1. Capturing Ηοw G is Expressed in Successive Developmental Phases
A 2-wave Longitudinal Study from 8 to 17 Years of Age
Mislav Stjepan Žebec, Zagreb, Croatia

2. Preliminary remarks The study:
is an outsiders developmental view on intelligence
came out from testing Demetriou at all Three-Level Theory of Developing Mind
tests some recent explanations (AACog) of intelligence development phenomena
tries to integrate experimental/cognitive and differential methodology
gives little bit more space to measures of attention

3. Introductory words (1)
The issue of developmental changes of cognitive abilities structure are already known from intelligence life span research of McArdle at al. (2002), Salthouse (1998, 2006), and others.
Qualitative differences in solving cognitive problems, related to several developmental phases, are also known from the work of many cognitive developmentalists (Piaget, Pascual-Leone, Case, Halford, Demetriou).

4. Introductory words (2) What was not known until recently?
How to integrate these two, independently produced, huge works:
Cognitive abilities with mental representations, relations among them and awareness about them
Continuous ability development with cognitive developmental phases
Differential methodology with the developmental one
Hierarchical intelligence models with developing domain specific cognitive structures?

5. Introductory words (3)
Possible solution of the integrational problem – recent theoretical model of Demetriou at al. and its empirical validation (2013, 2014):
common core of processes underlying Gf is always present in intellectual functioning;
this core involves 3 fundamental processes - abstraction, alignment, and cognizance (AACog)
AACog changes during development in the kind of representations that can handle, the relations that can build between representations, and the awareness about them
AACog evolves through 4 major developmental cycles (birth to 2 years, 2-6 years, 6-10 years, years), with two phases in each
relations of AACog to measures of processing and representational efficiency –processing speed, attention control and WMC - vary in development as a function of its current state

6. Aims
Testing Demetriou at al. psychometric-developmental integrational model by checking:
the existence of general factor (i.e. AACog) underlying all constructs (speed, attention, WMC, Gf and mathematical reasoning) across phases and testing waves;
whether the measures of speed, attention, WMC, Gf and mathematical reasoning show different developmental trajectories (thereby becoming the possible source of different relations between these measures and the general factor);
whether the general factor is differently expressed through processing efficiency, WMC and Gf at successive developmental phases (of the last two developmental cycle);
the nature of possible causal relations between information processing capacity development (speed, attention, WMC) and the development of problem solving ability (Gf, mathematics)

7. Design and participants
Design: 2-wave longitudinal study*
Participants: 478 right-handed students of public schools in Zagreb (Croatia), from 7 through 17 years of age (249 male) at first testing.

8. Cognitive tasks
Reaction time tasks → processing efficiency (processing speed, selective attention, divided attention)
manual answering
Digit span tasks → aspects of working memory capacity
oral answering
Raven SPM tasks → fluid intelligence
Arithmetic and algebra tasks → mathematical reasoning
paper - and - pencil test

9. Processing efficiency (1)
Measured by MID-KOGTESTER1 - computer based test battery that contains eight speeded cognitive tests.
First 6 tests are performed on the 1st response panel, and the last two included 2nd panel.
Answering ← two response panels:
1st = start + 5 target keys
2nd = start + 2 target keys
Stimuli generation and answers recording → laptop with software
Stimuli presentation → computer screen

10. Processing efficiency (2)
Processing speed = average decision time in three simple reaction time tests: SRT-RH (k=20 correct answered trials), SRT-LH (k=30), WR (k=30).
Fixation mark
Respond on vertically positioned target key in all 3 tests
Respond on any color!
Ignore distractor, respond on target word!

11. Processing efficiency (3)
Selective attention = selection-inhibition interference measured by the difference between average decision time in non-congruent Stroop tasks (Stroop, k=32) and color identification tasks (CRT-C, k=32), both designed in the form of choice reaction task: Stroop – CRT-C.
Respond on 4 non-vertically positioned target keys (1st panel), corresponding to the color of the stimulus!

