Mastery learning has been the subject of hundreds of research studies since Benjamin Bloom’s ground-breaking 1968 paper. The concept actually goes back way before Bloom, but it was Bloom’s prestige that finally put the subject permanently before the attention of educational researchers.
Fundamental Principles in Bloom’s Model
Bloom’s 1968 mastery-learning proposal includes these fundamental ideas:
- If we assume that, under the right circumstances, all students can master the content of a given course, then forced grading according to a normal curve should be eliminated and methods should be used that allow all students to earn high grades, not just those at the upper end of the spectrum of aptitude. Bloom writes, “… we proceed in our teaching as though only the minority of our students should be able to learn what we have to teach.” He goes on, “If we are effective in our instruction, the distribution of achievement should be very different from the normal curve.”
- Students should know there is an expectation of mastery and can be expected to achieve at higher levels when they do (confirmed by Ritchie and Thorkildsen (1994)).
- Since almost all students can learn specific content if given enough time, variable aptitude translates to variable time for students to reach mastery, Carroll (1963); high-aptitude students master course content faster than other students. Thus, in a mastery-learning environment the teacher should expect high-aptitude students to complete objectives earlier than other students and should have enrichment activities ready for them to undertake when they do.
- After an initial formative assessment, students are given feedback, correction, additional study time, and then are retested with another formative assessment.
- After the formative assessments, grades are established through a summative assessment.
- We should expect the result of this model to be that 90% of the students can earn scores formerly earned by only the top 10% of students.
Summary of Mastery-Learning Literature
The research literature on mastery learning is extensive. Since 1976, five metastudies of this literature have been conducted: Block and Burns (1976); Guskey and Gates (1986); Slavin (1987); Guskey and Pigott (1988); and Kulik, Kulik, and Bangert-Drowns (1990). All these except Slavin (1987) report strong, positive research findings in various areas associated with mastery learning, including student achievement, student retention, student affective variables, and teacher affective variables. Kulik, Kulik, and Bangert-Drowns (1990) include a detailed critique of the procedures and findings reported by Slavin (1987), discussed below.
In addition to the metastudies, several other significant analyses and discussions of the literature have been published, including:
- Slavin (1990)—an addendum to Slavin (1987), discussed below
- Davis and Sorrell (1995)—an extensive review of the metastudies
- Motamedi and Sumrall (2000)—a proposal to combine mastery learning with cooperative learning, computer technology, and constructivist principles
- Guskey (2005)—a thorough summary and discussion of mastery learning
- Zimmerman and DiBenedetto (2008)—a discussion of mastery learning in the context of high-stakes testing, including the No Child Left Behind program; also pertinent to the discussion surrounding Slavin (1987)
- Guskey (2010), Guskey (2011)—further elaboration on the implementation of mastery learning
Nearly all the writers mentioned so far hold that the extensive body of research literature supports the use of mastery-learning principles, Slavin (1987) being the single exception. In his 1987 metastudy, Slavin found positive results from mastery learning on criterion-referenced tests (i.e., teacher-written tests that measure student performance on learning objectives associated with the specific curriculum in use) but found no significant effect from mastery learning on student performance on norm-referenced tests (i.e., standardized tests). Here I will mention two issues associated with Slavin’s analysis. The first, noted by Kulik, Kulik, and Bangert-Drowns (1990), is that the selection criteria used by Slavin are problematic and that he unreasonably excludes from his analysis many of the studies that would lead to different results. The second concerns Slavin’s focus on norm-referenced tests. Kulik, Kulik, and Bangert-Drowns (1990) as well as Zimmerman and DiBenedetto (2008) argue that student performance on criterion-referenced tests is exactly what we should be concerned about, since criterion-referenced tests measure how well students have learned the specific content of what the teachers are teaching them.
I agree with the position expressed by Kulik, Kulik, and Bangert-Drowns (1990) and Zimmerman and DiBenedetto (2008). As a classroom teacher, my concern is exactly with how well students learn what I teach them. Of course, those teaching in public schools that mandate the administration of norm-referenced tests must be concerned with those results as well. However, unless one is specifically teaching to the test, I would not expect the mastery-learning methods used in short-term (one year or less) research studies to have much influence on performance on norm-referenced tests for the simple reason that such tests are designed to measure student development over the long term. I would expect a positive influence on performance on norm-referenced tests if mastery-learning methods were used over the course of years, and if the tests were designed to test what the schools are teaching, but this is not what the research studies have examined. In his short 1990 paper, Slavin concedes that “the findings of positive effects of mastery learning on experimenter-made measures can be interpreted as supporting the view that this technique can help focus teachers on a given set of objectives. Educators who value this have a good rationale for using group-based mastery learning.”
