Effortful Study Requires Mastery Learning

In my last post on making experts, we discussed how effortful study entails continually tackling challenges that lie just beyond the student's competence.

Let's see how effortful study might play out in an academic setting. One such program that I know of that employs effortful study techniques is the program described in Engelmann's Student-Program Alignment and Teaching to Mastery. This is not a DI program per se, but DI is certainly based on its principles. Engelmann calls his effortful study program mastery learning and describes it as such:

A program design that supports mastery does not present great amounts of new information and skill training in each lesson. Rather, work is distributed so new parts in a lesson account for only 10–15 percent of the total lesson. The rest of the lesson firms and reviews material and skills presented earlier in the program. The program assumes that nothing is taught in one lesson. Instead, new concepts and skills are presented in two or three consecutive lessons to provide students with enough exposure to new material that they are able to use it in applications. So a lesson presents material that is new today; material that is being firmed, having been presented in the last two or three lessons;and material that was presented even earlier in the sequence and is assumed to be thoroughly mastered. This material often takes the form of problems or applications that require earlier-taught knowledge.

Each new lesson contains a small amount (10-15%) of new material and lots of practice with previously presented material. Here's Engelmann's rationale.

The amount of new material is relatively small because most students are not capable of assimilating more. This design provides for some “overlearning,” but having the program err in the direction of providing too much practice is better than providing too little practice. Work on material presented in the preceding few lessons is needed to ensure that students are "automatic" with information or operations that were previously taught.

There goes the key word automaticity. Students are to learn the material so well that they are automatic with it. When knowledge is automatic it requires little cognitive toll to recall and use.

Student performance is judged on their first time correct responses, i.e., how well they respond to the material the first time it is predsented in a lesson. Engelmann has four criteria:

Criterion 1. Students should be at least 70% correct on anything that is being introduced for the first time. This percentage is based on the understanding that even the new skills or procedures that are being introduced are not composed entirely of material that is new. Much of it will be familiar. Therefore, the initial rate of correct responses should not drop below 70 percent. If students are at mastery on the preceding lessons, this outcome will occur in almost all cases. If students perform much below 70 percent, they are not learning the material. If they are only 50 percent correct, they may be at a chance level—guessing at the answers or the steps in the operation. Their responses are not generated by an overall understanding of what they are learning.

Criterion 2. Students should be at least 90% correct on the parts of the lesson that deal with skills and information introduced earlier in the program sequence. Criterion 2 is based on the fact that students must be completely at mastery on earlier-taught material. When earlier-taught material occurs in later lessons, no reteaching should be required. If substantial reteaching is needed, the amount of new learning that students must achieve to master the lesson becomes too great.

Criterion 3. At the end of the lesson, all students should be virtually 100% firm on all tasks and activities.

Criterion 4. The rate of student errors should be low enough that the teacher is able to complete the lesson in the allotted time. If students enter the lesson with skills that permit them to attain 70 percent correct on new material and 90 percent correct on material taught earlier, students should be able to achieve virtually 100 percent on all exercises presented in the lesson.

To meet these four criteria, Engelmann devised a system having the following seven requirements.

1. All students must be appropriately placed in each instructional program. All placements are based on first-time-correct performance. Mastery is not possible unless students are placed according to the criteria for first-time-correct performance.

2. All groups must be homogeneous with respect to the performance level of all students in the group. This requirement is an extension of the first-time-correct requirements. Unless all students in the group are appropriately placed, the teacher will not be able to bring the group to mastery in a reasonable amount of time. The teacher will have to spend time providing additional practice to students who should not be in the group. This additional practice tends not to serve students who need it nor the other students, who waste time while the teacher works on firming skills that they have already mastered.

3. There are actually three critical scheduling issues. The first is that adequate time must be scheduled on a daily basis for teaching each group each subject. The second is that the schedules must be coordinated to permit relatively easy movement of students from one instructional group to another, based on their performance. The third issue is that movement of students from one instructional group to another should occur frequently throughout the year. All schedules must be coordinated across classrooms and grades so that cross-class grouping and regrouping is possible.

4. Schedules must provide adequate time for each subject and each instructional group, and teachers must faithfully follow schedules. The schedules must include time for workchecks, so that students receive timely feedback on any mistakes they made, and so teachers receive information about any skills or items that need additional firming.

5. A group’s progress in mastering new material must be continuous throughout the year. If the group completes level 3 reading in the middle of February, students must begin level 4 within no more than two or three school days. Level 4 should not be delayed until the beginning of the next school year.

6. All teachers must enforce the same set of schoolwide management rules and practices for celebrating academic achievements. There should be rules for how students are to behave in the class, so that if students misbehave, they understand both the rule that they broke and the consequence. The system of rules should be designed so students receive reinforcement for complying with rules.

