This will remove all current structure and data information!
If you want to upload data for your current structure, please use the 'Upload Data'
menu point in the 'Response Patterns' tab.
Use a predefined structure
The numerous structrues available are grouped by source/topic.
If there are data provided for the structure
they are also automatically loaded
(Density, Matter, Doignon & Falmagne, Chess, ENDM).
For PISA, data are loaded and a surmise relation
can be generated from the data.
Your Structure
Your structure as is. It may be without
empty set or complete item set, i.e.
it may be no knowledge structure.
Knowledge Space including your Structure
Basis of the Corresponding Knowledge Space
Surmise Relation of the Corresponding Quasi-Ordinal Knowledge Space
Upload Data
This is for uploading data belonging to your current structure.
If you want to upload data to generate a structure fron, please use the
'select your structure' tab.
Compute a structure from response patterns
Simple structure generation
This procedure generates a knowledge structure from data
using a simple approach: take every response pattern with
a minimal frequency as knowledge space.
Please note that this requires a LARGE data set.
With a threshold of 1, the resulting structure is the set of unique response patterns.
Structure generation applying inductive item tree analysis (IITA)
This will compute a surmise relation and the corresponding knowledge structure
from the current data set applying the Inductive Item Tree Analysis (IITA).
See: Ünlü, A. & Sargin, A. (2010). DAKS: An R package for data analysis methods in
knowledge space theory.Journal of Statistical Software, 37(2), 1–31.
Simulation
Simulations are computed applying the BLIM model to your knowledge space
Data overview
Validation
Compute the discrepancy index DI and the distance agreement coefficient DA.
Download Structure or Response Patterns
An extension to the filename based on your filetype selection will be added automatically.
A Very Short Introduction to Knowledge Space Theory
Knowledge space theory is a set-theoretical framework for adaptive assessment and learning of knowledge. The basic
idea is to restrict the set of possibile knowledge states within a domain by prerequisite (or precedence) relationships.
A knowledge domain is represented by a set Q of items (or test problems). The individual learners are described
by the subset of items they can solve, their knowledge states. The set 𝒦 of all knowledge states in a population
is called a knowledge structure, by definition it always contains the empty set ∅ and the full item set
Q.
It seems reasonable that if there are two learners with knowledge states K and K' then there might also
be another learner with knowledge state K ∪ K', i.e. with their combined knowledge. A knowledge structure
𝒦 is called a knowledge space if it is closed under union, i.e. for any K, K' ∈ 𝒦,
their union K ∪ K' ∈ 𝒦. If a knowledge space is furthermore closed under intersection, i.e. for
any K, K' ∈ 𝒦, their intersection K ∩ K' ∈ 𝒦, it is called quasi-ordinal
knowledge space.
(Quasi-ordinal) knowledge spaces can be defined through prerequisite (or precedence) relationships. The first approach is
the surmise relation: If learners can solve item a, we can surmise that they can also solve item
b. We write b ⊑ a. ⊑ is a reflexive and transitive relation on Q, in
other words a quasi-order. There exists a one-to-one relationship between the set of surmise relations on
Q and the set of quasi-ordinal knowledge spaces on Q.
A more general approach than surmise relations are surmise mappings. They allow for alternative sets of
prerequisites fir an item, e.g. in the context of different solution paths. A surmise mapping assigns to each item
a nonempty family of nonempty subsets of Q, the clauses of q ∈ Q. If a learner masters
q s/he also masters all items of at least one clause of q. A surmise relation is a special case of
a surmise mapping where every item has exactly one clause. Surmise mappings fulfil extended versions of reflexivity and
transitivity plus incomparability axioms. There exists a one-to-one relationship between the set of surmise mappings on
Q and the set of knowledge spaces on Q.
References
{Major books on knowledge space theory]
Doignon, J.-P. & Falmagne, J.-C. (1985). Spaces for the assessment of knowledge. International Journal of
Man-Machine Studies, 23, 175-196.
Albert, D. (ed.) (1994). Knowledge Structures. Springer Verlag, New York.
Albert, D. & Lukas, J. (eds.) (1999). Knowledge Spaces: Theories, Empirical Research, Applications.
