User Models and Models of Human Performance - Assignment Example

User Models and Models of Human Performance "For what a man more likes to be true, he more readily believes." - Francis Bacon (quoted by Margulis (2005), cited in Stein, Larrabee, & Barman, 2008) 1. Introduction to Misconceptions Many errors made by novices learning a domain can be attributed to misconceptions. According to Fisher (1983), misconceptions are ideas that are at a variance with accepted views (as cited in Stein, Larrabee, & Barman, 2008). In common usage, this term refers to students ideas that differ from those accepted by experts in the field (Odom & Barrow, 1995, as cited in Stein, Larrabee, & Barman, 2008). Other labels associated with the term include "misunderstandings", "naïve understandings", "alternative frameworks", "alternative conceptions", and "personal models of reality" (Alexander, 1992; Stein, Larrabee, & Barman, 2008). Many studies have been conducted on misconceptions and their effects on learning in students. What role do they play in developing a students domain knowledge? 1.1 Role of misconceptions in domain knowledge development One of the most thoroughly researched aspects of misconceptions is their resilience - they are hard to eliminate (Champagne, Klopfer, & Anderson, 1980; Larkin, 1983; as cited in Alexander, 1992). One cannot just make them go away by giving new information to students. Alexander (1992) attributes this to the complex networks of related information associated with misconceptions. This connection of misconceptions to information associated with a domain could cause students to alter other concepts too (Duschl & Hamilton, 1992). As students do not know that these misconceptions exist, they often work towards reinforcing them (Alexander, 1992). For example, while solving a problem, a student with misconceptions in algebra would try to create an alternative process that would conform to the misconceptions. 1.2 Role of domain in misconception-related problems In well-structured domains such as mathematics, computer programming, physics, and physical sciences, misconceptions have been researched consistently (Alexander, 1992). While misconceptions are not limited to some domains, not much research exists on why studies focused on well-structured domains or how the impact of misconceptions changes with domains. According to Alexander (1992), misconceptions have a "dispersive quality" - the more central a misconception is in a domain, the greater its impact on domain knowledge. 2. Misconceptions in computer programming According to Johnson (1986), programs written by novices with misconceptions reflect the misconceptions through characteristic bugs. Novices in C programming often use "=" for equality testing, rather than the required "= =" (Bull, S. et al., 2008). A program to compare two numbers x=2 and y=4 with "=" for equality testing will yield "True" (Program 1). Program 1 #include main() { int x,y; scanf("The first number: ", &x); scanf("The second number: ", &y); if (x = y) printf("True"); else printf("False"); } In C language, "=" is used to assign values and "= =" to compare for equality. Students who are new to C are likely to use "=" to compare values, as they learnt in mathematics and other programming languages. 2.1 Consequences of this misconception While the statement "If (x = y)…else…" is syntactically correct, the value of "y" is copied to "x". This happens because of the "assignment by value" feature in C. No matter what the values of "x" and "y" are, the statement is always interpreted as true and the "else" part is ignored. In the above-mentioned program, the result printed is "True", irrespective of the values of "x" and "y". This misconception results in logical error. While compile-time errors like missing ";" and run time errors such as division by zero are caught easily, this category of errors are not easy to catch (Hubbard, 2000). The student would remain clueless as to what is wrong in the program unless someone with a better knowledge of C catches the bug and debugs the program. Also, students with this misconception may find it difficult to write a more complicated program such as calculating the factorial of a number or comparing ages. 2.2 User modelling systems to correct misconceptions According to Anderson (1990), tutoring systems using model-tracing technology follow the students cognitive states during problem solving in real time. Students problem solving is observed constantly and instructions are given on deviation from the solution path. Such a system checks not only the syntax, but also symbols used by the students (Anderson, 1990). 