CDSS: Course dependent skill structures

Description

The CDSS package provides functions for a complete workflow from skill assignment tables to surmise mappings on the sets of skills and learning objects, respectively.

Suggested workflow for the general case

1. Read the skill assignment using one of the read_skill_assignments_xxx() functions.

2. Check the compliance to the definition for skill assignments using cdss_sa_compliance().

3. Convert the skill assignment into a skill multi-assignment using cdss_sa2sma().

4. Close the skill multi-assignment under completion using cdss_sma2csma().

5. Compute the surmise function on skills using cdss_csma2sf().

6. Continue with functions from the kstMatrix package, e.g., to obtain a basis and further on a skill space.

Suggested workflow for the special case of one LO per skill

1. Read the skill assignment using one of the read_skill_assignments_xxx() functions.

2. Check whether the skill assignment allows for the derivation of a surmise relation using cdss_sa_describes_sr().

3. If yes, derive an attribution relation from the skill assignment using cdss_sa2ar_skill().

4. Close the attribution relation to a surmise relation using cdss_close_ar().

5. Continue with functions from the kstMatrix package, e.g., to obtain a basis and further on a skill space.

Data files

The installation of this package includes several data files as examples in the extdata sub directory (see the Examples below for how to access the files there). There are four data sets, KST, KST-Intro, SkillAssignment, and ErroneousSkillAssignment. The SkillAssignment data set is available in three formats, ODS, XLSX, and CSV (in CSV format, there are two files each, SkillAssignment-R.csv and SkillAssignment-T.csv, for required and taught skills, respectively). The other three data sets are available in ODS format only.

SkillAssignment and ErroneousSkillAssignment are small example data sets where the latter fails for cdss_sa_compliance(). KST contains a skill assignment for the course on knowledge space theory under https://moodle.qhelp.eu/. KST-Intro contains the reduction of KST to the first chapter of that course.

References

Hockemeyer, C. (2022). Building Course-Dependent Skill Structures - Applying Competence based Knowledge Space Theory to Itself. Manuscript in preparation.

Acknowledgements

The creation of this R package was financially supported by the Erasmus+ Programme of the European Commission through the QHELP project (https://qhelp.eu/).

Examples

library(readODS)
fpath <- system.file("extdata", "SkillAssignment.ods", package="CDSS")
sa <- cdss_read_skill_assignment_ods(fpath)
sa
sma <- cdss_sa2sma(sa)
sma
csma <- cdss_sma2csma(sma)
csma
sf <- cdss_csma2sf(csma)
sf

Compute a binary matrix product

Description

cdss_binary_matrix_product expects two binary matrices and computes there Boolean product.

Usage

cdss_binary_matrix_product(m, n)

Arguments

Value

Boolean matrix product of m and n

See Also

Other Utility functions: cdss_close_ar(), cdss_reduce_sf()

Vector of learning objects requiring and teaching the same skill

Description

cdss_circular_requirements expects skill assignment and returns a vector of learning objects which require a skill that they teach.

Usage

cdss_circular_requirements(sa)

Arguments

Value

Vector of learning objects

See Also

Other Functions testing validity of skill assignments: cdss_missing_los(), cdss_nonteaching_los(), cdss_sa_compliance()

Close an attribution relation to get a surmise relation.

Description

cdss_close_ar expects a quadratic binary matrix and closes it under reflexivity and transitivity.

Usage

cdss_close_ar(ar)

Arguments

Value

surmise relation or NULL

See Also

Other Utility functions: cdss_binary_matrix_product(), cdss_reduce_sf()

Derive a surmise function from a complete skill multi-assignment

Description

cdss_csma2sf expects a complete skill multi-assignment object and returns the corresponding surmise function on the set of skills.

Usage

cdss_csma2sf(csma)

Arguments

Value

Object of class cdss_csma.

Derive a surmise function between learning objects from a complete skill multi-assignment

Description

cdss_lo_csma2sf expects a complete skill multi-assignment and derives a surmise function on the set of learning objects.

Usage

cdss_lo_csma2sf(csma)

Arguments

Value

Object of class cdss_sf (attribution function).

See Also

Other functions building skill (multi) assignment matrices: cdss_lo_sa2af(), cdss_sa2sma(), cdss_tables2sa()

Determine Attribution function for LOs from a skill assignment

Description

cdss_lo_sa2af expects a skill assignment and derives an attribution function on the set of learning objects.

