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Curricular Competencies -- Proficiency Scales
- 1. Curricular Competencies Reasoning I can make sense of mathematics. Emerging Developing Pro fi cient Extending recognize repetition (patterns) predict what happens next (conjectures) fi gure out why repetition is happening (proofs) look for new occurrences of repeated reasoning notice structures discover shortcuts discover generalizations discover insights; fi nd faults in generalizations estimate a reasonable answer decide whether my actions and answers make sense (convince myself) decide whether my actions and answers make sense (convince a friend) decide whether my actions and answers make sense (convince a skeptic) build a logical progression of statements
- 2. Curricular Competencies Problem Solving I can fi gure out what do when I dont know what to do. Emerging Developing Pro fi cient Extending plan a way to approach a problem use a strategy to solve a problem use multiple strategies to solve a problem select the most e ffi cient or elegant strategy to solve a problem determine what is being asked and what information is needed to solve a problem evaluate progress and revise actions, if needed persevere until a problem is solved pose and solve new problems
- 3. Curricular Competencies Communicating I can explain and defend my ideas and decisions to others. Emerging Developing Pro fi cient Extending participate in mathematical discussions (pair, small-group, or whole-class) contribute to mathematical discussions (pair, small-group, or whole-class) share my thinking with others to advance collective knowing revise how I communicate my ideas to others, as needed describe my process for fi nding answers (play-by-play) explain my process for fi nding answers (colour commentary) back up my statements and actions with examples and reasoning construct and assess alternative arguments listen to the reasoning of others critique the reasoning of others use informal (but clear) intuitive language use formal (and precise) math language; attend to units, labels, etc. edit and organize my written work so that readers can follow it clearly (e.g., left to right, top to bottom; appropriate symbolic notation)
- 4. Curricular Competencies Representing I can show mathematical ideas in many ways. Emerging Developing Pro fi cient Extending use concrete and pictorial tools to approach problems and explore concepts and procedures e ff ectively use concrete and pictorial tools to solve problems and make sense of concepts and procedures select appropriate concrete and pictorial tools to solve problems and make sense of concepts and procedures consider advantages and limitations of a concrete or pictorial tool relate using concrete and pictorial tools to using symbols use prescribed symbolic representations to encode mathematical ideas move between di ff erent symbolic representations of the same mathematical idea select and use appropriate symbolic representations to encode mathematical ideas consider advantages and limitations of a symbolic representation
- 5. Curricular Competencies Connecting I can connect math concepts to each other, use math to understand our world, and build on my prior knowledge and experiences. Emerging Developing Pro fi cient Extending connect one part of math to another (within the same concept) connect one part of math to another (across di ff erent concepts and within the same strand) connect one part of math to another (across di ff erent strands) make math-to-math, math-to- world, and math-to-self connections that are novel and have value cite familiar real-world applications of mathematics use math to represent real- world situations use math to deepen my understanding of real-world phenomena connect new problems to previously solved problems express how new concepts and procedures are similar to and di ff erent from prior learning (partial) express how new concepts and procedures are similar to and di ff erent from prior learning (comprehensive)