The elementary mathematics program is guided by the belief that all students can learn and succeed in mathematics. On the path to becoming competent mathematicians, whether it is for future study and career or for functioning in everyday life, there are certain critical learning experiences in which all students will take part. These include learning that is related to concept development, procedural fluency, problem solving with real-life application, communication of mathematical processes and understanding, and fact fluency in the four basic operations. Concurrently, students will be immersed in mathematical process skills that deepen understanding and elevate cognitive demand. These include, but are not limited to, reasoning abstractly and quantitatively, critiquing the reasoning of others, modeling mathematics, looking for structure and pattern, and attending to precision.
Classroom lessons and assessments reflect instruction in each of these five areas. Achievement in each area is measured through a variety of assessment tools, problem-solving experiences, daily work, math projects, homework, and teacher observations.
The development of a sound understanding of mathematical concepts and relationships often takes place in physical contexts through the use of manipulative and concrete examples. These experiences are used to enable the student to make abstractions and to develop related skills. Instruction links concepts with the procedures they represent. Fully developed conceptual knowledge leads to increasing proficiency in problem solving.
Through procedural fluency instruction, students are taught various strategies and algorithms for written computation, mental computation, and for using a calculator. Students also learn how to decide if an exact calculation is needed or if an estimate is adequate. Estimation skills also assist students in determining whether answers are reasonable. While the math program often begins with exploring skills conceptually, lessons then move towards introducing more traditional, procedural methods.
The role of problem solving is vital to assist students in connecting mathematics with its application in the world, and to develop students’ understanding of mathematics as a discipline. Students experience specific strategies and are strongly encouraged to explore mathematical thinking in ways that make sense to them. With time, students tend to gravitate towards more efficient strategies as their exposure to various types of math problems expands. The ultimate goal is for students to reason through problems and think mathematically.
As recommended by the standards set forth by the National Council of Teachers of Mathematics, communication is a critical component of the math program. Math instruction does not stop when students figure out the right answer. Rather, students are required to communicate – first orally and later in writing – the process which was used or the reasoning used to arrive at the correct answer. Students are also asked to critique and compare other students’ methods. Lessons are rich with “math talk” and group discourse.
Fact Fluency is defined as using efficient and accurate methods when computing numbers. Paul Riccomini, a Clemson University mathematics researcher, best articulates why fact fluency in young students is important. He equates computational fluency in math to understanding letter-sound connections in reading. These connections are the foundational blocks from which reading knowledge grows and develops. A fluent knowledge of the basic facts in all four operations (addition, subtraction, multiplication, and division) can help move students from the concrete to more abstract math processes. Fact fluency instruction centers around strategies, rather than memorization. Daily practice occurs in a variety of ways depending on grade level and teacher preference. Weekly, timed quizzes are utilized to monitor growth in an operation over a semester.
The kindergarten mathematics program is designed to allow engaging, hands-on experiences with early numeracy and number sense skills. Kindergarten teachers may determine eligibility for support and enrichment opportunities dependent upon resource scheduling. Assessment of concept mastery is determined through observations and other tools, rather than through posttests.
Flexible grouping in mathematics in first through fourth grade allows for more responsive customization of the math program. For each topic rotation, students are placed by grade level teachers into flexible groups based on pretest scores, rates of acquisition, learner traits, and teacher observations of performance. This structure allows for class size variations, slight pacing adjustments, targeted instructional strategies, and focused assistance of building resource teachers for support and/or enrichment. All students are held accountable for mastering the PA Core Standards and all students are assessed with the same end of topic assessment.
At the elementary level, a small percentage of students qualify for math acceleration. The process guidelines and criteria for qualification are outlined in the math acceleration section of the Board approved document "Guidelines for Meeting Individual Needs".