| A Study on the Problem Representation of the Word-problem of theElementary School Students with Mathematic Learning Disabilitywhich is based on the PASS TheoryThe problem solving of the word problem is the main problem for the elementary studentswith mathematics learning disability (MLD).How to successfully solve mathematics wordproblem depends on how to appropriately represent the problem.Problem representation is a hottopic in the field of problem solving at present.However there are only a few studies with regardto the cognitive processing mechanism underlying problem representation specially related tostudents with MLD.In fact,exploring and comparing the cognitive mechanism and developmentalcharacteristics of the problem representation of students with MLD is critical for research foridentification of subtypes among MLD as well as the core deficit of mathematics disability.Consequently,proposal for the effective remediation of MLD can be constructed.PASS theorywhich focuses on the cognitive processing offers a sound theoretic framework with implication forapplication of the theory.Therefore it is meaningful to explore the problem representation of wordproblem of the students with MLD on the basis of PASS theory.This thesis mainly follows five phases on considering the above issues:In study one,the author aims at comparing the problem representation methods and itsefficiency of the word problem among the pupils with MLD.In study two,the author uses theChinese version of DN:CAS to make a comprehensive exploration of the relationship among theequation listing of the word problem,representation level,and the four PASS cognitive processesof MLD.The main results are summarized below.First,the students with MLD only performed better than those with mathematics and readingdisability (MRD) in the equation listing of the most difficult word problem.Similar results wereobtained in theproblem representation of medium and most difficult word problem.Secondly,the normal math learner and MLD in grade 3 and 4 mastered two or threerepresentation methods.The normal learner used more graph representation and relation representation but few rehearsal representation,direct translation representation andpre-representation methods In contrast,there was no difference in representation level and theusage of various problem representation between MLD and MRD.Thirdly,the representation methods used by the grade 4 students were more effective thanthose by grade 3 students,and the grade 4 students used more relation representation,but fewrehearsal representation.The grade 4 normal math learners made more progress than grade 3 inproblem representation level.But the grade 4 MLD only performed better than those in grade 3 inproblem representation level.There was no difference between the MRD of grade 3 and grade 4 inthe representation level.Finally,the four PASS processes could discriminate between the MLD and the normallearners.Specifically,Planning and Simultaneous could predict the equation listing and problemrepresentation level of the word problem.There was significant difference between the MLD onlyand MRD in Simultaneous,but no differences were found in Planning,Attention,Successive andthe Full Scale scores.Furthermore,the results showed the developmental trend from grade 3 tograde 4 among the four PASS processes.In the third study,the author compared the hitting frequency and reaction time among thenumber,relational term,variable name and other variables in three types of students;the objectivewas to determine the attention in the information apperception and retrieval phase among the threetypes of students.The results showed that the differences between the problem representation andattention of two types of MLD might be caused by the differences in Expressive Attention;theMLD only performed better in the attention selection and transference than MRD.There was nodifference in the attention scores in regard to problem information between the normal learnersand the two types of MLD.The attention scores of the MRD were comparatively low.The fourth study uses the self-designed and recomposed programs in order to investigate howMLD anticipate and regulate of the problem representation of the work problem.It is divided intotwo experiments.The results are as follows:First,there was no difference in planning between thetwo types of MLD.The MLD only anticipated the difficulty of problem poorly as a function ofage;there was no difference in the anticipation of problem solving and representation strategybetween the two grade students.No difference in performance of anticipation task was noticedbetween grade 3 and grade 4 MRD.Anticipation of comprehension ability,representation strategy, and task difficulty had significant impact on the equation listing scores of the word problem,themost influential was comprehension ability.Anticipation of representation strategy influencedproblem representation as well.Secondly,with regard to equation listing and problemrepresentation of word problem,verbal controls performed better than the non-verbal controls intwo types of MLD;the verbal controls of the normal group performed slightly better than thenon-verbal controls,but didn't reach the significant level.This showed that in case of the normalgroup (with high level planning),the advantage from verbalization was less significant than it wasfor the MLD (with low level planning).The MLD profited from verbalization more than the MRD.Finally,there was a significant difference in the rehearsal level among the three types of students.The normal math learner performed best,then followed by the MLD only and the MRD.In the fifth study,comprehension of word problem was investigated.The author designedsome multiple choices which were related to concerned problem in order to investigate the roleof simultaneous processing in problem representation.Results indicated that both the scale scoreand the subscale score of simultaneous of the two types of MLD were much lower than those ofnormal learners.Normal learners performed better than two types of MLD in all the tasks ofproblem comprehension and the MLD only performed better than MRD.There were nodifferences in the general comprehension of the problem between these two MLDs.There wassignificant difference in the selection of most important sentences in the MLD only between grade3 and grade 4.The MRD of grade 3 were significantly lower than grade 4 significant in the pictureselection.The important sentence,the general and specific comprehension of word probleminfluenced the representation ability greatly.The important sentence and the specificcomprehension of word problem influenced the performance of the equation listing,and theformer explained 37.2% of total variance of score of equation listing.After a further analysis based on the empirical results,a trial probe on the cognitiveprocessing mechanism of the problem representation of the word problem in two types of MLDwas made by the author.The MRD performed much poorer than the MLD only in the mostdifficult equation listing of word problem and the medium and most difficult problemrepresentation of word problem,which showed no difference in computation and comprehensionof simple meaning of the problem,but the gap between two types of MLD became wide as afunction of difficulty and cognitive loading.It indicated that the MLD only had some advantage over MRD for they used more cognitive skills to solve the problem.The author found that duringthe process of problem representation,there was no significant difference in Planning between twotypes of MLD,but the difference existed in Expressive Attention and the comprehension of theproblem.This implied that the differences in the equation listing and problem representation ofword problem could be caused by two factors:one was the difference of the attention selectionand transference in the information apperception and retrieval phase,the other was thesimultaneous processing in the course of problem representation.
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