Key Developmental Understandings in Mathematics: A Direction for Investigating and Establishing Learning Goals

By Martin A. Simon. 2006

194 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b19d7c11f9cc86f27da937189de3f70ff909a517

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Education

1. R. Vukovic
2. H. Johnson
3. C. Byerley
4. Patrick Thompson
5. Amy J. Hackenberg
6. P. Barmby
7. John Mason
8. Linda Siegel

In Statistics and Probability

1. R. Vukovic
2. C. Byerley
3. H. Johnson
4. Amy J. Hackenberg
5. P. Barmby
6. John Mason
7. Linda Siegel
8. Steven I. Higgins

Citations in the corpus

• Academic and Cognitive Characteristics of Persistent Mathematics Difficulty from First through Fourth Grade (2010, background): “There is growing recognition that traditional mathematics instruction that emphasizes skill and fact learning at the expense of developing children’s conceptual understanding does not lead to mathematically literate citizens (e.g., National Council of Teachers of Mathematics, 2000; Nunes, Schliemann”
• The array representation and primary children’s understanding and reasoning in multiplication (2009, methodology): “We can relate this to the notion of ‘key development understandings’ (KDUs), defined by Simon (2006 ) a s”
• Together yet separate: Students’ associating amounts of change in quantities involved in rate of change (2015, background): “…by the squareness example, a ratio as measure conception is more powerful than an identical groups conception of ratio, because it involves a conception of ratio as a single quantity, and thereby supports students’ deep understanding of other mathematical concepts, such as slope (Simon, 2006).”
• Mathematics Difficulty with and without Reading Difficulty: Findings and Implications from a Four-Year Longitudinal Study (2012, background): “Recognition is growing that traditional mathematics instruction that emphasizes skill and fact learning at the expense of developing children’s conceptual understanding does not lead to mathematical proficiency (e.g., National Council of Teachers of Mathematics, 2000; Simon, 2006).”
• The Actor-Oriented Transfer Perspective and Its Contributions to Educational Research and Practice (2012, background): “Partly, this is because what is challenging for students to understand early on in their development of an idea is often no longer apparent to an adult looking through the lens of sophisticated understanding (Simon, 2006).”
• NOTICING: Roots and Branches (2011, methodology): “For example, Simon (2006) described a conceptual advance as “one that changes students’ ability to think about and/or perceive particular mathematical relationships” (p. 362).”
• Secondary mathematics teachers’ meanings for measure, slope, and rate of change (2017, background): “Silverman and Thompson (2008) expanded this schemebased meaning of MKT by examining how teachers might create what they called Key Pedagogical Understandings from a basis of their personal, well-formed schemes— schemes which Simon (2006) called Key Developmental Understandings.”
• Students’ Reasoning With Reversible Multiplicative Relationships (2010, background): “In Silverman and Thompson's view of MKT, a first (but insufficient) step in its development is the construction of key developmental understandings ( Simon, 2006 ) in a particular mathematical area.”