Article

Rethinking what is "developmentally appropriate" from a learning progression perspective: The power and the challenge

Review of Science, Mathematics and ICT Education 01/2009;
Source: DOAJ

ABSTRACT Learning progressions have recently become increasingly visible in studies of learning and instruction in science. In this essay, I explore the power and considerable challenges in rethinking what may be developmentally appropriate for young children's learning science from the perspective of learning progressions. In particular, I examine the issues of: a) the design of promising learning progressions within the vast design space of potential progressions; b) identification of cognitive resources relevant to a progression; c) analysis of effort / payoff for particular competencies at different points in the progression; d) attribution of cognitive limitations and achievements; e) coordination and collaboration needed to support the design, utilization, and refinement of the learning progression; and f) absence of straightforward correspondence between a learning progression and trajectories of different children's knowledge-development.

0 Bookmarks
 · 
86 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: The goal of this classroom study of third-grade students was to support and document the emergence of multiple senses of mathematical similarity. Beginning with grounding metaphors of scale, magnification, and classification, the classroom teacher helped students redescribe their perceptions of these everyday experiences with the mathematics of similarity. Each sense of similarity was mediated by a distinct form of mathematical inscription: a ratio, an algebraic "rule," and a line in a Cartesian system. These forms of inscription were tools for externalizing and structuring children's perceptions of magnification and scale ("growing") and of classification ("same shape"). Children's interpretations of the mathematical meanings of the notational systems employed were supported by successive forms of signification, which Peirce (1898/1992) described as iconic, indexical, and symbolic. We tracked student sense making through 2 sequences of lessons, first involving 2- and then 3-dimensional forms. The shift in dimension supported students' integration of multiple senses of similarity as ratio and as-scale. The process of integration was assisted by resonances among diverse forms of inscription. Students' explorations of similarity served later in the year as a resource for modeling nature (e.g., by conducting explorations of density and growth). This shift toward modeling introduced a troublesome, yet ultimately rewarding, epistemological dissonance between mathematics and science. Postinstructional interviews suggested that most children came to appreciate the mathematical generalizations afforded by the algebraic and graphical forms of notation used to inscribe similar forms. A follow-up design experiment conducted in the fifth grade included some revisions to instruction that proved fruitful. Our concluding comments about design experiments and developmental corridors are motivated by a need to rethink these ideas in light of the contingent and historical nature of student thinking as it unfolded in these classrooms.
    Cognition And Instruction. 01/2002; 20(3):359-398.
  • Resonance 10(7).
  • [Show abstract] [Hide abstract]
    ABSTRACT: American high schools have never been under more pressure to reform: student populations are more diverse than ever, resources are limited, and teachers are expected to teach to high standards for all students. While many reformers look for change at the state or district level, the authors here argue that the most local contexts—schools, departments, and communities—matter the most to how well teachers perform in the classroom and how satisfied they are professionally. Their findings—based on one of the most extensive research projects ever done on secondary teaching—show that departmental cultures play a crucial role in classroom settings and expectations. In the same school, for example, social studies teachers described their students as "apathetic and unwilling to work," while English teachers described the same students as "bright, interesting, and energetic." With wide-ranging implications for educational practice and policy, this unprecedented look into teacher communities is essential reading for educators, administrators, and all those concerned with U. S. High Schools.
    The History Teacher 05/2003;

Full-text

View
3 Downloads