The epigenesis of mathematical thinking

By Rochel Gelman. 2000

70 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3060ae7804975cc9ae7ece5d0194b09ae420db50

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Education

In Statistics and Probability

Citations in the corpus

The Early Childhood Mathematics Education Revolution (2013, background): “A substantial body of research today holds that human brains are neurally programmed for basic number sense from birth (Gelman, 2000), and a common system of number representation is present and functional in 6-month-old infants (Xu, Spelke, & Goddard, 2005).”
Negative Integer Understanding: Characterizing First Graders' Mental Models (2014, background): “If asked to determine how many objects are in a small set, children reasoning at the predimensional level can use their enumeration structure to count the objects and identify the last word in the count as the cardinality of the set of objects or identify if someone has failed to complete this proce”
Mathematics Education for Young Children: What It is and How to Promote It (2008, background): “As Gelman (2000) puts it, “We can think of young children as self-monitoring learning machines who are inclined to learn on the fl y, even when they are not in school and regardless of whether they are with adults” (p. 26).”
Inhibiting natural knowledge in fourth graders: towards a comprehensive test instrument (2015, background): “This can result in problems and misconceptions when rational numbers are introduced, because the characteristics and rules accounting for rational numbers do not always correspond with those for natural numbers (Gelman 2000; Saxe et al. 2013; Smith et al. 2005; Vamvakoussi and Vosniadou 2004).”
How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation (2010, background): “Based on relevant empirical studies, Gelman ( 1994 , 2000 ) concludes that children by four or five years of age possess a principled understanding of number as counting number, which supports them to “invent solutions to novel counting problems, detect errors in counting trails generated by others”
Understanding the structure of the set of rational numbers: a conceptual change approach (2004, background): “There is increasing evidence from research with animals, human infants and individuals from different cultures (Butterworth, 1999; Dehaene, 1998; Gelman, 2000; Lipton & Spelke, 2003) that the domain of number is sustained by a specific, innately determined system.”
Defining Early Number Sense: A participatory Australian study (2005, background): “The informal mathematics of young children has been studied extensively; general conclusions are that children from different cultural and socio-economic backgrounds proceed through the same developmental pathway in their early intuitive understanding of mathematics ( Gelman, 2000; Ginsburg, 1982, ”
What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra (2012, background): “Students' number knowledge is based on their initial experience with counting numbers (see Gelman, 2000 ).”
Young children can add and subtract by predicting and checking (2004, background): “However, at that same young age, they can solve addition and subtraction problems with small numbers (e.g.,G lman, 1972; Hughes, 1981; Starkey & Gelman, 1982).”
Extending the conceptual change approach to mathematics learning and teaching (2004, background): “…based (developed through a long process of evol- ution), and that consists of certain core principles or presuppositions (such as the presupposition of discreteness in the number concept) that facilitate some kinds of learning but inhibit others (Dehaene, 1998; Gelman, 2000; Lipton & Spelke, 2003).”
Young American and Chinese Children's Everyday Mathematical Activity (2003, background): “It includes principles of counting that on one view develop from “skeletal” biological structures (Gelman, 2000).”
How Many Numbers are there in a Rational Numbers Interval? Constraints, Synthetic Models and the Effect of the Number Line (2007, background): “It has been argued that even before instruction children form a principled understanding of number that has its roots in the act of counting ( Gelman, 2000; Gelman & Gallistel, 1978).”
Naturally Biased? In Search for Reaction Time Evidence for a Natural Number Bias in Adults. (2012, background): “Similarly, the density tasks targeted a major conceptual difficulty in the shift from natural to rational numbers relating to the change from discrete to dense ordering (Gelman, 2000; Smith et al., 2005; Vamvakoussi & Vosniadou, 2010).”
What Fills the Gap between Discrete and Dense? Greek and Flemish Students' Understanding of Density. (2011, background): “From the students’ point of view, numbers are essentially discrete counting numbers that obey the successor principle and are grounded in additive reasoning (Vosniadou et al., 2008; see also Gelman, 2000; Ni & Zhou, 2005; Smith et al., 2005).”