Formative Assessments
Teachers use formative assessments to gather information about student knowledge. Then they adapt their instruction to address misunderstandings and shore up weaknesses. Formative assessments stand in contrast to summative assessments, which represent a summary of student knowledge at the end of a unit.


Mastery Standard
From the standpoint of the teacher who selected the mastery standard, a student who meets or exceeds this achievement level on an assessment has mastered the related objectives. The standard varies from course to course and teacher to teacher, but it should not be lower than the equivalent of a B letter grade. A common mastery standard is 90 percent.


For students who score below the mastery standard, mastery teachers offer support in the form of corrective activities, and they typically set aside some class time for activity completion, at least at the beginning of the year. The following correctives, described in greater detail in Guskey's Implementing Mastery Learning, illustrate the variety of activities available:


For students who score above the mastery standard, mastery teachers offer guidance on a challenging, exciting project. Enrichment students may simply get a head start on a project in which everyone will eventually participate, and they may be appointed project leaders.


Parallel Assessments
Assessments are considered parallel when they assesses the same skills in the same way, but their details differ. For example, parallel quizzes assess the same skills (e.g. multiplication) with the same types of questions (e.g. fill-in-the-blank), but the questions themselves differ (e.g. 11 x 4 = ?; 11 x 9 = ?).


A meta-analysis is a summary of the findings of a set of related studies. To conduct a meta-analysis, a researcher must first search databases for studies. After compiling a set of studies, the researcher reviews the studies. A study may be excluded from the meta-analyis if it was poorly designed or conducted. To produce the summary, the researcher retrieves data from the selected studies and then applies various statistical methods.


Good feedback typically includes information about what a student did right, what a student did wrong, and how the student can improve.


Controlled Experiment
A controlled experiment is a study with the following essential features: two (or more) separate groups of subjects, random assignment of subjects to groups, and manipulation of one variable (the independent variable) and control of all other variables. See the Frequently Asked Questions for an illustration.


Effect Size
An effect size indicates the practical significance of an effect. In the education world, a positive effect generally means an increase in student achievement while a negative effect means a decrease in student achievement. Most reforms are, of course, designed to increase student achievement, but relatively few produce large, positive effects. See the Frequently Asked Questions for information on how to read an effect size and how an effect size is calculated.


Pre-Test and Post-Test Means
Researchers often assess students both before and after they receive instruction. The pre-test means are the average scores of the students in the treatment and control groups before they receive instruction. And the post-test means are the average scores of the students in the same groups after they receive instruction. To infer the impact of instruction on a group, the researchers calculate the difference between the pre-test and post-test means.


Effect Size Level of Evidence
0.8 or more Strong
0.5 Moderate
0.2 or less Low


Mastery Learning

The need for differentiated instruction is acknowledged in theory, but neglected in practice. Students begin a course with different knowledge, abilities, and interests. In spite of their diversity, they usually receive uniform instruction. Clearly, students would benefit if their unique learning needs were met, so why don't most teachers provide differentiated instruction?

Simply put, teachers face constraints, and as usually depicted, differentiated instruction would be impractical, even burdensome, to implement. Teachers are justifiably wary of differentiated instruction because it represents a logistical nightmare. It is difficult enough for a teacher to plan and manage instructional activities for a few classes of students, let alone multiple subgroups within each class. Teachers need a workable model, not disconnected suggestions or a manifesto that amounts to little more than a wish list.

Mastery Models

Mastery models represent sensible solutions to a daunting problem, implementation of differentiated instruction. Mastery models promote a simple, systematic approach to assessment, and they do not prescribe or favor any particular instructional philosophy (e.g. direct instruction, guided discovery, etc.).

Do mastery models require more work on the parts of both teachers and students? Yes. However, the increase in work is well within reason, and the payoff is impressive, to say the least.

Mastery vs. Traditional Teaching
Model Type of Instruction % of Students Attaining Mastery
Mastery Differentiated Higher
Traditional Uniform Lower

Learning for Mastery and Personalized System of Instruction

Please select a section to learn about two mastery models, their effectiveness, and how mastery principles relate to recommendations from the Institute of Education Sciences.


