Study Skills: Interleaving & Spacing (Math)

INTERLEAVING AND SPACING

Are you looking to improve your ability to recall when to apply a specific formula, theorem, concept, or procedure?   Try the simple, yet effective, strategies of interleaving and spacing to better consolidate your learning and prepare for exams.

Many students use the blocked method, in which they practice a number of similar tasks in a long sequence.  As a simple example, the learner may practice solving multiplication problems for an hour then switch to practicing divisional problems. Blocked practice is effective when initially learning a new concept (as you need to repeat an equation or skill to adequately learn it) but has been proven to be less effective for solidifying a student's ability to discern the proper approach to solve different types of problems. 

Blocked practice

Cognitive science, however, demonstrates that practicing similar tasks in a row is less effective for long-term retention than mixing up (interleaving) tasks that require different strategies.  Interleaving exercises forces the student to choose the correct method to solve each question, whereas blocked practice simply requires the learner to duplicate the process again and again without thinking about which specific strategy is correct. In fact, students who rely solely on blocked practice disengage from learning as they may lose focus when repeatedly performing the same task.

When the learner has to concentrate on when to apply an approach their learning is strengthened because the necessary cognitive effort is required to identify similarities, differences, and connections between concepts.  In addition, when similar problem types are spaced out over time, retention increases because the student must recall the correct method. This approach requires the learner to pay more attention and significantly increases engagement.

Studies suggest not to interleave different subjects during interval study. Interleaving unrelated subjects (math and Spanish) can lead to frustration due to cognitive overload and can undermine retention and recall. Experts believe it is most beneficial to interleave content that is similar or related (e.g. math equations). 

Interleaving

It is also advisable to switch up the order or tasks (as done above) partway through your study session, as this involves even more cognitive effort and further improves retention.

We suggest the learner take a short (10-15-minute) break between each study interval and a longer break about halfway (e.g. before changing up the task order).  It is strongly recommended to do something active, such as take a brisk walk, as this helps consolidate your learning and recharges and refocuses your brain for the next interval.

It is helpful to further mix-up problem types when preparing for exams.  For example, over a 30-minute period, consider doing a few multiplication problems, then division, then fractions, then division, multiplication, followed by fractions.  This approach more closely mimics the format of most assessments. 

Spacing

Spaced learning is the idea that practicing a skill or retrieving information is more effective when spread over time, rather than repeated several times over a shorter period.  Research has proven that practicing over time with intervals in between specific problem types slows down the forgetting process and is critical to the consolidation of memories (recall and retrieval).  As the brain learns new information new neural connections (where memory is stored) are constructed.   Spaced out practice and review strengthen these pathways and best supports retrieval. While interleaving supports learning during a study session, it is recommended to space out your reviews of certain concepts, problems and information with intervals of days between, as opposed to concentrating your review over just a few days (e.g. avoid cramming).  We recommend that you not only review new learning but also take the time to review content from previous weeks to ensure you are consolidating your knowledge and eliminating the effects of forgetting caused by time.

Week 1

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