Teaching, Learning, and Employing Analytical Frameworks as Performance: Analysis of a Quantitative Literacy Event in Applied Mechanics

Competence		Examples/Elaboration
1 Knowing the conventions	1.1 Understanding verbal representations of quantitative concepts	This involves knowing the meanings of quantitative terms and phrases, and the mathematical and statistical concepts that these words refer to; it also includes knowledge of systems of units of measurement.
	1.2 Understanding symbolic representations of quantitative concepts	This involves knowing the conventions for the symbolic representation of numbers, measurements, variables and operations, for example: – representation of decimal numbers, and – symbols for operations such as exponentiation.
	1.3 Understanding visual representations of quantitative concepts	This involves knowing the conventions for the representation of data in tables, charts, graphs and diagrams (such as tree diagrams, scale and perspective drawings, and other visual representations of spatial or conceptual entities), for example: – bar, pie, scatter plots, – ways of showing scale on diagrams and maps, and – ways of representing 3D objects in perspective.
2 Identifying and distinguishing	2.1 Identifying connections and distinctions between different representations of quantitative concepts	This involves locating the relevant connections between different representations, for example: – locating the parts of a graph referred to in the verbal description of a process which is also represented graphically, – recognising that a table of data and a chart depict the same information, and – noticing significant differences between superficially similar representations.
	2.2 Identifying the mathematics to be done and strategies to do it	This involves identifying which mathematical concepts or methods are relevant in a context, for example: – knowing which arithmetic operations to perform, and – knowing when to formulate an equation.
	2.3 Identifying relevant and irrelevant information in representations	This involves identifying which information provided is relevant in a particular context, for example: – recognising which parts of a graph or chart contain the needed information, and – identifying misleading or redundant information.
3 Deriving meaning	3.1 Making meaning from representations	This includes understanding a verbal description of a quantitative concept, situation or process. It also involves deriving meaning from representations of contextualized data by, for example: – reading values off a chart, or – observing trends in tabulated data.
		Finally, it includes deriving meaning from graphical representations of relationships, for example: – using observations of the slope to derive information about rates, – reading off maximum or minimum values from a curve, and – translating between different representations of the same quantitative information.
4 Doing mathematics	4.1 Using mathematical methods	This involves using mathematical methods to solve a problem or clarify understanding, for example: – calculating, – modelling a situation algebraically, – finding rates of change, – calculating the slope of a graph, and – solving equations.
5 Higher order thinking	5.1 Synthesising	This involves synthesizing information or ideas from more than one source, for example, reading information from a chart and from a table and using them to understand a situation.
	5.2 Logical Reasoning	This involves identifying whether a claim is supported by the available evidence, formulating conclusions that can be made given specific evidence, and identifying the evidence necessary to support a claim.
	5.3 Conjecturing	This involves formulating appropriate questions and conjectures, in order to make sense of quantitative information, and recognizing the tentativeness of conjectures based on insufficient evidence.
	5.4 Interpreting and reflecting or evaluating	This involves interpreting quantitative information in terms of the context in which it is embedded by, for example, interpreting the results of the calculations in the original context.
6 Expressing quantitative concepts	6.1 Representing quantitative information using appropriate representational conventions	This includes choosing appropriate representations of quantitative information, and expressing quantitative information in a context: verbally, symbolically, graphically, diagrammatically or in tabular form.
	6.2 Describing quantitative ideas and relationships using appropriate language	This involves: identifying appropriate/correct descriptions of quantitative ideas, patterns, comparisons, trends, relationships; describing quantitative ideas, patterns, and comparisons between quantities, trends and relationships; and explaining reasoning (by linking evidence and claims).