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Mathematics

Introduction

The Iowa Core Essential Elements (EEs) are specific statements of knowledge and skills linked to the grade-level expectations identified in the Iowa Core Standards. The purpose of the EEs is to build a bridge from the content in the Iowa Core Standards to academic expectations for students with the most significant cognitive disabilities. A group of general educators, special educators, and content specialists from member states in the Dynamic Learning Maps (DLM) Consortium gathered to determine the essence of the Common Core State Standards (CCSS). The stakeholder group members were selected by their states to participate in this work. State education agency (SEA) representatives and SEA‐selected teachers collaborated to develop the EEs.

Beginning with the English Language Arts CCSS, stakeholders defined links to illuminate the precursors for the essential content and skills contained in the grade level CCSS standards and indicators. These EEs are not intended as a redefinition of the standards. Rather, they are intended to describe challenging expectations for students with significant cognitive disabilities in relation to the CCSS. The EEs clarify the bridge between grade‐level achievement expectations for students with significant cognitive disabilities who participate in alternate assessments and the CCSS.

Neither are the EEs intended to prescribe the beginning or end of instruction on the content and skills they represent; rather, they indicate the grade level at which initial mastery would be the target to be assessed. Students should begin instruction in content and skills at the earliest point possible and continue instruction until mastery is attained.

System Alignment

The EEs are intended to contribute to a fully aligned system of standards, curriculum, teaching, learning, technology, and assessment that optimize equity of opportunity for all students in each classroom, school, and local education agency to access and learn the standards. To the degree possible, the grade level EEs are vertically aligned and linked to the grade level Iowa Core Standards.

The linkages provided by the EEs to the Iowa Core Standards are intended to increase access to the general curriculum for all students with disabilities. Just as the EEs are designed to define achievement in academic content areas linked to the Iowa Core, the EEs reframe the expectations for foundational skills in pre‐academic and academic areas. Precursor/prerequisite and the unique enabling skills related to English language arts content is specified in the context of their roles as a foundation for students with significant cognitive disabilities to achieve skills related to academic content. The EEs are designed to allow students with significant cognitive disabilities to progress toward the achievement of state standards linked to grade level expectations. The relationship of standards and assessment to teaching and learning are depicted for use by teachers, assessment designers, and users of alternate assessment results.

Federal Guidance

The stakeholder group’s work was guided by the U. S. Department of Education’s Standards and Assessments Peer Review Guidance: Information and Examples for Meeting Requirements of the No Child Left Behind Act of 2001 [NCLB]), which requires that alternate academic achievement standards align with the alternate assessment. They must

  • knowledge and skills that link to grade level expectations,
  • promote access to the general curriculum, and
  • reflect professional judgment of the highest learning standards possible for the group of students with the most significant cognitive disabilities.

Although the grade‐level content may be reduced in complexity or modified to reflect prerequisite skills, the link to grade‐level standards must be clear. The Peer Review Guidance notes that the concept of alternate achievement standards related to grade level may be ambiguous. According to the Guidance, the descriptors

  • Should be defined in a way that supports individual growth because of their linkage to different content across grades;
  • Are not likely to show the same clearly defined advances in cognitive complexity as the general education standards when examined across grade levels;
  • Should rely on the judgment of experienced special educators and administrators, higher education representatives, and parents of students with disabilities as they define alternate achievement standards; and
  • Should provide an appropriate challenge for students with the most significant cognitive disabilities as they move through their schooling.

The Guidance requires links to grade‐level standards. The EEs were developed by DLM consortium states to differentiate knowledge and skills by grade level. This differentiation is intended to clarify the link between the grade‐level EEs and the grade‐level CCSS and to show a forward progression across grades. The progression of content and skills across years of instruction reflect the changing priorities for instruction and learning as students move from grade to grade. The differences from grade level to grade level are often subtle and progression is sometimes more horizontal than vertical.