The findings of the metastudies are well-summarized in Davis and Sorrell (1995). They report the finding from Block (1971) “that students with minimal prior knowledge of material have higher achievement through mastery learning than with traditional methods of instruction.” Other points noted in this paper are:
- Guskey and Gates (1986) “found that achievement results were overwhelmingly positive, but varied greatly from study to study. Students in mastery learning programs at all levels showed increased gains in achievement over those in traditional instruction program [sic]; effects were somewhat larger in elementary and junior high school classes than at the high school level. Effects in language arts and social studies classes were slightly larger than those attained in science and mathematics classes. Students retained what they had learned longer under mastery learning, both in short-term and long-term studies.”
- Low-aptitude students show higher performance gains than high-aptitude students, as reported by Kulik, Kulik, and Bangert-Drowns (1990).
- Higher levels of achievement are obtained with mastery learning when the students are aware that they are in a mastery-learning environment, as reported by Ritchie and Thorkildsen (1994).
- Public-school studies indicate that for mastery learning to realize its potential, the school “principal must take on the role of instructional leader. Instructional leadership involves an understanding of mastery learning principles, a commitment to preparing and supporting staff, constant awareness, and a system for setting and monitoring goals, directions, and results of the program.”
Davis and Sorrell conclude their study with a comment that is consistent with claims made in my own publications: “School systems must recognize that traditional methods of teaching and learning are unsuccessful for many students.”
The Bloom-Guskey Mastery-Learning Model
Early studies of mastery learning varied in the details of their applications of various mastery-learning models, making it difficult to summarize the models in terms of a set of common features. But over the years, the common features coalesced into a well-defined mastery-learning model, articulated primarily through the writings of Thomas Guskey, an educational researcher and leading proponent of mastery learning. Guskey (2005) notes that Bloom’s model is all about reducing variability in student achievement by increasing variability in instructional approaches and learning time. He also notes that from a researcher’s perspective, achievement gaps are matters of variation.
Guskey (2005) describes Bloom’s model with a list of essential elements and a flow chart similar to the one shown below. The flow chart illustrates the basic idea. A class is taught the material from a unit of instruction, using whatever high-quality instructional practices the teacher chooses. The students are then administered a formative assessment that measures students’ mastery of the material. (Formative assessments are used for learning instead of the usual assessments of learning.) Those who score below a mastery level of typically 80% or 90% on this assessment are given additional instruction consisting of tasks, known as correctives, specifically targeting the objectives for which mastery was not demonstrated. This additional instruction lasts for a couple of days and is not mere reteaching. Instead, instruction and correctives are individualized for each student to address students’ different “learning styles, learning modalities, [and] types of intelligence.” After the additional instruction and correctives, the students take a second formative assessment, this time targeting the specific skills addressed in the correctives. In this retest, problems and questions are similar but not identical to those on the first assessment. Those who demonstrate mastery are ready for the next unit; those who do not enter into a second set of correctives.
During the class time needed for correctives and retesting, students who scored at or above the mastery level on the first formative assessment are engaged in enrichment activities designed to broaden or deepen their knowledge of and experience with the material. The nature of the enrichment activities can vary widely, and student interest is one of the factors that guides the selection of particular activities.
Two comments about this process might be mentioned here, neither of which are mentioned in Guskey (2005). The first is that some students may take up to three formative assessments before moving to the next unit. Second, two different approaches to grading are mentioned in the mastery-learning literature. Guskey (2010) says that
Mastery learning teachers make a point of recognizing those students who do well on the initial formative assessments. But they also acknowledge that students who do well on the second assessment have learned just as much and deserve the same grades as those who scored well on their first try.
A second approach is suggested by Bloom:
Implicit in this way of defining the outcomes and preparing evaluation instruments is a distinction between the teaching-learning process and the evaluation process. At some point in time, the results of teaching and learning can be reflected in the evaluation of the students. But these are separate processes. That is, teaching and learning are intended to prepare the student in an area of learning, while evaluation (summative) is intended to appraise the extent to which the student has developed in the desired ways.