As Guskey chronicles in Implementing Mastery Learning (1996), Benjamin Bloom and Fred Keller independently developed mastery models during the 1960s. Bloom dubbed his model Learning for Mastery (LFM), and Keller dubbed his model the Personalized System of Instruction(PSI). Today, Bloom's Learning for Mastery is usually referred to as Bloom's Mastery Learning.

The two models share the following essential features:

But the models also differ in significant ways. See the table below for a quick comparison. Historically, K-12 teachers have overwhelmingly implemented Bloom's LFM, and college teachers have usually implemented Keller's PSI. Teacher needs, student needs, and practical constraints influence decisions about which mastery model to implement.

Learning for Mastery vs. Personalized System of Instruction
Mastery Model Pace Setter Social Context Remediation Enrichment
Learning for Mastery Teacher Group Strong Strong
Personalized System of Instruction Student Individual Strong Weak

The models are described in more detail below. Click on a model to reveal a summary and diagram. Click again to hide the summary and diagram.

Learning for Mastery

Bloom's Learning for Mastery (LFM) calls for teacher-paced, group instruction. Students move through the course as a group, and during each unit they receive the same instruction through the first assessment. Following the first assessment, students who meet the mastery standard receive enrichment while students who score below the mastery standard receive remediation.

Due to time constraints, LFM teachers generally only offer one opportunity to retake, revise, or redo an assessment. Quizzes are retaken; projects are revised; and performances are redone. (For quizzes in particular, parallel assessments should be used, not identical assessments.) Some teachers count the higher of the two scores while other teachers always count the score from the second assessment. For enrichment students, the second assessment may be optional.

Learning for Mastery process with decision point at Assessment A. Students who meet the mastery standard receive enrichment, and they decide whether or not to take Assessment B. Students who score lower than the mastery standard receive remediation, and they take Assessment B. At Assessment B, the paths of the two groups of students join, and everyone moves on to the next unit.
Learning for Mastery process

Personalized System of Instruction

Keller's Personalized System of Instruction (PSI) calls for self-paced, individualized instruction. It requires students to demonstrate mastery before moving on to the next unit, which in turn necessitates multiple opportunities to retake or revise an assessment. Hypothetically, students who always meet the mastery standard could complete a PSI course much more quickly than students who often score below the mastery standard and require remediation.

PSI teachers also face practical constraints, and they often decide to cap the number of assessment attempts. PSI teachers should construct parallel assessments in the same manner as LFM teachers.

Personalized System of Instruction process with decision point at the assessment. Students who meet the mastery standard proceed to the next unit, and students who score lower than the mastery standard receive remediation before taking the assessment again. Remedial students remain in this loop until they meet the mastery standard.
Personalized System of Instruction process


Since the late 1960s, researchers have performed dozens of studies on Bloom's Learning for Mastery (LFM) and Keller's Personalized System of Instruction (PSI), and several researchers have performed a meta-analysis of the studies in an attempt to summarize the available data. In 1990 Kulik, Kulik, and Bangert-Drowns reported the results of their meta-analysis, the most exhaustive ever conducted. Their goals were to gauge the effectiveness of mastery learning and identify the factors that impact its effectiveness.


After noting that mastery learning is not only effective, but also efficient (students in a mastery class typically spend just 2-3 minutes more per hour on their work), Kulik et al. concluded their analysis with the following remarks:

We recently reviewed meta-analyses in nearly 40 different areas of educational research. Few educational treatments of any sort were consistently associated with achievement effects as large as those produced by mastery teaching (p. 292).

The mastery model predicts higher examination scores, reduced variation in examination scores, and more positive academic attitudes with mastery teaching, and we found all of these effects in mastery classes. The effects, however, were not as large as sometimes claimed for mastery procedures (p. 292).

Kulik et al. found that a few factors were associated with strong achievement effects on local tests and moderate achievement effects on standardized tests. The factors included:

Mastery programs that lacked these characteristics generally produced weak achievement effects on standardized tests.

