Rubrics for NCATE Standards

Candidates know and understand number systems and number sense

K, S

Evidence indicates that:

• Candidates lack proficiency in the major concepts, procedures, or reasoning processes involved in number system and number sense
  

Evidence indicates that:

• Candidates are proficient in the major concepts, procedures, and reasoning processes involved with pre-number concepts, whole numbers, fractions, decimals, percents and their relationships; candidates apply the four basic operations to solve problems and develop computational algorithms
  
  
• Candidates apply number sequences and proportional reasoning along with estimation and checking reasonableness of results

Evidence indicates that:

• Candidates demonstrate multiple ways to explore and present number concepts
  
  
• Candidates are fluent and flexible
  
  
• Candidates balance and connect conceptual understanding and computational proficiency
  

Candidates know and understand geometry

K, S

Evidence indicates that:

• Candidates lack proficiency in the major concepts, procedures, or reasoning processes involved in geometry

Evidence indicates that:

• Candidates are proficient in the major concepts, procedures, and reasoning processes of geometry to describe and model mathematical ideas and real-world constructs, including two- and three-dimensional shapes, visualization, spatial reasoning, transformations, and symmetry

Evidence indicates that:

• Candidates demonstrate focused, coherent ways to advance their own understanding of geometry, posing conjectures and justifying them through reasoning and proof

Candidates know and understand measurement

K, S

Evidence indicates that:

• Candidates lack proficiency in the major concepts, procedures, or reasoning processes involved in measurement

Evidence indicates that:

• Candidates are proficient in the major concepts, procedures, and reasoning processes of measurement systems including time, money, temperature, two- and three-dimensional objects using non-standard and standard customary and metric units

Evidence indicates that:

• Candidates demonstrate the focused, coherent application of appropriate techniques, tools, and formulas to connect measurement ideas within mathematical areas and among other disciplines

Candidates know and understand statistics (data analysis) and probability

K, S

Evidence indicates that:

• Candidates lack proficiency in the major concepts, procedures, or reasoning processes involved in statistics (data analysis) and probability

Evidence indicates that:

• Candidates are proficient in the major concepts, procedures, and reasoning processes in data analysis and probability to formulate questions, collect, organize, represent, analyze, and interpret data by use of tables, graphs, and charts
  
  
• Candidates predict outcomes and conduct experiments to test predictions in real-world situations

Evidence indicates that:

• Candidates demonstrate a focused, coherent, resourceful approach to statistics (data analysis) and probability that examines relationships by formulating in-depth questions and designing experiments to test outcomes using calculator and computer simulations as appropriate

Candidates know and understand algebra

K, S

Evidence shows that:

• Candidates lack proficiency in the major concepts, procedures, or reasoning processes involved in algebra

Evidence shows that:

• Candidates are proficient in the major concepts, procedures, and reasoning processes to represent mathematical situations and relationships using algebraic symbols, patterns, relations, and functions

Evidence shows that:

• Candidates demonstrate a focused, coherent ability to analyze change in various contexts as it relates to quantitative and qualitative relationships in algebraic thinking

Candidates use major concepts, procedures, and reasoning processes to foster K-6 student learning

I

Evidence indicates that:

• Candidates lack proficiency in fostering K-6 student learning

Evidence indicates that:

• Candidates show positive impact on K-6 student learning by:
  
  (1) K-6 students’ appropriate use of patterns, quantities, and spatial relationships across the five content areas (number systems/number sense, geometry, measurement, algebra, statistics (data analysis) and probability), through the processes of problem solving, reasoning, communication, connection, and representation
  
  (2) K-6 student use of appropriate problem solving tools, including mental arithmetic, pencil-and-paper computation, a variety of manipulatives and visual materials, calculators, computers, electronic information resources, and other technologies pertinent to mathematics
  
  (3) K-6 students understanding the history of mathematics and the contributions of diverse cultures to that history
  
  (4) K-6 students communicating about and through mathematics by writing and orally using everyday language and mathematical language
  
  (5) analyzing K-6 students’ mathematical preconceptions, misconceptions, and error patterns and constructing ways for K-6 students to correct them

Evidence indicates that:

• Candidates facilitate K-6 students to be focused, coherent, and resourceful in:
  
  (1) the appropriate use of patterns, quantities, and spatial relationships by consistent in-depth use of problem solving, reasoning, communication, connection, and representation of mathematical ideas
  
  (2) the use of appropriate problem solving tools, including mental arithmetic, pencil-and-paper computation, a variety of manipulatives and visual materials, calculators, computers, electronic information resources, and other technologies pertinent to mathematics
  
  (3) understanding the history of mathematics and the contributions of diverse cultures to that history
  
  (4) communicating about and through mathematics by writing and orally using everyday language and mathematical language
  
  (5) analyzing their own mathematical preconceptions, misconceptions, and error patterns and constructing ways to correct their own learning