Information and processing from deductive mental models at
dyslectics
Summary
Introduction
The lack of good definitions make dyslexia to an interesting and
frustrating field of science.
Pegleg is a new contribution to look at eyemovement recordings and
logical sentences. The background are that there are not only the
eyemovements that are erratic among the dyslectics. Eyemovements
implicates more factors like fex. decoding- and probelmsolving more
strategies among dyslectics contra normal readers. Pegleg compares the
two different reading models: the staircase- and the connective reading
modelpattern.
The Language PegLeg
We shall consider a fragment of English called "PegLeg" consisting of the
atomic sentences "Peg has a leg" and "Bob is a snob", together with the
connectives "and", "or", "not". We also introduce the metalinguistic
variables "p", "q" which range over sentences, "A" which range over
connectives and "X", "Y" which range over models. Using brackets when
necessary, we shall allow the same well-formed-formulas as the
propositional calculus over the corresponding connectives. The semantics
will however differ. In general, the interpretation of q will not be
trith-value, but rather the operation of constructing one of its model.
E.G. my interpretation of "peg has a leg" is the construction of a mental
picture of Peg and her leg, my interpretation of "Bob is a snob" is the
construction of a mental picture of the snobbish Bob. In other words, we
have the semantical valuation:
"Peg has a leg":-construction of model of Peg having a leg.
"Bob is a snob":- construction of Bob being a snob.
"and":- operation of constructing a model embracing an arbitrary pair of
models (X,Y).
"or":- operation of constructing a model embracing at least one of a pair
of models (X,Y).
"not":-operation of constructig a model ruling uot an arbitrary model x.
We also include an operation we call EVALUATE. Given a binary string
"pAq" the evaluate is the operation of supplying (p,q) with a pair of
models (X,Y) and feeding these models to the operation associated with
"A". The evaluate of "Aq" is to supply q with a model X and apply the
operation associated with "A" to X.
In other words we sress that the semantical value of a sign is not a
model of it, but rather the operation of constructing a model in a given
context. The particualr model you get of a sentence depends on which you
choose to construct when you evaluate. E.G.
EVALUATE "Bob is a snob and Peg has a leg":- the mental picture of Bob
snobbishly commenting on Peg's (wooden ) leg.
EVALUATE"Not" (Bob is a snob and Peg has a leg)":-(a & b)
In the latter case, the interpreatation of the sentence is to construct a
paraphrase in propositional calculus.
Sentence are made up of physical sign. The semantical value of a sign is
an operation, an operation to be performed on objects of consciousness
(unconsciousness?) like perception (inkblots) and vizualizations.
Finally when you evaluate a sentence the machinery comes to life and
hopefully spewes out a model. Thus we distinguish between three
ontological levels: syntactical (physical signs), operational (mental acts)
object (mental objects).
Reasoning in PegLeg
When the subject has mastered the semantics of PegLeg he is ready to
reson about sentences. In general, the subject is presented with a list
of sentences to evaluate. E.g. is this proposition contradictary?
Peg has a leg and not: Peg has a leg.
Does the first proposition imply the second?
Peg has a leg and Bob is a snob.
Bob is a snob.
Are these propositions equivalent?
Not:(Bob is a snob and Peg has a leg).
(Not: Bob is a snob)or (not: Peg has a leg).
The resolution of problems of this type consists in the evaluation of the
sentences and comparison of their models in the obvious way. Succes
depends upon systematic evaluation. An effective strategy is
parametrization. This consists in singling out one or more atomic
sentences as parameters, and substitue their negations whenever they
occur. If evaluation of a sentence fails for all parametrizations, it is
demmed contradictary. If evaluation succeed for all parametrization, the
sentence is deemed tautological. If two sentences evaluates for a commen
parametrization they are deemed non-contradictary. Etc.
Backmapping and Skolem-models
We say that a sentence is a Skolem-model (in honour to him) if evaluate
p:-p. The notion is simple. A sentence, by the operational semantics of
its component signs, is an instruction to construct models.
These models are constructed out of elements of mind. If these elements
comprise the image of the sentence itself, the sentence is a Skolem-model.
The sentence thus enters two modes of representation; first, it
represents certain operations to be carried out, next, it represents a
structure upon which these operation is carried out. When a sentence becomes
a Skolem-model, we say the backmapping occurs. This duality may be
likened to the fifferent conceptions of meaning in Wittgenstein's
"Tractatus and Investigations".
