Math Pathways and Placement Overview

  • As a learning organization committed to continuous improvement and a focus on learning for every student, every day, we reflect on the instructional outcomes of our students through multiple data points, both formative (in-progress measures) and summative (end results). 

    Our teachers maintain the curriculum and design instruction to help students meet the expectations we have at each grade level (e.g. state academic standards), as well as to help them grow beyond that if they demonstrate readiness. We have renewed our commitment to both achievement and growth, noting the importance of differentiated instruction and engaging learning activities for students in alignment with the academic standards and assessments. This commitment is reflected in our 2023-2027 Strategic Plan.  

    We not only desire to see each student succeed and reach their potential, but we celebrate our students’ growth and commit to supporting them persistently through remediation, application, and enrichment, across all content areas. This is most visible within English Language Arts and Mathematics, where a robust multi-tiered system of support and multiple programs exist to ensure students meet with success based on their individual, unique needs.

    To help demystify the grades 2 - 5 math placement process where flexible math pathways exist, our team has created a Frequently Asked Questions (FAQ) document as a companion guide for the math pathways and placement process. We are sharing this document to ensure families’ familiarity with our process long before placements are made for the following year. All math placements are based on the student’s performance across multiple measures. Ensuring that families are aware of the criteria and grade level expectations can assist families in aiding their students in meeting with success as well. Our goal is to have each child most appropriately placed to feel their success and growth and to be appropriately challenged through scaffolding their learning so that it is “just out of reach” and then attained.  

    As an additional improvement, the math placement letters to students’ families have been updated and tailored by grade level. The matrix of various assessments used to determine a student’s placement has always been shared; however, specific student scores were not automatically sent to inform the families of the student’s performance on each of the measures reflected in the matrix. The letters shared this year will include a table with the possible and earned points for each assessment, as well as the weight assigned to each score in the overall placement process. The overall score attained by students is the determining factor for placement, as it reflects the full array of assessments and measures of achievement. 

    The overall factors included in the matrix vary by grade level, yet share similar characteristics. A review of the cumulative benchmark (reflective of the year’s content already learned), a diagnostic benchmark to assess mastery of content to be taught in the upcoming grade level, proficiency scores or grade point average in math throughout the current school year, standardized benchmark assessment scores, student attribute scores for the standards of math practice, and up until grade 6, basic math facts mastery levels. Given each of these factors, the overall score is calculated for each student.

    Students scoring above 95% or above on the matrix are provided with a secondary assessment to determine if they’ve also mastered the content that will be learned in the next year’s course. If the student scores 90% or above on that assessment, they are considered for subject acceleration in mathematics to help them continue to grow. Students scoring below 95%, but above our proficiency threshold, are placed in the compacted/extended class. This class is the same math course and curriculum, yet delivered in a more compact manner with additional learning extensions for applied learning. The current course is the expected grade level pacing and shares curriculum with the compacted/extended course. Both courses are reflective of the state academic standards and prepare students to demonstrate their mastery of content and successfully build upon it in future math courses. Within all math classes, the concept is to differentiate for the spectrum of student abilities, interests, and performance levels. Each student is supported and enriched regardless of course title, at the right level for their learning to occur. 

    Following the first semester, a committee of math teachers, gifted education/math enrichment teachers, and administrators came together to review the possible points, factor weights, and balance among the measures to ensure reasonable opportunities for consideration for both subject acceleration and placement into compacted/extended at the appropriate frequency and with ample opportunity to demonstrate mastery. Small revisions to our process were made to increase the likelihood of students scoring into and earning the opportunity to be placed in both of these courses (e.g. accelerated and compacted/extended), yet at a rate that should not decrease their chances of maintaining their levels of success.

    For example, students will be allowed to study the content from the next course up until July, when the secondary acceleration assessment would be given. We have found that students’ lack of exposure to math rules can hold them back, but once exposed to the rule, they can begin applying it immediately (e.g., a rate of acquisition that would match the accelerated pathway). Previously, each of these students would need to take the assessment before the end of the current school year, without exposure, or would need to enroll in an outside, accredited course over the summer, leveraging PRSD Board Policy 124. We believe this will allow many students the exposure to the curriculum that they would need to perform their best and aid the decision-making process for course placement. For those students qualifying to take the acceleration assessment, you will receive additional communication along with links to relevant materials. 

    Adjustments have also been made to the STAR 360 scaled scores required. Previously, the denominator for these assessments was reflected at the top of the rolling scaled score of 1400. We have now adjusted these scores to reflect the 90th percentile for the grade level (e.g. 90th percentile for grade 4 is a scaled score of 1075). Each grade level will now see a different number of points in the matrix based on this. We are confident that we are casting a broader net and allowing more students to sit for the potential acceleration assessment in the summer, should their families choose to do so. 

