User Models and Models of Human Performance - Coursework Example

User Models and Models of Human Performance Misconceptions When given a simple linear equation of the type a + b = x + c to solve for x, many sixth grade students give wrong answers. This could be an error, a faulty algorithm, or a misconception in their understanding of arithmetic (Li & Li, 2008). According to Hynd and Guzzetti (1993), researchers explain misconceptions as beliefs held contrary to known evidence (as cited in Taylor and Kowalski, 2004). Over 8000 studies on science education report existence of misconceptions or alternative conceptions, according to Duit (2007, as cited in Li & Li, 2008). Research suggests that misconceptions in students learning science may occur due to misrepresentation of objects belonging to one ontological group as members of another ontological group (e.g., students may treat heat and current as substances) (Chi 2005, as cited in Li & Li, 2008). In students learning mathematics, misconceptions occur due to inaccurate prior instructions and limited individual experience, observation, and interaction (Dole, 2000; Qian & Guzzetti, 2000, as cited in Taylor & Kowalski, 2004). 1.1 Difficulties caused by misconceptions Misconceptions do not change. Literature shows that misconceptions play a strong role in students pursuing academic study — once a misconception is formed, it is not likely to change (Taylor & Kowalski, 2004). Woodward and Howard (1994) suggest that misconceptions do not go away with more practice. Misconceptions cause students to introduce incorrect processes. According to Woodward & Howard (1994), misconceptions are fixed in the conscious process of "what to do next". For example, misconceptions in arithmetic problem solving process may cause the students to twist or invent an alternative, incorrect process (Woodward & Howard, 1994). Misconceptions result in flawed knowledge. Due to the highly persistent nature of misconceptions, which may last for several years, students knowledge of the subject remains flawed (Woodward & Howard, 1994). Dole (2000) proved that stronger misconceptions are likely to reduce comprehension of new material that is contrary to the misconception (as cited in Taylor and Kowalski, 2004). 1.2 Misconceptions and domain While misconceptions have been studied in some domains such as mathematics, physical sciences, biology, medicine, computer programming, and language education, evidence to suggest that effects of misconceptions are domain specific could not be found. However, Alexander (1992) says that effect of a misconception in a domain depends on whether the concept is fundamental to the particular subject. Misconceptions regarding the foundations or principles of a domain cause greater flawing of the domain knowledge. 2. Misconceptions in mathematics Li & Li (2008) cited (Falkner, Levi, & Carpenter, 1999) a misconception that occurred among sixth-graders solving a simple equation “8 + 4 = x + 5”. Many students filled the box with 12 or 17. The students could have overlooked “=” as part of an equation and interpreted it as “to do something”. Another misconception is to treat “8 + 4” as a computation process rather than an expression. Fifth graders moving from whole numbers to rational numbers also develop misconceptions. When asked to compare fractions 2/3 and 3/4, one student asserted that both are same as they have one part missing. A fifth grader who has only learnt whole numbers, is likely to compare these fractions with the whole number 1 and find a small part missing in both (Donovan & Bransford, 2005). Misconceptions in rational number system occur because the students have been taught to consider fractions as part of a whole. These misconceptions could affect equation and problem solving in mathematics and science. 2.1 Tutor systems to correct student misconceptions Tutoring systems with model tracing methodology minimize misconceptions in students. Such systems let students solve problems, keep track of their progress, and provide explanatory feedback when the student makes an error or asks for help (Merrill, 1992). Interactive systems do not just look at the solution per se, but record all the problem solving steps and analyze potential plans as well (Anderson et al., 1985, as cited in Merrill, 1992). The system also identifies the root of misconception and teaches the right concept required to find the solution. 3. User Models User models can simulate human performance, including misconceptions. 3.1. Some cognitive environments are designed to model misconceptions. Such applications find extensive use in training people in identifying and correcting errors. Some examples are: Sherlock II. Sherlock II developed by the Learning Resource and Development Center at the University of Pittsburg trains technicians of the U.S. Air Force to troubleshoot complex test equipment. First the trainee does a troubleshooting exercise getting instructions. Then Sherlock II tells them about their performance, points out the errors, and explains a better way of troubleshooting. This misconception modelling approach of Sherlock II helps Air Force technicians avoid mistakes in the trouble shooting process. According to an Air Force evaluation of Sherlock II, technicians who used the system for 20-25 hours were as proficient at testing equipment as those with over 4 years of real time testing experience (Lajoie, 1993, as cited in Kent, et, al., 2002). Circsim-Tutor. This cardiovascular physiology tutor was developed for medical students. Students take a test, after which the tutor analyzes the answers and goes to remedial mode. This system analyzes for unexpected answers, partially correct answers, too many answers, and redundancies (Kim, et. al., 1989, as cited in Kent, et. al., 2002). 