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Many of those who remain committed to Jean Piaget's cognitive developmental theory see important implications for our conceptions of readiness for formal aspects of school learning. The general principle of strong correlations between measures of cognitive development and school achievement is complemented by Piaget's proposal of a hierarchical sequence of four cognitive developmental stages: sensori-motor, pre-operational, concrete operational, and formal operational stages. In many Western school systems, the timing of the movement of children from the informal learning settings of kindergarten and pre-school to the first year of formal curriculum-based learning in primary or grade school coincides with the transition from pre-operational to concrete operational modes of thinking. Furthermore, the change in curriculum demands of theoretical mathematics, language, and science learning (for example) in high schools or secondary schools often occurs as students' minds are claimed to be in transition from concrete operational to formal operational thinking. However, whereas the timing of the school transitions is remarkably age-determined, the corresponding cognitive developmental transitions are merely age-related.

Three particularly important and widely implemented pedagogical outcomes of the study of cognitive developmental theory have been the play-based nature of preschool learning experiences, the hands-on approach to mathematics learning in the grade school years, and a problem-solving approach to high school science curricula. For almost two decades, two key U.S. journals, the Journal for Research Into Science Teaching and Science Education, were dominated by reports on the relationships between high school science learning and formal operational thinking. Researchers such as Anton Lawson, Warren Wollman, and Robert Karplus were foremost among researchers of that era. Although many would observe that the Piagetian influence in science education is well past its zenith in the United States, that is not the case in the United Kingdom, and that is certainly not the case for preschool education. The remarkable success of the team of Michael Shayer in the United Kingdom in applications to high school science pedagogy, in particular, and education in general, shows the benefit of theoretically informed long-term commitment. Preservice education of early years teachers remains under the sway of the Piagetian oeuvre and the early influence of Constance Kamii has been continued by others, such as Rheta Devries and Betty Zan.

Readiness for High School Science

Shayer and part of the Concepts in Secondary Mathematics and Science team at the University of London devised a cognitive demand taxonomy directly from the Barbel Inhelder and Jean Piaget book on the development of formal thought and used it to estimate the intellectual demands of the U.K. national high school science curriculum. Their subsequent representative national survey of children's cognitive development revealed a pedagogically important mismatch between the cognitive demands of the science syllabus content and the cognitive developmental capacity of high school students in the United Kingdom to understand that material. Therein lies the conceptualization of the relationship between cognitive development and lesson content as it relates to school readiness: The cognitive demands of the formal curriculum exceed the cognitive capacity of many students who have been promoted into that new school setting on the basis of some age-determined criterion. Two alternate resolutions for this mismatch seem possible in order to address the readiness for learning issue: reduce, reorganize, or reschedule the cognitive demands of the curriculum for all/many/some learners; or promote the students on the basis of cognitive readiness for learning rather than by age. In the face of intransigence of curriculum experts, or, in the U.K. situation, the demands of university entrance exams, a third, much more radical, solution seemed appropriate to Shayer's team. They developed the Thinking Science intervention to maximize the development of formal operational thinking structures in middle school and junior high school students. Really Raising Standards reported that not only were cognitive development rates improved, but students who received the special thought-provoking lessons later outperformed controls in science, mathematics, and language on the national public examinations used to decide access to universities. Lorna Endler found similar results for her replication of the project in Australia, which prompted a district-wide Goals 2000 implementation in Oregon in the United States. Stanbridge's research on her own radical constructivist science teaching over almost a decade revealed that understanding of core physical science concepts was constrained by the level of cognitive development of the learner; a cognitive ceiling on achievement was implied by Panizzon's research with high school, college, and university students.

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