In the former, a sentence is regarde as a picture or a diagram,
of a state of affairs. Its meaning consists in its use. Hypothetically,
backmapping occurs when the sentence is to complex for the subject to
form an internal
model. He then forms an external model by turning the sentence into a
Skolem-model. Thus hypothetically, backmapping occurs when the subjects
exceeds his capabilities for internal reasoning. Again hypothtically, if
the threshold is reached without the possibility of backmapping, the
current process of reasoning terminates.
Two models of reading
We have tried to look if there exsist a more systematic coordinated
readingpattern. We have made an index for constructed sytematic patterns.
In the traditional systematic or staircasepattern have dyslexics erratic
reading pattern. The reader fixate and sweeps his eyes is dependent of
the perceptual span. There is a saccade to the next fixation. If the
reader looks back we have a regression. Erratic eyemovementpatterns gives
a bad informationprocessing (Carpenter, 1991). But it depends if the
staircase models is right.
Contributions with the staircase reading-pattern.
1. The eyes moves from word to word because of the lexical processing
2. This model needs a lot of attention
3. This informationprocessing provokes much noise (noise def.= erratic
eyemovements which are not attached to a word with higher meaning E.G.
the context is a noisefactor that ruins the informationprocessing.
The connective model is an alternative model for eyemovements. A
linearlized automatic eyemovement reading pattern will be less effiancy
because it will not select out the right information. The connective
reading pattern means looking for logical operators to construct your own
meaning. These patterns are not automatic. The ey-brain coordination will
scan top-down to conceptualize meaning. The connectors brings the meaning
out of the sentence because the connectordiagram runs the attention to
meaning in the read text. This because the analytical sentence are
diveded into to parts; function and argument. The function are the
connectives and the argument all the other parts. Effiancy reading
deletes the argument and looks for the connectors like a computermodel
(E.G. if x,...then....y). Reading is in this case a part of boolian
mathematics.
The connective model
1. The attention and eyemovement are preselected towards the connectors
or logical operators
2. The visual perception has a noise killing filter.
3. The semantic decoding are serial.
It means that connectives are logical operators that are intentionality
towards a construction of meaning.
E.G. if, if....,then..., and, or,...and not controls the reading patterns.
We wanted to test those models and made a classical between-matched
experiment to match the experimental group (dyslectics) towards a normal
group. The background for the experiment was to compare dyslectics and
normal readers eyemovements. Part 1 of the experiment, the first
hypothesis are replication of Pavlidis (1981a) and the continuing of Just
and Carpenter (1980). There have never been a replication with such
sensetive equipment. Part 2 of the experiement is a continuing of
Johnson-Lairds mental models. Hypothesis 3 and 4 tries to make a new
perspective where we see the reading process as an informationdeductive
process-model. It means that there are some logical reading combinations
that are better than randomized searching for logical expressions. The
logical words if, if ...then, and , or and the negation not. The research
subject will read different deductions which are increasing in
complexity. Then we measure how often the subject look at logical
connectors. Do we read as computers?
The main problem reconsidered was:
Do dyslectics use the same reading techniques independent of the
complexity what they are reading.
Out of this problem we sat up different hypothesis to test the two samples.
Ha1. There are no fixation- or regression-differences between dyslectics
and normal readers when they are following a non-semantic point with
their eyes.
Ha2.There are no differences regarding to scanning behavior between
dyslectics and normal readers.
Ha3. The dyslectics look less at logical operator when they are trying to
solve deductive problems.
Ha4. There are differences between dyslectics and normal readers when
they are trying to solve deductive problems where the normal reader have
a better reading behavior and the dyslectics reader dont shift reading
technique when the complexity increases.
Methods
Design
<
br>
PegLeg experiment used a posttest only noneqiuvalent peer control group
design with predefined groups (Neale & Liebert, 1986) and looked at
differences between the experiment- and the normal group.
The independent variable was dyslexia. The dependent variables were
eyemovements, reading of deductive problems, solving deductive problems
and looking at logical operators. All the variable were on intervall
level and normally distributed. There were also added some
controlvariables from WMS-R and Ravens test.
Classification of the dyslectic reader
The dyslectic reader were classified from Carlsten & Langelands
discrepancy reading skill test for high school (4. ed, 1987). Carlsten &
Langelands discrepancy reading skill test takes the people that scores
1.5 SD below average and classify them as dyslectics readers.
Subjects
40 teenagers with normal etiology were studied. People with asthma,
diabetes, visionproblems and epilepsy were excluded. The experimentgroup
(n=20) had a mean age of 18,2 year and the controlgroup (n=20) with mean
age 18,19 year. Both samples were selected from a mechanical high school.
