Research & News

Dream Realizations follows current events and research in the field of mathematics and cognitive function relevant to subQuan.
Excerpts from Doug Clements "Subitizing: What is it? Why teach it?' (1999)

Three pictures hang in front of a six-month-old child. The first shows two dots, the others show one dot and three dots. The infant hears three drumbeats. Her eyes move to the picture with three dots.

Young children spontaneously use the ability to recognize and discriminate small numbers of objects (Klein and Starkey 1988).

Fitzhugh (1978) found that some children could subitize sets of one or two but were not able to count them. None of these very young children, however, was able to count any sets that he or she could not subitize. She concluded that subitizing is a necessary precursor to counting.

Others agreed that children develop subitizing later, as a shortcut to counting (Beckwith and Restle 1966; Brownell 1928; Silverman and Rose 1980). In this view subitizing is a form of rapid counting (Gelman and Gallistel 1978).

Researchers still dispute the basis for subitizing ability, with patterns and attentional mechanisms the main explanations (Chi and Klahr 1975; Mandler and Shebo 1982; von Glaserfeld 1982).

People are capable of viewing number and number patterns as units of units (Steffe and Cobb 1988). They can see the domino as composed of two groups of four and as "one eight".

"Subitizing is a fundamental skill in the development of students' understanding of number" (Baroody 1987, 115). Students can use pattern recognition to discover essential properties of number, such as conservation and compensation. They can develop such capabilities as unitizing, counting on, and composing and decomposing numbers, as well as their understanding of arithmetic and place value - all valuable components of number sense.

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Excerpt from the
A revolution in public education (8.20.2013)

• Recognition networks, the “what” of learning (how different learners pick up information). Since all learners perceive and comprehend information differently (there is no such thing as an average learner), there is no one way to represent information that will be successfully received by all learners. Consequently, presenting information and content in different ways, allows learning to occur.

Action and expression networks, the “how” of learning (how different learners act, demonstrate, express what they learned). Since all learners vary greatly in how they demonstrate what they learned, (again, there is no such thing as an average learner) there is no one means of expression that is optimal for all learners. Thus providing multiple ways for learners to express what they know, allows all learners to demonstrate their knowledge.

Engagement networks, the “why” of learning (how different learners get engaged/get excited or motivated by the learning situation). Since all learners vary greatly in ways that they can be engaged or motivated to learn, there is no one means of engagement that will be optimal for all learners. Providing multiple options of engagement allows learning to occur.

Based on these three key principles, teachers around the country are beginning to reassess how they design their goals, methods and materials in the classroom.

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