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Difficulty Analysis for Learners in Problem Solving Process based on the Knowledge Map. Rita Kuo, Wei-Peng Lien, Maiga Chang, Jia-Sheng Heh. Speaker: Rita Kuo. Multimedia Communication System Laboratory Dept. of Information and Computer Engineering

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## Difficulty Analysis for Learners in Problem Solving Process based on the Knowledge Map

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**Difficulty Analysis for Learners in Problem Solving Process**based on the Knowledge Map Rita Kuo, Wei-Peng Lien, Maiga Chang, Jia-Sheng Heh Speaker: Rita Kuo Multimedia Communication System Laboratory Dept. of Information and Computer Engineering Chung-Yuan Christian Univ., Chung-Li, 320, Taiwan**Outlines**• Basic Definition • Basic Problem Model • Problem Construction Steps • Knowledge and Problem Structure • Problem Difficulty Analysis • Difficulty Features • Difficulty Dimensions • Demonstration of Item Generating System • Brief Conclusion To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Basic Problem Model**• Inter-correlated Knowledge • Manipulation of inter-correlation among knowledge • Ex. Physics, Chemistry, and Mathematics • Knowledge Object • Way to analyze Inter-correlated Knowledge • Basic concept of a specific domain • Basic Problem Definition • One Core Knowledge Object • Example in Physics: Physics Phenomenon • Basic Problem Model To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Knowledge Base**Knowledge Map Concept Selection Knowledge Map Unknown Designation Problem Matrix Proposition Construction Problem Construction To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Knowledge Map**• Concept Hierarchy • Hierarchical structure of concepts Concept Map • Concept Schema • Attributes Schema • Definitions, Ability (Can-Fly), Property (Age) etc. To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Example of Knowledge Map**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Problem Matrix**• Manipulating concepts • Example in Physics: Physics Quantity • {“Displacement”, “Time”, “Velocity”, “Acceleration”} • Manipulating relations • Example in Physics: Physics Law • {“Displacement = 0.5 * Acceleration * Time ^ 2”,“Velocity = Acceleration * Time”} To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Example of Problem Construction**• Physics Phenomenon • Motion with constant velocity • Problem Matrix • tf: final time; si: initial position; ti: initial time; vi: initial velocity; sf: final position; d: distance To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Unknown Designer**• Select Physics Law • Set Attributes To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Problem Constructor (cont.)**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Analysis**• Difficulty Features According to the problem construction process • Selected Concepts • Knowledge Map • Attributes Setting • Problem Matrix • Difficulty Dimensions According to the problem solving steps • Problem Identification • Problem Elaboration • Problem Planning • Problem Execution To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Features**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Basic Definition**root: the root of Knowledge Map qi: ith concept Knowledge Map height(qi): the height of sub-tree from ith concept CS(qi): Concept Schema of ith concept size(CS(qi)): number of attributes in concept from full Concept Schema attrLS(CS(qi)): learning sequence attribute stored in Concept Schema Problem Matrix #given_attr: number of given attributes in the problem #unknown: number of unknown attributes in the problem attrmanip_cpt(qi): attributes extracted to manipulating concepts in Problem Matrix size(attrmanip_cpt(qi)): number of manipulating concepts in Problem Matrix attrmax_unknown(qi): maximum number of unknown in ith concept Attributes Definition To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Example**• In sky, raindrop proceeds the motion of constant acceleration. The initial velocity (vi) is 0 m/s. Acceleration (a) is 5 m/s^2. The final time (tf) is 5 s. Ask for the value of final velocity (vf). • Selected Concept • The motion of constant acceleration • Attributes Setting To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Attributes Definition – Knowledge Map**• size (CS (“Motion with Constant Acceleration”) ) = 11 • size (CS (“Free Fall”) ) = 13 • height (“Physics”) = 4 • height (“Motion with Constant Acceleration”) = 2 • attrLS(“Motion with Constant Acceleration”) = 2 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Attributes Definition – Problem Matrix**• #given_attr = 3 • #unknown = 1 • size(attrmanip_cpt(qi)) = 7 • attrmax_unknown(qi) = 2 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Features Calculation (1)**• gneed_attr = size(CS(qi)) / arg maxjKMsize(CS(qj)) = size(CS(“Motion with Constant Acceleration”)) / size(CS(“Free Fall”)) = 11 / 13 = 0.8 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Features Calculation (2)**• glearn_seq = attrLS(qi) / arg maxjsibling(qi) attrLS(qj) = attrLS(“Motion with Constant Acceleration”) / attrLS(“Motion with Constant Acceleration”) = 2 / 2 = 1 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Features Calculation (3)**• gcpt_depth = (height(root) – height (qi)) / height(root) = (height(“Physics”) – height (“Motion with Constant Acceleration”)) / height(“Physics”) = ( 4 – 2 ) / 4 = 0.5 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Features Calculation (4)**• ggiven_attr = (size(attrmanip_cpt(qi)) - #given_attr + 1) / size(attrmanip_cpt(qi)) = (size(attrmanip_cpt(“Motion with Constant Acceleration”)) - #given_attr + 1) / size(attrmanip_cpt(“Motion with Constant Acceleration”)) = (7 – 3 + 1) / 7 = 0.7 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Features Calculation (5)**• gunknown = #unknown / attrmax_unknown(qi) = #unknown / attrmax_unknown(“Motion with Constant Acceleration”) = 1 / 2 = 0.5 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Features Calculation (6)**• gelb_attr= (size(attrmanip_cpt(qi)) - #given_attr - #unknown + 1) / size(attrmanip_cpt(qi)) = (size(attrmanip_cpt(“Motion with Constant Acceleration”)) - #given_attr - #unknown + 1) / size(attrmanip_cpt(“Motion with Constant Acceleration”)) = ( 7 – 3 – 1 + 1) / 7 = 0.4 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Dimensions**• According to four steps of problem solving • Identification Difficulty (gidf) • Elaboration Difficulty (gelb) • Planning Difficulty (gpln) • Execution Difficulty (gexc) To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Dimensions (cont.)**• Identification Difficulty (gidf) • Position in Knowledge Map • Elaboration Difficulty (gelb) • Size of Concept Schema in Knowledge Map • Planning Difficulty (gpln) • Number of Manipulating Concepts • Execution Difficulty (gexc) • Number of Unknowns To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Difficulty Dimension Transformation**• gidf = w21 * glearn_seq + w31 * gcpt_depth= 0.5 * glearn_seq + 0.5 * gcpt_depth = 0.5 * 1 + 0.5 * 0.5 = 0.75 • gelb = w12 * gneed_attr + w42 * ggiven_attr + w62 * gelb_attr=0.3 * gneed_attr + 0.3 * ggiven_attr + 0.3 * gelb_attr = 0.3 * 0.8 + 0.3 * 0.7 + 0.4 * 0.4 = 0.61 • gpln= w53 * gunknown + w63 * gelb_attr = 0.5 * gunknown + 0.5 * gelb_attr = 0.5 * 0.5 + 0.5 * 0.4 = 0.45 • gexc= w54 * gunknown = 1 * gunknown = 1 * 0.5 = 0.5 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Demonstration**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Brief Conclusions**• Problem Construction Steps • Concept Selection • Unknown Designation • Proposition Construction • Problem Difficulties • Difficulty Features • Difficulty Dimensions • Item Generating System • Physics Domain To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Future Works**• Complex problem construction • Mathematical complexity analysis • Answer of the learners diagnosis To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**To Develop an Item Generating System with Analyzing the**Problem Model in the Inter-Correlated Knowledge**To Develop an Item Generating System with Analyzing the**Problem Model in the Inter-Correlated Knowledge**Presentations of Knowledge**• Concept • Basic element of knowledge • A atomic unit of knowledge pieces • Ex. “Free Fall”, “Constant Acceleration Motion”etc. • Relation • The aggregation of concepts • Ex. Is-A, Has-Aetc. • Proposition • An integration of concepts and relation • One relation with at least two concepts • Ex. “Free Fall”Is-A“Constant Acceleration Motion” To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Inter-correlated Knowledge**• Inter-correlated Knowledge • Manipulation of inter-correlation among knowledge • Ex. Physics, Chemistry, and Mathematics • Knowledge Object • Way to Analysis Inter-correlated Knowledge • Basic concept of a specific domain • Relations between Knowledge Objects • Ten types in The Frame Game [Clifford, 1981] To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**A graph composed with proposition**Relation among concepts in the problem Example Concept Set{"Object", "Free Fall", Displacement", "Time","19.6", "unknown"} PropositionsObject <proceeds> Free Fall,Object <has> Displacement,Object <has> Time, Displacement <is> 19.6, Time <is> Unknown An object proceeds Free Fall. After the phenomenon, the displacement of the object is 19.6. Ask for the procedure time of the object. Problem Structure 1: Problem Graph To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Problem Construction**• Basic Problem Model • Problem Construction Steps • Essential Data Structures To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Problem Matrix for Item Generation**• Extract manipulating concepts and attributes • Set Given and Unknown Attributes To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Problem Template**• Problem Format • Description Sequence • Possible Sentences To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Proposition Table**• Possible Sentences in problems • Corresponding syntax To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Item Generating System**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Problem Constructor**• Finding suitable Problem Template • Finding related proposition To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Item Generating System**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Conception Selection**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Problem Matrix Construction**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Physics Law Selection**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Physics Quantity Setting / Item Construction**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Knowledge Categories**• Grammatical Knowledge • usually has syntax, which has rules and formats in it. • Ex. Courses of Chinese, English, Music, and Art • Positioning Knowledge • lays stress on the location and direction among objects. • Ex. History and geography • Inter-Correlated Knowledge • attaches more importance to the manipulation of inter-correlation among knowledge. • Ex. Physics, Chemistry, and Mathematics To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge**Complex Problem Model**To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge

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