In other words, the scores on the formative assessments do not figure into the student’s final grade. The final grade is established by a summative assessment given later. As I note in the comparison section below, the manner in which student grades are established in my own mastery-learning model is distinct from both of these approaches. The justification for this grading policy is described below.
Guskey (2005) summarizes Bloom’s mastery-learning model as including two essential elements: 1) a feedback, corrective, and enrichment process, and 2) “instructional alignment.” The first of these is described above. Instructional alignment entails four components: a) learning objectives for each unit, b) instruction targeted at the objectives, c) formative assessments targeting the objectives, and d) feedback and correctives for objectives not mastered.
The FWTM Model
The FWTM model is described fully in From Wonder to Mastery, cited at the beginning of this paper. The goal of the FWTM model is to eliminate the Cram-Pass-Forget Cycle, the normal operating mode in most classrooms in America. When teachers and students operate this way, students cram for tests, pass them, and forget most of what they crammed in about three weeks. In the FWTM model, Cram-Pass-Forget behavior is replaced with a Learn-Master-Retain pattern:
- Learn—The initial stage in the process, focused on well-defined learning objectives.
- Master—Practice of learning objectives continues until proficiency has been obtained.
- Retain—Practice of both previous and new learning objectives continues throughout the course, effectively resulting in long-term retention.
The mastery component of the FWTM model may be implemented in any courses in any subject area. But the full FWTM framework applies to science instruction and includes these three major elements:
- Motivating all instruction by the innate human sense of wonder at the beauties and intricacies found everywhere in nature.
- Deep integration of four key themes throughout the learning objectives and assessment practices: epistemology (i.e., the nature of scientific knowledge as provisional and the nature of science as a cyclic, ongoing process), mathematics, history (the primary way students see the cyclic process of science in action), and language use.
- A teaching methodology designed to deliver mastery and long-term retention.
The power of the FWTM model resides in the unified orchestration of science classes around wonder, integration, and mastery. However, for the purpose of comparing the FWTM model to the Bloom model, we must focus the present discussion on the mastery or mechanical element of the FWTM model, since the Bloom model entails only the mechanics of teaching, testing, correctives, and retesting.
Implementation of the mastery element in the FWTM model requires specific attention in three areas:
- Proper placement is provided for all students, so that mastery is achievable for everyone. In secondary science and math, this essentially entails having separate grade-level and accelerated pathways for math beginning in eight grade and for science beginning in ninth grade.
- The curriculum is culled, so that the amount of material presented in the course may be mastered and not merely skimmed. This entails identifying the core topics for all subjects and focusing the curriculum on these.
- Learning objectives are published for each chapter in a given course. In particular, these are expressed in performance terms, so that students know exactly what they must be able to do on the assessments.
- A mastery mindset is cultivated among faculty and administration, and this mindset is continuously communicated to the students.
- Teaching strategies
- Major assessments are cumulative to the start of the year.
- Timed, weekly cumulative quizzes are used in grades 7–9; cumulative chapter exams with intermediate “spot-check” quizzes are used in grades 10–12.
- Grades are based largely (~85%) on the cumulative assessments, so that credit in the grading process depends very little or not at all on work associated with daily assignments.
- Enabling strategies
- Students are trained in effective study strategy and study habits based on practice, so that students capitalize on the phenomenon known as the practice effect.
- Teachers supply weekly review guides to students in grades 7–9 as a major tool for training students how to study.
- Teachers schedule regular drill/review days in grades 7–9.
Comparing Mastery-Learning Models
Both the Bloom model and the FWTM model result in significant gains in student achievement, significant increases in positive student affects, and significant increases in positive teacher affects. Both models also establish mastery as the expectation for students. However, the two models differ in key respects and, in my view, the differences result in some benefits that favor the FWTM model over the Bloom model. The purpose of this section is to make these distinctions and benefits clear. In the tables below, I compare the two models in several specific categories. For this comparison, I use the weekly quiz regimen described in From Wonder to Mastery and recommended for grades 7–9.