3. User Models Many tutoring systems are available to teach students. Tutoring systems that monitor students misconceptions help in improving students domain knowledge. Examples include: CMU LISP tutor. Students using the Carnegie-Mellon University LISP Intelligent Tutoring System (CMU LISP) learned programming faster and scored higher compared with their peers receiving traditional classroom instructions (Anderson et al., 1990, as cited in Merrill, 1992). This tutor uses the model tracing methodology, comparing students steps with those of a domain expert and giving continuous feedback. Students can diagnose and correct their errors using the feedback. The feedback is based on the solution, as well as prediction and analysis of the students potential problem solving plans (Anderson et al., 1985, as cited in Merrill, 1992). Systems using this methodology often have a database of different approaches to solve a problem, including errors and their causal misconceptions. The tutor analyzes students steps and compares with those in the database to predict plans. In diagnosis and feedback mode, the system verbalizes the misconceptions which cause the errors (Merrill, 1992). BUGGY. Brown and Burton (1978) developed the computer game BUGGY based on student error patterns in arithmetic (Polson, Richardson, & Soloway, 1988). In this game, students identify errors and misconceptions of "buggy" students, which are modelled by the computer. Students solve problems, checking continuously if their steps tally with those of the computer simulation. When there is a variance in steps, students can consider alternative steps in their procedure to simulate the errors. In doing so, they learn to debug others errors and to improve on their own concept knowledge (Polson, Richardson, & Soloway, 1988). Some user models do the teaching without modelling misconceptions: Lego Logo. Lego developed activity blocks controlled by a computer (Papert, 1986, as cited in Polson, Richardson, & Soloway, 1988). Children build racers with these kits and race them. This activity gives children an idea about speed, weight, and aerodynamics. Although this system doesnt teach concepts, students get to know the principles involved (Polson, Richardson, & Soloway, 1988). GIL. Although Graphical Instruction in LISP tutor has a model-tracing version to teach LISP programming to students, an exploration-based version is also available (Reiser, et al., 1991, as cited in Merrill, 1992). This version of the tutor does not provide feedback to students, who have to fend for themselves if they are stuck. According to Merrill (1992), students using this version of GIL took twice as long as those using the model-tracing version to complete their course, but were better at finding errors and debugging. Misconception modelling is of relevance in some adaptive systems, as shown in Table 1. Table 1. Summary of relevance of misconceptions Misconceptions are relevant Misconceptions may not be relevant Tools built to test students domain knowledge. Tools built to train students in testing. Tools that teach the principles without focusing on concepts. Tools that teach students to explore on their own. 4. Model Human Performance The Adaptive Control of Thought - Rational (ACT-R) model of human performance divides knowledge into two types: knowledge of facts or declarative knowledge and knowledge of how to do cognitive tasks or procedural knowledge. In this model, chunks of information correspond to declarative knowledge. Procedural knowledge involves using these chunks to perform tasks (Anderson & Schunn, 2000). In Section 2, a misconception among novices of C language was mentioned: usage of "=" in comparison. Consider the Program 2 to compare "x" and "y". Program 2 #include main() { int x,y; scanf("The first number: ", &x); scanf("The second number: ", &y); if (x = = y) printf("True"); else printf("False"); } If x =2 and y = 4, result is "False". In ACT-R like model, one should define declarative facts and corresponding production rules. 4.1. Declarative Facts Our knowledge of the comparison is the fact. A chunk of knowledge "Fact2==4" is defined, as in Table 2. Table 2. Declarative facts Fact details Chunk definition "Fact2==4" chunk Is of the type "comparison fact", with slots "comparand1", "comparand2" , and "result" Fact2==4 ISA comparison fact comparand1 2 comparand2 4 result false 4.2 Production rules A production rule maps our knowledge of "Fact2==4" in a procedure to compare two numbers. We define a production rule for the comparison, "compare_x,y" in Table 3. Table 3. Procedure and production rules. Procedure Production Rule If the goal chunk is of the type "find truth" and state slot is "truth" of an "expression" Where "expression" has left hand operand as "=x", right hand operand as "=y", and comparison operator is "==", And "=equality" is a comparison fact with left hand operand as "comparand1", right hand operand as "comparand2" and result "result", Then change the goal to state "result". p compare_x,y =goal> ISA find truth state truth =expression> ISA expression lho =x rho = y op == =equality> ISA comparison fact comparand1 =lho comparand2 =rho result =result ==> =goal> state result 5. Predicting errors In the Program 1, a result of "True" when x=2 and y=4 indicates an error. While the program may seem to give the correct result for 2 equal numbers, the error is caught only in when "x" and "y" are unequal. So, catching of the error depends on values of "x" and "y" (Table 4). Table 4. Program errors x y Result Error 2 2 True Not caught 2 4 True x = y = 4 To