numGen: A package for generating number series items.

Description

The numGen package provides 14 item models for generating number series items.

Item model 1

This number series generates simple linear sequences with a magnitude of up to 5000.
imOne

Item model 2

This number series generate sequences consist of elements belonging to two homogeneous groups with equal number of elements.
imTwo

Item model 3

This function allows you to select one of the four arithmetic operators following a sequence succession rule.
imThree

Item model 4

This create items that relates to comprehension of abstract object representation (Item model 5) and Identification of co-occurring relationships between elements (Item model 4).
imFour

Item model 5

Generate items with two sequences combined into one number series.
imFive

Item model 6

This model uses the addition and substraction (Arithmetic) operator, Linear pattern and Progressive coefficient to create the number series.
imSix

Item model 7

This function creates number series that is a combination of Arithmetic, Linear and Complex coefficient.
First logic of complex coefficient = i*x+y.
Second logic of complex coefficient = (i+x)*y.
imSeven

Item model 8

This is based on the categorical / pattern recognition rule. Neighbouring pairs or triads of objects are related, includes arithmetic operations.
imEight

Item model 9

This function creates Fibonacci sequences. The maximum number to be generated is 15 items.
imNine

Item model 10

The number series is a combination of Arithmetic, linear sequence and progressive coefficient.
First logic is combining sequences x y x y x y x y = one simple (cannot be controlled), one progressive.
Second logic is combining sequences x y x y x y x y = two progressive.
imTen

Item model 11

Neighbouring objects + 2-sequence coefficient.
This function creates number series that is a combination of Neighbouring objects + 2-sequence coefficient.
Multiplication and Division is removed since the calculated value is too big.
imEleven

Item model 12

This function creates number series that is a irregular combination of sequences a b b a b b a ...
Only the addition and substraction arithmetic operators are used to create the number series items.
imTwelve

Item model 13

Combination of sequences and ratios.
imThirteen

References

LeFevre, J. A., & Bisanz, J. (1986). A cognitive analysis of number-series problems: Sources of individual differences in performance. Memory & Cognition, 14(4), 287-298.

Holzman, T. G., Pellegrino, J. W., & Glaser, R. (1983). Cognitive variables in series completion. Journal of Educational Psychology, 75(4), 603.

Simon, H. A., & Kotovsky, K. (1963). Human acquisition of concepts for sequential patterns. Psychological Review, 70(6), 534.

Item Model 8

Description

This uses item model 8 to create number series items.

Usage

imEight(cat, n, items, arith)

Arguments

Details

This is based on the categorical / pattern recognition rule. Neighbouring pairs or triads of objects are related, includes arithmetic operations.

Author(s)

Aiden Loe and Filip Simonfy

Examples

imEight(cat=2,n=4,items=2, arith="add")

Item Model 11

Description

This uses item model 11 to create number series items - Identification of alternating coefficients of change.

Usage

imEleven(items = 1, fun1 = "add", fun2 = "add")

Arguments

Details

This function creates number series that is a combination of Neighbouring objects and 2-sequence coefficient. Multiplication and Division are removed since the calculated value is too big. Example: A sequence whose coefficient of change alternates between (add 6) and (multiply by 2). 1 7 14 20 40 46 (92) (98).

Author(s)

Aiden Loe and Filip Simonfy

Examples

#Draws 5 items randomly.
imEleven(items=5, fun1 = "add", fun2= "add")

Item Model 5

Description

This uses item model 5 to create number series items - Identification of co-occurring relationships between elements (with use of arithmetic skills)

Usage

imFive(arithOne = "add", arithTwo = "substr", n = 2, items = 4)

Arguments

Details

Logic analogous to the Item Model 4, but at least one sub-sequence involves the basic arithmetic operations. Sequences combine items from Item Families 1 and 3. The arithmetic operations change but the differences in value remains the name. Example: Odd elements of the sequence increase by 2 and even elements of the sequence are multiplied by 2. (2 12 4 24 6 48 8 (96) (10))

Author(s)

Aiden Loe and Filip Simonfy

Examples

imFive(arithOne="add",arithTwo="add",n=2,items=5)

Item Model 4

Description

This uses item model 4 to create number series items - Identification of co-occurring relationships between elements (without use of arithmetic skills)

Usage

imFour(items = 5, seed = 1)

Arguments

Details

Sequences which consist of regularly alternating parallel sub-sequences. Understanding of succession does not require use of algebraic skill. Sub-sequences involve items from Item Model 1. Example: Odd elements of the sequence are multiples of 1 and even elements of the sequence are multiples of 10. (1 10 2 20 3 30 (4) (40)) 2 simple linear (without arithmetic) 1 2 3 / 10 20 30 combine to form a number series item.

Author(s)

Aiden Loe and Filip Simonfy

Examples

## Not run: 

imFour(items=5, seed=5)


## End(Not run)

Item Model 9

Description

This uses item model 10 to create number series items - Identification of relationships within a chain of elements.

Usage

imNine(items)

Arguments

Details

Progressive sequences which involve relationships between multiple preceding objects (e.g. Fibonacci sequence). Example: Each element of the sequence is a result of addition of its two preceding elements (1 1 2 3 5 8 (13)). The maximum number to be generated is 15 items.

Author(s)

Aiden Loe and Filip Simonfy

Examples

imNine(items=3)

Item Model 1

Description

This uses item model 1 to create number series items - Elementary understanding of sequence succession.