    Please take some time to review the FAQ below to better understand the nuances and common questions and misconceptions related to the math placement process and courses Should you have any additional questions, we encourage you to reach out to your child’s math teacher, counselor, or building administrator to discuss their specific performance, experiences, and opportunities. Our grades 2 - 5 math placement assessments for the 2024-2025 school year will begin the week of May 13 and continue through May 24, 2024. Building teams will then be exporting the data and working on placement communications leading up to the week of June 4, 2024, when math placement letters will be activated in the Student Information System. A specific eBlast will be sent to families notifying them that this item is available for review. Additional information and opportunities to learn more about the math pathways will be shared by the building principals through the Friday Flash

     

Frequently Asked Questions

    1. What are the math pathways and why do they exist?

      During the 2014-2015 review of curriculum, our math educators commonly recognized that some students were prepared to move at a faster pace than others within the curriculum and that differentiating instruction for a classroom of students all at a different level of math could cause students frustration since pacing was not “just right” most of the time for them, but either felt “too slow” or “too fast”.

      Simultaneously, the math pathways were updated to allow for a “compacted/extended” mathematics course starting in Grade 3, which would utilize the same curriculum as the “current” (e.g. typical grade level course curriculum), yet allow for mastered topics to be compacted and extended, just as the name implies. The pacing could be adjusted slightly to allow for application of concepts at a deeper level.  Note that each of these pathways are flexible, with students retaining the ability to demonstrate mastery of content and to be considered for movement to the compacted/extended pathway during their Grades 3-8 mathematics experiences.

      Of note is that even within the “current” math pathway, students will reach calculus in grade 11 or 12, with opportunities for math electives in addition (e.g. business calculus). The mathematics programming at Pine-Richland School District is of an extremely high quality and scaffolds students to master the most complex math sub-disciplines by the time that they graduate; therefore, pushing students too far, too fast is not recommended and ends up becoming a race to nowhere, as even the math electives could be exhausted by a student who skips courses. Additionally, it behooves students to have algebra fresh in their minds when taking the SAT and ACT for college admissions. Our goal is to help our students learn, grow, and succeed on the life path that they choose to follow and even our “current” pathway for mathematics opens these doors for them.



    The department developed a math placement matrix to help review multiple assessment factors for students to assess students’ needs better through data. It was important that this process took into consideration more than just one snapshot of a student’s performance and demonstrated consistency and retention over time. The matrix reflects different tools assessing the same concepts, yet developmentally by grade level. The outcome of these assessments is an overall percentage of mastery (out of 100%). Students are assigned to current and compacted/extended course levels based on the overall matrix during the placement process in the spring of each year. At the elementary level, the matrix takes 6 or 7 individual data points into consideration. 



    Additionally, the District has a waiver system, whereby a family could request that their child be placed into compacted/extended, even if the student did not demonstrate a need for this instruction based on the math matrix. While a waiver is possible between the “current” and “compact/extended” pathways, waivers are not accepted in an effort to grade level accelerate a child (e.g. to skip a math course). All families requesting a course waiver will conference with their child’s principal to review the data available and make a determination regarding the right course for each student.

    Students demonstrating a strength in mathematics, as reflected as a 95% or above on the matrix, will receive an invitation for their family to consider pursuing acceleration through independent study until July, followed by a demonstration of at least 90% mastery of content on the cumulative benchmark assessment for the course that is proposed to be skipped during acceleration. Students must be available to assess on or before the provided dates to ensure standardization of the process and study timelines. Dates will be communicated to impacted families via personal communication during the final week of school. Provision for this process is made possible through Pine-Richland School District Board Policy #124 Alternative Instruction.  


    1. Will my child be able to change levels of math flexibly each year, based on their performance?

      Data is collected from various assessment points within mathematics each spring by each individual student for review on our math placement matrix to inform their next course pathway. It has been with careful study and planning over time that each of the dimensions of our math placement process and resulting, flexible course pathways were designed, beginning in 2014-2015 with a curriculum review. Through implementation of our recommendations outlined in the In-Depth Program Review for mathematics, we analyzed our processes and made revisions to the math placement matrix based on students’ lived experiences in each course through performance comparisons. The department identified the creation of knowledge gaps that led to students’ low performance in the accelerated pathway if they had waived into that level without data to support the move through mastery of knowledge and skills in the course that they skipped. At that point, it was determined that students could waive between courses for “current” and “compacted/extended” only, not in order to accelerate (e.g. skip a year of mathematics). Students are able to be assigned “current” in one school year and then to move up through their performance data to “compacted/extended”. Each year leads to a new review process, involving multiple measures of student performance to recommend the most appropriate course of study. Overemphasizing the course placement of your child is not recommended, as it is the learning that they experience within the course, not the course title that is most important. Our goal is to ensure that every child is in the “right course” for them at that time in their development and that they will continue to achieve and grow without feeling overwhelmed.


