5.8.1 Standards matrix Dimension A B C D E Identifying and communicating mathematical information The student work has the following characteristics: selection and effective use of mathematical information that is embedded in a range of texts and stimuli, including some that are unfamiliar and complex The student work has the following characteristics: selection and use of mathematical information that is embedded in a range of familiar and some unfamiliar texts and stimuli The student work has the following characteristics: selection and use of mathematical information that is embedded in some familiar and less familiar texts and stimuli The student work has the following characteristics: narrow selection and use of mathematical information that is embedded in familiar texts and stimuli The student work has the following characteristics: directed selection and use of mathematical information that is embedded in simple and familiar texts and stimuli accurate interpretation and use of whole numbers and fractions, decimal fractions and percentages embedded in a broad range of contexts, including some that are unfamiliar and complex interpretation and use of whole numbers and fractions, decimal fractions and percentages, embedded in a range of familiar and some unfamiliar contexts interpretation and use of whole numbers and familiar or routine fractions, decimal fractions and percentages, embedded in familiar or routine contexts identification and use of familiar whole numbers and simple, everyday fractions and percentages, embedded in familiar contexts identification of familiar whole numbers embedded in simple and familiar contexts effective use of oral and written informal and formal language, mathematical conventions, symbolism, abbreviations and diagrammatic representations to clearly communicate mathematical information and problem-solving process and results, in a broad range of contexts, including some that are unfamiliar and complex. use of oral and written informal and formal language, mathematical conventions, symbolism, abbreviations and diagrammatic representations to communicate mathematical information and problem-solving processes and results, in a of familiar and some unfamiliar contexts use of oral and written informal and formal language, mathematical conventions, symbolism, abbreviations and diagrammatic representations to communicate mathematical information and problem-solving process and results, in familiar or routine contexts. variable use of oral and written informal and formal language, mathematical conventions, symbolism, abbreviations and diagrammatic representations to communicate simple mathematical information and problem-solving process and results, in familiar contexts. unclear use of oral and written informal and formal language, mathematical conventions, symbolism, abbreviations and diagrammatic representations, in simple and familiar contexts.
Problem-solving and mathematical processes The student work has the following characteristics: selection and application of a range of mathematical processes and methods of solution to solve complex familiar and some unfamiliar problems The student work has the following characteristics: selection and application of a range of mathematical processes and methods of solution to solve familiar and some unfamiliar problems The student work has the following characteristics: selection and application of simple mathematical processes and methods of solution to solve familiar problems The student work has the following characteristics: some selection and application of simple mathematical processes and methods of solution to some familiar problems The student work has the following characteristics: directed selection and application of simple mathematical processes and methods of solution critical reflection on outcomes and the appropriateness of mathematical processes to tasks to validate decisions. informed reflection on outcomes and the appropriateness of mathematical processes to tasks using estimation and other assessment skills. reflection on outcomes and the appropriateness of mathematical processes to tasks using estimation and other assessment skills. some reflection on outcomes and the appropriateness of mathematical processes to tasks using estimation. cursory and unclear statements about outcomes and the appropriateness of mathematical processes to tasks. Learning The student work has the following characteristics: independent planning and application of practical strategies that facilitate learning in familiar and some unfamiliar contexts The student work has the following characteristics: planning and application of practical strategies that facilitate learning in familiar and some unfamiliar contexts The student work has the following characteristics: planning and application of practical strategies that facilitate learning in familiar contexts The student work has the following characteristics: planning and application of practical strategies that facilitate learning in simple, familiar and predictable contexts The student work has the following characteristics: simple planning and guided application of practical strategies that facilitate learning in simple, familiar and predictable contexts independent evaluation and adaptation of learning strategies in a of familiar and some unfamiliar contexts. evaluation and adaptation of learning strategies in a range of familiar and some unfamiliar contexts. evaluation and adaptation of learning strategies in a range of familiar contexts. evaluation of learning strategies in simple, familiar and predictable contexts. directed evaluation of learning strategies in simple, familiar and predictable contexts.
Appendix 1: Sample course of study Example 1: Self-directed student investigation The teacher and the student identify an area of student interest, then create a learning and assessing plan with timelines and deadlines, including dates for monitoring progress. (Note: 5E Instructional Model from: Rodger W. Bybee et al. 2006, The BSCS 5E Instructional Model: Origins, effectiveness, and applications—Executive summary, BSCS, <www.bscs.org/pdf/bscs5eexecsummary.pdf>). 5E Instructional Model phase and summary Possible learning experiences Assessment opportunity/ mode Facet of communication Formal/ informal Objective assessed Engagement — “The teacher or a curriculum task accesses the learners’ prior knowledge and helps them become engaged in a new concept through the use of short activities that promote curiosity and elicit prior knowledge. The activity should make connections between past and present learning experiences, expose prior conceptions, and organize students’ thinking toward the learning outcomes of current activities.” The student, in consultation with the teacher: devises an issue of interest raises questions and existing beliefs negotiates assessment opportunities creates a timeline for completion. Observation and monitoring of student plan Observation and interview Personal Cooperative Procedural Informal 1 Exploration — “Exploration experiences provide students with a common base of activities within which current concepts (i.e. misconceptions), processes, and skills are identified and conceptual change is facilitated. Learners may complete activities that help them use prior knowledge to generate new ideas, explore questions and possibilities, and design and conduct a preliminary investigation.” The student researches issue/ topic by: examining relevant information from online or printed sources categorising and collating relevant information constructing a concept map devising and implementing a survey for data collection developing a budget. Collation and presentation of information Personal Cooperative Technical Public Informal 3, 4, 5