7. The performance of students must be regularly monitored. The school must have systems for regularly monitoring students’ progress. The monitoring information may consist of weekly summaries of progress in each subject, summaries of student performance on in-program tests, and reports on daily independent work. The purpose of the monitoring is to guarantee that no students fall through the cracks and that all receive the best instruction that the school is able to deliver.

Finally, Engelmann has devised four rules for teaching to mastery in his system.

Rule 1: Hold the same standard for high performers and low performers. This rule is based on the fact that students of all performance levels exhibit the same learning patterns if they have the same foundation in information and skills.

Rule 2: At the beginning of the school year, place continuing students who have been taught to mastery no more than 5 lessons from their last lesson of the preceding year. If something is thoroughly learned and applied, it will be retained by lower performers as well as by higher performers.

Rule 3: Always place students appropriately for more rapid mastery progress. This fact contradicts the belief that students are placed appropriately in a sequence if they have to struggle--scratch their head, make false starts, sigh, frown, gut it out. According to one version of this belief, if there are no signs of hard work there is no evidence of learning. This belief does not place emphasis on the program and the teacher to make learning manageable but on the grit of the student to meet the “challenge.” In the traditional interpretation, much of the “homework” assigned to students (and their families) is motivated by this belief. The assumption seems to be that students will be strengthened if they are “challenged.”

This belief is flatly wrong. If students are placed appropriately, the work is relatively easy. Students tend to learn it without as much "struggle." They tend to retain it better and they tend to apply it better, if they learn it with fewer mistakes.

Rule 4: Move students as quickly and as reinforcingly as their performance permits. This rule opposes the notion that teaching to mastery is somehow synonymous with having picky or punishing standards.

According to Engelmann, mastery learning will confer the following benefits to students, teachers, and the school system.

Students benefit by becoming much more competent and by gaining options for their futures they otherwise would not have. Teachers benefit because students who are taught to mastery tend to succeed; therefore, teaching becomes easier. Schools benefit because students are much easier to teach in the upper grades if they have a solid mastery foundation starting in kindergarten. In the upper grades, students are able to learn new material at a good rate, and the bottom end of the student population performs more like traditionally taught students.

Two types of performance change occur in students. The most obvious is that students learn more material during a specified time period. The second change is in their ability to learn new material. There is a simple relationship between the amount of material they master and their overall facility to learn new material: The more success students have with a particular type of material, the better they become at it.

Teaching to mastery also instills self-confidence in students because they learn they are capable of learning whatever new skills or material the teacher presents. Their positive attitude is firmly grounded in experience. Because students have learned everything the teacher has taught, students understandably have confidence that it will happen the same way for future instruction.

Engelmann's mastery learning program works because it conquers the student's motivation problem. In Engelmann's program students are not only challenged every day with new material, but they also practice previously persented material until it is automatic. Students are placed, grouped and proceed at a pace in which they will have learned 100% of the material in each lesson by the end of the day. Student performance is continually monitored to ensure that students are in fact learning the material. The scope and sequence of the program is such that new material is based on previously presented material. Mastery learning ensures that students are successful in learning the material; therefore, students will be motivated to continue their success in learning new material. In short, motivation is not a problem in a properly designed and implemented mastery learning program.

Clearly, Engelmann's mastery learning program is based on sound cognitive science principles, rather than made-up faddish nonsense. We also know that it works because Engelmann's Direct Instruction program is based on these principles and it has been successfully shown to increase student achievement in numerous research studies involving thousands of children.

Of course, the instruction taht takes palce in most K-12 doesn't even come close to meeting the requirements of a mastery learning system as Engelmann has laid out. Predictably, motivational problems are rampant and all but a small faction of students are learning at the rigorous pace needed to succeed in college. Students don't retain information from one year to the next and the efficiency of the entire system is miserably low.

Who succeeds in our current system? The cognitive elite. Smart kids and not-as-smart kids with exceptional teachers and/or supportive parents. These kids learn quickly or have the support needed to learn at an acceptable pace. These kids don't require as much practice or get extra practice from their teacher and/or parents sufficient to master the material as it is presnted to them. these kids are successful learners and are motivated by their success and might be further encouraged by their teacher and/or parents.

Everyone else falls further and further behind as the years go on. this trend shows up clearly in NAEP and state exams. These kids are not mastering the material as it is presented. At best the material is partially mastered. Partial mastery is just another way of saying partial success which means partial failure. Failure kills motivation. Lack of motivation gets in the way of further learning. Eventually learning grinds to a halt or to a trickle. And, then its day care until diplomas are handed out.

So why don't more schools use mastery learning to increase student achievement? You'll find out in my next, and hopefully last, post on making experts.