17-04-2014, 12:56 PM
Mental Models for Math
Mental Models.pdf (Size: 1.19 MB / Downloads: 34)
Introduction
This workbook contains examples of mental models that teachers in middle school
through high school can use in explaining mathematical concepts.
The following information, taken from Understanding Learning: the How, the Why, the
What by Dr. Ruby K. Payne, explains the characteristics and purposes of mental models.
• Mental models are how the mind holds abstract information, i.e., information that
has no sensory representation.
• All subject areas or disciplines have their own blueprint or mental models.
• Mental models tell us what is and is not important in the discipline. They help the
mind to sort.
• Mental models often explain the “why” of things working the way they do.
• Mental models tell the structure, purpose, or pattern of the discipline.
• Mental models are held in the mind as stories, analogies, movements, or
two-dimensional drawings.
• Mental models “collapse” the amount of time it takes to teach/learn something.
Movement Mental Models
An example of a movement mental model in
mathematics is where students use a smile and
frown to identify right-side-up and upside-down
parabolas. If the parabola opens up, the leading
coefficient is positive and matches the smile.
If the parabola opens down, the leading coefficient
is negative and matches the frown. A movement
mental model reflects a concept, generalization,
or discipline.