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Math Taxonomy

Classification of Topic Areas and Behaviors in K-12 coursework. Used to analyze textbook expository content and problems.

This page supports research by Mary Ann Huntley in collaboration with Maria Terrell

Table of Contents

Page Status:

  • Still a bit rough.
  • Some of the automatically generated links have errors due to illegal search symbols in the original descriptions.
  • Definitely usable for poking around.
  • I have added some initial observations in the comment area below.
  • You can add your own comments to this page below.

Taxonomy with links to a corresponding searches in Mathworld:Mathworld , Wordnet:Wordnet , Wikipedia:Wikipedia

Code Mathworld Wordnet Wikipedia Description of code
000 MW WN WP EXCEPTION -- No Appropriate Code
100 MW WN WP NUMBER SENSE /Properties/ Relationships
101 MW WN WP Place value
102 MW WN WP Whole numbers and Integers
103 MW WN WP Operations
104 MW WN WP Fractions
105 MW WN WP Decimals
106 MW WN WP Percents
107 MW WN WP Ratio and proportion
108 MW WN WP Patterns
109 MW WN WP Real and/or Rational numbers
110 MW WN WP Exponents and scientific notation
111 MW WN WP Factors, multiples, and divisibility
112 MW WN WP Odd/even/prime/composite/square numbers
113 MW WN WP Estimation
114 MW WN WP Number Comparisons (order, magnitude, relative size inverse, opposites, equivalent forms, scale or number line)
115 MW WN WP Order of operations
116 MW WN WP Computational Algorithms
117 MW WN WP Relationships between operations
118 MW WN WP Number Theory (e.g. base-ten and non-base-ten systems)
119 MW WN WP Mathematical properties (e.g., distributive property)
190 MW WN WP OTHER NUMBER SENSE
200 MW WN WP OPERATIONS
201 MW WN WP Add/subtract whole numbers and integers
202 MW WN WP Multiply whole numbers and integers
203 MW WN WP Divide whole numbers and integers
204 MW WN WP Combinations of operations on whole numbers or integers
205 MW WN WP Equivalent and non-equivalent fractions
206 MW WN WP Add/subtract fractions
207 MW WN WP Multiply fractions
208 MW WN WP Divide fractions
209 MW WN WP Combinations of operations on fractions
210 MW WN WP Ratio and proportion
211 MW WN WP Representations of fractions
212 MW WN WP Equivalence of decimals, fractions, and percents
213 MW WN WP Add/ subtract decimals
214 MW WN WP Multiply decimals
215 MW WN WP Divide decimals
216 MW WN WP Combinations of operations on decimals
217 MW WN WP Computing with percents
218 MW WN WP Computing with exponents and radicals
290 MW WN WP OTHER OPERATIONS
300 MW WN WP MEASUREMENT
301 MW WN WP Use of measuring instruments
302 MW WN WP Theory (arbitrary, standard units and unit size)
303 MW WN WP Conversions
304 MW WN WP Metric (SI) system
305 MW WN WP Length and perimeter
306 MW WN WP Area and volume
307 MW WN WP Surface Area
308 MW WN WP Direction, Location, Navigation
309 MW WN WP Angles
310 MW WN WP Circles (e.g., pi, radius, area)
311 MW WN WP Mass (weight)
312 MW WN WP Time and temperature
313 MW WN WP Money
314 MW WN WP Derived measures (e.g., rate and speed)
315 MW WN WP Calendar
316 MW WN WP Accuracy and Precision
390 MW WN WP OTHER MEASUREMENT
400 MW WN WP CONSUMER APPLICATIONS
401 MW WN WP Simple interest
402 MW WN WP Compound interest
403 MW WN WP Rates (e.g., discount and commission)
404 MW WN WP Spreadsheets
490 MW WN WP OTHER CONSUMER APPLICATIONS
500 MW WN WP BASIC ALGEBRA
501 MW WN WP Absolute value
502 MW WN WP Use of variables
503 MW WN WP Evaluation of formulas, expressions, and equations
504 MW WN WP One-step equations
505 MW WN WP Coordinate Planes
506 MW WN WP Patterns
507 MW WN WP Multi-step equations
508 MW WN WP Inequalities
509 MW WN WP Linear and non-linear relations
510 MW WN WP Rate of change/slope/line
511 MW WN WP Operations on polynomials
512 MW WN WP Factoring
513 MW WN WP Square roots and radicals
514 MW WN WP Operations on radicals
515 MW WN WP Rational expressions
516 MW WN WP Multiple representations
590 MW WN WP OTHER BASIC ALGEBRA
600 MW WN WP ADVANCED ALGEBRA
601 MW WN WP Quadratic equations
602 MW WN WP Systems of equations
603 MW WN WP Systems of inequalities
604 MW WN WP Compound Inequalities
605 MW WN WP Matrices and determinants
606 MW WN WP Conic sections
607 MW WN WP Rational, negative exponents/radicals
608 MW WN WP Rules for exponents