|Expectation of Mastery|
|Bloom Model||FWTM Model|
|Students are expected to master content by scoring at or above a fixed score (typically 80% or 90%) on frequent (approximately weekly) formative assessments. Students are informed that they are in a mastery-learning environment.||Students are expected to master content by being prepared to answer questions from present and previous chapters on weekly quizzes that function as both formative and summative assessments. Students are informed that they are in a mastery-learning environment.|
|Consequence of Scoring Below the Mastery Standard|
|Bloom Model||FWTM Model|
|Students engage in additional instruction and corrective activities, followed by taking another formative assessment. This cycle might be repeated again if mastery is still not demonstrated.||There is no specific score indicating a mastery standard and no specific consequence of a given weekly score. If students are not mastering content and practicing for long-term retention of older material, their scores will decline over time (as they forget older material) and they will not pass the course. Students know this and know they need to be prepared to see similar questions and problems again and again week after week. Accordingly, a quiz score below 80 motivates students to engage in more study and practice, or to obtain additional instruction.|
|Bloom Model||FWTM Model|
|Assessments target objectives for the present unit of study.||Weekly quizzes target objectives for all units of study completed to date.|
|Bloom Model||FWTM Model|
|Instructional alignment entails four components: a) learning objectives for each unit, b) instruction targeted at the objectives, c) formative assessments targeting the objectives, and d) feedback and correctives for objectives not mastered.||Instructional alignment entails four components: a) learning objectives for each unit, b) instruction targeted at the objectives, c) formative assessments targeting the objectives from all units studied to date, and d) from the feedback of returned quiz papers, students seek assistance or engage in additional self-study (e.g., practice) for objectives not mastered.|
|Extra Time (variable aptitude = variable time to reach mastery)|
|Bloom Model||FWTM Model|
|The extra time for students who have not mastered all objectives for a given formative assessment occurs in class. Students are given correctives, including additional instruction and new assignments, and this work is assumed to require a day or two.||The extra time for students who have not achieved mastery, including additional practice and review, occurs outside of regular class hours. Tutorial assistance occurs during the teacher’s tutorial times.|
|Bloom Model||FWTM Model|
|While correctives are being given to students who have not achieved mastery, teacher-developed enrichment activities are given to those who have.||Since correctives and additional time occur outside regular class hours, there are no specific occasions when some students are engaged in enrichment activities while others are engaged in correctives.|
|Bloom Model||FWTM Model|
|Students receive feedback about the objectives assessed on the formative assessment for which they did not demonstrate mastery.||Initial feedback occurs as students receive their graded quizzes each week and look them over. Additional feedback occurs as the teacher reviews the quiz together with the class.|
|Bloom Model||FWTM Model|
|The teacher prepares individualized correctives for each student who does not demonstrate mastery. These activities are targeted at the specific objectives not mastered.||As needed, the teacher works with one or more students during the teacher’s tutorial hours, or during class, providing whatever assistance may be required. In certain cases, the teacher may decide to prepare additional sets of questions or problems for a student to engage with.|
|Bloom Model||FWTM Model|
|The teacher writes a second formative test targeting the specific objectives not previously mastered. Since the non-mastered objectives may vary from student to student, these retests may be unique for each of the students in the correctives sessions.||No special retests are offered. The new check for mastery occurs the next time a question or problem related to a specific objective occurs on a quiz. Since all quizzes are cumulative, quiz content addressing the objectives from older chapters occurs regularly and students are tested on objectives from all chapters over and over.|
|Bloom Model||FWTM Model|
|As mentioned above, student grades are either based on a summative assessment that occurs at some point after the formative assessments are completed, or students are awarded the same grades.||The average of the weekly quiz scores comprises 80–85% of the student’s grade. All quiz scores are included (see below). Lab reports and homework assignments (for younger students) comprise the remaining 10–15%. Students who study and practice correctly will likely earn an A or B as a result.|
|Bloom Model||FWTM Model|
|Longer retention is a consequence of higher initial achievement. Research focuses on retention over relatively short periods, such as four weeks. A small number of studies have reported improvement in retention over four months.||Improved long-term retention is a result of the practice effect, which itself comes into play because the weekly quizzes are cumulative to the beginning of the course. Students see similar questions and problems week after week on the quizzes. They also routinely practice answering questions and solving problems from previous chapters in order to be prepared for questions from older chapters.|
Some additional discussion is warranted on some of the differences between Bloom’s model and the FWTM model.
