January 26, 2007

On Improving the Traditional Curriculum

(Cross posted at KTM-II)

Here's a question I've been struggling with for some time now:

Under the traditional curriculum why didn't mastery learning become the norm?

With the exception of the haphazard presentation of material is some of today's constructivist texts, traditional texts typically present a lesson, provide some practice, and then move on to the next topic in the sequence. Many students learned the material using this approach, but there was no effort to get the student to master the material and firmly place the material into the student's long term memory where it is somewhat protected against the ravages of forgetfulness. The inevitable result is that the student partially or fully forgets much of the material once the class moves on, unless the skills taught are used in subsequent lessons (like in elementary math). It was rare that we ever got a cumulative exam at the end of the year which was probably intentional because most of the students had forgotten the material taught in the first half of the year. This practice was mitigated to an extent by the fact that much of the material was retaught year after year--a precursor to today's spiral curriculum.

Nonetheless, this seems to be a horribly inefficient way of teaching to me. Yet it seems the have developed as the dominant form of (pre-constructivist) instruction by the latter half of the 20th century.

The question is why did it develop this way? Why not mastery learning?

Before you answer take a look at this blurb from Engelman's new book (pp. 30-31):

Mastery is essential for lower performers. Unless the practice children receive occurs over several lessons, lower performers will not retain information the way children from affluent backgrounds do. Prevailing misconceptions were (and are) that children benefit from instruction that exposes them to ideas without assuring that children actually learn what is being taught. If you present something new to advantaged children and they respond correctly on about 80 percent of the tasks or questions you present, their performance will almost always be above 80 percent at the beginning of the next session. In contrast, if you bring lower performers to an 80 percent level of mastery, they will almost always perform lower than 80 percent at the beginning of the next session.

The reason for this difference is that higher performers are able to remember what you told them and showed them. The material is less familiar to the lower performers, which means they can’t retain the details with the fidelity needed to successfully rehearse it. After at-risk children have had a lot of practice with the learning game, they become far more facile at remembering the details of what you showed them. When they reach this stage, they no longer need to be brought to such a rigid criterion of mastery. At first, however, their learning will be greatly retarded if they are not taught to a high level of mastery.

This trend was obvious in the teaching of formal operations. At first, the low- and high-performing groups were close in learning rate. Later, there were huge differences. Group 2 was able to learn at a much higher rate, largely because it was not necessary to bring them to a high level of mastery. On several occasions, I purposely taught the children in Group 2 to a low level of mastery (around 60 percent). I closed the work on the topic with one model of doing it the right way, and I assured the children that this was very difficult material. At the beginning of the next lesson, almost all of them had perfect mastery.

So, I think the answer to my question as to why mastery learning didn't become the norm is simply that it wasn't needed. Why go through all the effort of mastery learning when the higher-performers really didn't need it to learn? If the teacher is basing their performance on the feedback they are receiving from the successful students (only 60% mastery is needed), it's easy to see how one could reach the false conclusion that that's all the teaching a student needs to learn. And human nature being what it is, why teach more when less will do.

Nonetheless, I think we now know enough about how the brain works to know that retention of learned material is greatly enhanced when the learner engages in distributed practice after the initial mass practice. All students would benefit from distributed practice. So why haven't traditional educators changed their ways to offer more distributed practice?

I understand there is a philosophical objection to distributed practice (i.e., drill and kill)at the elementary school level. But what about at the secondary and post-secondary level where traditional education is still the norm? At this level, distributed practice just means giving a a couple of additional independent work problems that keeps previously taught material alive for the student until the material is better retained in long term memory. So why are classes at these levels still taught like the need for distributed practice doesn't exist?

Moreover, if the goal is to eradicate the worst practices of constructivist teaching, wouldn't it be beneficial to improve traditional teaching methods to incorporate techniques that will improve student performance? One of the reasons why constructivism has gained the foothold it has is due to the underperformance of the traditional curriculum, especially among lower-performers.



Anonymous said...

Kill and drill. One cannot master the material needed to understand the next level of material in my class-chemistry-without lots and lots and lots of practice that cannot take place inside the 88 minute every-other-day classroom time. Period.

Students MUST be automatic (not having to figure it out all over again) in their work on all previous material in order to learn the new material. Students MUST know the symbols of the elements in order to determine their electron configuration so they may determine how they will bond with other elements. Having to figure out what Na is about when asked to show how it bonds with Cl will ALWAYS lead to failure in chemistry.

Homework not needed? Only if you truely desire FAILURE for the children.

Anonymous said...

The funny thing about "Drill and Kill" is that every musician and athlete knows it as "Practice Makes Perfect." No pianist or football player would dream of running through a sonata/game plan once and then not doing it again until concert/game time.

However, I am not sure where I stand on homework. Sure, practice is necessary. But if students don't know what they are doing, they will inadvertently reinforce their own mistakes, and make it all the more difficult to learn the "right" way to do things later. At least in the classroom, an instructor is theoretically there to say "no, you've missed step X." With elementary school topics, subject matter is often simple enough for parents to offer assistance.

That being said, I like the way homework is handled in my son's class. They get a packet that is due a week later. Anything that doesn't get done in class has to be done at home. Advantage one, kids don't fall behind as easily. Advantage two, parents have a crystal clear idea where their child's weak areas are (and has the opportunity to offer an help).

Anonymous said...


A quibble: Practice does not make perfect. Rather, the perfect practice makes perfect. That is, a student must repeatedly do something correctly in order to master it.

This relates to your HW discussion. I teach 6th grade math. I give HW nearly every night -- usually 5 to 10 problems related to the day's lesson -- and go over them the next day. I do a cursory check to ensure that the HW was done with appropriate effort. I may focus on a problem or two as I travel around the room to see if there is a systemic misunderstanding or if certain students are making the same mistake. We evantually go over the HW as a class. It is incumbent upon the students to correct wrong answers so they can engage in a "perfect practice".

Anonymous said...

NYC Math Teacher:

You are of course correct. It doesn't matter how much you "practice" or "drill" if you aren't doing it correctly to begin with. Unfortunately it took me too long to get to that idea. Of course most academic subjects are more like French (where if you don't practice, you forget it) than riding a bike (which we keep hearing is a skill you never really forget).

I hope when you go through the correct answers to HW, you go through the steps to get there instead of merely "Number one was 862. Number two was -71." If they can't figure out what part of the problem was practiced imperfectly... well you get the idea.

Unknown said...

One of the reasons why constructivism has gained the foothold it has is due to the underperformance of the traditional curriculum, especially among lower-performers.

Amen, Brother Ken.

KDeRosa said...

I knew you'd like that line.

Anonymous said...

It's Liz from I Speak of Dreams.

The forum members at Schwab Learning have a question that I don't know the answer to, and I imagine you might:

SchwabLearing Parent Forum.

Are there research-based math instruction programs like the reading programs? having difficulty finding info.

16yo with math disability. School's choices are SpEd math (not appropriate) or regular class. But how do we ensure what they're doing will meet needs?

KDeRosa said...

Hi Liz,

There ias not nearly as much math research as there is reading research. The WWC has started to go through it and so far, it's not very encouraging.

The only large scale research on math programs that I know of was Project Follow Through which is know 30 years old. The effect size was about a standard deviation, but only grades K-3 were tested. The successor to that math program is SRA's Connecting Math Concepts which is a K-6 program.