#### Mastery Learning

# Ensuring Every Student Succeeds

## What is Mastery Learning?

A mastery learning approach relies on the idea that education should focus on the time needed for each student to master concepts, rather than focusing on the students’ differing abilities when given the same amount of time to learn (like our current system of A-F grading does). It proposes that students need to master preliminary concepts before they should be allowed to move on to more complex subjects.

In a normal classroom, where students are given the same amount of instruction, grades and test scores generally match a normal distribution, represented by the bell curve on the left in Figure 4.

Most students will achieve scores in the middle, while lower and higher scores are achieved by a smaller number of students who have relatively low or high aptitudes for the subject.

Most universities even use a normal bell curve to distribute grades for tests and courses. The assumption is that it is completely normal for half of the students to achieve failing grades, no matter their performance!

Mastery learning however challenges the assumption that achievement must conform to a normal distribution. Instead, it asserts that most students can achieve a high level of mastery if given enough time and individualized instruction. Proponents argue that if mastery learning is properly implemented, the distribution curve of aptitude will remain normal, while the distribution of student achievement will have a peak that is shifted to the right, like the curve on the right in Figure 4.

Figure 4

Benjamin Bloom said in his 1968 paper Learning for Mastery, "There is nothing sacred about the normal curve… if we are effective in our instruction, the distribution of achievement should be very different from the normal curve." Bloom then went on to predict that in mastery classes, 90% of the students would achieve at the level previously reached only by the top 10%.

At gt.school, we expect even more impressive results from our students! We expect that mastery learning, combined with the other learning techniques we employ, will enable every gt.school student to perform at or above the 99th percentile level.

## Is Mastery Learning Effective?

Mastery learning and its effects have been extensively studied. To get a good idea of the effects of the approach we can look at several meta-studies that have been published, each of which examined anywhere from 40 to almost 100 mastery learning studies at once.

Block and Burns (1976) was one of the earliest meta-studies published. They looked at 97 studies that compared average achievement test scores between mastery-taught and non-mastery-taught students. They found that mastery-taught students scored higher 89% of the time and their scores were on average 5/8ths of a standard deviation higher.

Guskey and Pigott (1988) looked at a further 43 studies of mastery learning that were conducted after the Block and Burns review. Almost all of the studies showed positive effects: the test score differences for the 43 studies ranged from 0.02 to greater than 1.70 standard deviations.

In 1990, Kulik, Kulik, and Bangert-Drowns conducted another meta-study, this time on 36 Learning For Mastery (LFM) studies and 67 Personalized System of Instruction studies (or PSI, another type of mastery learning). They found that over 90% of programs produced results that were favorable to mastery learning. The average standard deviations of test scores were 0.48 for PSI studies and 0.59 for LFM studies (Figure 5).

Figure 5

Adapted from "Effectiveness of Mastery Learning Programs: A Meta-Analysis" by CL. Kulik, J. Kulik, and R. Bangert-Drowns, 1990, Review of Educational Research, 60:2, 265-299.

The researchers concluded that “Few educational treatments of any sort were consistently associated with achievement effects as large as those produced by mastery learning. ... In evaluation after evaluation, mastery programs have produced impressive gains.”

## How Can We Implement Mastery Learning?

Although Bloom is credited with inventing the term “mastery learning”, his initial paper did not give too much guidance on how to implement mastery learning in classrooms. Two key practices which he recommended were breaking up the curriculum into smaller units and conducting “formative evaluations,”, frequent progress tests to determine whether or not the student has mastered the unit and what, if anything, the student must still do to master it.

Interestingly, not only do regular assessments give teachers and students information about what the students know and what they still need to learn, but the actual act of undertaking regular exams produces a positive learning impact that we now know as the Testing Effect!

The processes of mastery learning have become more defined over time by Bloom and many other researchers. Now, most mastery learning programs use a combination of diagnostic pre-tests, regular progress tests, enrichment activities for students who have mastered the current unit and corrective instruction for those who have not yet mastered the unit.

