the mathematics curriculum k-12

1、a standards-based search for coherencejohn a. dosseyillinois state universityjeremy kilpatrickuniversity of georgiacurriculum not just a syllabus or textbook includes aims content methods assessment procedures depends on ones position plan experience a linear path through a multi-dimensional domainw

2、hat is a curriculum? a plan of action directing the content and delivery of a program of mathematics learning for a specified group of students this plan consists of an articulated set of statements that provide: general goals for the plan a structure of content domains and cognitive processes to be

3、 developed a philosophy concerning the general conditions of learning expected a listing of general standards and specific outcomes of learning related to levels of schooling germane to the population for which the curriculum is intendedthe importance of mission“a discussion of mathematical educatio

4、n, and of ways and means of enhancing its value, a precise and comprehensive formulation of the of such education. only on such basis can we approach intelligently the problems relating to the selection and organization of material, the methods of teaching and the point of view which should govern i

5、nstruction.” (the reorganization of mathematics in secondary education, 1923)source of goalssociety/workforcedisciplinepsychologymathematics educationassessmentsmost curricula do not answer who?, what?, where?, why? situating a curriculum nctm and pisa discuss: personal life, workplace, cultural and

6、 societal, and scientific and technological. college board standards for college success: mathematics and statistics: “college board presents these standards as a guide to provide all students with the rigorous education that will prepare them for success in college, opportunity in the workplace, an

7、d effective participation in civic life.”recommendation 1 what is the purpose of the curriculum? who is it to serve? what are the intended outcomes in: broad brush strokes (overview) unit level content and processes (teachers and materials) specific concepts, principles, and skills (specialist and r

8、esource guide level)previous periods of curricular reform early 1900scommissions . late 1950slate 60s“new math” late 1980s90sstandards early 2000s based on assessmentstoday & recent past nclb and state “curriculum” reforms college boards standards for college success: mathematics and statistics (200

9、9) nctm curriculum focal points (pre-k8) (2006) & focus in high school mathematics: reasoning and sense making (912) (2009) nga & ccsso release draft of college- and career-readiness standards (2009), the first stage of the common core state standards initiative - a move toward a curriculumhttp:/www

10、./structuring a curriculum how are the “levels” laid out? how is the “content” divided? how are the “processes” described and interwoven? how is knowledge itself related to intended learning (and to envisioned pedagogy)? problems: connection linearity differentiation choiceproviding

11、 structurecontent content domainsdomainscognitivecognitiveprocessesprocessescontent domains number & operations algebra & functions geometry & transformations measurement data analysis chance be careful to: avoid straying too far from a concise list because that rapidly leads to a lack of focus make

12、 sure there are ample areas to connect!e.g., algebra is algebra? margaret kendal and kaye stacey in the future of the teaching and learning of algebra: the 12th icmi study (stacey et al., 2004): “dont take your countrys curriculum and approach to teaching algebra for granted and dont assume all othe

13、r educational jurisdictions operate in a similar waythey conspicuously do not.” striking differences in who takes algebra whether integrated or layered across years emphasis put on generality and pattern attention to symbolism, formalism, and abstraction whether approached through functions and mult

14、iple representations role played by technologyinterconnected content domains & cognitive processescontentdomainsconceptsrelationshipsprocedurefactsrecommendation 2 keep the lists of content and processes focused and concise do not stray greatly from current models without strong justificationit just

15、 makes work for teachers and costs moneylittle real change make sure statements of goals, standards, and outcomes have clarity and reflect a range of cognitive processesa philosophy of pedagogy reasoning and sense making teaching should value and emphasize reflective reasoning (sense making) on the

16、part of the student in order to promote construction of new mathematical concepts based on previously learned concepts and new ideas. teaching should help students see the need for justifying their work and help students to develop justification strategies. problem solving and mathematical modeling

17、teaching should engage students in solving open-ended problems, in groups and individually, to illustrate the need for mathematics and demonstrate the connectedness of mathematical ideas. teaching with a problem-solving approach should encourage students to investigate mathematical models as a vehic

18、le for analyzing problems, making sense of related content and structures, and finding problem solutions.a philosophy of pedagogy (cont.) multiple perspectives teaching should develop students capabilities to look at mathematical situations and outcomes from multiple perspectives, compare and critiq

19、ue methods, and reflect on the value of each. teaching mathematics should encourage students to employ appropriate tools and techniques such as computing, graphing, and other analytical methods. mathematical autonomy teaching mathematics should support student development and ownership of mathematic

20、al ideas. teaching mathematics should strengthen students capability to illustrate and communicate their mathematical ideas, imbuing each student with the belief that they have the foundations and related capabilities required to succeed in mathematics.pedagogical framework while the instructional implementation is a partially separate matter, a broad statement of the boundaries and shape of the program should be included. “what you learn reflects how you learned it.” such a framework also reflects the approaches and conditions for achieving “depth of unde