs for drawing, children's own maps, emergent writing and those of Children's Mathematical Graphics. These signs are those that children use intentionally, and to which they attach personal meanings.

     

    Signify (verb)

    To mean, indicate, show, or suggest. 

     

    Socio-cultural theory

    Vygotsky’s socio-cultural theory is an essential element of emerging cognition. This theory emphasises that learning is profoundly entrenched in social interactions, and dialogue is fundamental to this process. For these reasons, in Children’s Mathematical Graphics, socially interactive contexts that involve children and/or adults freely interacting, are valuable, and one of the richest play contexts is child-initiated, free and spontaneous pretend play.

     

    Symbol

    We use the word 'symbol' when referring to standard (formal) abstract signs such as alphanumerical symbols (e.g., t, B, 2, 17) and other standard mathematical symbols (including = and +). A symbol is a sign that is arbitrary or purely conventional - so that the relationship must be learnt (e.g., the word 'stop', a red traffic light, a national flag, a number).

     

    Symbolic tools

    Like spades, hammers, spoons or tooth brushes, the graphical signs children use to communicate their mathematical thinking are tools, signs that carry out a specific role in making and conveying meaning, and are often referred to in the literature as symbolic tools. They may also be variously referred to as external representations (in contrast with internal signs), inscriptions; notationscultural tools; psychological tools; emergent models; schematisations; visual signs;  and (from Worthington & Carruthers, 2003), Children’s Mathematical Graphics.

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