Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades

Self Cite

In this report, we discuss background research on the development of student understanding of quadratic functions and present a provisional learning progression for quadratic functions and quadratic equations. We also describe task shells that are linked to the learning progression. The learning progression and task shells can be used as a starting point to develop tasks that assess student standing with respect to the theory of development. The intention is that this report should find an audience in both researchers and test developers.

Section: The Learning Progression For Quadratic Functions and Quadratmentioning

confidence: 99%

“…As part of the CBAL ® learning and assessment tool research initiative at Educational Testing Service (ETS; Bennett, ; Bennett & Gitomer, ), an LP was developed for linear functions (Arieli‐Attali, Wylie, & Bauer, ; Graf & Arieli‐Attali, ). The current work can be viewed as a sequel to this work.…”

mentioning

confidence: 99%

The Development of a Quadratic Functions Learning Progression and Associated Task Shells

Graf

Fife

Howell

et al. 2018

Self Cite

“…The presentation concluded with a description of the linear functions LP (Arieli-Attali, 2011;Arieli-Attali et al, 2012), which served to review and further clarify the materials that had been sent in advance (see also Graf & Arieli-Attali, 2015).…”

Section: Methodsmentioning

confidence: 99%

“…For mathematics, we used a linear function LP for middle school students, which is described in further detail by Arieli-Attali, Wylie, and Bauer (2012) and Graf and Arieli-Attali (2015). The levels in this LP are shown in Table 2.…”

Section: Learning Progressionsmentioning

confidence: 99%

Agreement of Teachers on Evaluating Assessments of Learning Progressions in English Language Arts and Mathematics

Rijn¹,

Graf

Arieli‐Attali

et al. 2018

Self Cite

In this study, we explored the extent to which teachers agree on the ordering and separation of levels of two different learning progressions (LPs) in English language arts (ELA) and mathematics. In a panel meeting akin to a standard‐setting procedure, we asked teachers to link the items and responses of summative educational assessments to LP levels. We evaluated four types of agreement among teachers, with test developers, and with trained raters. Although the results were quite mixed, agreement on the LP levels of mathematics items was generally better than that for ELA tasks. The agreement on the LP levels of ELA sample responses was generally better than that for mathematics. Implications of the results are discussed.

Validating Classifications From Learning Progressions: Framework and Implementation

Attali

Arieli‐Attali

2019

Learning progressions (LPs) have seen a growing interest in recent years due to their potential benefits in the development of formative assessments for classroom use. Using an LP as the backbone of an assessment can yield diagnostic classifications of students that can guide instruction and remediation. In operationalizing an LP, assessment items are classified as measuring specific LP levels and, through the application of a measurement model, students are classified as masters of specific LP levels. To support the use of LPs in instructional planning and formative assessment, the reliability and validity of both item and student classifications should stand up to scrutiny. Reliability of classifications refers to their consistency. Validity of classifications refers to alignment of these classifications with test data. A framework for testing these classifications is proposed and implemented in a validation study of a rational number LP for elementary school mathematics. As part of this study, 400 items were classified in terms of LP level of understanding, a cognitive diagnostic model of student mastery level within the LP was fitted to the data, and analyses were conducted to assess the reliability and validity of these classifications.