# Difference: MathTaxonomy (1 vs. 2)

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# Math Taxonomy

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

#### Revision 12009-06-24 - DickFurnas

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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

## 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.

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

Code Mathworld Wordnet Wikipedia Description of code
`<-- -->`
714 MW WN WP 3-D relationships
501 MW WN WP Absolute value
316 MW WN WP Accuracy and Precision
213 MW WN WP Add/ subtract decimals
206 MW WN WP Add/subtract fractions
201 MW WN WP Add/subtract whole numbers and integers
600 MW WN WP ADVANCED ALGEBRA
800 MW WN WP ADVANCED GEOMETRY
1309 MW WN WP Amplitude
1200 MW WN WP ANALYSIS
806 MW WN WP Analytic Geometry
R1 MW WN WP Analyze
309 MW WN WP Angles
710 MW WN WP Angles
A MW WN WP Applying
306 MW WN WP Area and volume
902 MW WN WP Bar graph and histograms
500 MW WN WP BASIC ALGEBRA
1301 MW WN WP Basic ratios
701 MW WN WP Basic terminology
1108 MW WN WP Binomial distribution
610 MW WN WP Binomial theorem
1005 MW WN WP Bivariate distribution
908 MW WN WP Box plots
315 MW WN WP Calendar
1011 MW WN WP Central Limit Theorem
1009 MW WN WP Chi Square
709 MW WN WP Circles
310 MW WN WP Circles (e.g., pi, radius, area)
910 MW WN WP Classification and Venn diagrams
216 MW WN WP Combinations of operations on decimals
209 MW WN WP Combinations of operations on fractions
204 MW WN WP Combinations of operations on whole numbers or integers
609 MW WN WP Complex numbers
1511 MW WN WP Composition
604 MW WN WP Compound Inequalities
402 MW WN WP Compound interest
1102 MW WN WP Compound probability
116 MW WN WP Computational Algorithms
K3 MW WN WP Compute
1604 MW WN WP Computer programming
218 MW WN WP Computing with exponents and radicals
217 MW WN WP Computing with percents
1103 MW WN WP Conditional probability
1006 MW WN WP Confidence intervals
704 MW WN WP Congruence
606 MW WN WP Conic sections
400 MW WN WP CONSUMER APPLICATIONS
1203 MW WN WP Continuity
303 MW WN WP Conversions
804 MW WN WP Coordinate Geometry
505 MW WN WP Coordinate Planes
1007 MW WN WP Correlation
900 MW WN WP DATA DISPLAYS
1010 MW WN WP Data Transformation
105 MW WN WP Decimals
314 MW WN WP Derived measures (e.g., rate and speed)
1206 MW WN WP Differentiation
308 MW WN WP Direction, Location, Navigation
215 MW WN WP Divide decimals
208 MW WN WP Divide fractions
203 MW WN WP Divide whole numbers and integers
1104 MW WN WP Empirical probability
212 MW WN WP Equivalence of decimals, fractions, and percents
205 MW WN WP Equivalent and non-equivalent fractions
113 MW WN WP Estimation
503 MW WN WP Evaluation of formulas, expressions, and equations
000 MW WN WP EXCEPTION -- No Appropriate Code
9999 MW WN WP EXCEPTION -- Out of Topic Area
1107 MW WN WP Expected value
1508 MW WN WP Exponential
110 MW WN WP Exponents and scientific notation
611 MW WN WP Factor/remainder theorem
512 MW WN WP Factoring
111 MW WN WP Factors, multiples, and divisibility
612 MW WN WP Field properties of real number system
1409 MW WN WP Fractals
104 MW WN WP Fractions
1500 MW WN WP FUNCTIONS
R2 MW WN WP Generalize
700 MW WN WP GEOMETRIC CONCEPTS
1008 MW WN WP Hypothesis testing
1305 MW WN WP Identities
1106 MW WN WP Independent vs. dependent events
508 MW WN WP Inequalities
1600 MW WN WP INSTRUCTIONAL TECHNOLOGY
1207 MW WN WP Integration
1510 MW WN WP Inverse
1406 MW WN WP Iteration and recursion
R4 MW WN WP Justify
K MW WN WP Knowing
1304 MW WN WP Law of Sines and Cosines
305 MW WN WP Length and perimeter
1202 MW WN WP Limits
905 MW WN WP Line graphs
1003 MW WN WP Line of best fit
909 MW WN WP Line plots
1503 MW WN WP Linear
509 MW WN WP Linear and non-linear relations
1404 MW WN WP Linear programming
802 MW WN WP Loci
1507 MW WN WP Logarithmic
1402 MW WN WP Logic
801 MW WN WP Logic, reasoning, and proofs
311 MW WN WP Mass (weight)
1403 MW WN WP Mathematical induction
119 MW WN WP Mathematical properties (e.g., distributive property)
605 MW WN WP Matrices and determinants
1205 MW WN WP Maxima, Minima, and Range
1001 MW WN WP Mean, median, and mode
300 MW WN WP MEASUREMENT
304 MW WN WP Metric (SI) system
A3 MW WN WP Model
713 MW WN WP Models
313 MW WN WP Money
507 MW WN WP Multi-step equations
516 MW WN WP Multiple representations
613 MW WN WP Multiple representations
214 MW WN WP Multiply decimals
207 MW WN WP Multiply fractions
