The problem / intent

Pattern to be used to embed mathematical conents in a game.

The context

It applies in all the situations where one is interested in a particular mathematical content and wants it to be embedded in a game for educational pourposes. It may be the case of researchers or of teachers, however, we derive it from our experience as researchers who tried to embed mathematical contents in eduational software.

Here we assume a very general meaning for the expression "embedding mathematical knowledge": Given an artefact, by embedded knowledge we mean any knowledge that has been somehow employed by the creator of the object in the process that led to its existence" Cerulli (2004, chapter 2, pg. 11-12). The basic assumption is that as artefacts are made by human, there is always some knowledge behind them, as humans don't build artefacts "randomly"; they use some ratio but also some knowledge to build artefacts, could it simply be for instance a knowledge of the difference between meterials in order to choose the best one.
The point then is how all this knowledge relates to the knowledge which is the object of an educational activity. One may assume that if some mathematical knowledge is embedded in game (which is an artefact itself), then such knowledge can be learnt by students thanks to some kind of activities that involve the game, in other words, such knowledge can be evoked Cerulli (2004, chapter 2, pg. 12) for educational purposes. As a consequence, one may want to deliberatley embed a specific knowledge in a game, in order to make it learnable by pupils. Here we don't make any particular assumption on "how" the knowledge embedded in a game can be learnt, we only assume that somehow it can be learnt through some un-specified activity that involve the game.     
Suppose you want students to learn a given mathematical knowledge, thenyou can use this pattern design ad hoc a game that embeds such  knwoledge,  instead  of searching for other games that  embeds the same knowledge. Sometimes it may be the case that no game exists embedding the knowledge one is interested in, thus this pattern can be again used to design new games ad hoc.

 

Mathematical content	content domain, Skill Domain
Learning and instruction	Mathematical content, relationship, How embedded,  Characteristics of toy, Characteristics of rules. Metaphor,Modalities of employiment
Educational context	type of learning activity
Games	games as genres
Interface + interaction	-
Software design	Game Design/ Specification

The pattern

1. Identify the main characteristics of the game to be designed as follows (for each step below try to focus strictly on the aim of embedding the content in the game, not all details are needed at this stage, only thoe key characteristics of the game that allow embedding the chosen content):
   
   • Describe/characterise the mathematical content to be embedded in the game.
   • Use the Learning and instruction typology to define the main ideas of how the game should embed the mathematical content, with reference to the game's educational use and to theoretical assumptions. Characterise the game in terms of the following: relationship, How embedded,  Characteristics of toy, Characteristics of rules. Metaphor,Modalities of employiment
   • Define the nature of the game, according to the typology Games, if this is relevant to the mathematical content to be embdded
   • Define the nature of the interface and/or of the interaction, according to the typology Interface + interaction: for instance a certain modality of interaction might represent some mathematical actions relevant to the content that has to be embedded in the game.
     
2. Apply a design pattern that takes into account the above choices; for instance use one of the patternes that elaborate this one.

Related patterns

Note the relationship to other patterns, using the appropriate qualifiers from this set -
Leads to: Content embedding in toy, Content Embedding in Rules
Follows: content morph, rejigging, Microworld
Elaborates: Concept Development
Elaborated by: Content Embedding in Rules, Content Embedding in toy .

Notes

Examples

In the Guess my garden case study  content was embedded both in rules and in features of the used microworld