The first issue relates to the way student grades are established. As noted above, Bloom held that formative assessments should not count in the students’ grades, which should be based instead on a summative assessment after the learning process is complete. I certainly understand the principle involved here, that learning and assessment of learning are separate processes. (This is why one should assign little or no grade credit for homework—homework is a necessary learning activity but not a legitimate assessment of whether learning has occurred.) However, there is an inevitable decrease in motivation for some students when they know that if they don’t score high enough on a quiz the grade won’t count. I have implemented mastery-learning programs in both math and science that have run for many years. While I was developing the FWTM model for use in science classes, I developed a separate model for mathematics that we applied in middle and high school to all math classes and all students from pre-algebra through algebra 2. The model we used was similar to Bloom’s and required students to take a retest if they didn’t score at least 83 on the chapter test. Early on, we discovered a fundamental property of student psychology: many students are not motivated to apply themselves diligently to prepare for a test if they know the test grade doesn’t count. If the score doesn’t count, there is no penalty for not being prepared for the test. This results in some students not taking the steps they need to take in order to be prepared for the test; they are content simply to retest over and over until they finally hit the magic 83. This experience persuaded us that it is essential that scores on all quizzes and tests must be included in the students’ grades.
Second, a closely related psychological flaw resides in the use of required retesting itself. In our mathematics mastery program, we found that over time an increasing number of students discovered that even if all the scores were counted in the grade they could game the system by essentially not studying or working at all, other than showing up at the required after-school tutorial sessions. Thus, the teacher became the one doing all the work writing retests, scoring retests, and tutoring students while the students sat more or less passively listening in the belief that sooner or later they would have seen a problem worked enough times that the student finally scores the 83 by some accident. Needless to say, the load on teachers when some students require five or six retests is enormous. There is no remedy for this problem other than forcing students to accept a failing grade if they don’t score at the mastery standard within a specific number of test attempts, and such a policy would be politically very unpopular.
Third, without a requirement for cumulative assessments, the Cram-Pass-Forget Cycle—the enemy of education—still occurs. Since the Bloom model does not require cumulative assessments, the higher achievement does not translate well into students taking what they have learned with them into future years and courses. Research does show improved retention, but the studies measure this in terms of only a few weeks (four months in a few cases). Thus, the model addresses the level of initial achievement, not the tendency to forget things after a few weeks. The cumulative nature of the assessments is at the very core of the success of the FWTM model and results in students remembering things for months or years into the future.
Fourth, Guskey remarks that for a student to be engaged in additional tutoring and practice on older material while simultaneously moving on to new material is an “impossible situation” that should be avoided. However, I have used the FWTM mastery-learning model in the classroom for a decade myself and I have not found this to be at all the case. When students study correctly in the first place, they do not fall behind and do not need much in the way of tutoring. I found that each year a few students did fall behind in their practice of older material and did have to work hard to get caught back up. But never once did any student or parent complain that a mastery standard requiring students to get tutoring on their own time when needed was an unreasonable challenge.
Benefits of the FWTM Model
Structuring mastery learning around cumulative assessments instead of retests results in several benefits that make the FWTM model successful and preferable. I conclude by itemizing a few of these.
- There is no need for teachers to write, administer, and score retests.
- There is no need for teachers to devise enrichment activities.
- All students remain together; there is no separation of the class into those in enrichment and those engaged in correctives.
- There is no need to establish a mastery standard at a specific percentage and there is no potential for anxiety about a requirement that everyone score at or above a certain score. Almost all students end up with grades of A or B simply because of the weekly review practice they engage in.
- Long-term retention is very strong due to the ongoing action of the practice effect, enabling teachers to depend on students’ knowledge from previous mastery-learning courses.
