Two Types of Mathematical Knowledge and Their Relation

Robotics projects and learning concepts in science, technology and problem solving

“…Mathematics educators (Rittle-Johnson and Alibali 1999;Haapasalo and Kadijevich 2000;Ben-Hur 2006) regard procedural knowledge as the ability to answer questions or solve problems by manipulating particular rules, algorithms and procedures. In contrast, conceptual knowledge has to do with understanding general concepts and recognizing their application in various situations, or the ability to transfer knowledge between situations.…”

Associative and reflective connections between the limit of the difference quotient and limiting process

“…Thus, this classification into the associative and the reflective connections takes into account the crucial role of the consciousness emphasized by Hiebert and Lefevre (1986) and Haapasalo and Kadijevich (2000). Hiebert and Lefevre (1986) stress that a person's knowledge is conceptual only if he or she recognizes its connections to other pieces of knowledge (p. 4).…”

“…Hiebert and Lefevre (1986) stress that a person's knowledge is conceptual only if he or she recognizes its connections to other pieces of knowledge (p. 4). Haapasalo and Kadijevich (2000) highlight that the consciousness of the applied actions play a crucial role when distinguishing between the procedural and conceptual knowledge: procedural knowledge often calls for unconscious steps, but conceptual knowledge requires conscious thinking (p. 141). Therefore, the reflective connections seem to correspond to conceptual knowledge and the associative connections to procedural knowledge.…”

“…Connections, links, and relations between representations or pieces of knowledge as well as students' ability to move, change, or translate among representations are important characteristics of learning and problem solving (Dreyfus, 1991;Goldin, 1998;Haapasalo & Kadijevich, 2000;Hiebert & Lefevre, 1986;Tall & Vinner, 1981;Zimmermann, 2005). Many studies discuss the fact that students are able to make particular connections but few explain the distinctions between different types of connections.…”

Reading-enhanced word problem solving: a theoretical model

“…However, a balance of conceptual (comprehension) and procedural (syntax/semantics) skills is needed in instruction as students begin to solve math word problems. The majority of prior research and theory has focused on whether conceptual or procedural knowledge emerged first (e.g., Haapasalo and Kadijevich 2000;Rittle-Johnson et al 2001). This debate over which type of knowledge developed first tends to obscure the gradual development of conceptual and procedural knowledge, where each influences the other in integrated and mutually supportive ways.…”