The meta-analysis is described in more detail below. Click on a section of the study to reveal a summary. Click again to hide the summary.

Selection Criteria

After scouring the available literature and compiling studies, Kulik et al. evaluated each study. To be included in the meta-analysis, a study had to meet the following criteria:

The researchers selected 108 studies for analysis. One third of the studies involved Bloom's LFM, and two-thirds involved Keller's PSI. College students were the subjects in 91 studies. K-12 students were the subjects in 17 studies, all focused on Bloom's LFM.

Pie graph showing breakdown of selected studies (See text.)
Breakdown of studies selected

Achievement Measure

To facilitate comparison of student achievement across studies, Kulik et al. retrieved student test means from every study and calculated the effect size. Whenever possible, the researchers retrieved both pre-test and post-test means to estimate growth. Post-test means from end-of-instruction assessments (local tests, standardized tests, or both) were obtained from 103 studies. Five PSI studies did not report post-test means.


Kulik et al. calculated mean effect sizes of 0.59 and 0.49 for Bloom's LFM and Keller's PSI, respectively. And they calculated a combined mean effect size of 0.52, or an average increase of 0.52 standard deviations. The typical mastery student scored at the 70th percentile on the end-of-instruction assessment whereas the typical traditional student scored at the 50th percentile. This is an achievement effect of moderate strength.

Although Keller's PSI had a small negative effect on course completion, Kulik et al. found no connection between course completion and student achievement. The researchers asserted, "Higher student achievement in PSI classes is not an illusion created by the withdrawal of the weaker students before final-examination time" (p. 286).

To view a table that will help you interpret the effect sizes, click the button below.

Effect Size Table

Histogram of Bloom's Learning for Mastery effect sizes with peak near 0.5 and right skew
Achievement with Learning for Mastery
Histogram of Keller's Personalized System of Instruction effect sizes with peak near 0.5
Achievement with Personalized System of Instruction

IES Practice Guide

In 2007 the Institute of Education Sciences (IES), the US Department of Education's research center, published a practice guide by Pashler et al. entitled Organizing Instruction and Study to Improve Student Learning. The purpose of an IES practice guide is to offer concrete recommendations that are feasible, evidence-based, and coherent.

The practice guide makes seven recommendations. More than half of the recommendations relate to mastery learning, and a couple recommendations are straight out of the mastery learning playbook:

IES Recommendations
Recommendation Level of Evidence Related Mastery Learning Practice(s)
1. Space learning over time. Moderate N/A
2. Interleave worked example solutions with problem-solving exercises. Moderate Both: Following Assessment A, teachers provide worked examples (e.g. demonstrations and/or answer keys with worked answers). Remedial students perform targeted activities prior to Assessment B.
3. Combine graphics with verbal descriptions. Moderate N/A
4. Connect and integrate abstract and concrete representations of concepts. Moderate N/A
5a. Quizzing: Use pre-questions to introduce a new topic. Low N/A
5b. Quizzing: Use quizzes to re-expose students to key content. Strong Both: Teachers offer students who score below the mastery level on Quiz A an opportunity to take Quiz B, a parallel quiz.

Bloom's LFM: Teachers are encouraged to select a few important questions from past units' quizzes and place them on the current unit's quizzes.
6a. Self-Management: Teach students how to use delayed judgments of learning to identify content that needs further study. Low N/A
6b. Self-Management: Use tests and quizzes to identify content that needs to be learned. Low Both: Both teachers and students use Quiz A to diagnose student learning needs. Students then perform targeted remedial activities in preparation for Quiz B.

Bloom's LFM: Teachers reteach difficult concepts, procedures, processes, etc.
7. Ask deep explanatory questions. Strong Both: Teachers align objectives, instruction, and assessment.

Bloom's LFM: When designing each unit, teachers are encouraged to use Bloom's Taxonomy, which promotes high-level objectives.
Overlap of IES Practice Guide recommendations and principles of Bloom's Learning for Mastery (LFM) and/or Keller's Personalized System of Instruction (Highlighted rows indicate strong congruity.)