The samples were only boys with a range from 17 to 21 years.
Apparatus and stimuli
The program Orbital infra red scanning version
1.31 were installed on a IBM PC. PC with 486DX processor with 33 Mhz
frequenz. The visual stimuli were presented on a computerscreen VGA 640 X
400 70Hz (Model MAG Technology CO. No:Mx17S, 1992).
Horizontal and vertical eyemovements were recorded by means of OberII, a
system based on
Infrared reflection from the eye. There were produced different stimuli
in both eyes. The stimuli text were produced using the «Nyström»
language. There were used fixation frames to prevent artifacts from
headmovements. Systeminstallations were:
Measuring frequenz: 100HZ
Frame frequenz: 350ms
Sensitivity: < 5 degrees
Measure rangable: 30 degrees horisontally and 20 degrees vertically
Infrared density: 0.76mW/cm2
Stimulusmaterials
For measuringing voluntary saccades there were used a white moving diode.
Ober2 standard interface were used when defing balance, gain calibration
and linearization.
Horisontal saccades: Follow a horisontal moving spot with the eyes
(Pavlidis, 1981a).
Vertical sacades: Follow a vertical moving spot with the eyes.
Smooth pursuit: Follow a ballistic moving target.
Scanning: Scan after letters in a number matrise.
Pegleg: Read and solve the deductive problem.
WMS-R (Figur memory, verbal association and visual span) and Ravens
matrisetest (IQ control)
Procedure
The subjects were instructed to wear a pair of infrared goggles and gaze
at the computerscreen 580 mm in front of them. The subjects gazed at the
computerscreen and the first tasks were exposed of 4 different stimuli.
In the first task the subject were supposed to follow a horisontaly
moving dot with the eyes. In the second task the subject were supposed to
follow a verticaly moving dot with the eyes. In the third task the
subject should follow a dot that moved with constant speed in the x and y
axes. In the fourth task the subject were supposed to follow a ballistic
moving dot in the x axes. These tasks took approximatley 3 min. Task
situation 2. The letters were replaced with x`s, which were presented on
the screen as words. The subjects were supposed to replace the x`s with
real letters. After that the subject should scan after 2 letters hidden
in a number matrise as soon as possible.
Task situation 3. There were presented 9 different logical expressions
with increasing complexity. The subject were supposed to tell if the
sentences were true or false. This part of the task took 8 to 14 min.
The subjects were later tested on WMS-R and Ravens matrisetest.
Results
There were no significantly difference between experiment and the control
group when they looked and fixated at a nonsemantic sign ( T2(38) =
.518, p = .476, Mse = 68,53 ). There were no significantly difference
between experiment and the control group regarding to regressions at a
nonsemantic sign ( T2(38) = .876, p = .355, Mse = 8,50 ).
Scanning behavior in a matrise
There were no significantly difference between experiment and the control
group when they scanned after letters in a X-matrise ( T(38) = 1.42, p =
.247 ).
Numbers looking at a logical operator
Looking at logical operators there were significantly differences between
the groups,
but only when the deductive problems were increasing in complexity.
In the first logical problems there were no differences between the
groups if the saw more on the logical operators ( F(1, 37) = 1.48, p =
.232, Mse = 12,98 ). The difference between the group grew bigger when
the problems increased in complexity. The control group saw significantly
more on the logical operators regarding to modus ponens problemes ( F(1,
37) = 9.95, p = .003, Mse = 3,39 ), regarding to modus tollens problems (
F(1, 37) = 10.36, p = .003, Mse = 10,27 ) and when the modus tollens
problems were presented with a wrong grammer ( F(1, 37) = 24.16, p =
.000, Mse = 7,60 ).
There were no covariate interactionseffects between Gfaktor and looking
at the logical operators ( T(38) = .237, p = .388 ).
Readingbehavior when trying to solve deductive problems
There were no difference betwenn experiment- and control group reagarding
to read simple logical expressions ( F(1, 37) = 2.06, p = .160, Mse =
0,0001 ). The difference were significantly when presenting a modus
ponens problem ( F(1, 37) = 35.39, p = .000, Mse = 0,00028 ), regarding
to the modus tollens problems ( F(1, 37) = 45.09, p = .000, Mse = 0,00006
) and when the semantic notation were changed together with a logical
expression
the significant differences were a fact ( F(1, 37) = 116,93, p = .000,
Mse = 0,00004 ).
