hints, learning styles, and learning orientations
TRANSCRIPT
Hints, Learning Styles, and Learning Orientations
SYLVIA ENCHEVAStord/Haugesund University College
Faculty of Technology, Business and Maritime SciencesBjørnsonsg. 45, 5528 Haugesund
SHARIL TUMINUniversity of Bergen
IT DeptP.O. Box 7800, 5020 Bergen
Abstract:Evaluation of hints related learning styles and learning orientations is in the main focus of this work. Ahint is regarded as useful to a student if the student has succeeded to solve a problem after using it. The decisionmaking process is based on the common assumption that if given a choice between two alternatives, a person willchoose one.
Key–Words:Ordered sets, help functions, intelligent systems
1 Introduction
Developing a cognitive tutor involves creating a cog-nitive model of student problem solving by writingproduction rules that characterize the variety of strate-gies and misconceptions students may acquire. Cog-nitive Tutors have been successful in raising students’math test scores in high school and middle-schoolclassrooms, but their development has traditionally re-quired considerable time and expertise, [8].
The Cognitive Tutor, [7] is able to understandstudent knowledge and problem-solving strategiesthrough the use of a cognitive model. A cognitivemodel represents the knowledge that an ideal studentwould possess about a particular subject. An investi-gation of whether a cognitive tutor can be made moreeffective by extending it to help students acquire help-seeking skills can be found in [14].
The process of delivering hints in an intelligenttutoring system has been discussed in [20]. A taxon-omy for automated hinting is developed in [19]. Therole of hints in a Web based learning systems is con-sidered in [6].
This work is intended to facilitate automated pro-vision of hints via an intelligent tutoring system, ap-plying mathematical methods from partially orderedsets. Our approach to evaluate help functions willavoid the influence of the above mentioned subjectivefactors since a help function in this work is regardedas useful to a student if the student has succeeded tosolve a problem after using it.
The rest of the paper is organized as follows. Sec-tion 2 contains definitions of terms used later on. Sec-tion 3 is devoted to ordered sets. Section 4 explainshow to rank hints according to learning styles and ori-
entations and Section 5 is devoted to a system descrip-tion. Section 6 contains the conclusion of this work.
2 BackgroundA method enabling the instructor to do a post-test cor-rection to neutralize the impact of guessing is devel-oped in [12]. The theory and experience discussed inthe above listed literature was used while developingassessment tools.
A personalized intelligent computer assistedtraining system is presented in [16].
Applying many-valued logic in practical deduc-tive processes related to knowledge assessment, eval-uating propositions being neither true nor false whenthey are uttered, [11].
2.1 Learning Styles and Orientations
Learning styles describe the influence of cognitivefactors where learning orientations describe the influ-ence of emotions and intentions.
In [13] learning styles are defined as the ”com-posite of characteristic cognitive, affective, and phys-iological factors that serve as relatively stable indica-tors of how a learner perceives, interacts with, andresponds to the learning environment,” while in [18]they are considered to be the ”educational conditionsunder which a student is most likely to learn.”
Learning styles group common ways that peoplelearn, [9]. The following seven learning styles are pre-sented there: visual, aural, verbal, physical, logical,social and solitary.
The learning orientations model in [15] refers tofour categories of learning orientations: transforming,
Proceedings of the 9th WSEAS International Conference on TELECOMMUNICATIONS and INFORMATICS
ISSN: 1790-5117 189 ISBN: 978-954-92600-2-1
performing, conforming, and resistant learners.Learning orientations describe an individual’s
disposition to approach, manage, and achieve learningintentionally and differently from others, [24]. Thefollowing factors having impact on intentional learn-ing success and influence individual learning differ-ences are listed: affective learning focus, learningindependence, and committed strategic planning andlearning effort.
2.2 Hints in Intelligent Tutoring Systems
Student navigation in an automated tutoring systemshould prevent students from becoming overwhelmedwith information and losing track of where they aregoing, while permitting them to make the most of thefacilities the system offers, [10].
A proliferation of hint abuse (e.g., using hints tofind answers rather than trying to understand) wasfound in [14].However, evidence that when used ap-propriately, on-demand help can have a positive im-pact on learning was found in [17].
The process of delivering hints in an intelligenttutoring system has been discussed in [20]. A taxon-omy for automated hinting is developed in [19]. Therole of hints in a Web based learning systems is con-sidered in [6].
3 Ordered SetsTwo very interesting problems are considered in [4],namely the problem of determining a consensus froma group of orderings and the problem of making sta-tistically significant statements about ordering.
