One of the most distinguishing characteristics of an expert tutor is their considerable attention given to motivating students as well as providing cognitive information to them. They seem to have a working model of each tutee on when they need more emotional support, and when they need to be challenged in their state of knowledge construction. Lepper and Woolverton proposes the INSPIRE model which highlights seven critical characteristics of expert tutors:
I - intelligent. Expert tutors know their subject well and are able to guide their tutees in knowledge construction.
N - nurturant. Expert tutors are highly supportive and nurturing of their students.
S - Socratic. Expert tutors engage their students using questions rather than directions or assertions, they provide hints and not answers.
P - progressive. Expert tutors carefully plan their tutoring sessions of increasing difficulty and complexity, but they are also flexible in adjusting their session in response to the student's learning.
I - indirect. Expert tutors deliberately avoid overt criticism of their students' mistakes but rather often pose questions that imply the existence of the errors.
R - reflective. Expert tutors ask their students to reflect aloud on what they have just done immediately after a successful attempt in their problem solving.
E - encouraging. Expert tutors keep their students' interest / attention / involvement high by instilling confidence and a sense of curiosity.
Reference:
Lepper, M. and Woolverton, M. (2002). "The Wisdom of Practice: Lessons Learned from the Study of Highly Effective Tutors" in Improving Academic Achievement. Elsevier Science, pp 135 - 158.
27 August 2009
22 August 2009
Framing
Solving problems usually involve a variety of concepts and skills. Some problems can be approached from a number of angles but usually, when one goes down a "wrong track", it may take sometime to recover unless one is aware of the backtracking points and be able to try alternate paths. The perception / judgment that is used in problem solving is called epistemological framing. It refers to the class of tools and skills that one would bring to a particular situation or context for problem solving. As a simple example, some students may rely on memorized facts to solve a problem, while others may rely on logical reasoning, etc.
Bing and Redish (2009) identify four common framing clusters that students commonly use of mathematics to solve physics problems: calculation, physical mapping, invoking authority, and math consistency. Calculation refers to the algorithmic use of established computational steps to derive a solution, e.g. calculus rules, geometry rules, algebraic rules, etc. Physical mapping refers to the mapping between mathematics with the student's intuition of the physical or geometrical situation at hand to support their arguments and reasoning. Invoking authority points to the resource / book / journal / quote / person / etc. to support a claim. Math consistency appeals to the other math ideas and concepts that are demonstrably consistent to offer validation of an argument.
As I reflect on these four framing clusters, I wonder how these clusters can be detrimental for beginning computer science students. Take for example, calculation, the meaning of "=" in math as equating two entities, like x = y, is so different from computer science use of assigning one value to a variable. Similarly, there is hardly any connection between how computer science models physical objects, like tree, or student, and how we intuitively understand and interact with them. Students are also often surprised at what they can do and cannot do with a programming language. They lack the source(s) of "authority" to guide them in their learning. One comment that I often hear from students when they are learning a new programming language is "I didn't know you can do that!". Finally, although computer science students know that computers are consistent and logical, the subtleties of programming language syntax and the precision of logic that is also highly dependent on the sequence of execution in a program can be frustrating and overwhelming to them. Identifying some of these framing clusters that students bring into the classroom may help in their learning process.
Reference:
Bing, T. J. and E. F. Redish (2009, Jul). Analyzing problem solving using math in physics: Epistemological framing via warrants. Available at http://arxiv.org/pdf/0908.0028.
Bing and Redish (2009) identify four common framing clusters that students commonly use of mathematics to solve physics problems: calculation, physical mapping, invoking authority, and math consistency. Calculation refers to the algorithmic use of established computational steps to derive a solution, e.g. calculus rules, geometry rules, algebraic rules, etc. Physical mapping refers to the mapping between mathematics with the student's intuition of the physical or geometrical situation at hand to support their arguments and reasoning. Invoking authority points to the resource / book / journal / quote / person / etc. to support a claim. Math consistency appeals to the other math ideas and concepts that are demonstrably consistent to offer validation of an argument.
As I reflect on these four framing clusters, I wonder how these clusters can be detrimental for beginning computer science students. Take for example, calculation, the meaning of "=" in math as equating two entities, like x = y, is so different from computer science use of assigning one value to a variable. Similarly, there is hardly any connection between how computer science models physical objects, like tree, or student, and how we intuitively understand and interact with them. Students are also often surprised at what they can do and cannot do with a programming language. They lack the source(s) of "authority" to guide them in their learning. One comment that I often hear from students when they are learning a new programming language is "I didn't know you can do that!". Finally, although computer science students know that computers are consistent and logical, the subtleties of programming language syntax and the precision of logic that is also highly dependent on the sequence of execution in a program can be frustrating and overwhelming to them. Identifying some of these framing clusters that students bring into the classroom may help in their learning process.