12. Processing efficiency (4)
Divided attention = dual-task interference measured by the difference between mean decision time in Divided Attention Test (Task 2 performed “together” with the Task 1) and mean decision time in Object Size Classification Test (Task 2 performed separately) and mean decision time in SRT-LH (Task 1 performed separately).
SRT-LH test
OSC-test
DA-test
SRT-LH → respond 1st panel
OSC → respond 2nd panel
DA → respond 1st + 2nd panel

13. Processing efficiency (5)
General properties of measurement:
Individual measurement with practice trials at the beginning (practice ended when the criterion of 10 or 12 correct answers was met);
error responses were very limited (mean errors over all tests were 8.7% of the total number of responses) and speed-accuracy trade off was not registered;
Test presentation order was changed across participants and items order was randomized within tests;
Precision was high (RTs were recorded at 1 ms measurement scale) and test-retest reliability (across the two testing waves) varied between 0.7 (CRT-C) and 0.85 (DA)

14. Working memory capacity (WMC)
The extended version of forward (FDS) and backward digit span (BDS) test included in WISC
FDS = 10 pairs of digit sequences varying from 2 to 11 digits and primarily addressed to the STM component of WM (the phonological loop)
BDS = 8 pairs of digit sequences, varying from 2 to 9 digits and measured WMC (it activates the central executive component together with the phonological loop)
Test-retest reliability across the two testing waves was satisfactory both for the FDS (0.69) and the BDS (0.66).

15. Fluid intelligence (Gf)
Raven SPM
Applied in group (regular school class), during minutes

16. Mathematical reasoning
Arithmetic
Algebra
participants were asked to specify the operations (*, $) missing from simple arithmetic equations:
5 * 3 = 8 (level 1)
{4 # 2} * 2 = 6
{3 * 2 # 5= 7
2} o 4 = {12 $ 1} * 2 (level 4)
participants were required to specify one or more unknowns in an equation:
a + 5 = 8, a =? (level 1)
u = f + 3; f = 1; u =?
If (r = s + t) and (r + s + t = 30), specify r =?
When is true that {L + M + N} = {L + P + N}? (level 4)
The battery was applied in group (regular school class), during 30 minutes.
Good psychometric and developmental properties, shown in several studies (Demetriou et al., 1996): Cronbach α=.92, split-half=.95

17. Results: Processing and representational efficiency development
Speed
Selective attention
Divided attention
FDS
BDS

18. Results: Gf, arithmetic and algebra development
In order to be comparable, performance has been standardized to difficulty level, varying from 0 to 4.

19. Results: Developmental relations of G (AACog), Gf, mathematical reasoning, processing and representational efficiency
Models obtained with SEM performed on both measurement waves simultaneously
Multiple-groups analysis on age groups corresponding to developmental phases 8-10 (N=159), (N=150) and (152)
Across groups equality constraints were imposed assuming that the task-factor relations were equal across the three age groups.
The result of testing of big number of models made in EQS (A. Demetriou)

20. Results: General factor underlying processing and representational efficiency, Gf and mathematical reasoning across phases and testing waves
The relations between the 1st-order factors and the general 2nd-order G factor were allowed to vary freely across the groups (the strength of the G factor may vary with age)
Acceptable results: χ2(1074) = , p < .001, CFI = .93, RMSEA = .056, model AIC =

21. Results: G is differently expressed through processing efficiency, WMC and Gf at successive developmental phases (of the last two developmental cycle)
G loadings differences across factors & across phases
Time stability of Ind. Diff. not accounted by G & increment across phases (Maths*)
Phase decrement except for Maths
Processes that contribute to the formation of G differ across phases

22. Results: possible causal relations between information processing capacity development and the development of problem solving ability
7 models fully exhausted all combinations of pairs of processes at the 2nd testing with trios of processes at the 1st testing
all CFIs = ; all χ2/df < 2; all RMSEAs < .08

23. Results: possible causal relations (2)
Results suggest 3-level cognitive organization:
Processing efficiency → top-down change
Representational efficiency → top-down & bottom-up change
Inference → top-down change
Different patterns of change across developmental phases

24. Implications of the study
Developmental:
age boundaries marking transitions in mental organization and functioning are well preserved (i.e., 8, 11, and 14 years) and may reflect important dynamics in brain and organismic development;
theories assuming a single chain of effects from simpler to more complex processes during development only grossly captured a part of the causal forces driving intellectual development
Psychometric:
general processes do exist however they are called, but their profiles varies with developmental phase;
changes in Ggrand imply that the core of general processes might run through AACog
individual differences in practically important aspects of intelligence varies extensively depending upon the cycle or phase concerned → diagnostic tools for intellectual assessment might need to adjust so that they can capture these variations