To completely understand the Iowa Core standards for mathematics you must first explore the 3 shifts in the mathematics standards: focus, coherence and rigor.
Focus
Focus strongly where the standards focus.
The Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom.
We focus deeply on the major work of each grade so that students can gain strong foundations:
conceptual understanding
procedural skill and fluency
apply math to solve real-world problems
Focus looks different in high school. Rather than eliminating topics, we focus on the structure that ties them together.
Think across grades and link to major topics within grades
Through coherence, we take advantage of focus to actually pay attention to sense-making in math. Coherence speaks to the idea that math does not consist of a list of isolated topics.
The Standards themselves, including curriculum and instruction, should:
Build new understanding on foundations built in previous years
Begin with conceptual understanding of core content
Recognize that each standard is not a new event, but an extension of previous learning
Appendix A - Common Core State Standards for Mathematics
At the high school level, standards are not organized by grade level, but instead by conceptual categories. Appendix A is a useful resource to illustrate possible approaches to organizing the content of the Iowa Core into coherent and rigorous courses that lead to college and career readiness.
In major topics, pursue conceptual understanding, procedural skill & fluency, and application with equal intensity.
The Common Core Shift of Rigor doesn't just mean "harder" or "trickier", but a balance of conceptual understanding, procedural skill and fluency, and application in math instruction. All three components need to be addressed for students to be able to reach the depth of learning that is expected by the Iowa Core.
The three aspects of rigor are not always separate. Conceptual understanding provides the foundation for fluency work; fluency can be practiced in the context of applications; and applications can build conceptual understanding. Nor are the three aspects of rigor always together. Fluency requires dedicated practice. Rich applications cannot always be squeezed into the mathematical topic of the day.
It is important that all students have access to grade level instruction based on the Iowa Core mathematics standards. High-quality mathematics instruction has an intentional lesson design that engages teachers and students in mathematical practices to promote reasoning and problem solving, mathematical discourse, and procedural fluency built upon conceptual understanding.
A balanced assessment system is critical to supporting students’ success in mathematics. A balanced assessment system includes: universal screening, progress monitoring, diagnostic, formative and summative assessments. Formative Assessment
Universal Screeners
Universal Screeners Reviewed List
Universal screening assessments are characterized by the administration of quick, low-cost, repeatable testing of age-appropriate skills typically administered to all students three times a year.
This is not meant to be a complete list of screeners available. Keystone neither endorses nor recommends a particular screener.
Universal Screeners List (coming soon)
Questions on Universal Screeners can be directed to Keystone math consultants: Sarah Sieck or Gertie Monat.
Diagnostic
Diagnostic assessment is a distinct form of measurement, used to evaluate the exact skills a student has and does not have in order to plan for intervention.
Diagnostic Assessment List (coming soon)
PLEASE NOTE: Some diagnostic assessments could act as interventions.
Additional instruction and support may be necessary for students to be successful in grade-level content. Math intervention consists of both classwide and small-group intervention based on the needs of individual students and classrooms.
Principles and Standards for School Mathematics (NCTM, 2000) states, “Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose,understand and can explain these methods, and produce accurate answers efficiently.”
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