Reference:
Bing, T. J. and E. F. Redish (2009, Jul). Analyzing problem solving using math in physics: Epistemological framing via warrants. Available at http://arxiv.org/pdf/0908.0028.
06 August 2009
What can we learn from Video Games?
How do we motivate people to learn? Well, Gee (2005) notes that "[u]nder the right conditions, learning, like sex, is biologically motivating and pleasurable for humans (and other primates)." It is the same hook that game designers use to attract gamers (see link), so we can learn a great deal about learning from video games. Gee organized these attributes in video games in 3 categories and for each category a number of principles:
Empowered Learners - gamers / learners need to have some sense of control
They feel that they are co-designers of the game or learning, they can customize their game play or learning experience, they can take on a new identity (and for learners to adopt the culture and role of a biologist / computer scientist / etc.), and be able to manipulation and distributed knowledge in the game virtual world or in the real world.
Problem Solving - gamers / learners need to be exposed to appropriate information and problems
They need to be exposed to well-organized problems that are not too complex nor too trivial, and problems should be pleasantly frustrating and there is payoff. There should be cycles of practice to help them develop their expertise, information is given 'on demand' and 'just in time' so they don't feel overwhelmed, they are exposed to fish tanks and sandboxes (simplified versions of the game / learning content) so they can understand a simple system or try out things without any risk first, and they see their practice of skills as strategies to accomplish their goals.
Understanding - gamers / learners make sense of their world
They want to look at the big picture and be able to think of the system at large, they can attach meanings to their past experiences.
Reference:
Gee, J. (2005). "Learning by Design: good video games as learning machines." E-Learning, 2(1). pp 5 - 16.
Empowered Learners - gamers / learners need to have some sense of control
They feel that they are co-designers of the game or learning, they can customize their game play or learning experience, they can take on a new identity (and for learners to adopt the culture and role of a biologist / computer scientist / etc.), and be able to manipulation and distributed knowledge in the game virtual world or in the real world.
Problem Solving - gamers / learners need to be exposed to appropriate information and problems
They need to be exposed to well-organized problems that are not too complex nor too trivial, and problems should be pleasantly frustrating and there is payoff. There should be cycles of practice to help them develop their expertise, information is given 'on demand' and 'just in time' so they don't feel overwhelmed, they are exposed to fish tanks and sandboxes (simplified versions of the game / learning content) so they can understand a simple system or try out things without any risk first, and they see their practice of skills as strategies to accomplish their goals.
Understanding - gamers / learners make sense of their world
They want to look at the big picture and be able to think of the system at large, they can attach meanings to their past experiences.
Reference:
Gee, J. (2005). "Learning by Design: good video games as learning machines." E-Learning, 2(1). pp 5 - 16.
Situated Learning
Much learning is done within contexts. An average 17 year old would have learned her vocabulary at a rate of 5000 words per year for over 16 years by listening, talking, reading, and interactions. In contrast, if vocabulary were taught simply by abstract definitions and sentences taken out of context, it is hardly even possible to learn 100 to 200 words per year.
Students should be exposed to and then adopt the culture of which the tools they are taught to use. This requires the support of a community, and learning is a process of enculturation. The activities that the students will be exposed to will be authentic (i.e. ordinary practices of the culture, and not just classroom or toy problems), and these activities are framed by its culture.
While we want our students to have practical knowledge on how to use the tools and develop practical skills, we also want them to develop deep thinking and cognitive sills. Within the context of situated learning, this is called cognitive apprenticeship. It begins with problems and practice in situ, and moves them beyond the traditional practices by emphasizing that practices are not absolute, and students are encouraged to generate their own solutions with other members of the culture, which we sometimes call a community of practice.
Reference:
Brown, J., Collins, A., Dugid, P. (1989). "Situated Cognition and the Culture of Learning". Educational Researcher. 18(32). pp 32 - 42.
Students should be exposed to and then adopt the culture of which the tools they are taught to use. This requires the support of a community, and learning is a process of enculturation. The activities that the students will be exposed to will be authentic (i.e. ordinary practices of the culture, and not just classroom or toy problems), and these activities are framed by its culture.
