Math
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Math Shifts
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.
2020-2021 Priority Instruction Content for Mathematics
Coherence
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
- Set students up for success in high school
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.
Rigor
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.
Standards
Designing High School Mathematics Courses Based on the Common Core State Standards (Appendix A)
Standards for Mathematical Practice by Grade Level
- Preschool SMPs
- Grades K-5 (PDF)
- Grades 5-12 (PDF)
- Standards for Mathematical Practice Progression through Grade Levels (PDF)
- Standards for Mathematical Practice Grade Level Emphasis (PDF)
- Standards for Mathematical Practice Questions for Teachers to Ask (PDF)
- Standards for Mathematical Practice I Can Statements (Elementary Level) (PDF)
- Standards for Mathematical Practice Look-Fors (Kansas) (PDF)
- Standards for Mathematical Practice Look-Fors (NCSM) (PDF)
Universal Instruction
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.
Instructional Practices in Mathematics
8 Mathematical Teaching Practices (coming soon)
Number Sense Routine (coming soon)
Assessment
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.
Progress Monitoring
Intervention Central Math Worksheet Generator
Create probes/worksheets by skill; can include more than one skill; choose number of problems
Basic Fact Assessment Considerations (Kling & Bay-Williams):
- Flexibility
- Efficiency
- Appropriate strategy use
- Accuracy
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.
13 Rules that Expire (Elementary) from National Council of Teachers of Mathematics
12 Rules that Expire (Middle School) from National Council of Teachers of Mathematics
Circumventing the Rules that Expire (High School) from National Council of Teachers of Mathematics
Classwide Interventions (coming soon)
Small-Group Interventions (coming soon)
Fluency
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.”
Fluency: Simply Fast and Accurate? I Think Not!
Fact Fluency (coming soon)
Number Talks (coming soon)
Math Updates
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Learning and networking opportunities for math teachers
Learning and networking opportunities for math teachers
Learning and networking opportunities for math teachers
Learning and networking opportunities for math teachers
Resources/Tools/Professional Development to Support the Universal Tier Tools and K-8 Building Blocks in Mathematics