Part I. Experimental Studies: 2. Experiment in psychology 3. Experiments on perceiving III Experiments on imaging 4-8. Experiments on remembering: (a) The method of description (b) The method of repeated reproduction (c) The method of picture writing (d) The method of serial reproduction (e) The method of serial reproduction picture material 9. Perceiving, recognizing, remembering 10. A theory of remembering 11. Images and their functions 12. Meaning Part II. Remembering as a Study in Social Psychology: 13. Social psychology 14. Social psychology and the matter of recall 15. Social psychology and the manner of recall 16. Conventionalism 17. The notion of a collective unconscious 18. The basis of social recall 19. A summary and some conclusions.

Remembering. A Study in Experimental and Social Psychology, Cambridge (University Press) 1964.

In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

Thinking fast and slow.

The power of feedback.

/pdf/semi-supervised-learning-literature-survey-4ccxy3rmmj.pdf

Semi-Supervised Learning Literature Survey

Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: * Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. * Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.

Adding It Up: Helping Children Learn Mathematics

The authors propose that conceptual and procedural knowledge develop in an iterative fashion and that improved problem representation is 1 mechanism underlying the relations between them. Two experiments were conducted with 5th- and 6th-grade students learning about decimal fractions. In Experiment 1, children's initial conceptual knowledge predicted gains in procedural knowledge, and gains in procedural knowledge predicted improvements in conceptual knowledge. Correct problem representations mediated the relation between initial conceptual knowledge and improved procedural knowledge. In Experiment 2, amount of support for correct problem representation was experimentally manipulated, and the manipulations led to gains in procedural knowledge. Thus, conceptual and procedural knowledge develop iteratively, and improved problem representation is 1 mechanism in this process.

https://psych.wisc.edu/alibali/home/Publications_files/Rittle-JohnsonSieglerandAlibali2001.pdf

Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process.

Spontaneous gestures that accompany speech are related to both verbal and spatial processes We argue that gestures emerge from perceptual and motor simulations that underlie embodied language and mental imagery We first review current thinking about embodied cognition, embodied language, and embodied mental imagery We then provide evidence that gestures stem from spatial representations and mental images We then propose the gestures-as-simulated-action framework to explain how gestures might arise from an embodied cognitive system Finally, we compare this framework with other current models of gesture production, and we briefly outline predictions that derive from the framework

https://link.springer.com/content/pdf/10.3758/PBR.15.3.495.pdf

Visible embodiment: Gestures as simulated action

I. GENERAL PERSPECTIVES ON CHILDREN'S THINKING. 1. An Introduction to Children's Thinking. 2. Piaget's Theory of Development. 3. Information-Processing Theories of Development. 4. Sociocultural Theories of Development. II. SIX SPECIFIC ASPECTS OF CHILDREN'S THINKING. 5. Perceptual Development. 6. Language Development. 7. Memory Development. 8. Conceptual Development. 9. Social Cognition. 10. Problem Solving. 11. Development of Academic Skills. 12. Conclusions for the Present Challenges for the Future. References. Author Index. Subject Index.

Children's Thinking

ages understand and what they struggle to learn, and examine how instruction influences children's acquisition of both concepts and procedures. The purpose of the present study was to explore the relations between conceptual and procedural knowledge in children learning the principle that the two sides of an equation represent the same quantity. Specifically, the study investigated how instruction about the concept of mathematical equivalence influences children's problem-solving procedures and how instruction about a problem-solving procedure influences children's conceptual understanding of equivalence. In addressing these issues, we also identified what aspects of equivalence fourth- and fifth-grade students understand, what aspects they do not understand but can easily learn, and what aspects they have difficulty learning.

Conceptual and procedural knowledge of mathematics: Does one lead to the other?

Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based in perception and action, and it is grounded in the physical environment. We present evidence for each of these claims drawn from the gestures that teachers and learners produce when they explain mathematical concepts and ideas. We argue that (a) pointing gestures reflect the grounding of cognition in the physical environment, (b) representational gestures manifest mental simulations of action and perception, and (c) some metaphoric gestures reflect body-based conceptual metaphors. Thus, gestures reveal that some aspects of mathematical thinking are embodied.

Martha W. Alibali

Papers

Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process.

Visible embodiment: Gestures as simulated action

Children's Thinking

Conceptual and procedural knowledge of mathematics: Does one lead to the other?

Embodiment in Mathematics Teaching and Learning: Evidence From Learners' and Teachers' Gestures