Lawrence Erlbaum Associates, Mahwah, NJ.
Falmagne, J.-C., Albert, D., Doble, C., Eppstein, D., & Hu, X., editors (2013). Knowledge Spaces: Applications
in Education. Springer, Heidelberg.
Heller, J. & Stefanutti, L., editors (2024). Knowledge Structures: Recent Developments in Theory and Application,
volume 7 of Advanced Series on Mathematical Psychology. World Scientific, Singapore.
Hockemeyer, C., Heller, J., Spoto, A., Stefanutti, L., & Wickelmaier, F. (2018).
Knowledge Space Theory.
Moodle course produced in the TquanT and
QHELP projects.
Using this App
The WorkKST app offers various functions to work with knowledge spaces.
Below you find its menu structure.
Select your structure
Pre-defined: Select one of the predefined structures or data sets.
Upload: Upload your own structure or data file. Please note that this
drops all existing structure and data information in your session.
If you want to upload data and keep existing structure information, please
use the Upload Data panel unter "Response Patterns".
Structure info: These panels allow you to compute and show the various
representations of your structure
Your structure: Show your original uploaded/selected structure.
Knowledge space: Compute and show your knowledge space, i.e. the closure
under union of your structure.
Basis: Compute and show the basis of your structure.
Surmise relation: Compute and show the surmise relation of your structure.
Response Patterns: Various functions dealing with data.
Upload data: Upload a data set for your structure. Please note that
Your structure is preserved (as opposed to the "Upload" function under
"Select ypour structure").
You current structure in the system and the uploaded data set must have the
same number of items.
Compute a structure from data: Two different procedures are offered:
Simple approach.
Inductive Item Tree Analysis (IITA; may take quite some time).
Simulation: Simulate response patterns from your knowledge space applying
the BLIM (Basic Local Independence Model).
Data overview: This panel currently only shows the top part of your data set.
Validation: Compute a few validity coefficients.
Download: You can download the produced data/structures.
Clear data: Clear ALL data.
Settings: You can select limits for tables and plots.
Introduction & help: Information about the App
Knowledge Space Theory: A very short introduction to KST - basically
it is assumed that people using this app know already something about it.
Usage: How to use the app – this page
File formats: The different file formats usable with the functions
About the data: The app includes a lot of empirical data available through
the various R packages for KST. This page gives information on their sources.
About the app: Basic information about the WorkKST app.
Please not that the server does not store any information, i.e. all data and
structures are automaticall deleted after your session ends.
File Formats
[This page was taken from the kstIO Package documentation (Hockemeyer, 2018).]
Over time and in different research groups with
knowledge space theory, different file formats have evolved.
Matrix Format
The probably simplest and most direct approach
is to store the information in a binary ASCII matrix where a "1"
in row i and column j means that item j is element of state/response
pattern i.
There is no separating character between the columns,
and there should be no trailing whitespace at the end of the line.
The last line of the matrix must carry an EndOfLine - in most editors
(except vi) this means an empty line after the matrix.
KST Tools Format
This format (Hockemeyer, 2001) extends the
matrix format by two preceding header lines containing the number of
items and the number of states/response patterns, respectively.
SRBT Tools Format
This format (Pötzi & Wesiak, 2001) extends
the KST tools format by yet another preceding header line with format and
content metadata. This new header line has the format
#SRBT v2.0 <struct> ASCII <comment>
where <struct> specifies the type of data stored in the
file and <comment> is an optional arbitrary comment.
The following data types are supported by the respective
kstIO functions:
basis
data
space
structure
For kbase files, the encoding information "ASCII" is
missing because kbase files are always in ASCII format.
Base Files
Base files are available only in KST and
SRBT tools format. Their matrix part differs from the other files
in that it contains "0", "1", and "2". A "1" means that the state
is minimal for the item and a "2" means that it is not (but contains
the item). A "0" stands (as always) for the state not containing
the item.
Please look at the respective package documentation for more details.
CAD (Dwoling)
Six experts were queried about prerequisite relationships between 28 AutoCAD knowledge
items (Dowling, 1991; 1993). A seventh basis represents those prerequisite relationships on
which the majority (4 out of 6) of the experts agree (Dowling & Hockemeyer, 1998).