Solving deductive problems
The relation between solving deductive problems and Gfaktor (Raven) were
P = .362 (One tailed). There were differences between experiment and the
control group regarding to the total score for solving the logical
deductive problems ( T(38) = -4.7, p = .000 ). There were no differences
between experiment and the control group regarding to the solving of
Ravens matrisetest ( T(38) = .37, p = .439 ).
Discussion
The conclusion of the PegLeg experiment are that the controlgroup had
better solving capacity of logical deductive problems than the
experimentalgroup. The experimentgroup had less readingbehavior when they
were going to read the diffucult deductive problems. They saw less at the
logical operators/connectives than the controlgroup on all tests. There
were no difference between experiment and the control group measured with
fixations and regression when the subjects followed a moving dot. There
were either no difference in scanningbehavior to look after different
letters.
The results from the PegLeg-experiment contributes hypothesis 1 that the
dyslexics dont make more fixations and regressions when they follow a
moving target. The results is opposite to Pavlidis (1981a, 1985). He
claims that the dyslexics has more regressions and fixations. We used
more sensetive eyemovementrecording equipment than Pavlidis and we can
not conlude that the dyslexics do make more fixations and regression,
this supports findings from Olson, Wise, Connors & Rack (1989). The
reason we dont find anything is maybe because that to follow a basic
target you dont have to use much cognitive operations.
The results contributes hypothesis 2, there are no differences in
scanningpatterns. E.G. there may be different scanning techniques but
there were equal fixations and regressions in both groups. The critics
against this task may be that there were to small digitframe that the
subjects should scan over. If there were a bigger frame the dyslexics
would have made more fixations and regressions.
Taking the view of hypothesis 3 we notice that the average normale
reader gazes more at logical operators then the dyslexic-group. The
reason may be that for the dyslexics reader all written information is
equal because of the word-to-word lexical processing. The dyslexcis cant
differ between a logical operator and related words. It means that they
read in a staircase pattern, are more unsure and process the sentences
argument as the function. There may be some formal elements that are missing.
The results from hypothesis 4 contributes that normal readers have a
better reading behavior when reading complex logical deductive problems.
The results induce that the dyslexic reader makes more fixations, more
regressions and more saccades. The reason is because that normal readers
use the connective model of reading when solving logical problems and the
dyslexics use the staircasepattern and they cannot filter out the noise.
Therefor we have the beginning staircasepattern among the dyslexic
readers and because of the cannot locate the logical operators they fail.
My view on the results implicates that the dyslexics has a more passive
perception as written in Held & Richards (1972). This because the
dyslexics has more cognitive lag than normal readers. E.G. that the
eye-mind delay are not zero. This is against Just & Carpenters
immediacy-hypothesis (1980). The conclusion from PegLeg are that
linguistic processing does not happen at the fixationpoint.There may be a
physiological eye-mind delay. The experimentalgroup has not problems with
their eyemovements as Pavlidis said (1990). The behavior of the eye
depence of the lexical processing from word to word. It is the step
between signal to symbol where the dyslexics fails. If the reader does
not understand the problem the insigtinformation stays out because the
reader cant rerepresent the problem to his own language. E.G. the reader
get stucked in his own Hoeffding step.
Artifacts from the PegLeg experiment
You dont have scientific control over the independet variable. Since we
dont have the developmental history of the subjects it means that we
cannot say anything bout a casual structure (Neale & Liebert, 1986).
There is impossible to say anything about causality and dyslexia from an
abductive point of view because the system is too complex (Catch 22). We
cannot induce dyslexia in some subjects and the n after measure the
manupulation of the independent variable. There are also more problems in
this design do we measure dyslexia or ability to solve logical deductive
problems. We wanted to measure the dyslectics reading behavior when the
decoded the deductive information blocks.
The dyslexia definition is not outstanding. There is a lack of a general
dyslexiadefinition in the field of dyslexia research. You could choose
between discrepancycriterias, multivariate definitions,
exlusionprinciples. Carlsten & Langeland is a discrepancy definitions
which not is solid but it takes a stand. Therefor we got the problems
with the intelligens. We try to control it with the Ravens test but maybe
it isnt enough. A sceptical person will claim that measuring of logical
deductions will be controlled by the intelligence (Johnson-Laird, 1991).
When there were no difference between the groups in Ravens test, there
may be a conclusion that deductions also is a matter of reading as
boolian mathematics. PegLeg may be the new standard to measure dyslexia.
You could make diagnosis when measuring the eyemovements under reading of
logical expressions. You could then easily control the subjects
fixations/regressions with comparisons with a normated mean fixations or
regressions. We need to standardise the fixations and regressions.