Usage

cdss_lo_sa2af(sa)

Arguments

Value

Object of class cdss_af (attribution function).

See Also

Other functions building skill (multi) assignment matrices: cdss_lo_csma2sf(), cdss_sa2sma(), cdss_tables2sa()

Create an attribution relation on learning objects from a skill assignment.

Description

cdss_lo_sa2ar expects a skill assignment and derives an attribution relation on learning objects if the skill assignment fulfills the necessary conditions, i.e. if there is only one teaching LO per skill.

Usage

cdss_lo_sa2ar(sa)

Arguments

Value

attribution relation or NULL

See Also

Other functions deriving skill structures from skill assignments: cdss_sa2ar_skill(), cdss_sa_describes_sr()

Vector of skills without teaching learning objects.

Description

cdss_missing_los expects a skill assignment and returns a vector of skills which are not taught by any learning object.

Usage

cdss_missing_los(sa)

Arguments

Value

Vector of skills

See Also

Other Functions testing validity of skill assignments: cdss_circular_requirements(), cdss_nonteaching_los(), cdss_sa_compliance()

Vector of learning objects not teaching any skills.

Description

cdss_nonteaching_los expects a skill assignment and returns a vector of learning objects which do not teach any skill.

Usage

cdss_nonteaching_los(sa)

Arguments

Value

Vector of learning objects

See Also

Other Functions testing validity of skill assignments: cdss_circular_requirements(), cdss_missing_los(), cdss_sa_compliance()

Read an assignment of taught and required skills for a set of learning objects from CSV-files.

Description

cdss_read_skill_assignment expects two CSV-files with two columns each. The first column contains the IDs of learning objects and the second row the IDs of single skills required or taught, respectively, by this learning object. It returns a list of two binary matrices, "taught" and "required". Each matrix has one row per learning object and one column per skill. The cells contain a "1" if the skill is taught or required, respectively, by the learning object and a "0" otherwise,

Usage

cdss_read_skill_assignment_csv(
  taught,
  required,
  header = TRUE,
  sep = ",",
  dec = ".",
  warnonly = FALSE,
  verbose = TRUE
)

Arguments

Value

List of two binary matrices, "taught" and "required".

See Also

Other functions reading skill assignments: cdss_read_skill_assignment_ods(), cdss_read_skill_assignment_xlsx(), cdss_wf_read_skill_assignment()

Read an assignment of taught and required skills for a set of learning objects from an ODS-file.

Description

cdss_read_skill_assignment_ods expects an ODS-file with two sheets assigning taught and required, respectively, skills to learning objects with two columns each. The first column contains the IDs of learning objects and the second row the IDs of single skills required or taught, respectively, by this learning object. It returns a list of two binary matrices, "taught" and "required". Each matrix has one row per learning object and one column per skill. The cells contain a "1" if the skill is taught or required, respectively, by the learning object and a "0" otherwise,

Usage

cdss_read_skill_assignment_ods(
  filename,
  taughtname = "Taught",
  requiredname = "Required",
  warnonly = FALSE,
  verbose = TRUE
)

Arguments

Value

List of two binary matrices, "taught" and "required".

See Also

Other functions reading skill assignments: cdss_read_skill_assignment_csv(), cdss_read_skill_assignment_xlsx(), cdss_wf_read_skill_assignment()

Read an assignment of taught and required skills for a set of learning objects from an XLSX-file.

Description

cdss_read_skill_assignment_xlsx expects an XLSX-file with two sheets assigning taught and required, respectively, skills to learning objects with two columns each. The first column contains the IDs of learning objects and the second row the IDs of single skills required or taught, respectively, by this learning object. It returns a list of two binary matrices, "taught" and "required". Each matrix has one row per learning object and one column per skill. The cells contain a "1" if the skill is taught or required, respectively, by the learning object and a "0" otherwise,

Usage

cdss_read_skill_assignment_xlsx(
  filename,
  taughtname = "Taught",
  requiredname = "Required",
  warnonly = FALSE,
  verbose = TRUE
)

Arguments

Value

List of two binary matrices, "taught" and "required".

See Also

Other functions reading skill assignments: cdss_read_skill_assignment_csv(), cdss_read_skill_assignment_ods(), cdss_wf_read_skill_assignment()

Reduce a surmise function with respect to item equivalence

Description

cdss_reduce_sf takes a surmise function and returns its reduction to non-equivalent items.

