Developmental Continuum for Mathematics
Developmental Continuum for Mathematics (.doc) prints on legal size sheet 11''x 14 ''
Developmental Continuum for Mathematics (.pdf) prints on legal size sheet 11" x 14" at 100% / 8.5" x 11" at 67.1%
Portraits of Mathematicians (.doc)
Mathematics Developmental Continuum by Discovery School is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Based on a work at www.discovery-school.org.
Permissions beyond the scope of this license may be available at www.discovery-school.org.
The Creation Process
Discovery School began using the Developmental Continuums for Reading and Writing by Bonnie Campbell Hill in fall, 2006, following a one-and-half-year staff development process. Discovery School embraced a child-centered, constructivist, developmental philosophy of teaching and learning in our classrooms and sought out an assessment tool to match and facilitate demonstrating growth over the course of a student’s career at the school.
In 2009, after successfully using the Continuums for Reading and Writing for 3 years, the school faculty began a curriculum review of Mathematics with an eye to potentially creating a parallel document, a Developmental Continuum for Mathematics. The process which the staff worked through was to first analyze and list the current mathematics curriculum, identifying skills, and listing when students are exposed, introduced, develop and practice, and master each skill and concept. With this raw data, teachers discussed any inconsistencies and also reviewed the current NCTM standards for correlations. During the second year of work those long lists of skills were mined for core concept development. Next we had considerable discussion about the nature of mastery in mathematics and the issues of re-visiting and building on skills and concepts (spiraling curriculum). We found and embraced the document from NCTM/California State Standards about “mathematical apprenticeships,” defining the role of problem solving and inquiry in mathematics teaching/learning. We arrived at terms, which are in the continuum - with guidance (skill introduced), demonstrates skills (develop and practice), and demonstrates skills independently (mastery, maintain, and apply) – to distinguish a student’s progress with various skills. This language is also found in the continuums for reading and writing. Finally we wrote Profiles of the Mathematicians at each of the levels, using the same levels as the reading and writing continuums. After considerable editing to get everything to fit onto a page of legal size paper, the final product is done.
Unfortunately the school, an independent, not-for-profit corp., was struggling during the hard economic times and had to close for lack of sufficient tuition-paying students. We have decided to publish this assessment tool with a Creative Commons license to allow its use by other educators and schools and to share our work and inspiration. You are allowed to use the Continuum, and attribute its development, and you may adapt it for your specific setting. No commercial product will be allowed, this is a share and share alike of the work of fellow educators.