While we want our students to have practical knowledge on how to use the tools and develop practical skills, we also want them to develop deep thinking and cognitive sills. Within the context of situated learning, this is called cognitive apprenticeship. It begins with problems and practice in situ, and moves them beyond the traditional practices by emphasizing that practices are not absolute, and students are encouraged to generate their own solutions with other members of the culture, which we sometimes call a community of practice.
Reference:
Brown, J., Collins, A., Dugid, P. (1989). "Situated Cognition and the Culture of Learning". Educational Researcher. 18(32). pp 32 - 42.
05 August 2009
Interactive Engagement vs. Traditional Methods
A study of 6,542 students (Hake, 1998) who took introductory physics courses in high schools, colleges and universities was conducted to compare the effectiveness of interactive engagement in the classroom as compared to traditional lecture style presentations. Not surprisingly, the average gain (measured as per Halloun-Hestenes Mechanics Diagnostic test, Force Concept Inventory, and Mechanics Baseline test) due to interactive engagement delivery is significantly higher than traditional courses.
In another paper by Hake (1997), he lists several interactive engagement methods that have been used successfully for teaching physics. These include collaborative Peer Instruction, microcomputer-based labs, concept tests, modeling, active learning problem sets or overview case studies, physics-education-research based text or no text, and socratic dialogue inducing labs.
It should be noted that interactive engagement is "necessary but not sufficient for marked improvement over traditional methods" (Hake, 1997) since there are a number of colleges which have marginal gain even when interactive engagement activities were used.
I like the Epilogue that Hake included in his 1997 article:
I am deeply convinced that a statistically significant improvement would occur if more of us learned to listen to our students....By listening to what they say in answer to carefully phrased, leading questions, we can begin to understand what does and does not happen in their minds, anticipate the hurdles they encounter, and provide the kind of help needed to master a concept or line of reasoning without simply "telling them the answer."....Nothing is more ineffectually arrogant than the widely found teacher attitude that ’all you have to do is say it my way, and no one within hearing can fail to understand it.’....Were more of us willing to relearn our physics by the dialog and listening process I have described, we would see a discontinuous upward shift in the quality of physics teaching. I am satisfied that this is fully within the competence of our colleagues; the question is one of humility and desire.
Arnold Arons, Am. J. Phys. 42, 157 (1974)
I often wonder whether this applies to Computer Science. Afterall, don't we know pretty well how our students think? ... or do we?
Reference:
Hake, Richard. (1997). "Interactive engagement methods in introductory mechanics courses". Retrieved on August 6, 2009 from http://www.physics.indiana.edu/~sdi/IEM-2b.pdf.
Hake, Richard. (1998). "Interactive-engagement versus Traditional Methods: A six-thousand-student survey of mechanics test data for introductory physics courses". American Association of Physics Teacher. 66(1), pp64-74.
In another paper by Hake (1997), he lists several interactive engagement methods that have been used successfully for teaching physics. These include collaborative Peer Instruction, microcomputer-based labs, concept tests, modeling, active learning problem sets or overview case studies, physics-education-research based text or no text, and socratic dialogue inducing labs.
It should be noted that interactive engagement is "necessary but not sufficient for marked improvement over traditional methods" (Hake, 1997) since there are a number of colleges which have marginal gain even when interactive engagement activities were used.
I like the Epilogue that Hake included in his 1997 article:
I am deeply convinced that a statistically significant improvement would occur if more of us learned to listen to our students....By listening to what they say in answer to carefully phrased, leading questions, we can begin to understand what does and does not happen in their minds, anticipate the hurdles they encounter, and provide the kind of help needed to master a concept or line of reasoning without simply "telling them the answer."....Nothing is more ineffectually arrogant than the widely found teacher attitude that ’all you have to do is say it my way, and no one within hearing can fail to understand it.’....Were more of us willing to relearn our physics by the dialog and listening process I have described, we would see a discontinuous upward shift in the quality of physics teaching. I am satisfied that this is fully within the competence of our colleagues; the question is one of humility and desire.
Arnold Arons, Am. J. Phys. 42, 157 (1974)
I often wonder whether this applies to Computer Science. Afterall, don't we know pretty well how our students think? ... or do we?
Reference:
Hake, Richard. (1997). "Interactive engagement methods in introductory mechanics courses". Retrieved on August 6, 2009 from http://www.physics.indiana.edu/~sdi/IEM-2b.pdf.
Hake, Richard. (1998). "Interactive-engagement versus Traditional Methods: A six-thousand-student survey of mechanics test data for introductory physics courses". American Association of Physics Teacher. 66(1), pp64-74.
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