Research on the different stages of instructional approach for young children, and how symbols play a role in learning and teaching
concrete-representation-abstract instructional approach
concrete stage: teacher begins instruction by modeling each mathematical concept with concrete materials
representational stage: may involve drawing pictures; using circles, dots... etc.
abstract stage: models concepts at a symbolic level, using only numbers
want to incorporate both concrete and representational, but omit the abstract; combination of the "doing" stage and the "seeing" stage
for example, to read and write fractions, the goal for teachers is to have the student develop the spatial organization, visually and kinesthetically
http://www.k8accesscenter.org/training_resources/CRA_Instructional_Approach.asp
Electronic Media, Attention, and Visual Spatial Skills
ie: Tetris, third graders experimental group showed improved scores on a paper&paper test of mental-rotation skills
Electronic Media and Problem-Solving Skills
transfer from television is possible, as long as 1. children must understand the content of the program; 2. must create an abstract mental representation of that content; 3. must remember the content and see its relation to the new problem; 4. must apply the remembered content to the new problem.
Fisch recommends program repetition of the same content in multiple contexts, to increase the likelihood of transfer of learning.
http://futureofchildren.org/futureofchildren/publications/journals/article/index.xml?journalid=32&articleid=57§ionid=256&submit
Child Psychology
concrete objects can help young children understand symbol-referant relations, but ultimate goal must remain to help children comprehend more abstract relations
the best concrete object symbols may well be ones that possess elements of their own destruction, designed to become less necessary or relevant as children come to understand the more abstract representation
http://books.google.com/books?id=reWupx_OJs8C&pg=PA190&lpg=PA190&dq=children+%22abstract+representation%22+cognition+OR+perception+OR+learning&source=bl&ots=0s0lpSbhdw&sig=rVzxft-9su7lvIIlaqC1ROS-T4c&hl=en&ei=lvCtTKSGHY60sAO6tqWvBw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCsQ6AEwAw#v=onepage&q=children%20%22abstract%20representation%22%20cognition%20OR%20perception%20OR%20learning&f=false
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