3.2. Some environments educate users without modelling misconceptions: The Adventures of Jasper. This video series was developed by the Cognition and Technology Group at Vanderbilt University (CTGV). Each videodisc in the series helps students to identify and solve a complex problem with all the required data incorporated in the story (Jones & Idol, 1990). The series is based on the concept of Anchored Instruction to help students develop problem solving skills in students. Learning skills are enhanced by connecting the problem at hand with previous experiences. This teaching model has two goals (Jones & Idol, 1990): 1. To help students understand problems and opportunities encountered by experts in their fields and to see how the experts tackle these problems using their knowledge. 2. To help students assimilate their knowledge by viewing the situation from different perspectives. In this model, a learner-centred instructional environment is created to help students get the most out of on their strong suits as learners. Individual strengths and needs are identified and students are taught to exploit their strengths. 3.3. Relevance of Misconception Modelling In Adaptive Systems The two examples mentioned in 3.1 - Sherlock II and Circsim-Tutor, are tutoring systems designed specifically to test and improve students subject knowledge. In order to spot and correct students misconceptions, these systems model misconceptions in their reflective modes. In such systems whose goal is to correct errors in students, modelling misconceptions is a priority. On the other hand, the example in 3.2, The Adventures of Jasper, was developed to build on younger students strengths in order to teach them basic problem solving skills. The "experts" in such a system model students strengths. Here, the focus is not on misconception modelling. 4. Model Human Performance The Adaptive Control of Thought – Rational (ACT-R) model finds applications in cognitive tutoring systems to predict difficulties a student has in academic study and to help students overcome misconceptions. This human cognition model is based on the production system theory. According to this theory, a cognitive skill consists of conditional statements called production rules (Anderson, 1993, as cited in Lebière, Anderson, & Reder, 1994). Two different long-term memories are used in this theory: declarative memory comprising facts and procedure memory comprising our knowledge of how to do things. In the ACT-R model, declarative facts are represented as chunks and procedures as productions consisting of production rules. Syntax is defined to represent facts and productions (Budiu). Consider the equation: 8 + 4 = x + 5 which was discussed in Section 1. This is a linear equation of the form a + b = x + c To develop the basic components of an ACT-R model, we need to represent the declarative facts and map facts to tasks using production rules. 4.1 Declarative facts To solve this equation, we require the facts 8 + 4 = 12. We form a chunk of declarative knowledge called "Fact8+4", whose chunk type is "addition-fact" and slots are "addend1", "addend2", and "sum". Table 1 Representing the facts Fact8+4 ISA addition-fact addend1 eight addend2 four sum twelve "Fact8+4" chunk Is of the type "addition-fact", "addend 1" is 8, "addend 2" is 4, And "sum" is 12. 4.2 Production Rules The equation a + b = x + c is simplified toy = x + c where y = 12 To solve the equation, we use the productions “solve_y=x+c” and “compute_y-c”. For “solve_y=x+c”, left hand side y is a number and right-hand side is the term x+c. So “c” is subtracted from both sides. Subtraction of “c” in the right-hand side isolates x. In the next step, “compute_y-c”, the difference between “y” and “c” is calculated as y-c=x. The production rules are encoded as in Table 2. The table also explains how we formed the production rules. Table 2 Production rules Encoding Explanation Encoding Explanation p solve_y=x+c =goal> ISA solve-equation rht =term lht =y =term> ISA term rho x op + lho =lho ==> =difference> ISA term lho =y op - rho =lho =goal> rht x lht =difference If the goal chunk is of the type "solve equation", and right-hand term is "=term" and left hand term is "=y" Where "term" has x as right-hand operand, "+" operator and left hand operand as"=lho", And, "difference" is a term whose left hand operand is "=y", operator is "-", and right hand operand is "=lho" Then, change the goal so that right hand term is x and left hand term is "=difference" p compute_y-c =goal> ISA solve-equation rht x lht =term =term> ISA term lho =lho op - rho =rho =lho-rho> ISA subtraction-fact arg1 =lho arg2 =rho difference =difference ==> =goal> lht =difference If the goal is a solve equation to compute "y-c", then