    1. Can my child accelerate and skip a grade level course in mathematics in elementary school?

    Annually, students are assessed for acceleration and must achieve a 95% or above on the multi-dimensional math matrix for their current grade level and math course. Students performing at that threshold are then invited to sit for an acceleration assessment and demonstrate at least 90% mastery of content on the cumulative benchmark assessment for the course that is proposed to be skipped during acceleration. Provision for this process is made possible through Pine-Richland School District Board Policy #124 Alternative Instruction. While this acceleration process is possible, oftentimes it is not recommended by our educational team based on the already rigorous math pathways in place, allowing students to take calculus by the time they graduate, even if they’re in the “current” pathway. 

    As a district, we have the ability to monitor student performance and progress longitudinally and determine it is commensurate with the expectations in the standards. After accelerating and skipping an entire grade level course, gaps are often created that do not surface until Algebra and beyond, which in some cases can become a very stressful situation to the student who is used to performing well and understanding content. It is for this reason that a waiver is not acceptable for course acceleration and that only those opportunities to learn content through approved programming and a retention and mastery of content, as demonstrated on our benchmark assessment, can lead to skipping an entire grade level mathematics course.

    Additionally, students with a Gifted Individualized Education Program (GIEP) with a documented strength that is above average or exceptional in mathematics and quantitative reasoning are considered for programming options evidenced within their formal Gifted Written Referral (GWR) and in consultation with their GIEP and the building-based MTSS team. Gifted students are not automatically placed into compacted/extended nor accelerated math courses, as their area of giftedness may not fall within the quantitative reasoning domain. The typical math placement process is in place for all students to assess the recommended level of math placement. 


    1. Can my child accelerate and skip a math course at the secondary level?

    Students in grades 7-12, or taking an accelerated course from the secondary program of studies, may take courses outside of Pine-Richland School District for the purpose of moving ahead in mathematics, science, or world language pathways. A student will not receive credit for the outside course, but the student may move to the next course in the pathway. The timelines and criteria of Policy #124 must be adhered to in this instance. A student may accelerate in a course pathway, provided:

      1. The student assumes responsibility for all fees including tuition and textbooks.

      2. The building principal approves the course in advance.

      3. The course is offered by an institution approved by the Superintendent or designee.

      4. The student demonstrates readiness to move into the new pathway course.  The student must earn a 70% on the corresponding Pine-Richland comprehensive assessment.  In order to enter an honors or Advanced Placement (AP) course, the student must also meet the criteria outlined in the course requirements from the Program of Studies.

    Waivers are not accepted for course acceleration.


    1. How can I stay informed about my child’s progress throughout the year?

    A number of sources for performance data exist for each child. The most obvious access points are logging into the Sapphire portal to review grades, assignment and assessment scores and data, and the results of benchmark assessments at both the local (e.g. STAR 360) and state (e.g. PSSA/Keystone) levels. 

    Additionally, several public tools exist to help understand the expectations of performance by grade level, against which you can assess or evaluate your child’s own performance strengths and weaknesses. The academic standards for mathematics and the Standards of Mathematical Practice created by the state, serve as a framework of expected outcomes for each grade level. Similarly, the parent-facing curricular information on the Pine-Richland School District website, provides a good gauge of the topics to be addressed by each course. 

    Open communication with your child’s teacher through parent-teacher conferences, reviewing work samples, and following along with their test performance and retention can be the most effective manners of monitoring student performance. Students in Grades K-5 also have access to Freckle Math (and ELA) as well as RedBird as computer adaptive tools, aligned to the standards, which can be leveraged from home and include incentives for students to continue mastering additional skills and content. For additional recommendations, connect with your child’s math teacher.


    1. What types of interventions are available to help my child continue growing?

    For students in need of support and possibly remediation, your child’s teacher, counselor, and principal may follow up with you to invite your child to be a part of an intervention group during RAM Time. In order for students to participate, parental permission is sought formally. Once permission is provided, students’ assessment data is reviewed to determine the area(s) of need and the best type of intervention program to support them. While receiving supports, progress monitoring is completed to determine if your child is making progress and continuing to grow. These data points are shared with families to foster collaboration between home and school as the child’s specific needs are remediated to close gaps, while they continue to receive grade level instruction with their classmates (e.g., core instruction plus additional intervention, not in lieu of core instruction). 

    For students in Grades 1 and 2, prior to the math pathways existing, math enrichment groups are run by semester. All students take the STAR 360 assessments, which produce reports reflecting students’ progress with regard to the state standards. For students demonstrating strengths, an additional secondary assessment is given to determine if they would benefit from math enrichment once per week with grade level peers from across classrooms. This is meant to provide a boost in mathematics and to encourage critical thinking, problem-solving, computational thinking, and to foster the math skills reflected in the standards of math practice. It is always our goal to ensure that students are growing and this differentiation outside of the classroom can help support these efforts for students not hitting the “just right” level of challenge within their core instruction.

     

Math Pathways Presentation

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