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Elementary Mathematics

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. To view the PreK-12 Mathematics PA Core Standards, click here.

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.

What it Means for Students?

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.

What Does that Look Like In the Classroom?

K to 12 Standards for Mathematical Practice

  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics.
  • Use appropriate tools strategically.
  • Attend to precision.
  • Look for and make use of structure.
  • Look for and express regularity in repeated reasoning.

In Upper Perkiomen School District, the new PA Core State Standards for Math mean deeper, more meaningful learning for our students.

How is this different from what students have done in the past?

The new standards will ask students to think more conceptually, and to think deeper and even more thoroughly about what they're learning. The new standards go beyond basic memorization to help students truly understand what they are learning.

Previously, students might have been given a word problem that required them to memorize a formula to calculate something like "area."

For example:

Under the old PA Standards, students might have been asked the follow:

  • 6 x 6
  • Mrs. Brown's class has a rabbit pen that is 6 feet long by 6 feet wide. How much room do the rabbits have to run around?

Under the new Common Core Standards, a word problem will more likely look like this:

Mrs. Brown's class has 24 feet of fencing to build a pen for rabbits. They want the rabbits to have as much room as possible. How long will each of the sides be?

The first problem simply requires a calculation: "Area" is defined by calculating length times width (for a rectangle or square.) In this case, simply multiply 6 x 6. The second problem requires the same calculation, but requires much more in depth thinking.

What is some of the knowledge and what are some of the questions that students need to know and answer to solve the problem?

  • What "perimeter" means (how many sides/combinations should they examine - should the pen be a rectangle, an oval, etc. and which would give the rabbits the most space)
  • How do you calculate the area of various shapes?

In order to solve this problem, the student may have to experiment with several formulas and concepts. They have to work through the problem. This process is referred to in educational circles as "productive struggle" or "brain sweat." This is the process of taking prior knowledge and working through the problem individually and then in small groups, during which time a teacher circulates throughout the class to help guide thinking pathways and conversations.

The workforce demands that children go beyond rote memorization and be able to solve real world problems. The programs selected by Upper Perkiomen School District staff and administration are aligned to the PA Core Content and Practices, create a cohesive K to 12 math program, provide "productive struggle", and challenge students at higher levels while providing more intensive help for students who need more time to learn.

To ensure that students were prepared to master these standards, the mathematics departments adopted the Everyday Mathematics program in grades K-5 during the most recent department curriculum review.

Everyday Mathematics is a comprehensive Pre-K through grade 6 spiral mathematics program developed by the University of Chicago School Mathematics Project and published by McGraw-Hill Education. Every year in the U.S., about 220,000 classroom are utilizing Everyday Mathematics.

What is a spiral curriculum?

In a spiral curriculum, learning is spread out over time rather than being concentrated in shorter periods. In a spiral curriculum, material is revisited repeatedly over months and across grades. Different terms are used to describe such an approach, including “distributed” and “spaced.” A spiral approach is often contrasted with “blocked” or “massed” approaches. In a massed approach, learning is concentrated in continuous blocks. In the design of instructional materials, massing is more common than spacing.

Why does Everyday Mathematics spiral?

Everyday Mathematics (EM) spirals because spiraling works. When implemented as intended, EM’s spiral is effective: EM students outscore comparable non-EM students on assessments of long-term learning, such as end-of-year standardized tests. Spiraling leads to better long-term mastery of facts, skills, and concepts.

Spiraling is effective with all learners, including struggling learners. Learning difficulties can be identified when skills and concepts are encountered in the early phases of the spiral and interventions can be implemented when those skills and concepts are encountered again later in the spiral.

What is the research basis for spiraling?

The “spacing effect” – the learning boost from distributing rather than massing learning and practice – has been repeatedly found by researchers for more than 100 years. Findings about distributed learning are among the most robust in the learning sciences, applying across a wide range of content and for all ages from infants to adults. “Space learning over time” is the first research-based recommendation in a recent practice guide from the U. S. Department of Education’s Institute of Educational Sciences (Pashler et al., 2007). In a recent review of the literature, Lisa Son and Dominic Simon write, “On the whole, both in the laboratory and the classroom, both in adults and in children, and in the cognitive and motor learning domains, spacing leads to better performance than massing” (2012).

Why does spacing work better than massing?

The reasons for the “spacing effect” are not fully understood. One possibility is that massing reduces attention so that learning is weaker. Another possibility is that effortful processing of the sort involved in spaced learning enhances long-term retention. Easy learning often doesn’t lead to the best retention; more difficult learning can lead to more robust encoding of information and better long-term learning (Schmidt & Bjork, 1992). This explanation identifies the spacing effect as an example of a “desirable difficulty” that enhances learning. A third possibility is that spiraling helps learners make connections over time, which creates more robust pathways for recalling information. Multiple, strategically spaced and strategically progressing learning experiences may produce deeper, more conceptual learning.

Everyday Mathematics curriculum emphasizes:

  • Use of concrete, real-life examples that are meaningful and memorable as an introduction to key mathematical concepts.
  • Repeated exposures to mathematical concepts and skills to develop children’s ability to recall knowledge from long-term memory.
  • Frequent practice of basic computation skills to build mastery of procedures and quick recall of facts, often through games and verbal exercises.
  • Use of multiple methods and problem-solving strategies to foster true proficiency and accommodate different learning styles.

Each grade of the Everyday Mathematics curriculum is carefully designed to build and expand a student’s mathematical proficiency and understanding. The goal is to build powerful mathematical thinkers!