PegLeg is a no-budget study. If we could choose samples after CT-scanning
or other physiological test it would be a benefit for the
dyslexia-research. The consequences of the artifacts may have been
different if there were full control over the variables.
The conclusion of the PegLeg experiment were that logical operators in
the language may be a step between the neuron-signal to the
language-symbol were the dyslectics fail. The dyslecitic reader doesnt
understand the logical problems and the lack of insighti nformation means
that the reader cannot rerepresent the mental model to his own language.
The mental model fail and the dyslecitc reader get stucked in his own
Höffding step.
APPENDIX
XXX.testen
This is a X-matrise. Lettertype Times New Roman size 14. Pretend that
the x`s are words.
xxx xx x xxxxxx xxx xxxx xx xxxxxxx xx.
xxx xx xxxxxxxxxx, x xxx xxx x xxxxx xxx
xxxxxx xxxxx. x xxx xxxx xxx xxxxxxxxxxx
xx xxx xxxx. xxxxxx xxxxxxx xxxxxxxxx, x
xxxxxxxxxxxx xx xx xxxx. xxxxx xxxxxxxx
xxxx xxxxxx xxx xxx xxxx xxx xxxx xx xx.
Scanning
This is the scanning task. The subject search for 2 letters in the
number-matrise. Lettertype Courier New size 14.
1 2 3 4 5 5 5 5 4 5 6 7 7 8 8 6 5 4 3 3 2
3 4 5 6 7 9 9 8 9 7 6 5 3 5 6 5 6 7 4 5 3
1 3 x 4 5 6 7 5 4 3 8 9 6 2 4 5 3 4 x 1 3
3 4 5 1 3 5 4 6 4 3 2 2 5 6 3 6 3 7 8 7 6
3 5 1 5 9 5 8 5 2 2 8 9 5 3 4 5 2 4 5 2 4
PegLegexperiments deductiontasks. Lettertype Times Roman size 14 on the
computerscreen.Task 1. 1. Are
proposition 1 and 2 contradictory? 1. Per is at school.
2. Kari is at school. Task 2.2. Are proposition
1 and 2 contradictory?1. Per or Kari is at school.2. Per is at school.
Task 3.3. Are proposition 1 and 2 contradictory?1. Kari is at school and
Per is not at school.2. Per is at school.Task 4.4. Are proposition 1 and
2 contradictory?1. Kari is at school or Per is not at school.2. Per is at
school. Task 5.5. Are proposition 1 and 2 contradictory?1. If Per is at
school, then Kari is at school.2. Per is at school.Task 6.6. Is
proposition 3 true if 1 and 2 are true?1. Kari is home or at school.2.
Kari is not home.3. Kari is at school.Task 7.7. Are proposition 1 and 2
contradictory?1. If not Per is home then Kari is home.2. If not Kari is
home then Per is home.Task 8.8. Is the following proposition true? Not
both Per and Kari are at school, if Kari is at school then Per is at
school.Task 9.9. Is the following proposition true? Per or Kari are at
school, if not Per is at school, then Kari is at school.
REFERENCES
Carpenter, J.R. (1991). Eye Movements. Vol 8. (General editor
J.R.Cronly-Dillon), Macmillian Press.
Held, R. & Richards, W. (1972). Perception : mechanisms and models /
with introductions by Richard Held and Whitman Richards. San Francisco :
Freeman
Johnson-Laird, P. & Byrne R.M.J. (1991). Deduction. LEA Hillsdale.
Just, M.A. & Carpenter, P.A. (1980). A theory of reading: from eye
fixation to comprehension. Psychological Review, 87, 329-354.
Neal, J.M. & Liebert, R.M. (1986). Science and behaviour. An introduction
to methods and research. Prentice Hall 3.ed.
Olson, R.K., Wise, B., Conners, F.A. & Rack, J.P. (1989). Organization
heritability, and remediation of component word recognition and language
skills in disabled readers. I Carr T.H. & Levy B.A (Eds): Reading and its
development: component skills approaches. NYAP.
Pavlidis, G. Th. (1981). Dyslexia research and its applications to
education / edited by George Th. Pavlidis and T. R. Miles. Chichester: Wiley.
Pavlidis, G.Th. (1985). Eye movements in Dyslexia:Their diagnostic
significance.
Journal of learning disability,vol 18.nr.1:42-49.
Pavlidis, G. Th. (1990). Perspectives on dyslexia.Chichester, Wiley.
Skolem, Th. (1970). Selected works in logic; edited by Jens Erik Fenstad.
Oslo .