Introduction

This Precalculus Concept Assessment (PCA) instrument is a 25-item multiple-choice instrument that assesses a student's understanding of the central ideas of precalculus mathematics.

Both the assessment items and every answer choice for PCA have been evaluated in research studies conducted by the instrument's authors over the past 15 years. The PCA taxonomy articulates the reasoning abilities, understandings and analytic abilities that are assessed by the 25-item test.

PCA is unique in several ways. Each question assesses an ability that research studies have revealed students must possess in order to understand the central ideas of calculus. Each answer choice for each PCA item emerged from qualitative studies that revealed the precise misconceptions that commonly lead students to give that answer. The researchers identified these answer/misconception pairings by conducting dozens of clinical interviews in which they prompted students to explain the thinking that led to their answer choices.

PCA is highly predictive. Studies have revealed that more than 85% of students who complete the PCA instrument as a pre-test for calculus and score 13 or higher go on to complete Calculus I with a grade of C or better.

PCA Taxonomy

PCA Literature References

PCA Assessment Items with Video Clips and Transcripts

Support provided by the National Science Foundation, and Arizona State Universiy.