Definition 1 An ordered set (or partially ordered setor poset) is an ordered pair(P,≤) of a setP and abinary relation≤ contained inP ×P called the order(or the partial order) onP such that
1. The relation is≤ reflexive. That is, each elementis related to itself;∀p ∈ P : p ≤ p
2. The relation≤ is antisymmetric. That is, ifp isrelated toq and q is related top, thenp mustequalq; ∀p, q ∈ P : [(p ≤ q)∧(q ≤ p)] ⇒ (p =q)
3. The relation≤ is transitive. That is, ifp is relatedto q and q is related tor, thenp must equalr;∀p, q, r ∈ P : [(p ≤ q) ∧ (q ≤ r)] ⇒ (p ≤ r).
A relationI is anindifferencerelation when givenAIB neitherA > B norA < B has place in the com-ponentwise ordering. A partial ordering whose indif-ference relation is transitive is called aweak ordering.
If given two alternatives, a person is finally choos-ing only one. The natural extension to more than twoelements is known as the ’majority rule’ or the ’Con-dorcet Principle’. A relationR(L1, L2, ..., Lk) is con-structed by saying that the pair(a, b) ∈ R if (a, b)belong to the majority of relationsLi.
The linear orderingsa b c, b c a, andc a bleading toR = {(a, b), (b, c), (c, a)} (three-way tie),illustrate the ’paradox of voting’.
3.1 Social Welfare Function
If given a choice between two alternatives , a personwill choose one. Thus obtained partial orderings ap-peared to be all linear orders since each pair of alter-natives is compared. A social welfare function acts onk-tuples representing either weak or linear orderingsof k individuals form alternatives. The representa-tion of an individual’s ordering can be thought of asa column vector in which an integer in positioni rep-resents the preference level the individual asigns toalternativei. Thusk individuals presented withm al-ternatives can illustrated byk-tuples of orderings in am × k matrix A of integers of preference levels.
Theorem 2, [4] provides an existing social welfarefunction.
Theorem 2 There is a unique social welfare functionsatisfying Axioms 0-4. It is given by:i is preferred toj if and only if the sum of the row ofA correspondingto j is larger than the the sum of the row ofA cor-responding toi, and otherwise the social ordering isindeferent betweeni andj.
Two elementsa andb wherea 6= b anda, b ∈ Pare comparable ifa ≤ b or b ≤ a, and incomparableotherwise. If∀a, b wherea, b ∈ P are comparable,thenP is chain. If∀a, b wherea, b ∈ P are incompa-rable, thenP is antichain.
4 Ordering of Help FunctionsIn this scenario students are suggested to solve prob-lems via an intelligent tutoring system. The systemprovides assistance in a form of help functions on auser request. Three types of help functions calleda, b, andc respectively are available. They can con-tain f. ex. theoretical rules, hints and solutions ofsimilar problems. The students’ responses are savedin a database. The goal is to find out in which orderhelp functions related to a particular problem shouldbe presented to a new student and in which order helpfunctions should be presented to a student who hasbeen using the system when the student is requesting
Proceedings of the 9th WSEAS International Conference on TELECOMMUNICATIONS and INFORMATICS
ISSN: 1790-5117 190 ISBN: 978-954-92600-2-1
b c
a level 1
level 2
Figure 1: Two levels case where one of the elementsa, b, c is ranked higher than the other two while thosetwo are of equal importance
help with respect to a new problem. The system rec-ognizes a help function as a useful one if a studentprovides a correct answer after that function has beenpresented to her/him.
Using nested parentheses one can represent thepartial ordering structure in an application internally.Let the alphabets in this definition be ’( ), a, b, c’. Theuse of parentheses is to signify the position of orderingof a particular element ’a’, ’b’, or ’c’, where ’( )’signifies level 1 - the top most level, ’(( ))’ signifieslevel 2, and ’((( )))’ signifies level 3.
Since the distance between partial orderings isunique than the distance between ’adjacent orderings’is 1, [4]. Based on students’ responses a contentprovider can follow the process of responses cluster-ing and make appropriate adjustments in contents ofa problem or the related help functions or both. TheIt can also be used to track down the effect of helpfunctions to each student and thus provide better indi-vidualized assistance.
When a pattern of clustering does not show anysignificant value but is evenly distributed amongst thetwelve ordering pattern then one can conclude thatnone of the help functions were helpful for the stu-dents study progress. The help functions need to beredesigned.
4.1 Distances Between Orderings WhereTwo of the Functions are Considered tobe Equally Helpful
The observed distances between two orderings in acase two of the functions are considered to be equallyhelpful are either 2 or 4. Illustration details:
Orderings (a(bc)) and ((ac)b)In the first ordering we observe one function on level1 and two functions on level 2, Fig. 1. In the secondordering we observe two functions on level 1 and onefunction on level 2, Fig. 2.