Block, James H. and Burns, Robert B. (1976), Mastery Learning, Review of Research in Education, 4, 3–49
Bloom, Benjamin. (1968), Learning for Mastery, Evaluation Comment, 1, 2, 1–11
Davis, Denese and Sorrell, Jackie. (1995), Mastery Learning in Public Schools, Educational Psychology Interactive, December, accessed http://www.edpsycinteractive.org/files/mastlear
Guskey, Thomas and Gates, Sally L. (1986), Synthesis of Research on the Effects of Mastery Learning in Elementary and Secondary Classrooms, Educational Leadership, 43, 8, 73–80
Guskey, Thomas and Pigott, Therese D. (1988), Research on Group-Based Mastery Learning Programs: A Meta-Analysis, The Journal of Educational Research, 81, 4, 197–216
Guskey, Thomas. (2005), Formative Classroom Assessment and Benjamin S. Bloom: Theory, Research, and Implications, paper presented at the 2005 Annual Meeting of the American Educational Research Association
—— (2010), Lessons of Mastery Learning, Educational Leadership, 68, 2, 52–57
—— (2011), Response-to-Intervention and Mastery Learning: Tracing Roots and Seeking Common Ground, The Clearing House, 84, 249–255
Karpicke, Jeffrey D. and Roediger III, Henry L. (2007), Repeated retrieval during learning is the key to long-term retention, Journal of Memory and Language, 57, 2, 151–162
Kulik, Chen-Lin C.; Kulik, James A.; and Bangert-Drowns, Robert L. (1990), Effectiveness of Mastery Learning Programs: A Meta-Analysis, Review of Educational Research, 60, 2, 265–299
Mays, John D. (2021), From Wonder to Mastery: A Transformative Model for Science Education, Centripetal Press/Classical Academic Press
Motamedi, Vahid and Sumrall, William J. (2000), Mastery Learning and Contemporary Issues in Education, Action in Teacher Education (Association of Teacher Educators), 22, 1, 32–42
Roediger III, Henry L. and Butler, Andrew C. (2011), The critical role of retrieval practice in long-term retention, Trends in Cognitive Sciences, 15, 1, 20–27
Rowland, C.A. (2014), The effect of testing versus restudy on retention: A meta-analytic review of the testing effect, Psychological Bulletin, 140, 6, 1432–1463
Slavin, Robert. (1987), Mastery Learning Reconsidered, Review of Educational Research, 57, 2, 175–213
—— (1990), Mastery Learning Re-Reconsidered, Review of Educational Research, 60, 2, 300–302
Zimmerman, Barry J. and DeBenedetto, Maria K. (2008), Mastery Learning and Assessment: Implications for Students and Teachers in an Era of High-Stakes Testing, Psychology in the Schools, 45, 3, 206–216
 Bloom (1968).
 We have Benjamin Bloom to thank for the elimination, at the secondary level at least, of grading according to a normal curve.
 Bloom (1968), p. 2.
 Davis and Sorrell (1995), p. 4.
 Note that while mastery learning adapts instruction to variability in aptitude by accommodating the different rates at which students learn, the spread in aptitude for secondary mathematics is still so wide that multiple tracks or pathways are essential.
 Kulik, Kulik, and Bangert-Drowns (1990) comment that “the demonstrably superior performance of LFM [Learning For Mastery] students on locally developed tests is not offset by demonstrably poorer performance on standardized tests. LFM students perform as well as conventionally instructed students on standardized tests, and they perform at a clearly higher level on the locally developed tests used in most LFM evaluations.” p. 290–291.
 ibid., p. 288–290.
 ibid., p. 291; Zimmerman and DiBenedetto (2008), p. 207–208.
 Slavin (1990), p. 301.
 Davis and Sorrell (1995), p. 1.
 ibid., p. 2.
 ibid., p. 3. This is not surprising: low-aptitude students have a wider range of improvement available to them.
 ibid., p. 4.
 ibid., p. 6.
 ibid., p. 6.
 Guskey (2005), p. 1.
 I have modified Guskey’s diagram to show the possibility of more than one pass through the correctives. This possibility is not mentioned in Guskey (2005) but is included in Zimmerman and DiBenedetto (2008).
 Guskey (2010), p. 55.
 Guskey (2005), p. 6.
 Zimmerman and DiBenedetto (2008), p. 208.
 Guskey (2010), p. 56.
 Bloom (1968), p. 8.
 Guskey (2005), p. 5, 7.
 Mays (2021).
 The practice effect: “[R]epeated recall of previously recalled items enhanced retention by more than 100% relative to dropping those items from further testing. Repeated retrieval is the key to long-term retention,” Karpicke and Roediger (2007), p. 151. See also Rowland (2014), p. 1432 and Roediger and Butler (2011), p. 20.
 These are the major enabling strategies. There are many more minor enabling strategies described in From Wonder to Mastery.
 Guskey (2010), p. 56.
John D. Mays
Centripetal Press/Novare Science/Classical Academic Press
Much of this article originally appeared as an appendix in the author’s book From Wonder to Mastery: A Transformative Model for Science Education © Classical Academic Press®, 2021. All rights reserved. Reprinted by permission from Classical Academic Press.