How should students most effectively allocate their time in order to truly comprehend a subject such as math? Studies on cognitive learning show that students have greater retention when they are exposed to a topic more frequently, in shorter timeframes and extended over a long period of time. Cramming is the least effective method of learning. Due to the linear nature of math and the connection between the fundamental building blocks and more advanced learning in the subject, retention and comprehension of previous topics is essential for a student to grow in math.
The two methods of learning are known as Massed Practice and Distributed Practice. Mass Practice involves less frequent and longer sessions compacted into a shorter time period. Distributed Practice refers to spreading out a lesson over a longer period with shorter but more frequent sessions. Research demonstrates that distributing learning results in a better understanding and recall of a subject. This has been referred to by Cognitive Scientists as the “spacing effect.”
The theory of the spacing effect was developed by Herman Ebbinghaus in 1885. He was credited with performing the first scientific studies on memory. The spacing effect has held up to numerous testing by researchers over the years. In 1967, Geoffrey Keppel tested the spacing effect on college students using words paired with adjectives in a nonsensical manner (e.g., lum-happy). Half the subjects were tested using massed practice while the other half used distributed practice to learn these word pairings. The results demonstrated that there was a considerable loss of knowledge in the students that used the massed practice after a week. However, after the same rest period between learning and testing, the students the distributed practice group displayed a higher retention with these word pairings.
The spacing effect is not only applicable to college students. Studies have been performed on high school as well as elementary school students. In one study of third grade students, those employing a distributed practice method of learning showed a significant performance enhancement on a test (70% correct) over those using massed practice (53% correct). Studies have also been conducted over more extended periods of time and support the position that students achieve greater learning by having their lessons distributed over a period of time.
As stated earlier, retention of previous topics in math is essential for more advanced learning. Continued practice on the building blocks of math –numerical fluency and number sense –at an early age is essential for a child to develop into a strong math student in later years. “Regular practice, in moderation, is not what drives children away from math. What really makes them dislike and fear math is not understanding it . . . The antidote to such anxiety is greater familiarity with Math. And such familiarity comes from repeated exposure," said William Bennett, former US Secretary of Education. “Since each lesson builds on those that came before, students must retain a solid understanding of what was taught previously. Even as new operations and principles are being introduced, children spend time practicing old ones . . . Assignments may consist of three problems like those worked last week, three like the ones worked yesterday, and six problems dealing with the concept the teacher introduced today." Madeline Hunter, author of Retention and associated with S.C.'s PET program-Program For Effective Teaching, wrote "Once something has been learned, distributing practice usually ensures longer retention."
At Mathnasium, we employ Distributed Practice in our teaching methods. Through the assessment process, we determine areas in which students need assistance or extra practice. From this assessment, we develop a learning plan of prescriptive kits (or PKs) consisting of packets of worksheets assigned to students so that they can practice the specific areas in which they demonstrated weak abilities. Students practice each topic over several visits as they work towards mastering a concept. This process assures that virtually every Mathnasium student develops a thorough understanding of each concept before moving onto their next step in learning math. With this mastery, each student’s foundational skills will be strong for future learning.
Call today 303-840-1184 to schedule your child's no risk assessment and find out the areas in which they could use some Distributed Practice.
