"Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common." - Albert Einstein

Wednesday, January 28, 2015

Why Cramming Does Not Work

Back in high school, we had regular weekly quizzes on current events. The quizzes were based on the contents of a bulletin that we were required to buy and read. Since the questions required a simple retrieval of information, I often read and memorized as much as I could within an hour before the quiz. After all, the quiz was only measuring a sciolistic or superficial knowledge of what was in the news. Whether I would retain the information hours after I took the quiz did not really matter.

A quiz that requires only frivolous pieces of information is where cramming works best. It does not work in mathematics or in the sciences, especially when problem solving is expected. To solve problems requires first and foremost a correct choice of strategy. A final exam in chemistry, for instance, can cover so many chapters and a large part of the exam relies on a student correctly recognizing what topic is being covered by the question and choosing the appropriate approach. This is likewise true in mathematics. Cramming only involves memorizing large amounts of information in a short period of time. Due to lack of practice and time to digest, it is not possible for a student who only crams to relate and identify different strategies and problems.

Courses in schools are usually structured into various lessons. Lessons are drawn based on topics. It is therefore common to see lessons that focus on a topic or two. In third grade, students may spend some time, for example, four weeks, learning multiplication. Then the next four weeks may be devoted to learning fractions. And another four weeks may be focused on decimal places. With cognitive load in mind, it is important to lecture on one topic at a time. With regard to activities and homework, it is not necessary to limit an assignment within the topic currently discussed or taught in class. It is possible to add questions from topics previously covered. Doing this allows for students to see problems of various kinds. Questions are not necessarily on the topic at hand. It is only through this mixing that a student receives an opportunity to practice identifying problems, making choices, and drawing appropriate strategies. Rearranging problems in students' activities or homework so that the questions do not belong to one topic is called interleaved practice.

Several studies have shown that interleaved practice is superior to blocked practice (activities or homework that focus only on one topic or one style of problem). For instance, a recent study published in the Journal of Educational Psychology, shows that interleaved practice leads to better results even when a review session is provided. This study takes place in a middle school in Florida. The lessons covered include graphing and calculating slopes. One group of students receives practice problems that are solely on the topics covered while another group has to work on problems from previous topics such as fractions, proportions, percentages, statistics and probability in addition to the problems on graphing and slopes. Both groups are provided a review session a day (or thirty days) before the unannounced test on graphs and slopes.

And the results are summarized in the graph below:

Above copied from Rohrer et al.
After a month has passed after the review session, students who are taught in an interleaved fashion demonstrate far better retention of what is learned during the lessons on slopes and graphs.

During my high school years, I would have probably remembered more and understood better what was going on if those quizzes were based not only on the weekly bulletin at hand but also on previous ones. Seeing a concrete example of an interleaved activity is perhaps useful at this point so I am sharing here a homework that my son has just received from his teacher. My son is just beginning to study division at the moment. His class has finished addition and subtraction with numbers containing multiple digits, fractions, making estimates, decimal places, and number lines. The homework below obviously does not contain only division questions:

Seeing the above set makes it quite obvious that a student working on this homework needs to identify the problem first. From there, a student then chooses the appropriate strategy. The questions do not fit under one topic or category. This practice, based on controlled studies such as the one published by Rohrer et al., leads to better performance and a longer retention of knowledge and skills.

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