609 MW WN WP Complex numbers
610 MW WN WP Binomial theorem
611 MW WN WP Factor/remainder theorem
612 MW WN WP Field properties of real number system
613 MW WN WP Multiple representations
690 MW WN WP OTHER ADVANCED ALGEBRA
700 MW WN WP GEOMETRIC CONCEPTS
701 MW WN WP Basic terminology
702 MW WN WP Points, lines, rays, segments, and vectors
703 MW WN WP Patterns
704 MW WN WP Congruence
705 MW WN WP Similarity
706 MW WN WP Parallels
707 MW WN WP Triangles
708 MW WN WP Quadrilaterals
709 MW WN WP Circles
710 MW WN WP Angles
711 MW WN WP Polygons
712 MW WN WP Polyhedra
713 MW WN WP Models
714 MW WN WP 3-D relationships
715 MW WN WP Symmetry
716 MW WN WP Transformations (e.g., flips or turns)
717 MW WN WP Pythagorean Theorem
790 MW WN WP OTHER GEOMETRIC CONCEPTS
800 MW WN WP ADVANCED GEOMETRY
801 MW WN WP Logic, reasoning, and proofs
802 MW WN WP Loci
803 MW WN WP Spheres, cones, and cylinders
804 MW WN WP Coordinate Geometry
805 MW WN WP Vectors
806 MW WN WP Analytic Geometry
807 MW WN WP Non-Euclidean Geometry
808 MW WN WP Topology
890 MW WN WP OTHER ADVANCED GEOMETRY
900 MW WN WP DATA DISPLAYS
901 MW WN WP Summarize data in a table or graph
902 MW WN WP Bar graph and histograms
903 MW WN WP Pie charts and circle graphs
904 MW WN WP Pictographs
905 MW WN WP Line graphs
906 MW WN WP Stem and Leaf plots
907 MW WN WP Scatter plots
908 MW WN WP Box plots
909 MW WN WP Line plots
910 MW WN WP Classification and Venn diagrams
911 MW WN WP Tree diagrams
990 MW WN WP OTHER DATA DISPLAYS
1000 MW WN WP STATISTICS
1001 MW WN WP Mean, median, and mode
1002 MW WN WP Variability, standard deviation, and range
1003 MW WN WP Line of best fit
1004 MW WN WP Quartiles and percentiles
1005 MW WN WP Bivariate distribution
1006 MW WN WP Confidence intervals
1007 MW WN WP Correlation
1008 MW WN WP Hypothesis testing
1009 MW WN WP Chi Square
1010 MW WN WP Data Transformation
1011 MW WN WP Central Limit Theorem
1090 MW WN WP OTHER STATISTICS
1100 MW WN WP PROBABILITY
1101 MW WN WP Simple probability
1102 MW WN WP Compound probability
1103 MW WN WP Conditional probability
1104 MW WN WP Empirical probability
1105 MW WN WP Sampling and Sample spaces
1106 MW WN WP Independent vs. dependent events
1107 MW WN WP Expected value
1108 MW WN WP Binomial distribution
1109 MW WN WP Normal curve
1190 MW WN WP OTHER PROBABILITY
1200 MW WN WP ANALYSIS
1201 MW WN WP Sequences and series
1202 MW WN WP Limits
1203 MW WN WP Continuity
1204 MW WN WP Rates of change
1205 MW WN WP Maxima, Minima, and Range
1206 MW WN WP Differentiation
1207 MW WN WP Integration
1290 MW WN WP OTHER ANALYSIS
1300 MW WN WP TRIGONOMETRY
1301 MW WN WP Basic ratios
1302 MW WN WP Radian measure
1303 MW WN WP Right triangle trigonometry
1304 MW WN WP Law of Sines and Cosines
1305 MW WN WP Identities
1306 MW WN WP Trigonometric equations
1307 MW WN WP Polar coordinates
1308 MW WN WP Periodicity
1309 MW WN WP Amplitude
1390 MW WN WP OTHER TRIGONOMETRY
1400 MW WN WP SPECIAL TOPICS
1401 MW WN WP Sets
1402 MW WN WP Logic
1403 MW WN WP Mathematical induction
1404 MW WN WP Linear programming
1405 MW WN WP Networks
1406 MW WN WP Iteration and recursion
1407 MW WN WP Permutation combinations
1408 MW WN WP Simulations
1409 MW WN WP Fractals
1490 MW WN WP OTHER SPECIAL TOPICS
1500 MW WN WP FUNCTIONS
1501 MW WN WP Notation
1502 MW WN WP Relations
1503 MW WN WP Linear
1504 MW WN WP Quadratic
1505 MW WN WP Polynomial
1506 MW WN WP Rational
1507 MW WN WP Logarithmic
1508 MW WN WP Exponential
1509 MW WN WP Trigonometric and circular
1510 MW WN WP Inverse
1511 MW WN WP Composition
1512 MW WN WP *transformations
1590 MW WN WP OTHER FUNCTIONS
1600 MW WN WP INSTRUCTIONAL TECHNOLOGY
1601 MW WN WP Use of calculators
1602 MW WN WP Use of graphing calculators
1603 MW WN WP Use of computers and internet
1604 MW WN WP Computer programming
1605 MW WN WP Use of Spreadsheets
1690 MW WN WP OTHER INSTRUCTIONAL TECHNOLOGY
9999 MW WN WP EXCEPTION -- Out of Topic Area
K MW WN WP Knowing
K1 MW WN WP Recall
K2 MW WN WP Recognize
K3 MW WN WP Compute
K4 MW WN WP Retrieve
K5 MW WN WP *Recount
A MW WN WP Applying
A1 MW WN WP Select
A2 MW WN WP Represent
A3 MW WN WP Model
A4 MW WN WP Solve (Routine Problems)
R MW WN WP Reasoning
R1 MW WN WP Analyze
R2 MW WN WP Generalize
R3 MW WN WP Synthesize/Integrate
R4 MW WN WP Justify
R5 MW WN WP Solve (Non-routine Problems)

