Mathematics

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: 

1. Make sense of and persevere in solving complex and novel mathematical problems;
2. Use effective mathematical reasoning to construct viable arguments and critique the reasoning of others;
3. Communicate precisely when making mathematical statements and express answers with a degree of precision appropriate for the context of the problem/situation;
4. 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
5. 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.

• 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.

Beginning with the 2012-2013 school years Keystone Exams will be administered for Algebra I, Literature and Biology. In future years, pending funding, additional Keystone Exams will be administered.

The Algebra 1 Resource Page was created to support the Algebra I Keystone Exam and contains materials that align with the Keystone Exam, provide instructional content for educators and provide subject-specific activities that students can use to prepare for the assessment.

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