Usage

imOne(items = 5, seed = 1)

Arguments

Details

Simple linear sequences which do not require use of advanced arithmetic operations, such as ordered multiples of 1, 10, or 100. Example: A sequence of ordered multiples of 10. (10 20 30 40 (50)).

Author(s)

Aiden Loe and Filip Simonfy

Examples

imOne(items=5, seed=5)

Item Model 7

Description

This uses item model 7 to create number series items - Identification of complex coefficients of change

Usage

imSeven(vOne = 1, vTwo = 3, items, seed = 1, logic = "one",
  random = FALSE)

Arguments

Details

This function creates number series that is a combination of Arithmetic, Linear and Complex coefficient. Ability to identify complex coefficients; the coefficient of change involves a combination of arithmetic operations (e.g. addition and multiplication) applied serially.
There are two logic to calculate the number series. First logic of complex coefficient = i*x+y.
Second logic of complex coefficient = (i+x)*y.
. Example: Each element in the sequence is derived from the preceding by adding two and multiplying the result by two. (2 8 20 44 92 (188)).

Author(s)

Aiden Loe and Filip Simonfy

Examples

#Draws 5 items randomly.
imSeven(vOne=1,vTwo=3,items=5,seed=2,logic="one",random=TRUE)

# Calculates all combinations
# Items and seed arg is ignored.
imSeven(vOne=1:2,vTwo=1:3,items=5,seed=2,logic="one",random=FALSE)

Item Model 6

Description

This uses item model 6 to create number series items - Identification of progressively evolving coefficients of change.

Usage

imSix(items)

Arguments

Details

Non-linear progressive sequences which require a higher level of abstraction; the coefficient of change between two neighbouring elements is not invariable and its elements form a sequence. The coefficient sequences correspond to items from Item Families 1 and 3. Example: The coefficient of change between each pair of neighbouring elements in the sequence increases by 1. (2 4 7 11 16 (22))

Author(s)

Aiden Loe and Filip Simonfy

Examples

imSix(items=3)

Item Model 10

Description

This uses item model 10 to create number series items - Combined identification of parallel sub-sequences and progressively evolving coefficients of change.

Usage

imTen(items, logic = "one", n = 2, arith = "add")

Arguments

Details

The number series items are a combination of Arithmetic, linear sequence and progressive coefficient.
First logic is combining sequences x y x y x y x y = one simple (cannot be controlled), one progressive .
Second logic is combining sequences x y x y x y x y = two progressive. The minimum number of items that will be generated is 2.
Logic analogous to the Item Model 5, but at least one sub-sequence involves a progressively evolving coefficient. Sub-sequences involve items from Item Families 1, 3, and 7. Example: The coefficient of change between odd elements in the sequence increases by 1. The coefficient of change between even elements increases by -1. (2 8 4 7 7 5 11 2 16 (-2) (22)).

When using the first logic, n corresponds to the change in the progressive pattern. However, the simple pattern is fixed and hence drawn randomly.

Author(s)

Aiden Loe and Filip Simonfy

Examples

#Draws 10 items randomly.
imTen(10,logic="one", n=2,arith="add")

Item Model 13

Description

This uses item model 13 to create number series items - Combined identification of unevenly ordered sub-sequences and non-successive relationships between elements.

Usage

imThirteen(items)

Arguments

Details

This function creates number series creates a combination of sequences and ratios. TLogic analogous to the Item Model 13, but the second sequence belongs to the Item Model 9. As a result, pairs of elements following certain rule are embedded into a progressive sequence. Example: Sequence with coefficient of (+ 1) is interposed with pairs of elements which differ by 3. 1 5 8 2 209 212 3 41 (44) (4). Only the addition and substraction arimethic operators are used to generate the number series items.

Author(s)

Aiden Loe and Filip Simonfy

Examples

#Draws 10 items randomly.
imThirteen(10)

Item Model 3

Description

This uses item model 3 to create number series items - Use of basic algebraic skills.

Usage

imThree(items, n, arith = "add")

Arguments

Details

Each element in the sequence is derived from the preceding by applying one of four basic arithmetic operations - addition, subtraction, multiplication, or division. Coefficient of change is invariant across the sequence. 20 18 16 14 (12). Currently it only displays up to a series of 9.

Author(s)

Aiden Loe and Filip Simonfy

Examples

imThree(items=4,n=2,arith="add")

Item Model 12

Description

This uses item model 12 to create number series items - Identification of unevenly ordered sub-sequences

Usage

imTwelve(items)

Arguments

Details

This function creates number series that is a irregular combination of sequences a b b a b b a ... Only the addition and substraction arithmetic operators are used to create the number series items.

Author(s)

Aiden Loe and Filip Simonfy

Examples

#Draws 10 items randomly.
imTwelve(10)

Item Model 2

Description

This uses item model 2 to create number series items - Understanding of object categorisation.

Usage

imTwo(cat = 2, items = 4, random = FALSE)

Arguments

Details

Sequences consist of elements belonging to two homogeneous groups with equal number of elements. Missing element belongs to the group with fewer elements present in the sequence. For example, 1 1 1 5 5 (5).

Author(s)

Aiden Loe and Filip Simonfy

Examples

imTwo(cat=2,items=4,random=FALSE)