The cerebellum-driven\xa0social basis of mathematics: implications for one-on-one tutoring of children with mathematics learning disabilities

Larry Vandervert,Kimberly Moe

doi:10.1186/s40673-021-00136-2

Abstract

The purpose of this article is to argue that the patterns of sequence control over kinematics (movements) and dynamics (forces) which evolved in phonological processing in inner speech during the evolution of the social-cognitive capacities behind stone-tool making that led to the emergence of Homo sapiens are homologous to the social cerebellum’s capacity to learn patterns of sequence within language that we refer to as mathematics. It is argued that this evolution (1) selected toward a social cognitive cerebellum which arose from the arduous, repetitive precision patterns of knapping (stone shaping) and (2) that over a period of a million-plus years was selected from mentalizing toward the kinematics and dynamics as observed and modeled in Theory of Mind (ToM) of more experienced stone knappers. It is concluded that components of this socially-induced autobiographical knowledge, namely, (1) segmenting events, (2) sequencing events, and (3) sequencing event clusters, all at various levels of abstraction, can inform optimum approaches to one-on-one tutoring of children with mathematical learning disabilities.

Highlights

Based on the works of Ito [1,2,3,4], Leiner, Leiner and Dow [5, 6], Leggio and Molinari [7], Van Overwalle and Mariën [8] and Van Overwalle et al [9], Vandervert [10,11,12] proposed that the foundations of our scientific knowledge of patterns that constitutes mathematics1 evolved in the human brain during approximately 1.7 million years of rigorous, repetitive social interaction required in stone-tool making
Within this perspective, it is further argued that the learning of mathematics, like the learning of stone-tool making, takes place predominately in cerebellar internal models of inner speech in the child that are based on patterns of the kinematics and dynamics of social interaction as modeled in Theories of Mind (ToM) of the teacher
The efficacy of one-on-one teaching/learning of mathematics (e.g., [19]) is predominantly (1) based on the learning of constantly new phonological representations in inner speech, and (2) this phonological process can be optimized in children with mathematics learning disabilities (MLDs) including dyscalculia when taught with an emphasis on (ToM) autobiographical components identified by Van Overwalle et al [9]

Summary

Introduction

Based on the works of Ito [1,2,3,4], Leiner, Leiner and Dow [5, 6], Leggio and Molinari [7], Van Overwalle and Mariën [8] and Van Overwalle et al [9], Vandervert [10,11,12] proposed that the foundations of our scientific knowledge of patterns that constitutes mathematics evolved in the human brain during approximately 1.7 million years of rigorous, repetitive social interaction required in stone-tool making Within this theoretical perspective he argued that the patterns which constitute mathematics (1) evolved in cerebellar internal models of repetitive patterns of sequences (a la [7]) of detailed cause-and-effect related kinematics and dynamics of socially modeled stone-tool making [12] and (2) evolved as the basis for mentalized forms of knowledge [within Theory of Mind (ToM)]through the phonological loop of inner speech representing the socially modeled kinematics and dynamics of other bodies in (1). Within this perspective, it is further argued that the learning of mathematics, like the learning of stone-tool making, takes place predominately in cerebellar internal models of inner speech in the child that are based on patterns of the kinematics and dynamics of social interaction as modeled in Theories of Mind (ToM) of the teacher. Third, it is proposed that the efficacy of one-on-one teaching/learning of mathematics (e.g., [19]) is predominantly (1) based on the learning of constantly new phonological representations (new words) in inner speech, and (2) this phonological process can be optimized in children with mathematics learning disabilities (MLDs) including dyscalculia when taught with an emphasis on (ToM) autobiographical components identified by Van Overwalle et al [9]

Objectives

Conclusion