Analysis of the Intended Mathematics Curriculum as Represented in State-Level Standards: Consensus or Confusion? Barbara J. Reys Center for the Study of Mathematics Curriculum The intended curriculum: What mathematics should students learn and when should they learn it?
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Center for the Study of Mathematics Curriculum
The intended curriculum: Represented in State-Level Standards:
What mathematics should students learn and when should they learn it?
Each state is required to:
Prior to NCLB, many states did not have curriculum standards that specified mathematics that students should learn (and what teachers should teach) at each grade level.
2006 4 states
2005 9 states
2004 13 states
2003 8 states
2002 4 states
2001 4 states
2000 2 states
pre-2000 7 states (FL, 1999)
For many states, their most recent curriculum standards represent increased specificity of learning expectations compared to previous standards.
The standards carry additional “weight” or influence since they are tied to NCLB-mandated annual assessments in grades 3-8.
Teachers and state department leaders acknowledge the increased influence of state standards in determining curriculum focus at the classroom level.
http://www.mathcurriculumcenter.org/states.php standards that specified mathematics that students should learn (and what teachers should teach) at each grade level.
To what extent are the elementary and middle (K-8) grade-level learning expectations described in state-level mathematics curriculum standards similar in terms of content and grade placement?
Example of Variation in grade-level learning expectations described in state-level mathematics curriculum standards similar in terms of content and grade placement?Number of GLEs (grain size)
Mean number of GLEs by grade level across all 42 state documents: 47
Grade placement variation regarding
Whole number computation
Emphasis on calculators/technology
The “national” 4th grade mathematics curriculum
*For this summary, we used the culminating learning expectation that indicated students were working with common and uncommon denominators when adding and subtracting fractions.
General Finding: subtract, multiply and divide fractions?*There exists considerable variation across the state curriculum standards with regard to the grade placement of key number and operation learning expectations.
Fordham Foundation conveyed within the state standards documents?(The State of Math Standards, 2005)
Searched all state-level elementary and middle grades GLE documents:
Our analysis of the state GLE documents does not support the finding of the Fordham Foundation report regarding emphasis on calculators.
- For teacher preparation and professional development?- For development of textbooks?- For comparisons of student performance?
At each grade, we recommend a general statement of major goals for the grade. These general goals may specify emphasis on a few strands of mathematics or a few topics within strands. These general goals should be coordinated across all grades, K-8, to ensure curricular coherence and comprehensiveness.
The set of learning expectations per grade-level should be manageable given the school year. Along with the statement of general goals and priorities for a particular grade, we suggest that the set of learning expectations per grade be limited to 20-25.
We recommend that learning expectations be expressed succinctly, coherently, and with optimum brevity, limiting the use of educational terms that may not communicate clearly to the intended audience of teachers, school leaders, and parents.
Provide guidance within particular learning goals or as part of an overall philosophical statement regarding the role of technology - specifying when it is an appropriate tool for computing and/or developing or representing mathematical ideas.
Fifty states with 50 state standards documents increases the likelihood of large textbooks that treat many topics superficially. In order to increase the likelihood of focused curriculum materials, states will need to work together to create some level of consensus about important learning goals and expectations at each grade.
Variation in learning goals across states directly influence the quality and coherence of commercially developed textbook materials. It also limits our ability to develop and provide focused professional development for teachers.
Many models of curriculum standards exist for review, refinement and/or adoption.
Full report of the study will be available in October 2006. on mathematics to be learned
Information Age Publishing Company:
http://mathcurriculumcenter.org on mathematics to be learned`