Effects of Spacing and Mixing Practice Problems
Blocked Practice Vs. Mixed Practice Blocked practice are all problems drawn from the preceding lesson or topic, they are distributed or spaced across many practice sets. Mixed Practice are a mixture of problems from different lessons or topics that are intermixed within one practice set. Blocked practice is less demanding on students because every problem is based on the immediately preceding lesson Mixing improves students ability to pair a problem with the appropriate concept or procedure. Mixed practice is more demanding because students have to link a problem to a preceding concept ; however, the apparent benefit of mixing problems suggest that this easily adopted strategy is underused.
Blocked Practice a.k.a Over Learning PROS CONS Test performance is improved if learners immediately continue to practice that same task after one success instead of quitting after first success. Affects of over learning dissipates with time, and additional over learning has little affect in further increasing performance. High scores on quizzes and tests administered in less than one week period. Experiments has shown that requiring students to work more than a few consecutive problems of the same type would boost subsequent test scores by negligible amounts when tests were delayed.
Experiment # 1 <ul><li>Students were asked to do 3 or 9 problems immediately after a lesson was introduced with each attempt followed immediately by a visually presented solution. Students returned 1 to 4 weeks later for a test that included problems of the same kind. </li></ul><ul><li>These are the average of the scores 3 problems vs 9 problems </li></ul><ul><li>1 week later 69% vs. 67 % </li></ul><ul><li>4 weeks later 28% vs. 27% </li></ul><ul><li>The additional 6 problems provided a negligible benifit. </li></ul>
Conclusion to Experiment 1 <ul><li>Even if heavy repetition did boost test scores, it would not be advisable unless the benefit was greater than that derived from a different use of time devoted to additional repetition. </li></ul><ul><li>The utility of learning strategy should be judged not by its effectiveness but by its efficiency. The data of this study provides no support the heavy repetition that is common in blocked schedules. </li></ul>
Effects of Spacing <ul><li>Spacing is a type of mixed review where the practice problems are distributed across many sets. For example, rather than working 10 problems on the same topic in one session, a student can divide the same problem across two or more sessions. Spacing has been demonstrated with a range of tasks, like learning foreign language, spelling, and mathematics. </li></ul><ul><li>The effects of spacing has shown to be one of the largest and most robust finding in learning research. However, most of the learning studies has involved college students, it has been shown to benefit elementary and middle school students as well. </li></ul>
Spacing Experiments <ul><li>The key of spacing experiments are longer test delays after learning a certain procedure. </li></ul><ul><li>In this experiment students were assigned problems that were either spaced or massed across two sessions separated by a week. The practice problems were allotted a given time and were followed by a visual representation of the complete solution. </li></ul><ul><li>After 1 week testing Spacing vs. Massing (74% vs. 49%) </li></ul><ul><li>After 4 weeks (64% vs. 32%) </li></ul><ul><li>Spacing works by reducing the rate of forgetting , as evidenced by the fact that its benefits increase with longer test delays. </li></ul>
Spacing Conclusion <ul><li>The benefits of spacing have been observed over a wide range ages, tasks, settings, and time periods, where large effects has been discovered. </li></ul>
Effects/Benefits of Mixing <ul><li>Spacing provides temporal separation of problems on a single topic. Mixed practice includes a variety of problems on different topics. </li></ul><ul><li>In both math/non-math subjects there is evidence of improving student performance. These are some of its benefits </li></ul><ul><li>Ensures that a student knows the appropriate strategy for a problem before solving it. </li></ul><ul><li>Pair a mathematical problem with appropriate procedure or concept. </li></ul><ul><li>Improves discrimination ability because it gives the student the opportunity to recognize which features of a problem are relevant. </li></ul><ul><li>Blocked practice require students to know how to perform a procedure, Mixed practice require them to know which procedure to apply and that is key to problem solving </li></ul><ul><li>All of the above benefits are common problems during midterm or final exams, and standardized tests. </li></ul>
Mixed Experiments <ul><li>Students learned how to find the volume of four obscure solids. Every student saw the same practice problem and the same correct solution. Four practice types of practice problems (a, b, c, d) were assigned and arranged as follows: </li></ul><ul><li>Unmixed: a a a a , b b b b , c c c c , d d d d </li></ul><ul><li>Mixed : a b c d , b d a c , c a d b , d c b a </li></ul><ul><li>One week later the students were assessed on the four kinds of problems. Scores on the test given one week later revealed that mixed practice tripled the test scores (63% vs. 20%) </li></ul><ul><li>Similar experiments were done on 9 and 10 year old students on four types of problems on prisms and again the mixed practice group`s performance was far greater 78% vs. 38% </li></ul><ul><li>Both experiments confirm that the benefits of mixing reflects an improved ability to pair problems and strategies. </li></ul>
Limitations of the Experimental Data <ul><li>Although the mathematics learning studies summarized in the experiments above favour mixed review over blocked practice, all of these studies rely on procedural (steps needed to solve a problem) rather than conceptual (concerning underlying principals). </li></ul><ul><li>The tasks at hand still require d routine expertise; solving problems quickly and accurately with or without understanding ; rather than adaptive expertise; ability to apply meaningfully learned procedures flexibly and creatively. </li></ul><ul><li>Further research is still being conducted to determine whether mixed review prompt such expertise to lesser or greater degree than blocked practice. </li></ul>
Retrieval Practice <ul><li>Mixed review is a blend of spacing and mixture that also increases students` reliance on a strategy known as retrieval practice in which to be learned information is retrieved from memory. Retrieval practice boosts retention even after the retrieval fails, given that the student sees correct answers soon after. </li></ul><ul><li>Mixed review increases the retrieval practice in two ways. First, students must retrieve the appropriate concept or procedure from memory. Second, once the correct concept is recalled the student has to recall how to apply the procedure; in contrast, when students confront a series of problems involving the same concept or procedures, such retrievals are required only for the first problem . </li></ul>
Impaired Practice Performance <ul><li>Although spacing and mixing often boosts test scores, each feature impairs practice performance. The test benefits of mixing (63% vs. 20%) occurred even though the mixed practice performance was worse than the mixed practice performance ( 60% vs. 89%) </li></ul><ul><li>A feature that decreases practice performance and increases test performance is known as desirable difficulty. Students and teachers sometimes avoid desirable difficulties because there is a false belief that inferior practice performance yields inferior learning. </li></ul>
Mixed Review and the teacher <ul><li>The use of mixed problems can alter the demand placed on teachers. Normally teachers devote a portion of the lesson to the discussion of the set of yesterdays homework problems that are related to that topic. </li></ul><ul><li>With mixed review the teacher will likely encounter a greater number and a variety of questions. On the other hand; mixed review ensures that the students who failed to understand a lesson or miss a class or two will still encounter many problems on this topic that might address that gap. </li></ul><ul><li>Mixed review does not require any changes in the way teachers present their materials or in the way they teach new concepts. It might only require the teacher to rethink the amount of blocked vs. mixed problems to assign for practice. </li></ul>