Usage

cdss_reduce_sf(sf)

Arguments

Value

Surmise function reduced by equivalences

See Also

Other Utility functions: cdss_binary_matrix_product(), cdss_close_ar()

Create an attribution relation on skills from a skill assignment.

Description

cdss_sa2ar_skill expects a skill assignment and derives an attribution relation on skills if the skill assignment fulfills the necessary conditions, i.e. if there is only one teaching LO per skill.

Usage

cdss_sa2ar_skill(sa)

Arguments

Value

attribution relation or NULL

See Also

Other functions deriving skill structures from skill assignments: cdss_lo_sa2ar(), cdss_sa_describes_sr()

Convert skill assignment matrices to skill multi-assignment

Description

cdss_sa2sma expects a list of two matrices (taught and required) of a skill assignment. It returns a skill multi-assignment object.

Usage

cdss_sa2sma(sa)

Arguments

Value

Object of class cdss_sma.

See Also

Other functions building skill (multi) assignment matrices: cdss_lo_csma2sf(), cdss_lo_sa2af(), cdss_tables2sa()

Check whether a skill assignment is compliant to the CDCS conditions.

Description

cdss_sa_compliance expects a skill assignment and checks whether it is compliant to the conditions for CDCS.

Usage

cdss_sa_compliance(sa, warnings = FALSE)

Arguments

Value

Boolean

See Also

Other Functions testing validity of skill assignments: cdss_circular_requirements(), cdss_missing_los(), cdss_nonteaching_los()

Check whether a surmise relation can be derived from a given skill assignment.

Description

cdss_sa_describes_sr expects a list of two matrices (taught and required) of a skill assignment. It returns TRUE if the skill assignment describes a surmise relation (i.e. there is only one teaching LO per skill) and FALSE.

Usage

cdss_sa_describes_sr(sa, verbose = FALSE)

Arguments

Value

Logical value

See Also

Other functions deriving skill structures from skill assignments: cdss_lo_sa2ar(), cdss_sa2ar_skill()

Complete a skill multi-assignment

Description

cdss_sma2csma expects a skill multi-assignment object and returns the corresponding complete skill multi-assignment. If this would involve cycles, the function stops by default - except if allowcycles is set to TRUE. In that case, the result may be ill-defined!

Usage

cdss_sma2csma(sma, allowcycles = FALSE)

Arguments

Value

Object of class cdss_csma.

Build matrices of taught and required, respectively, skills for learning objects from respective tables.

Description

cdss_tables2sa expects two data frames with two columns each. The first column contains the IDs of learning objects and the second row the IDs of single skills required or taught, respectively, by this learning object. It returns a list of two binary matrices, "taught" and "required". Each matrix has one row per learning object and one column per skill. The cells contain a "1" if the skill is taught or required, respectively, by the learning object and a "0" otherwise.

Usage

cdss_tables2sa(taught, required)

Arguments

Value

List of two binary matrices, "taught" and "required".

See Also

Other functions building skill (multi) assignment matrices: cdss_lo_csma2sf(), cdss_lo_sa2af(), cdss_sa2sma()

Read an assignment of taught and required skills for a set of learning objects from file and do the whole workflow up to a surmise function on skills

Description

cdss_wf_read_skill_assignment expects an ODS or XLSX file with two sheets assigning taught and required, respectively, skills to learning objects with two columns each. Alternatively, two CSV files can be specified. In the sheets/CSV files, the first column contains the IDs of learning objects and the second row the IDs of single skills required or taught, respectively, by this learning object. It returns a list of two binary matrices, "taught" and "required". Each matrix has one row per learning object and one column per skill. The cells contain a "1" if the skill is taught or required, respectively, by the learning object and a "0" otherwise,

Usage

cdss_wf_read_skill_assignment(
  filename,
  filename2 = NULL,
  filetype = "auto",
  taughtname = "Taught",
  requiredname = "Required",
  header = TRUE,
  sep = ",",
  dec = ".",
  warnonly = FALSE,
  verbose = TRUE
)

Arguments

Value

List of four elements: sfs (surmise function between skills), sfl (surmise function between learning objects) srs (surmise relation between skills, if available; NULL otherwise) srl (surmise relation between learning objectrs, if available; NULL otherwise)

See Also

Other functions reading skill assignments: cdss_read_skill_assignment_csv(), cdss_read_skill_assignment_ods(), cdss_read_skill_assignment_xlsx()