The concept of practicing has always been a key step in the learning process. How we practice is worth a close look. When I did my thesis for my masters degree in the 1990's, I based it on what I had witnessed using the Saxon series of textbook. An article describing this approach is 'interleaving'.

Interleaving purposely mixes multiple problem types from more than one topic into one practice session to force the student to differentiate between topics, types of problems and problem solving techniques. This is different from 'massed' or 'blocked' practice where a student practices many problems based on the new concept(s) in one session. The book "Make it Stick: The Science of Successful Learning" discusses interleaving and research examples in more detail.

Going back to my experience with Saxon, interleaving proved to be very effective in both the learning process and forming long term connections which provided recall well after the course was completed. Students were given time to grasp a concept in depth before applying it to more complex situations and the constant review seemed to provide effortless recall of topics in the long term.

But you don't need a textbook that utilizes interleaving to incorporate it in your classes. When I accepted a teaching position at another school where the texts were selected for the district, I still utilized the concept. While others were doing the chapters in order, I skipped the first four chapters of the text which were monotonous review of what had been covered in previous courses and we jumped to the new topics. I interleaved the topics of the first chapters into the new topics to help the students recall and relearn in a timely fashion. As for assignments, the new topics accounted for about one-third of the assignment while the rest of the problems were selected from past topics to provide a mixture of recall.

How can we adopt an interleaving approach to practice in developmental mathematics or other courses? Here's an example of one process used to interleave the assignments of Intermediate Algebra.

Click on each step for additional information.