Access to Instruction and Assessment

The EEs developed by the DLM consortium states are intended to create the maximum possible access to the CCSS for students with significant cognitive disabilities. The way in which information is presented for instruction and assessment and the manner in which students demonstrate achievement is in no way intended to be limited by statements of EEs. To that end, modes of communication, both for presentation or response, are not stated in either the EEs unless a specific mode is an expectation. Where no limitation has been stated, no limitation should be inferred. Students’ opportunities to learn and to demonstrate learning should be maximized by providing whatever communication, assistive technologies, augmentative and alternative communication (AAC) devices, or other access tools that are necessary and routinely used by the student during instruction.

Students with significant cognitive disabilities include a broad range of students with diverse disabilities and communication needs. For some students with significant cognitive disabilities, graphic organizers similar to those used by students without disabilities provide useful access to content and are adequate to maximize opportunities to learn and demonstrate achievement. Other students require a range of assistive technologies to access content and demonstrate achievement. For some students, AAC devices and accommodations for hearing and visual impairments will be needed. As with other physical disabilities, students with visual impairments may perform some expectations using modified items, presentations, or response formats. A few items may not lend themselves to such modifications. Decisions about the appropriate modifications for visual impairments are accounted for in the design of the assessments.

The access challenge for some is compounded by the presence of multiple disabilities. All of these needs, as well as the impact of levels of alertness due to medication and other physical disabilities which may affect opportunities to respond appropriately, need to be considered.

The Alignment Process

The process of aligning the learning map and the EEs began by identifying nodes in the maps that represented the essential elements in mathematics and English language arts. This process revealed areas in the maps where additional nodes were needed to account for incremental growth reflected from an essential element in one grade to the next. Also identified were areas in which an essential element was out of place developmentally, according to research, with other essential elements. For example, adjustments were made when an essential element related to a higher-grade map node appeared earlier on the map than an essential element related to a map node from a lower grade (e.g., a fifth-grade skill preceded a third-grade skill). Finally, the alignment process revealed EES that were actually written as instructional tasks rather than learning outcomes.

This initial review step provided the roadmap for subsequent revision of both the learning maps and the EEs. The next step in the DLM project was to develop the claims document, which served as the basis for the evidence-centered design of the DLM project and helped to further refine both the modeling of academic learning in the maps and the final revisions to the EEs.

Claims and Conceptual Areas

The DLM system uses a variant of evidence-centered design (ECD) as the framework for developing the DLM Alternate Assessment System. While ECD is multifaceted, it starts with a set of claims regarding important knowledge in the domains of interest (mathematics and English language arts), as well as an understanding of how that knowledge is acquired. Two sets of claims have been developed for DLM that identify the major domains of interest within mathematics and English language arts for students with significant cognitive disabilities. These claims are broad statements about expected student learning that serve to focus the scope of the assessment. Because the learning map identifies particular paths to the acquisition of academic skills, the claims also help to organize the structures in the learning map for this population of students. Specifically, conceptual areas within the map further define the knowledge and skills required to meet the broad claims identified by DLM.

The claims are also significant because they provide another means through which to evaluate alignment between the EEs and the learning map nodes and serve as the foundation for evaluating the validity of inferences made from test scores. EEs related to a particular claim and conceptual area must clearly link to one another, and the learning map must reflect how that knowledge is acquired. Developing the claims and conceptual areas for DLM provided a critical framework for organizing nodes on the learning maps and, accordingly, the EEs that align with each node.

EEs are represented with codes that reflect the strands in mathematics with the strand listed first, followed by the standard. For example, EE.1.NBT.2 is the EEs that align with Numbers and Operations in Base Ten in first grade.
Clearly articulated claims and conceptual areas for DLM served as an important evidence-centered framework within which this version of the EEs was developed. With the claims and conceptual areas in place, the relationship between EEs within a claim and conceptual area or across grade levels is easier to track and strengthen.

For more information please refer to pages 1-24 of the Iowa Core Essential Elements Mathematics for Students with Significant Cognitive Disabilities.