KNOWLEDGE
25%
 Algorithms
 Estimation; appropriate
rounding of numbers
 Theorems
 Straight recall
 Identifying from data
sheet
 Simple mathematical
facts
 Know and use of
appropriate vocabulary
 Knowledge and use of
formulae (substitution)
All of the above will be based
on known knowledge
MATHEMATICS
COGNITIVE LEVELS
ROUTINE PROCEDURES
COMPLEX PROCEDURES
30%
30%
 Problems are not
 Problems are mainly
necessarily unfamiliar
unfamiliar and learners
and can involve the
are expected to solve by
integrating different LOs
integration of different LOs
 Perform well known
 Problems do not have a
procedures
direct route to the solution
 Simple applications and
but involve :
calculations which may
o Using higher level
have many steps and may
calculation skills and
reasoning to solve the
require interpretation from
given information
problem
 Identifying and
o Mathematical
manipulating of formulae
reasoning processes
All of the above will be based
 The problems are not
on known procedures
necessarily based on real
world contexts and may be
abstract requiring fairly
complex procedures in
finding the solutions.





SOLVING PROBLEMS
15%
Solving non-routine,
unseen problems by
demonstrating higher
level understanding and
cognitive processes
Interpreting and
extrapolating from
solutions obtained by
solving problems based in
unfamiliar contexts
Using higher level
cognitive skills and
reasoning to solve nonroutine problems
Being able to break down
a problem into its
constituent parts –
identifying what is required
to be solved and then
using appropriate method
in solving the problem
Non-routine problems
based on real contexts
Action verbs associated with the taxonomy for cognitive levels (Bloom's Taxonomy) and their relevance within
Mathematics
The following shortened version attempts to describe the levels in the taxonomy (McCormick and Pressley 1997)
Cognitive level
Knowledge
Comprehension
Application
Analysis
Synthesis
Evaluation
Description
The ability to recall specific facts, common terms, basic concepts, principles and
theories
The ability to demonstrate understanding, to explain and to interpret
The ability to demonstrate application of facts and concepts in new situations and to
solve problems
The ability to break down a situation into its component parts, to distinguish between
facts and inferences, and to identify the organisational structure of the whole
The ability to integrate many ideas into a solution, a conclusion or a generalisation
The ability to judge the quality of something based on criteria or standards
Currently we notice a shift in focus to classifying on the basis of action verbs rather than cognitive level. So a strategy to
compile a set of action verbs related to each cognitive skill may assist to operationalise this shift in focus It needs to be
stated however, that the list of skills associated with these cognitive skills depends on at least 3 aspects (J.S. Paterson,
2001):
 Educational level
 Context of the user
 The subject under consideration
Patterson compiled the following list for mathematics, based on a search on the web:
Knowledge
Name
Define
Identify
State
Select
Write
show
draw
Comprehensio
n
Explain
Describe
Estimate
Classify
Rewrite
Convert
Extend
Express
Identify
illustrate
give
Application
Analysis
Synthesis
Evaluation
Solve
Use
Demonstrate
Apply
Show
Illustrate
Calculate
Predict
Construct
Sketch
find
Compare
Analyse
Differentiate
Select
Break down
Identify
Calculate
deduce
Evaluate
Solve
estimate
Formulate
Modify
Combine
Write
Rearrange
Devise
Construct
Integrate
Generate
Rewrite
deduce
Asses
Compare
Evaluate
Justify
Select
Choose
Estimate
Interpret
Explain
Determine
Verify
In many cases the action verb does not indicate clearly which cognitive skill is involved (see the verb in bold). This may
lead one to the conclusion that action verbs are not as appropriate to classifying cognitive skills levels in Mathematics as
they may be in other subjects. This is because as going on the definition of the verb only does not take into account the
context in which the verb is being used.
Reference:
Linking on-line assessment in mathematics to cognitive skills (Jane S Paterson, 2001)