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Core Principles of Mathematics
The grades K-12 progression of mathematics learning expectations in the Hawaiʻi Common Core Standards for Mathematics (HCCS-M) is designed so that every student in the State of Hawaiʻi can achieve mathematical competence through a curriculum that emphasizes fluency, sense-making, problem-solving, communication, the strategic use of technology and the application of mathematics in real-world contexts and to other disciplines.
To ensure that students from all racial, ethnic, linguistic, gender, and socioeconomic groups meet the HCCS-M, schools must establish a culture of access and equity.
Math teachers work collaboratively with special education and English language teachers, and colleagues across disciplines to build effective teaching practices that close the achievement gap (NCTM, 2018).
Students routinely have opportunities to experience high-quality differentiated instruction and learn rigorous mathematics content in a safe learning environment that promotes creativity, collaboration, and a growth mindset (Emersonkress, 2015).
Teachers regularly monitor student progress and make strategic real-time adjustments to support and optimize student learning.
The HCCS-M has two equally important sets of expectations: the Content Standards and the Standards for Mathematical Practice.
Content Standards
The design principles for the content standards (often referred to as "the three shifts") are focus, coherence, and rigor (Achievethecore.org).
Focus: Each grade level has "critical areas of focus" that inform teachers of the high-priority learning targets for that grade level. Teachers should FOCUS on the high-priority learning targets for their grade, devoting more learning time to address the depth of these standards.
Coherence: The standards are a progression across grade levels. Concepts and skills scaffold from one grade to the next. Instruction should intentionally relate new concepts to students’ prior skills and knowledge (across grade levels). Additionally, within a grade level, teachers should intentionally make connections between related concepts (e.g., multiplication and area in grade 3, or statistics and functions in grades 8 and 9).
Rigor: The balance between conceptual understanding, fluency with skills and procedures, and application. The Standards for Mathematical Practice are critical to ensuring that rigor is in the mathematics classroom.
Standards of Mathematical Practice
describe the various types of expertise and habits of mind that students should develop as they engage with mathematics. They describe what we want to see STUDENTS doing as they engage with mathematics. "Encouraging these practices in students of all ages should be as much a goal of the mathematics curriculum as the learning of specific content" (Common Core State Standards Initiative, 2010).
should inform teachers’ decision-making when planning learning opportunities for students and when creating class norms and structures that promote a culture for learning in the mathematics classroom. Formative feedback will be constructive to promote student growth regarding the Practices; however, a summative grade should not be given regarding the Practices.
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