A student’s journey in a mastery learning classroom looks like the flow in Figure 6.

Figure 6

Adapted from "Formative Classroom Assessment and Benjamin S. Bloom: Theory, Research, and Implications" by T. Guskey, 2005, page 4

## How Do Adaptive Apps Teach for Mastery?

All of this seems a bit theoretical though… isn’t gt.school using learning apps rather than teachers and classrooms? Can apps really replicate all the elements we need to implement mastery learning?

Absolutely, they can and they do!

Let’s look at each element of mastery learning to see how apps can enable mastery learning:

**Diagnostic Pre-Tests**

Many apps require students to take an initial assessment before they can begin any material for a course. This ensures that the student is only presented with material that they have not yet mastered, and is also not too difficult for them to master.

For example, ALEKS issues students an “Initial Knowledge Check” when they first log on to a course, which is effectively a placement test to determine which concepts the student has already fully learned and which still need to be mastered.

Figure 7

**Quality Group Instruction**

… Well actually, this one we don’t need to replicate- apps do one better, in the form of individual instruction! As we have discussed, adaptive learning apps can be just as effective as 1:1 tutoring.

**Regular Progress Tests **

Most adaptive learning apps also regularly assess students to determine if they have mastered the material that they have been working on. For example, Khan Academy uses regular quizzes and a Unit Test at the end of each block of material to assess a student’s mastery.

**Enrichment Activities**

In a classroom setting, enrichment activities are used because not all students will be ready to move on to new material at the same time. Students who master concepts before others then complete enrichment activities to ensure that they remain engaged.

However, with adaptive learning apps, students can progress at their own pace, so there is no need for enrichment activities to keep quicker students occupied. Instead, students can move right on to learning the next concept!

**Corrective Instruction**

Adaptive apps approach feedback and corrective instruction in different ways, depending upon the design of the app.

Corrective instruction is usually applied by apps even before the student has reached the testing stage. When students submit the answers to practice problems, feedback can be given as a) a hint as to why their answer is incorrect and a prompt to try again, or b) a verbal or written explanation of how to correctly solve the problem.

For example, in Knowre’s math courses, when students submit incorrect answers they are first prompted to try again. After they submit a second incorrect answer, the app walks the student through the incorrect answer to help them understand how to solve the problem. This helps the student to work through subsequent problems.

Figure 8

Once the student has taken a more formal assessment, if the material has not been mastered, the student will be assigned more material on the same topic until they have gained mastery. Depending on the app, this might be more material of the same level of difficulty, or even easier material to bring students back to foundation concepts that they might need to revisit.

**Further Progress Tests**

Apps that are based on mastery learning principles do not allow students to progress to the next topics until they have reached a certain performance level on previous topics

(this could be anywhere from 80-100%, depending on the app). If the student does not demonstrate mastery on assessments, corrective instruction is then applied and after practicing, the student can re-attempt the progress test to show that they have mastered the material.

This iterative process is present in Khan Academy. There are multiple ways for students to achieve mastery- students can ace the Unit Test two times in a row to move on right away, or if they need more practice, they can complete more practice problems and quizzes. They can then re-attempt the unit test to prove that they are ready to move on.

**Student Motivation**

### The Science of Motivation

## References

- Block, J. H., & Burns, R. B. (1976). 1: Mastery Learning. Review of Research in Education, 4(1), 3–49.
- Thomas R. Guskey & Therese D. Pigott (1988) Research on Group-Based Mastery Learning Programs: A Meta-Analysis, The Journal of Educational Research, 81:4, 197-216.
- Guskey, T. (2005). Formative classroom assessment and Benjamin S. Bloom: Theory, research, and implications.
- Kulik, C.-L. C., J.A. Kulik & R.L.Bangert-Drowns. (1990). Effectiveness of Mastery Learning Programs: A Meta-Analysis. Review of Educational Research, 60(2), 265–299.