Common Core State Standards for Mathematics and the Standards for Mathematical Practice

The Common Core State Standards for mathematics are organized by content standards, which address topics, content, and skills. The Standards for Mathematical Practice address ways of thinking about mathematics, persevering in problem solving, use of appropriate tools, and mathematical reasoning. The balance of both content and conceptual understanding is essential in the development of proficiency for all students.

COMMON CORE STATE STANDARDS
The Common Core State Standards are organized by grade level and identify the content students will be learning that particular year. When the standards were constructed, an emphasis was placed on coherence and rigor to ensure that student learning builds from one grade to the next.  The development of mathematical reasoning begins in Kindergarten and supports students to articulate their thinking and apply multiple strategies to solve problems.

Mathematics: Kindergarten
Mathematics: Grade 1
Mathematics: Grade 2
Mathematics: Grade 3
Mathematics: Grade 4
Mathematics: Grade 5
Mathematics: Grade 6
Mathematics: Grade 7
Mathematics: Grade 8
Mathematics: Algebra
Mathematics: Geometry

STANDARDS FOR MATHEMATICAL PRACTICE
The Standards for Mathematical Practice describe “processes and proficiencies” that students should acquire as their math learning progresses. These standards require students to articulate their reasoning, provide proof for solutions, persist in problem solving, and make connections across mathematical ideas. 

The Standards for Mathematical Practice

FIVE STRANDS OF MATHEMATICAL PROFICIENCY
In its publication, Adding it Up, The National Research Council highlighted the importance of developing the five strands of mathematical proficiency: strategic competence, adaptive reasoning, conceptual understanding, procedural fluency, and productive disposition.  All five strands are considered to be intertwined and essential for overall math proficiency.

Descriptions of the Five Strands of Mathematical Proficiency

D90 VISION FOR MATHEMATICS EDUCATION
District 90 believes that all students are capable of achieving high levels of mathematics, and that the following elements are essential for providing the highest quality math learning for all:

High-Quality Learning Environment values
●      a growth mindset
●      mistakes and views them as learning opportunities
●      student collaboration and discourse
●      all learners as individuals and avoids labeling
●      multiple approaches to problem-solving

High-Quality Curriculum and Materials
●      are based on the standards
●      provide coherent student learning progressions that are vertically and horizontally aligned
●      are student-centered
●      provide a balance of both content and mathematical practices
●      embed student collaboration
●      place emphasis on authentic, real-world problem solving
●      emphasize application of both math skills and concepts (content and practices)
●      provide multiple entry points for students
●      offer hand-on opportunities and access to a range of tools for problem-solving
●      emphasize solving problems in multiple ways

High-Quality Classroom Instruction provides
●      all students access to the same high-quality learning goals
●      student collaboration as an established routine
●      instruction that is differentiated to meet the range of learners
●      flexible grouping opportunities within the classroom setting (not exclusively based on readiness)
●      appropriate scaffolds
●      high levels of student engagement
●      common language across grade levels
●      time

High-Quality Assessment Practices provide
●      formative assessment that drives instruction and provides ongoing information
●      authentic problem-solving to engage students
●      alignment to established learning goals
●      opportunity for students to transfer learning to new and novel situations

High-Quality Professional Development includes
●      intentional, meaningful, and timely collaboration
●      collaboration across and within grade levels
●      research and best practices instruction as drivers for decision-making
●      differentiated opportunities to meet the range of teacher needs and interests
●      is ongoing

MATHEMATICS TEACHING PRACTICES
The National Council for Teachers of Mathematics (NCTM) has worked for the last twenty-five years to push for rigorous, coherent, and systemic math learning to ensure that all students have access to high-quality math learning.  In its publication, Principles to Actions: Ensuring Mathematical Success for All, NCTM highlights essential mathematics teaching practices:

MATHEMATICS TEACHING PRACTICES
Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.
Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and tools for problem solving.
Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.
Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to asses and advance students’ reasoning and sense making about important mathematical ideas and relationships.
Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.
Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

 

 

 

 

 

 

 

 

 

 

 

Source: Principles to Actions: Ensuring Mathematical Success for All. National Council for Teachers of Mathematics (2014).

PRODUCTIVE BELIEFS ABOUT TEACHING AND LEARNING MATHEMATICS
In addition to identifying mathematical teaching practices, The National Council for Teachers of Mathematics (NCTM) also highlights the required shift in mathematics instruction to effectively support productive math learning for all students.

Beliefs About Teaching and Learning Mathematics
Unproductive Beliefs	Productive Beliefs
Mathematics should focus on practicing procedures and memorizing basic number combinations.	Mathematics learning should focus on developing the understanding of concepts and procedures through problem solving, reasoning, and discourse.
Students can learn to apply mathematics only after they have mastered the basic skills.	All students need to have a range of strategies from which to choose in solving problems, including general methods, standard algorithms, and procedures.
Students can learn to apply mathematics only after they have mastered the basic skills.	Students can learn mathematics through exploring and solving contextual and mathematical problems.
The role of the teacher is to tell students exactly what definitions, formulas, and rules they should know and demonstrate how to use this information to solve mathematics problems.	The role of the teacher is to engage students in tasks that promote reasoning and problem solving and facilitate the discourse that moves students towards shared understanding of mathematics.
The role of the student is to memorize information that is presented and then use it to solve routine problems on homework, quizzes, and tests.	The role of the student is to be actively involved in making sense of mathematics tasks by using varied strategies and representations, justifying solutions, making connections to prior knowledge or familiar contexts and experiences, and considering the reasoning of others.
An effective teacher makes the mathematics easy for student by guiding them step by step through problem solving to ensure that they are not frustrated or confused.	An effective teacher provides students with appropriate challenge, encourages perseverance in solving problems, and supports productive struggle in learning mathematics.

Source: Principals to Action: Ensuring Mathematical Success for All, National Council for Teachers of Mathematics (2014).

ACCELERATED MATHEMATICS IN THE MIDDLE SCHOOL
Roosevelt Middle School offers four different mathematics pathways for students in order to meet the diverse needs of all our learners.  The accelerated program, also known as ATP, provides math instruction at a faster pace of instruction. Eligibility is determined through the following means:

• Silicon Valley Math Initiative Tasks: students complete five problem-solving tasks, one for each of the five mathematical  “big ideas” to assess grade-level proficiency with concepts, use of multiple strategies, creative problem solving, and ability to explain math reasoning.  University of Illinois at Chicago’s Metro Chicago Math Initiative (MCMI) scores the completed tasks and proficiency levels are determined by norms established annually by the Silicon Valley Math Initiative.
• Measures of Academic Progress (MAP): eligible students must attain 90% on the math section of the assessment to be considered for ATP-1 or 95% for ATP-2.
• Teacher Assessment: teachers complete a checklist related to how student engage in mathematics (ability to persevere in problem solving, use of multiple strategies, ability to explain math thinking).

Roosevelt Middle School Mathematics Pathways

RESOURCES FOR PARENTS TO SUPPORT THEIR CHILD’S MATH LEARNING
The Council of Great City Schools has developed content and grade-specific parent roadmaps that provide detailed information for parents about the expectations of the Common Core in Mathematics. These roadmaps include examples of grade-level focus in the content area and can be accessed via this link https://www.cgcs.org/page/244.

The National PTA has partnered with the National Education Association to develop guides to help families support their children.

Helping Your Child with Today’s Math