Mathematics in Pennsylvania stresses both procedural skills and conceptual understanding to ensure students are learning and applying the critical information they need to succeed at higher levels. The introduction at each grade level articulates a small number of critical mathematical areas that should be the focus for that grade. At the end of their high school education, students will be able to use their mathematical knowledge independently to:
- Make sense of and persevere in solving complex and novel mathematical problems;
- Use effective mathematical reasoning to construct viable arguments and critique the reasoning of others;
- Communicate precisely when making mathematical statements and express answers with a degree of precision appropriate for the context of the problem/situation;
- Apply mathematical knowledge to analyze and model situations/relationships using multiple representations and appropriate tools in order to make decisions, solve problems, and draw conclusions; and
- Make use of structure and repeated reasoning to gain a mathematical perspective and formulate generalized problem solving strategies.
Although it is an interesting and enjoyable study for its own sake, mathematics is most appropriately used as a tool to help organize and understand information from other academic disciplines. Because our capacity to deal with all things mathematical is changing rapidly, students must be able to bring the most modern and useful technology to bear on their learning of mathematical concepts and skills.
Standards Aligned System
The Standards Aligned System (SAS) is the Pennsylvania Department of Education digital curriculum and instruction resource site. The SAS is a comprehensive, researched-based resource to improve student achievement. The SAS is comprised of six distinct elements which provide a common framework for continuous student, teacher, and school and district growth. The elements are Standards, Assessment, Curriculum Framework, Instruction, Materials and Resources and Safe and Supportive Schools. Numerous resources for teaching and developing high quality mathematics education programs are available on the Standards Aligned System website. The SAS portal is designed to organize and deliver educational content carefully aligned to Pennsylvania Academic Standards.
Professional Learning Community
Professional Learning Communities (PLC) provide users with the ability to communicate and collaborate with educators from across the Commonwealth via threaded discussion forums and blogs. Learning Communities may be comprised of educators who teach the same subject areas or grade levels, or may focus on a particular instructional strategy or professional interest.
We encourage you to join the Mathematics Learning Community. The Mathematics Learning Community provides a collaborative environment to extend and enhance the discussion of important issues, challenges, and ideas that promote success in the teaching and learning of mathematics throughout the commonwealth as well as access to numerous resources. Join the Mathematics PLC by becoming a registered user of the Standards Aligned System. Once you are a registered user, sign-in to your account, select Teacher Tools, My Communities.
PA Core Standards
The State Board of Education adopted the Core Standards in July 2010. Since that time, the decision was made to craft a set of PA Core Standards in English Language Arts and Mathematics. A group of Pennsylvania educators created a draft set of PA Core Standards. These new standards mirror the content and rigor of Common Core, but reflect the organization and design of the PA Academic Standards. Additionally, the Core Standards for English Language Arts and Literacy in History/Social Studies and Science/Technical Subjects will be appended to their respective PA Academic Standards. The PA Core Standards are currently being reviewed within the regulatory review process.
The PK-12 PA Core Standards for Mathematics cannot be viewed or addressed in isolation, as each standard depends upon or may lead into multiple standards across grades; thus, it is imperative that educators are familiar with both the standards that come before and those that follow a particular grade level. These revised standards reflect instructional shifts that cannot occur without the integrated emphasis on content and practice. Standards are overarching statements of what a proficient math student should know and be able to do. The Pennsylvania Assessment Anchors and Eligible Content closely align with the revised standards and are an invaluable source for greater detail.
Key Points in Mathematics:
- The standards stress both procedural skills and conceptual understanding to ensure students are learning and applying the critical information they need to succeed at higher levels.
- K–5 standards, which provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions, and decimals, help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into application. They also provide detailed guidance to teachers on how to navigate their way through topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade.
- Having built a strong foundation at K–5, students can do hands-on learning in geometry, algebra, and probability and statistics. Students who have mastered the content and skills through the seventh grade will be well-prepared for algebra in grade 8.
- High school standards emphasize applying mathematical ways of thinking to real world issues and challenges.
Teachers shall expect that students know and can apply the concepts and skills expressed at the preceding level. Consequently, previous learning is reinforced but not re-taught. Students who achieve these mathematical standards will be able to communicate mathematically.
PA Core Curriculum Framework
The Curriculum Framework specifies what is to be taught for each subject in the curriculum. In Pennsylvania, Curriculum Frameworks include Long Term Transfer Goals, Big Ideas, Concepts, Competencies, and Essential Questions aligned to Standards and Assessment Anchors and where appropriate, Eligible Content.
