Plenary Address: Language and Mathematics, A Model for Mathematics in the 21 st Century

"Human language and thought are crucially shaped by the properties of our bodies and the structure of our physical and social environment. Language and thought are not best studied as formal mathematics and logic, but as adaptations that enable creatures like us to thrive in a wide range of situations" (Feldman, 2006, p. 7). Language and Mathematics: A Complex Symbiotic for Learning In order to know how to use this language correctly requires an integrated knowledge of multiple facets of communicative competence and mathematical knowledge. Walshaw and Anthony Explicating a Model Language and competence in mathematics are not separable. The model that is presented in this paper [See (2) Heuristic methods, i.e., search strategies for problem analysis and transformation (e.g., decomposing a problem into subgoals, making a graphic representation of a problem) which do not guarantee, but significantly increase the probability of finding the correct solution. (3) Meta-knowledge, which involves knowledge about one's cognitive functioning (metacognitive knowledge; e.g., knowing that one's cognitive potential can be developed through learning and effort), on the one hand, and knowledge about one's motivation and emotions (metavolitional knowledge; e.g., becoming aware of one's fear of failure when confronted with a complex mathematical task or problem), on the other hand. (4) Positive mathematics-related beliefs, which include the implicitly and explicitly held subjective conceptions about mathematics education, about the self as a learner of mathematics, and about the social context of the mathematics classroom. (5) Self-regulatory skills, which embrace skills relating to the self-regulation of one's cognitive processes (metacognitive skills or cognitive self-regulation; e.g., planning and monitoring one's problem-solving processes), on the one hand, and skills for regulating one's volitional processes/activities (metavolitional skills or volitional self-regulation; e.g., keeping up one's attention and motivation to solve a given problem), on the other hand. (p. 20-21)