Theory Name: Situation Problem Solver (SPS)

Authors (Last, First): Reusser, Kurt

Associate Learning Theory:
Cognitive constructivist: The theory focuses on cognitive learning process including comprehending, simulating process of the understanding (mental representation) and solving by accessing knowledge and applying strategies with mathematical text, word, or story problems (MSPs). Tracing the comprehension, mathematization, and solution process are generated by the situation problem solver (SPS). Instruction with SPS focuses on the bridging of abstract, symbolic problem solving with concrete, situational reasoning. Students need instruction on how to use representational systems and languages to express their situational and mathematical understanding of a problem in meaningful and cognitively efficient ways.

Model Description:
The theory focuses on designing computer-based system for learning and instruction. The design of computer-based educational system should be based on two foundations: on content-specific research on learning and comprehension, and on a pedagogical model of the learner and the learning process. The pedagogical design includes the didactic analysis of key concepts, structures, and representations; learning methods, skills, and strategies; as well as patterns of instruction related to a task or domain. This theory offers 6 design principles for didactically intelligent computer-based tools and cognitive-instructional task analysis of content. Based on the theoretical framework, the author developed a cognitive tool, HERON for supporting the reified planning and construction of a mathematical problem model.

Specification of Theory
(a) Goals and preconditions
The theory is intended to provide design principles of cognitive tools for intentional learner in the mathematical story-problem comprehension tasks.

(b) Principles
1) Design intelligent technologies as cognitive tools for thoughtful teachers and learner; 2) Stimulate and facilitate students’ effort toward domain-knowledge construction, understanding, and skill acquisition by providing expert procedural and domain conceptual assistance; 3) Provide students with intelligible representational tools of thought and communication; 4) Provide as much learner control as possible and as much control of the learner as needed-or provide learners with some guidance according to the principle of variable control and minimal help; 5) By their potential as extracortical mirrors of the mind (Pee, 1985), computers should allow students to express and communicate their mental models and to reflect on their own processes and products of learning; 6) Extend computer-based instruction from individual to cooperative contexts of learning.

(c) Condition of learning
Mathematical text, word, or story problems (MSPs), which are used to assess students’ application of mathematical knowledge and skills, consist of two interwoven semiotic worlds: a storylike description of a nonmathematical situation or event, and an implicit web of mathematical relations.

(d) Required media
Computer based programs or multimedia to support cognitive modeling process (e.g., HERON: a mouse-driven, graphics-based problem-solving tool for understanding and solving complex mathematical story problems.

(e) Role of facilitator
Essential roles of teachers include adaptive structural and procedural role models, domain experts and scaffolds for expert learning, and impulse givers and facilitators of learning.

(f) Instructional strategies
The process of mental representations generated in the Situation Problem Solver as follows:
1) a text base as a prepositional representation of the task extracted from the textual input
2) an episodic situation model as a goal- and task-specific, qualitative representation of the elaborated nonmathematical situation denoted by the story text
3) a mathematical problem model capturing the inferred gist of the mathematical situation, that is, the elements and relations of the episodic situation model that are relevant from the point of view of a mathematical question to be answered
4) a formal equation as the densest form of the mathematical situation inherent in a word problem.

(g) Assessment method
Assessment on problem solving process using computer-based tools: e.g., Solution Tree- a graphical format for problem representation and planning in HERON system. Solution Tree provides students with a constraining format for planning and generating their solutions and, for expressing their understanding of the problem in situational and mathematical forms.

Formative Research & Application
(a) Tested context: K-12 (Staub, Stebler, Reusser, & Pauli, 1994)
(b) Research method: Mixed
(c) Research description: Staub et al. (1994) compare pairs of fifth-grade students solving word problems with and without the HERON system in an intervention study. The results indicate that HERON was easily accepted by teachers and students, and that using the system was beneficial to the students in at least three ways: with respect to (a) an improvement in understanding and solving relatively complex story problems in a posttest, (b) the mindfulness of dialogue among the co-working students and (c) the quality of cooperation in maintaining a mutually shared understanding of the problem
(d) Resources
Reusser, K. (1990). From text to situation to equation: Cognitive simulation of understanding and solving mathematical word problems. In H. Mandl, E. De Corte, N. Bennett, & H. F. Friedrich (Eds.), learning and instruction in an international context (Vol. 2, pp. 477-498). NY: Pergamon

Reusser, K. (1996). From cognitive modeling to pedagogical tools. In S, Vosniadou, E. D. Corte, R. Glaser, & H. Mandl (Eds.), International perspectives on the design of technology-supported learning environments (pp. 81-103). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.

Staub, F. C., Stebler, R., Reusser, K., & Pauli, C. (1994, April). Improving understanding and solving of math story problems through collaborative use of a computer tool (HERON). Paper presented at the annual meeting of the American Educational Research Association AERA, New Orleans.