Provided by the kstMatrix package.
Chess (Schrepp)
Held, Schrepp and Fries (1995) derived several knowledge structures (DST1, DST3, and DST4)
for the representation
of 92 responses to 16 chess problems. See Schrepp, Held and Albert (1999) for a detailed
description of these problems.
Provided by the pks package.
Fractions (Baumunk)
Three experts were queried about prerequisite relationships between 77 items on fractions
(Baumunk & Dowling, 1997). A forth basis represents those prerequisite relationships on
which the majority of the experts agree (Dowling & Hockemeyer, 1998).
Provided by the kstMatrix package.
PISA
This dataset is part of the empirical 2003 Programme for International Student Assessment
(PISA) data. It contains the item responses by 340 German students on a 5-item dichotomously
scored mathematical literacy test.
Provided by the DAKS package.
Probability Problems (Anselmi & Wickelmaier)
This data set contains responses to problems in elementary probability theory observed
before and after some instructions.
Provided by the DAKS package.
Read/Write (Dwoling)
Three experts were queried about prerequisite relationships between 48 items on reading
and writing abilities (Dowling, 1991; 1993). A forth basis represents those prerequisite
relationships on which the majority of the experts agree (Dowling & Hockemeyer, 1998).
Provided by the kstMatrix package.
School Arithmetics (de Chiusole, Stefanutti, & Brancaccio)
23 fraction problems were presented to 191 first-level middle school students (about 11
to 12 years old). A subset of 13 problems is included in Stefanutti and de Chiusole (2017).
Eight subtraction problems were presented to 294 elementary school students and are described
by de Chiusole and Stefanutti (2013).
Provided by the DAKS package.
Taagepera
A five items subtest of the density test, and a five items subtest of the conservation
of matter test by Taagepera et al. (1997).
Provided by the pks package.
Ficticious
xpl
Small example space with simulated data (N = 500).
Provided by the kstMatrix package.
Doignon & Falmagne
Fictitious data set from Doignon and Falmagne (1999, chap. 7). Response patterns of
1000 respondents to five problems. Each respondent is assumed to be in one of nine
possible states of the knowledge structure 𝒦.
Provided by the pks package.
ENDM & ENDM K2
Knowledge structures and 200 artificial responses to four problems that were used to
illustrate parameter estimation in Heller and Wickelmaier (2013).
Provided by the pks package.
References
Baumunk, K. & Dowling, C. E. (1997). Validity of spaces for assessing knowledge about
fractions. Journal of Mathematical Psychology, 41, 99–105.
Dowling, C. E. (1991). Constructing Knowledge Structures from the Judgements of Experts.
Habilitationsschrift, Technische Universität Carolo-Wilhelmina, Braunschweig, Germany.
Dowling, C. E. (1993). Applying the basis of a knowledge space for controlling the
questioning of an expert. Journal of Mathematical Psychology, 37, 21–48.
Dowling, C. E. & Hockemeyer, C. (1998). Computing the intersection of knowledge spaces
using only their basis. In Cornelia E. Dowling, Fred S. Roberts, & Peter Theuns, editors,
Recent Progress in Mathematical Psychology, pp. 133–141. Lawrence Erlbaum Associates
Ltd., Mahwah, NJ.
Held, T., Schrepp, M., & Fries, S. (1995). Methoden zur Bestimmung von Wissensstrukturen –
eine Vergleichsstudie. Zeitschrift für Experimentelle Psychologie, 42(2), 205–236.
Schrepp, M., Held, T., & Albert, D. (1999). Component-based construction of surmise relations for
chess problems. In D. Albert & J. Lukas (Eds.), Knowledge spaces: Theories, empirical research,
and applications (pp. 41–66). Mahwah, NJ: Erlbaum.
The R Shiny appWorkKST offers
a graphical user interface to various functions for knowledge spaces.
It uses the
R packages
DAKS,
kst,
kstIO,
kstMatrix, and
pks.
WorkKST was inspired by an earlier web-based system at the
CSS (Cognitive Science Section
at University of Graz).
This app is a long–term project and still under construction.