The shuffling of mathematics problems improves learning

  title={The shuffling of mathematics problems improves learning},
  author={Doug Rohrer and Kelli M Taylor},
  journal={Instructional Science},
In most mathematics textbooks, each set of practice problems is comprised almost entirely of problems corresponding to the immediately previous lesson. By contrast, in a small number of textbooks, the practice problems are systematically shuffled so that each practice set includes a variety of problems drawn from many previous lessons. The standard and shuffled formats differ in two critical ways, and each was the focus of an experiment reported here. In Experiment 1, college students learned… 

The benefit of interleaved mathematics practice is not limited to superficially similar kinds of problems

It is concluded that interleaving improves mathematics learning not only by improving discrimination between different kinds of problems, but also by strengthening the association between each kind of problem and its corresponding strategy.

Interleaved Practice Improves Mathematics Learning.

In the experiment reported here, 126 seventh-grade students received the same practice problems over a 3-month period, but the problems were arranged so that skills were learned by interleaved practice or by the usual blocked approach.

The Scarcity of Interleaved Practice in Mathematics Textbooks

A typical mathematics assignment consists of a block of problems devoted to the same topic, yet several classroom-based randomized controlled trials have found that students obtain higher test scores

The effects of spacing and mixing practice problems

Sets of mathematics problems are generally arranged in 1 of 2 ways. With blocked practice, all problems are drawn from the preceding lesson. With mixed review, students encounter a mixture of

Spaced Retrieval Practice Imposes Desirable Difficulty in Calculus Learning

After being taught how to perform a new mathematical operation, students are often given several practice problems in a single set, such as a homework assignment or quiz (i.e., massed practice). An

Interleaved practice enhances memory and problem-solving ability in undergraduate physics

In a domain that entails considerable amounts of problem-solving, replacing conventionally arranged homework with interleaved homework can (despite perceptions to the contrary) foster longer lasting and more generalizable learning.

A randomized controlled trial of interleaved mathematics practice.

We report the results of a preregistered, cluster randomized controlled trial of a mathematics learning intervention known as interleaved practice. Whereas most mathematics assignments consist of a

Spaced mathematics practice improves test scores and reduces overconfidence

Correspondence Doug Rohrer, University of South Florida, Psychology PCD4118G, Tampa, Florida 33620. Email: Abstract The practice assignments in a mathematics textbook or course can be

The effects of interleaved practice

Previous research shows that interleaving rather than blocking practice of different skills (e.g. abcbcacab instead of aaabbbccc) usually improves subsequent test performance. Yet interleaving, but



The effects of cumulative practice on mathematics problem solving.

Cumulative practice of component skills is an effective method of training problem solving in basic algebra rules teaching to college students.

Learning “How” Versus Learning “When”: Improving Transfer of Problem-Solving Principles

Experiments examined how instructing learners about when to apply problem-solving principles may later improve performance and found that subjects who received applicability instructions made fewer confusion errors when learning the similar problem pair.

Effects of Massed and Distributed Practice on the Learning and Retention of Second-Language Vocabulary

AbstractHigh school students enrolled in a French course learned vocabulary words under conditions of either massed or distributed practice as part of their regular class activities. Distributed

The Effect of Overlearning on Long-Term Retention

Once material has been learned to a criterion of one perfect trial, further study within the same session constitutes overlearning. Although overlearning is a popular learning strategy, its effect on

Timing of Information Presentation in Learning Statistics

Simultaneous presentation ofprocedural information before and supportive information during practiceled to the most efficient learning.

Application of the Testing and Spacing Effects to Name Learning

SUMMARY Four experiments investigated the effects of testing and spacing on the learning of face-name stimulus-response pairs. Experiments 1a and 1b compared the recall of names following intervening

Motor schema formation and retention in young children.

The variability-of-practice hypothesis, a major prediction of Schmidt's (1975) motor schema theory, was tested in an attempt to investigate motor-schema formation and transfer to novel tasks in the same movement class.

Distributed Versus Massed Practice in High School Physics

An analysis of the effects of distributed practice in physics was undertaken. The subjects were 41 students, nearly equal numbers of males and females, in two suburban high school physics classes.

3 Optimizing Long-Term Retention and Transfer

  • Education
This chapter considers training conditions that do or do not facilitate posttraining performance. We focus on two aspects of posttraining performance: its durability (long-term retention), that is,

New Conceptualizations of Practice: Common Principles in Three Paradigms Suggest New Concepts for Training

We argue herein that typical training procedures are far from optimal. The goat of training in real-world settings is, or should be, to support two aspects of posttraining performance: (a) the level