Conceptual Measures

On this page, we provide a brief summary of the conceptual measures and a link to one of the forms. See the information at the bottom of the page to access the full set of 12 forms of each type of measure.

Concept of Variable – The items included in the CoV measure address comparing the relationship of algebraic expressions with generalized quantities, determining the effects of changing the value of variable(s) in expressions, finding solutions of related equations, and applying properties of equality. The CoV measure includes concepts that students proficient in algebra could use without applying symbolic manipulations.

CoV Form A

Proportional Reasoning – The items in the PR measure include (1) ordering rational numbers; (2) interpreting proportional relationships; (3) determining equivalent ratios; (4) comparing ratios using continuous and discrete quantities; and (5) analyzing expressions with variable quantities.

PR Form A

Translations, Functions, and Graphs – The TRFG measure requires students to demonstrate the ability to link representations of the same function (tables, graphs, and equations) and to use the characteristics or parameters given by a text or narrative description, function, graph, or table to determine another representation.

TFG Form A

To Access the Free Conceptual Measures:

Please complete the user agreement and email it to When we receive your completed user agreement, we will email you zip files containing the administration directions, measures and keys for each of the three types of conceptual measures developed in ASPM.

Please note that our research results in the schools participating in ASPM did not indicate sufficient technical adequacy for using the conceptual measures in a progress monitoring context. At this time, we encourage teachers to use the items and measures for instructional or diagnostic purposes, rather than for monitoring student growth over time.

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ASPM project team