model this error, we need a procedure "transform" that assigns the value of "y" to "x" instead of comparing "x" and "y" (Table 5). Table 5. Procedure transform If the goal is to transform an expression whose left hand operand is "=x", right hand operand is "=y" and operator is "==" And "rule" is a rule that sets left hand operand as "=lho", the right hand operand as "=rho", and new operator as "=new op", Then set "new expression" as an expression with left hand operand as "x", operator as "new op" and right hand operand as "=rho" And change the goal to retrieve left hand term as "x" and right hand term is "= rho". p transform =goal> ISA transformation =expression> ISA expression lho =x rho =y op == =rule> ISA rule lho =lho rho =rho new op =new op ==> =new expression> ISA expression lho =x op =new op rho =rho =goal> lht =x rht =rho Chunk encoding rule x=y rule ISA rule lho =x op == rho =y new-op = Chunk "x=y" is a rule with left hand operand "x", operator "==", "right hand operand "y" and new operator "=" 6. Errors and misconceptions In Section 2, Program 1 has no syntax errors, but gives the wrong answer when x = 2 and y = 4. However, Program 2 in section 4 gives the right answer when x = 2 and y = 4. How does the ACT-R like representation explain these changes? In the production rule "compare_x,y", the procedure checked for an expression with "x" as the left hand operand, "y" as the right hand operand and "= =" as the operator. When the expression "x= =y" was transformed to "x=y" in the production rule "transform", "x" was assigned the value of "y". The misconception which transforms the expression, results in a logical error. Table 6. Error classification Error Classification Reason if (x =y) Logical error Misconception in comparison operators gives erratic output. Conclusion An ACT-R like model was used to simulate the comparison operator misconception in C-language. References Alexander, P.A. (1992). Domain knowledge: Evolving themes and emerging concerns. Educational Psychologist. 27(1) p. 51. Retrieved March 5, 2009 from www.questia.com. Anderson, J.R. (1990). Analysis of student performance with the LISP tutor. In N. Frederiksen, R. Glaser, A. Lesgold, & M.G. Shafto, eds. Diagnostic Monitoring of Skill and Knowledge Acquisition. Hillsdale, NJ: Lawrence Erlbaum Associates. Retrieved March 7, 2009 from http://www.questia.com/read/91976713. Anderson, J. R., Boyle, C. F., & Reiser, B. J. (1985). Intelligent tutoring systems. Science. 228, pp. 456-462. Anderson, J. R., Boyle, C. F., Corbett, A. T., & Lewis, M. W. (1990). Cognitive modeling and intelligent tutoring. Artificial Intelligence, 42, 7-49. Anderson, J.R. & Schunn, C.D. (2000). Implications of the ACT-R learning theory: No magic bullets. Advances in instructional psychology, 5. Hillsdale, NJ: Lawrence Erlbaum Associates. Retrieved March 5, 2009 from http://www.lrdc.pitt.edu/Schunn/research/papers/NoMagicBullets.pdf. Brown J. S. & Burton R.R. (1978). 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Proceedings of the International Seminar on Misconceptions in Science and Mathematics. Ithaca, NY: Cornell University. Hubbard, J.R. (2000). SCHAUMs OUTLINE of Theory and Problems of Programming with C++. New York: McGraw-Hill. Johnson, W.L. (1986). Intention-Based Diagnosis of Novice Programming Errors. CA: Morgan Kaufmann. Retrieved March 5, 2009 from http://books.google.co.in/books?id=dGdie63ZYOAC&pg=PA16 Larkin, J.H. (1983). Teaching problem solving in physics: The psychological laboratory in the practical classroom. In D.T. Tuma & F. Reif. eds. Problem solving and education: Issues in teaching and research. Hillsdale, NJ: Lawrence Erlbaum Associates. Margulis, L. (2005). Science, the rebel educator: I. American Scientist. 93(6), 482. Merrill, D.C. (1992). Effective Tutoring Techniques: a Comparison of Human Tutors and Intelligent Tutoring Systems. Journal of the Learning Sciences. 2. Retrieved March 6, 2009 from www.questia.com Odom, A.L. & Barrow, L.H. (1995). Development and application of a two-tier diagnostic test measuring college biology students understanding of diffusion and osmosis after a course of instruction. Journal of Research in Science Teaching. 32(1), 45-61. Papert, S. (1986). Rethinking mathematics learnability in a computer culture. The Karl de Leeuw Memorial Lecture, Stanford, 2 May, 1986. Stanford, CA: Stanford University. Polson, M.C., Richardson, J.J., & Soloway, E. (1988). Foundations of Intelligent Tutoring Systems. Hillsdale, NJ: Lawrence Erlbaum Associates. Retrieved March 7, 2009, from http://www.questia.com/read/47609932? Reiser, B. J., Beekelaar, R., Tyle, A., & Merrill, D. C. (1991). GIL: Scaffolding learning to program with reasoning-congruent representations. In The International Conference of the Learning Sciences: Proceedings of the 1991 conference. Evanston, IL: Association for the Advancement of Computing in Education. Stein, M., Barman, C., & Larrabee, T. (2008). A study of common beliefs and misconceptions in physical science. Journal of Elementary Science Education. 20(2). Retrieved March 6, 2009 from http://www.questia.com/read/5027566798 Read More