Assessment
The Pennsylvania System of School Assessment (PSSA) includes assessments in English Language Arts and Mathematics which are taken by students in grades 3, 4, 5, 6, 7 and 8. Students in grades 4 and 8 are administered the Science PSSA. The English Language Arts and Mathematics PSSAs include items that are consistent with the Assessment Anchors/Eligible Content aligned to the Pennsylvania Common Core Standards in English Language Arts and Mathematics. The Science PSSA includes items that are aligned to the Assessment Anchors/Eligible Content aligned to the Pennsylvania Academic Standards for Science, Technology, Environment and Ecology.
The Keystone Exams are end-of-course assessments designed to assess proficiency in various subjects. The Keystone Exams are one component of Pennsylvania’s proposed system of high school graduation requirements. Keystone Exams will help school districts guide students toward meeting state standards.
Project Based Assessments are alternative assessments for students who are unable to meet Chapter 4 requirements relating to high school graduation requirements through the Keystone Exams.
STEM
STEM education is an intentional, integrative approach to teaching and learning in science, technology, engineering, and mathematics. Students become adept problem solvers, innovators, and inventors who are self-reliant by asking questions, investigating, making informed decisions about how they live their daily lives and engage in their vocations and communities.
Regulations
The Pennsylvania State Board of Education Curriculum Regulations Title 22, Chapter 4 details the requirements for all public schools within Pennsylvania.
Certification
Certification and Staffing Policy Guidelines (CSPG) that pertain to mathematics education certification and course assignment are CSPG 50 – Mathematics and CSPG 53 – Middle Level Mathematics.
Questions regarding certification requirements should be directed to Bureau of School Leadership and Teacher Quality.
Teacher/Student Resources
Classroom Resources - National Council of Teachers of Mathematics (nctm.org)
S.O.S. MATHematics is a free resource for math review material from Algebra to Differential Equations! This is a study site for high school, college students and adult learners. Get help to do homework, refresh your memory, or prepare for a test.
Khan Academy is a not-for-profit with the goal of changing education for the better by providing a free world-class education for anyone anywhere. All of the site's materials and resources are available to anyone completely free of charge.
HippoCampus is a project of the Monterey Institute for Technology and Education (MITE). The goal of HippoCampus is to provide high-quality, multimedia content on general education subjects to high school and college students free of charge.
Math Playground is an action-packed site for elementary and middle school students. Play a math game, solve a logic puzzle, and have some fun!
LearnZillion is a learning platform that combines video lessons, assessments, and progress reporting. Each lesson highlights a Common Core standard, starting with math in grades 3-9.
Curriculum Resources
The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.
Illustrative Mathematics provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.
CK-12 provides open-source content and technology tools to help teachers provide learning opportunities for students globally. Free access to high-quality, customizable educational content in multiple modalities allow teachers, students and others to innovate and experiment with new models of learning.
The Mathematics Assessment Program (MAP)aims to bring to life the Common Core State Standards (CCSSM) in a way that will help teachers and their students turn their aspirations for achieving them into classroom realities.
The Partnership for Assessment of Readiness for College and Careers (PARCC) is a consortium of 22 states plus the U.S. Virgin Islands working together to develop a common set of K-12 assessments in English and math anchored in what it takes to be ready for college and careers.
Smarter Balanced is a state-led consortium developing assessments aligned to the Common Core State Standards in English language arts/literacy and mathematics that are designed to help prepare all students to graduate high school college- and career-ready.
National Resources
The National Council of Teachers of Mathematics supports teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
The Pennsylvania Council of Teachers of Mathematics is the statewide organization in Pennsylvania for teachers of mathematics. Its primary purpose is to promote and support the teaching of mathematics at all levels within the state of Pennsylvania.
The Trends in International Mathematics and Science Study (TIMSS) provides reliable and timely data on the mathematics and science achievement of U.S. 4th- and 8th-grade students compared to that of students in other countries. Additional TIMSS information is available from the TIMSS and PIRLS International Study Center.
The National Assessment of Educational Progress (NAEP) is the largest nationally representative and continuing assessment of what America's students know and an do in various subject areas. Assessments are conducted periodically in mathematics, reading, science, writing, the arts, civics, economics, geography, U.S. history, and beginning in 2014, in Technology and Engineering Literacy (TEL).
The Council of Chief State School Officers (CCSSO) is a nonpartisan, nationwide, nonprofit organization of public officials who head departments of elementary and secondary education in the states, the District of Columbia, the Department of Defense Education Activity, and five U.S. extra-state jurisdictions. CCSSO provides leadership, advocacy, and technical assistance on major educational issues. The Council seeks member consensus on major educational issues and expresses their views to civic and professional organizations, federal agencies, Congress, and the public.