Note that the function on level 1 in the first order-ing is still on level 1 in the second ordering while oneof the functions on level 2 in the first ordering is onlevel 1 in the second ordering, Fig. 3. The distance is2.
From ordering (ab(c)) to ordering (c(ab))
a b
c
level 1
level 2
Figure 2: Two levels case where two of the elementsa, b, c are of equal importance and are ranked higherthan the third
b c
b
c
level 2
level 2
level 1
Figure 3: One the elementsa, b, c is changing levelsof belonging
All functions change their levels of belonging, Fig. 4.The distance is 4.
From ordering (a(bc)) to ordering (b(ac))Both orderings have the same structure, Fig. 5.
Two of the functions exchange their levels’ be-longing, one of them from level 1 to level 2 and theother one from level 2 to level 1, Fig. 6. The distanceis 4. The position of the third function is unchanged.
4.2 Distances Between Orderings Where AllFunctions Are Considered to Have Dif-ferent Level of Helpfulness
The observed distances between two orderings whereall hints are considered to have different level of help-fulness. Illustration details
From ordering (a(c(b))) to ordering (c(a(b)))Both orderings have the same structure. Two of thefunctions exchange their levels’ belonging, one ofthem from level 1 to level 2 and the other one fromlevel 2 to level 1, Fig 7. The distance is 2.The posi-tion of the third function is unchanged. The position
a b
c
b
c
a
level 1
level 2
level 1
level 2
Figure 4: Elementsa, b, c are changing levels of be-longing
Proceedings of the 9th WSEAS International Conference on TELECOMMUNICATIONS and INFORMATICS
ISSN: 1790-5117 191 ISBN: 978-954-92600-2-1
b
ca
level 1
level 2
b c
a level 1
level 2
Figure 5: Elementsa, b, c have the same structure inboth orderings
b
a
level 2
level 1
a
b
level 2
level 1
Figure 6: Two the elementsa, b, c are changing levelsof belonging within the same structure
a
c
b
c
a
b
level 1
level 2
level 3
level 1
level 2
level 3
Figure 7: Two the elementsa, b, c are changing levelsof belonging within the same structure of three differ-ent levels of helpfulness
a
c
b
c
b
a
level 1
level 2
level 3
level 1
level 2
level 3
Figure 8: All elementsa, b, c are changing levels ofbelonging within the same structure of three differentlevels of helpfulness
a
c
b
b
c
a
level 1
level 2
level 3
level 1
level 2
level 3
Figure 9: Two of the elementsa, b, c are changing lev-els of belonging within the same structure of three dif-ferent levels of helpfulness
of the third function is unchanged.From ordering (a(c(b))) to ordering (c(b(a)))
All functions change their levels of belonging, Fig 8.The distance is 4.
From ordering (a(c(b))) to ordering (b(c(a)))The first and the third functions exchange their lev-els of belonging, while the second function keeps thesame level of belonging in both orderings, Fig 9. Thedistance is 6.
5 System DescriptionA system prototype is build as a Web-based appli-cation using Apache HTTP server modpython mod-ule, and SQLite database. The modpython moduleprovides programmable runtime support to the HTTPserver using Python programming language. Thewhole application components are Web-based usersinterface, application logic and application interfaceswritten in Python, and relational database.
The users, i.e. expert tutors, teachers, and stu-dents interact with the system using Web forms. Be-fore any interaction with the system can take place,a user needs to be authenticated first. Experts andteachers can submit and update data, while studentscan only view information.
For a particular subject, an expert tutor will firstsubmit data that will be used to construct a data table.
Proceedings of the 9th WSEAS International Conference on TELECOMMUNICATIONS and INFORMATICS
ISSN: 1790-5117 192 ISBN: 978-954-92600-2-1
Figure 10: Recommendation of a new topic
The system will then check that there are no du-plicate attribute combinations and insert the contextdata in to the database.
The system provides recommendations onwhether or not a student needs to take additionalclasses (courses) based on fuzzy dependencies.
In this framework supporting personalized learn-ing a new topic is recommended to a student (Fig. 10)after assessing his/her knowledge. The system re-sponds to students’ needs according to their learningpreferences and orientations.
6 ConclusionEvaluating help functions based on students’ re-sponses is more accurate than using questionnaires.Such an approach is not affected by subjective opin-ions and provides useful feedback to content develop-ers.
The presented automated tutoring system is a re-sponse to the the increased demand for the neces-sity of developing effective learning tools that can besmoothly integrated in the educational process.
The system uses each student’s diagnostic re-ports on miscalculations, misconceptions, and lack ofknowledge and offers advice in the form of additional
reading, hints and tests and recommends an interac-tion with the human tutor when needed.
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