202 MW WN WP Multiply whole numbers and integers
1405 MW WN WP Networks
807 MW WN WP Non-Euclidean Geometry
1109 MW WN WP Normal curve
1501 MW WN WP Notation
114 MW WN WP Number Comparisons (order, magnitude, relative size inverse, opposites, equivalent forms, scale or number line)
100 MW WN WP NUMBER SENSE /Properties/ Relationships
118 MW WN WP Number Theory (e.g. base-ten and non-base-ten systems)
112 MW WN WP Odd/even/prime/composite/square numbers
504 MW WN WP One-step equations
103 MW WN WP Operations
200 MW WN WP OPERATIONS
511 MW WN WP Operations on polynomials
514 MW WN WP Operations on radicals
115 MW WN WP Order of operations
690 MW WN WP OTHER ADVANCED ALGEBRA
890 MW WN WP OTHER ADVANCED GEOMETRY
1290 MW WN WP OTHER ANALYSIS
590 MW WN WP OTHER BASIC ALGEBRA
490 MW WN WP OTHER CONSUMER APPLICATIONS
990 MW WN WP OTHER DATA DISPLAYS
1590 MW WN WP OTHER FUNCTIONS
790 MW WN WP OTHER GEOMETRIC CONCEPTS
1690 MW WN WP OTHER INSTRUCTIONAL TECHNOLOGY
390 MW WN WP OTHER MEASUREMENT
190 MW WN WP OTHER NUMBER SENSE
290 MW WN WP OTHER OPERATIONS
1190 MW WN WP OTHER PROBABILITY
1490 MW WN WP OTHER SPECIAL TOPICS
1090 MW WN WP OTHER STATISTICS
1390 MW WN WP OTHER TRIGONOMETRY
706 MW WN WP Parallels
108 MW WN WP Patterns
506 MW WN WP Patterns
703 MW WN WP Patterns
106 MW WN WP Percents
1308 MW WN WP Periodicity
1407 MW WN WP Permutation combinations
904 MW WN WP Pictographs
903 MW WN WP Pie charts and circle graphs
101 MW WN WP Place value
702 MW WN WP Points, lines, rays, segments, and vectors
1307 MW WN WP Polar coordinates
711 MW WN WP Polygons
712 MW WN WP Polyhedra
1505 MW WN WP Polynomial
1100 MW WN WP PROBABILITY
717 MW WN WP Pythagorean Theorem
601 MW WN WP Quadratic equations
1004 MW WN WP Quartiles and percentiles
1302 MW WN WP Radian measure
510 MW WN WP Rate of change/slope/line
403 MW WN WP Rates (e.g., discount and commission)
1204 MW WN WP Rates of change
107 MW WN WP Ratio and proportion
210 MW WN WP Ratio and proportion
1506 MW WN WP Rational
515 MW WN WP Rational expressions
607 MW WN WP Rational, negative exponents/radicals
109 MW WN WP Real and/or Rational numbers
R MW WN WP Reasoning
K1 MW WN WP Recall
K2 MW WN WP Recognize
K5 MW WN WP *Recount
1502 MW WN WP Relations
117 MW WN WP Relationships between operations
A2 MW WN WP Represent
211 MW WN WP Representations of fractions
K4 MW WN WP Retrieve
1303 MW WN WP Right triangle trigonometry
608 MW WN WP Rules for exponents
1105 MW WN WP Sampling and Sample spaces
907 MW WN WP Scatter plots
A1 MW WN WP Select
1201 MW WN WP Sequences and series
1401 MW WN WP Sets
705 MW WN WP Similarity
401 MW WN WP Simple interest
1101 MW WN WP Simple probability
1408 MW WN WP Simulations
R5 MW WN WP Solve (Non-routine Problems)
A4 )?topicparent=MH.MathTaxonomy;nowysiwyg=0" rel="nofollow" title="MW (this topic does not yet exist; you can create it)">MW )?topicparent=MH.MathTaxonomy;nowysiwyg=0" rel="nofollow" title="WN (this topic does not yet exist; you can create it)">WN )?topicparent=MH.MathTaxonomy;nowysiwyg=0" rel="nofollow" title="WP (this topic does not yet exist; you can create it)">WP Solve (Routine Problems)
1400 MW WN WP SPECIAL TOPICS
803 MW WN WP Spheres, cones, and cylinders
513 MW WN WP Square roots and radicals
1000 MW WN WP STATISTICS
906 MW WN WP Stem and Leaf plots
901 MW WN WP Summarize data in a table or graph
307 MW WN WP Surface Area
715 MW WN WP Symmetry
R3 MW WN WP Synthesize/Integrate
602 MW WN WP Systems of equations
603 MW WN WP Systems of inequalities
302 MW WN WP Theory (arbitrary, standard units and unit size)
312 MW WN WP Time and temperature
808 MW WN WP Topology
1512 MW WN WP *transformations
716 MW WN WP Transformations (e.g., flips or turns)
911 MW WN WP Tree diagrams
707 MW WN WP Triangles
1509 MW WN WP Trigonometric and circular
1306 MW WN WP Trigonometric equations
1300 MW WN WP TRIGONOMETRY
1601 MW WN WP Use of calculators
1603 MW WN WP Use of computers and internet
1602 MW WN WP Use of graphing calculators
301 MW WN WP Use of measuring instruments
1605 MW WN WP Use of Spreadsheets
502 MW WN WP Use of variables
1002 MW WN WP Variability, standard deviation, and range
805 MW WN WP Vectors
102 MW WN WP Whole numbers and Integers

`<--/commentPlugin-->`
• Math World In poking around Math World, it appears they have serious aspirations to cover Math and Math education at all levels.
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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