Ecological dynamics as a theory of mathematics learning: mathematical concepts emerge from guided discovery of sensorimotor schemes oriented on attentional anchors¶

Theory · All theories
Evidence · no claims cited

Description¶

Ecological dynamics blends dynamical systems theory and ecological psychology's theory of affordances; the article applies it to mathematics education, modeling learning as 'the complex and adaptive self-organizing of subject –environment dynamical systems' rather than as sequences of disembodied symbolic propositions. On this view, mathematical meanings are cultural constructs that agents build by developing and then signifying motor-action coordinations oriented on discovered attentional anchors. The authors contend the framework offers tools for designing, implementing, and analyzing pedagogical interactions in embodied-interaction environments, and position it as extending constructivist and socio-cultural perspectives.

Design Implications¶

Context¶

Requirements¶

• Learning environments must present situated motor-action problems whose solution is a target sensorimotor scheme, with semiotic means interpolated into the action problem space afterwards

Constraints¶

• The article notes extant frameworks lack analytical specificity for sensorimotor schemes, and the authors' focus on motor-action coordination is not a disavowal of the symbolic register's formative role

Target Learners¶

• Grade 4–6 mathematics students

Target Learning Objectives¶

• proportional equivalence and proportional reasoning

Claims¶

• Students Discover Interval Attentional Anchor Mitp [+M]

Related Theories¶

• Affordance-based assessment framework: linguistic ability as emergent property of organism-environment interaction

Examples¶

• Mathematical Imagery Trainer for Proportion (MIT-P): an embodied-interaction environment where the screen turns green only when cursor heights relate by a target ratio
• Tutor–student co-enactment: distribute or co-operate the control devices, negotiate leadership silently, and progressively hand over agency until the student solo-enacts

Key Sources¶

• Dor Abrahamson & Raúl Sánchez–García. (2015). A Call to Action: Towards an Ecological-Dynamics Theory of Mathematics Learning, Teaching, and Design. Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. http://www.tinyurl.com/FreeMITP