right hand term is x and left hand term is "=term" Where term has left operand "=lho", operator "-", and right operand "=rho" And "lho-rho" is a subtraction-fact where arg1 is "=lho", arg2 is "=rho" and difference is "=difference" Then change the goal to retrieve "=difference" as the left hand term 5. Predicting Errors In the equation a + b = x + c, (where a = 8, b = 4, and c = 5), whose solution is x = a + b -c, many errors are possible. In Section 2, two errors were described, as in Table 3. Table 3 Solution errors Error Result a + b = x or y = x 12 a + b + c = x or y + c = x 17 The error a + b = x occurs due to omission of the production “compute_y-c”. In order to model algebraic error a + b + c = x, we have to use a production that retrieves a different algebraic expression. In place of “compute_y-c”, the production “transform”, which yields “y + c” is used. Table 4 Production “transform” p transform =goal> ISA solve-equation rht x lht =term =term> ISA term rho =rho op =op lho =lho =rule> ISA rule rho =rho lho =lho new op =new op ==> =new term> ISA term rho =y op =new op lho =lho =goal> rht =x lht =new term If the goal is to transform a solve equation whose right hand term is x and left hand term is "=term", Where term has right hand operand "=rho", operator "=op", and left hand operand "=lho" And "rule" is a rule that sets right hand operand as "=rho", left hand operand as "=lho" and new operator as "=new op" Then set "new term" as a term with "right hand operand" as "y", operator as "=new op" and left hand operand as "=lho" And change the goal to retrieve right hand term as x and left hand term as "=new term" Chunk encoding rule y + c rule ISA rule lho y op + rho =c new-op + Chunk "y +c" is a rule with left hand operand "y", operator "+", "right hand operand "c" and new operator "+" 6. Classifying errors as misconceptions In section 2, while solving the equation 4 + 8 = x + 5, two erroneous results were obtained, 12 and 17. Table 3 lists how the errors were obtained. Table 5 compares and classifies the errors as misconceptions and faulty algorithms. Table 5 Error classification Error Classification Reason(s) a + b = x Misconception Misrepresenting “=” as “to do something” rather than as part of an equation. Treating “a + b” as a computation process rather than an expression. a + b + c = x Faulty algorithm The “+ c” when shifted to right-hand side was not changed to “-c”. References Anderson, J.R. (1993). Rules of the Mind. Hillsdale, NJ: Erlbaum. Anderson, J. R., Boyle, C. F., & Reiser, B. J. (1985). Intelligent tutoring systems. Science. 228, pp. 456-462. Alexander, P.A. (1992). Domain Knowledge: Evolving Themes and Emerging Concerns. Educational Psychologist. 27 (1). Budiu, R. (n.d.). ACT-R: About. Retrieved February 23, 2009, from http://act-r.psy.cmu.edu/about/ Chi, M. T. H. (2005). Commonsense conceptions of emergent process: Why some misconceptions are robust. The Journal of the Learning Science. 14, pp. 161-199. Donovan S., & Bransford J (2005). How Students Learn: History, Math, and Science in the Classroom. National Academies Press. Duit, R. (2007). http://www.ipn.unikiei.de/aktuell/stcse/stcse.html. Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Childrens understanding of equality: A foundation for algebra. Teaching Children Mathematics. 6, 232-236. Hynd, C. R., & Guzzetti, B. J. (1993). Exploring issues in conceptual change. In D. J. Leu & C. K. Kinzer (Eds.), Examining central issues in literacy research, theory and practice (pp. 374-381). The National Reading Conference. Jones, B.F., & Idol L. (1990). Dimensions of Thinking and Cognitive Instruction. NJ: Lawrence Erlbaum Associates. Kent, A., Hall, C. M., & Lancour, H. (2002). Encyclopedia of Library and Information Science: Vol. 71(34). Boca Raton: CRC. Retrieved February 24, 2009 from http://books.google.co.uk/books?id=saa39p6C538C Kim, N., Evens, M., Michael, J., & Rovick, A. (1989) An intelligent tutoring system for circulatory physiology. In H Maurer, ed. Computer Assisted Learning. Springer-Verlag. Kowalski, P., & Taylor, A. (2004). Naive psychological science: The prevalence, strength, and sources of misconceptions. The Psychological Record. 54(1). Lajoie, S. Computer environments as cognitive tools for enhancing learning (1993). In S. Lajoie & S. Derry, eds., Computers as Cognitive Tools. NJ: Lawrence Erlbaum Associates. Lebière, C., Anderson, J.R., & Reder, L.M. Error modelling in the ACT-R production system. The 1994 Cognitive Science Conference. Retrieved February 23, 2009, from http://act-r.psy.cmu.edu/papers/Lebiere_And_Red94-abs.html Li, X., & Li, Y. (2008). Research on students misconceptions to improve teaching and learning in school mathematics and science. School Science and Mathematics. 108 (1). Merrill, D.C. (1992). Effective Tutoring Techniques: a Comparison of Human Tutors and Intelligent Tutoring Systems. Journal of the Learning Sciences. 2. Qian, G., & Guzzetti, B. (2000). Conceptual change learning: A multidimensional lens. Reading & Writing Quarterly. 16, pp. 1-3. Regian, J.W., & Shute, V.J. (1992). Cognitive Approaches To Automated Instruction. NJ: Lawrence Erlbaum. Woodward, J., & Howard, L. (1994). The misconceptions of youth: errors and their mathematical meaning. Exceptional Children. 61. Read More