Add your Comments here.

 
  • Math World In poking around Math World, it appears they have serious aspirations to cover Math and Math education at all levels.
    http://mathworld.wolfram.com/about/
    Clearly they began as a resource for Research and Professional Mathematicians and are only more recently working their way into College level and High School.
    http://mathworld.wolfram.com/classroom/
    One item of particular interest is a note that all pages in Math World are tagged with classification information for both
    Dublin Core: http://www.ams.org/mathscinet/msc/msc.html and Mathematics Subject Classification (MSC): http://www.ams.org/mathscinet/msc/msc.html -- DickFurnas - 08 Jun 2009
  • Mathematics Subject Classification (MSC) may be just what the doctor ordered as far as a taxonomy. The coding philosophy has pieces of your notion of "find THE one" but allows for identifying other areas of interest as well. A coding team which had three people coding each question or narrative piece, along the lines we were talking about at dinner, could probably just use the MSC schema and use a voting system to assign THE one in a manner consistent with the MSC.
    State standards and exams could be similarly coded with a direct, well-supported basis for comparison of problems, curriculum materials and research brought together using these tools and other efforts. -- DickFurnas - 08 Jun 2009

  • American Institutes for Research (AIR) in DC: My son, Ben, did a brief stint as a freelance writer of Math questions for the Assessment division of (AIR) in DC:
    http://assessment.air.org/default.aspx
    By Ben's account, AIR provides a whole set of training manuals with
    • skeletons of questions
    • Behaviors/Cognitive Domains
    • Notions of difficulty all explicitly spelled out, enabling AIR to give him very specific assignments that will fit into their assessment schema. Ben was under the impression that AIR provies questions to various state testing entities and maybe some of the commercial testing companies as well. -- DickFurnas - 08 Jun 2009
  • Unnecessary Reverse Engineering? In my discussion with Ben, we both found ourselves wondering about the extent to which some of the classification task at hand amounted to reverse engineering things for which the original engineering may be readily available. If only the right places could be found to ask... AIR might be a significant resource in that regard. -- DickFurnas - 08 Jun 2009
  • Consensus for definitions One possible way to achieve a consensus for definitions: Use the training time to have people find the entry in Math World which corresponds to what wants to be understood under the topic in the taxonomy. The Math World entry then becomes the basis for a natural definition, or more likely the corresponding entry in the printed version: CRC Concise Encyclopedia of Mathematics, Second Edition by Eric W. Weisstein (Hardcover - Dec 12, 2002) Amazon:978-1584883470 . This process will result in separating out the various collection topics in the taxonomy, but they will easily translate back to any taxonomy. -- DickFurnas - 08 Jun 2009
  • Wikipedia and Wordnet can be of great help in casting about for synonyms or searchable terms to find appropriate definition pages in Mathworld. My initial impression is that Wikipedia does a better job of producing an appropriate hit for the more ordinary parlance of the K-12 curriculum taxonomy, but the lack of a printed reference is problematic for the research purposes. -- DickFurnas - 08 Jun 2009
  • The math jargon used in Math World is different, often stricter usage than that inherited from the taxonomy so some translation and experimentation with searches using different words is required to find the Math World entry which corresponds to the desired topic. -- DickFurnas - 08 Jun 2009

-- DickFurnas - 08 Jun 2009

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Topic revision: r2 - 2009-09-18 - 02:27:45 - DickFurnas
 
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