PhysPort Implementation Guide - Precalculus Concept Assessment (PCA) - Version 1

Aug 30, 2026

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PhysPort’s Precalculus Concept Assessment (PCA) Implementation Guide (Version 1) explains how to evaluate foundational precalculus knowledge linked to understanding core ideas of beginning calculus. It details intended course level, assessed mathematics content (rate of change, function processes, and covariational reasoning), and recommended administration time of 30–45 minutes. The guide provides access and purchase information, administration as pre- and post-tests, participation incentives to reduce anxiety, scoring via percent correct from 25 items, and guidance for interpreting results using typical scores, normalized gain, and effect size.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Implementation

Purpose of the PCA

Course Level: What kinds of courses is it appropriate for?

Content: What does it assess?

Timing: How long should I give students to take it?

Example Questions

Access: Where do I get the assessment?

Versions and Variations: Which version of the assessment should I use?

Administering: How do I give the assessment?

Scoring: How do I calculate my students’ scores?

Clusters: Does this assessment include clusters of questions by topic?

Typical Results: What scores are usually achieved?

Interpretation: How do I interpret my students’ scores in light of typical results?

Resources

Translations: Where can I find translations of this assessment in other languages?

Background

Similar Assessments

Research: What research has been done to create and validate the assessment?

PhysPort Implementation Guide: Precalculus Concept Assessment (PCA) Version 1 Implementation Guide by Adrian Madsen Table of Contents Implementation Purpose of the PCA Course Level: What kinds of courses is it appropriate for? Content: What does it assess? Timing: How long should I give students to take it? Example Questions Access: Where do I get the assessment? Versions and Variations: Which version of the assessment should I use? Administering: How do I give the assessment? Scoring: How do I calculate my students’ scores? Clusters: Does this assessment include clusters of questions by topic? Typical Results: What scores are usually achieved? Interpretation: How do I interpret my students’ scores in light of typical results? Resources Translations: Where can I find translations of this assessment in other languages? Background Similar Assessments Research: What research has been done to create and validate the assessment? Research Validation Research Overview Developer: Who developed this assessment? References ©[2026 PhysPort.org-Last updated August 26](2026 PhysPort.org-Last updated August 26), 2026 1 Purpose of the PCA To assess essential knowledge that mathematics education research has revealed to be foundational for students’ learning and understanding of the central ideas of beginning calculus. Course Level: What kinds of courses is it appropriate for? Intro college Content: What does it assess? Mathematics Content knowledge (rate of change, function, process view of functions, covariational reasoning) Timing: How long should I give students to take it? 30-45 minutes Example Questions Example question from the PCA (Carlson, Oehrtman, and Engelke, 2010) . Access: Where do I get the assessment? The PCA, also known as the Algebra and Precalculus Concepts Readiness test (APCR), is available from DigitalEd for a fee of $20 per student as part of their Placement Test Suite. Email <[info@digitaled.com](info@digitaled.com)> for instructions on how to access and purchase the PCA/APCR. Versions and Variations: Which version of the assessment should I use? The most recent version of the PCA, version 1, was released in 2010. Administering: How do I give the assessment? Give it as both a pre-and post-test. This measures student learning. Give the pre-test before you cover relevant course material. Give the post-test at the end of the term. Use the whole test, with the original wording and question order. This makes comparisons with other classes meaningful. Make the test required, and give credit for completing the test (but not correctness) . This ensures maximum participation from your students. Tell your students that the test is designed to evaluate the course (not them), and that knowing how they think will help you teach better. Tell them that correctness will not affect their grades (only participation) . This helps alleviate student anxiety. Refer to the test by a generic title like "Precalculus Survey" to prevent students from looking up the answers. For more details, read the PhysPort Guides on implementation: PhysPort Expert Recommendation on Best Practices for Administering Concept Inventories ([www.physport.org/expert/AdministeringConceptInventories/](www.physport.org/expert/AdministeringConceptInventories/)) Scoring: How do I calculate my students’ scores? ©[2026 PhysPort.org-Last updated August 26](2026 PhysPort.org-Last updated August 26), 2026 2 Download the answer key from PhysPort ([www.physport.org/key/PCA](www.physport.org/key/PCA)) Each student's score is their percentage correct out of 25 questions. See the PhysPort Expert Recommendation on Best Practices for Administering Concept Inventories for instructions on calculating normalized gain and effect size ([www.physport.org/expert/AdministeringConceptInventories/](www.physport.org/expert/AdministeringConceptInventories/)) Clusters:

FAQs

What is the purpose of the PCA?

The PCA assesses essential precalculus knowledge identified by mathematics education research as foundational for students’ learning of central ideas in beginning calculus.

How should instructors administer the PCA?

Administer it as both a pre-test and a post-test: the pre-test before relevant course material and the post-test at the end of the term, using the original wording and question order.

How are PCA scores calculated and interpreted?

Each student’s score is the percentage correct out of 25 questions. Interpretation can incorporate typical results plus measures such as normalized gain and effect size when comparing pre- and post-test changes.

Aug 30, 2026

Upload by James