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Article Excerpt
This paper describes the global feedback in ACTIVEMATH, a Web-based adaptive learning environment for mathematics and beyond. It addresses some of the cognitive foundations and the architecture of the suggestion mechanism with its components. This architecture separates components for diagnosis from components for suggestions and different types of information: the observable facts about the student, implied non-observable diagnoses about the student's actions, suggestions implied from the observable and non-observable diagnoses, and the actual rendering of the suggestions. This mechanism is highly adaptive.
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INTRODUCTION
Human tutors react to a student's learning activities such as reading, understanding examples, or problem solving attempts. Similarly, an intelligent tutoring system should provide such reactions, non-verbal as well as verbal ones. As the granularity and type of the student's activities vary, the tutorial responses do not only depend on the learner's actions but also on what the system delivered in the time interval to which the feedback responds. For instance, responses can be given on problem solving steps, on an overall exercise performance, or on a lesson. Obviously, reactions for navigation deviations will have to differ from a response to a misconception. In addition, responses may depend on the learning goal, the pedagogical strategy, and on the learner's characteristics.
Feedback is a reaction to a student's learning behavior. It can consist of a verbal tutorial reaction and of non-verbal reactions, such as pointing, attention-drawing, offering of next steps, etc. Cognitive and pedagogical psychology research has primarily investigated feedback, in problem solving exercises. This includes questions such as: Is feedback effective for learning and for which students? Is feedback indeed used as expected? How should feedback be designed and when should it be offered to the student to achieve the largest possible learning gains?
The following summarizes results on feedback types that appeared to be useful inside exercises (this summary is adopted from Jacobs (2001), which is based on a myriad of scientific articles). There are several types of feedback:
* Knowledge of result (KR) means a feedback that states whether a solution is correct or incorrect. This feedback has proved to be the minimal one. For strong students, KR might suffice to stimulate further elaboration.
* Knowledge of correct result (KCR) provides a correct solution. This is recommended for students with little prior knowledge, little ability, many errors, and relatively simple learning goals.
* Answer until correct (AUC) asks the student to try again until the answer is correct. It proved valuable, for complicated tasks and for students with sufficient ability to solve the exercise.
* Instruction-based elaboration (IBE) may include an explanation of the correct solution, correction of errors (local), or the presentation of the original instruction.
Several investigators (Aleven & Koedinger, 2000; Narciss & Huth, 2004) found that delivering KCR immediately--without any effort by the learner--is counterproductive. Therefore, they suggest inhibiting KCR as long as the learner does not try to follow KR and hints.
For multi-step problem solving, Farquhar (1995) shows that elaborate feedback improves learning time and learning results more than the pure KCR does. For Farquhar, elaborate feedback might comprise several of the following: notification of error, reason for incorrectness, brief description of appropriate subgoal, list of steps to complete the subgoal, indication of progress, or identification of next step. Certainly, elaborate feedback could contain other actions as well, e.g., a counter example or a description of consequences of a mistake.
Extra-instructional elaboration (EIE) in problem-solving may include a variety of information. Examples include the following:
* Strategic help (Dempsey, Driscoll, & Swindell, 1993)
* Meta-level feedback such as prompts for self-explanation (Chi, DeLeeuv, Chiu, & Lavancher, 1994; Chi, 2001; Stark, 2000; Sandoval, Trafton, & Reiser, 1995) or prompts for summarizing and elaborating.
The content of a tutorial reaction matters. In addition, the point in time when it is delivered to a particular student and the method of delivery (e.g., positive vs. negative feedback) is important. Some relevant aspects for the actual delivery of feedback are:
* Feedback is particularly useful when an error has occurred. Weak students benefit more from feedback than do strong students. One paper (Webb, Stock, & McCarthy, 1994) describes a beneficial effect of positive feedback.
* Feedback may be used inappropriately by learners and may not improve learning because the user just receives the correct solution without any thinking effort (Aleven & Koedinger, 2000b; Clariana, 1999). The learner may use this information only for judging performance (in competition) rather than for reasoning about mistakes and for correcting errors.
* As with any learning, the understanding of feedback can be supported by referring to knowledge familiar to the student, by asking questions, and by prompting the student to deliver explanations, to find new examples, to make notes, or to draw a concept map (Jacobs, 2001).
* Feedback or help should be sparsely provided, only if needed (Bunt, Conati, Huggett, & Muldner, 2001), and mainly as a guidance for poor learners. Feedback should be brief and relevant (Jacobs, 2001). Some researchers found questions to be superior to statements (Chi, Siler, Jeong, Yamauchi, & Hausmann, 2001).
* Often, feedback is better acknowledged by the student when it is personalized by pictures of the teacher or a friend, and tailored to the student (by name etc).
The question of whether immediate or delayed feedback is more effective does not currently have a clear answer. The diverging results may be caused by the influence of characteristics of the learner and of the learning situation. See more on immediate vs. delayed feedback in the section on Local and Global Feedback below.
Most of the mentioned reactions in feedback are conveyed verbally. A (non-verbal) form of reaction to a student's learning activities is the selection of new exercises by the tutor. Although most of the results were obtained for feedback in exercises only, this brief summary shows that there are many aspects to be investigated for appropriate and useful tutorial reactions.
This brief introduction shows that there are many cognitive aspects to be investigated for appropriate and useful tutorial reactions. The Web-based, adaptive, and interactive learning environment, ACTIVEMATH, strives to support the learning of mathematics, currently at a university or college level (and soon to also include a school version). For true learning, interactivity and feedback are two key ingredients that can be offered by e-Learning (Schulmeister, 2004). Therefore, we are developing components of ACTIVEMATH, which can deliver intelligent feedback on interaction. One of these components--the suggestion mechanism--is presented in this paper. In order to generate feedback that helps learning, the cognitive empirical results must be respected in the design of the suggestion mechanism and in the actual suggestions. In addition, the technological problems need to be solved, such that, e.g.,...
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