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Seven Instructional Strategies Every Teacher Needs to Know, Part 2: Mixing Solved and Unsolved Problems
posted by: Melissa | May 19, 2016, 05:00 AM   


Last week, we started a series on techniques that are available to every teacher, require only minor tweaking to teaching style, and have been identified by IES to have a significant impact on student learning. Unfortunately, these techniques are often overlooked in professional development or in teacher preparation yet they are worthy of being covered.  We started with distributing practice over time, and continue today with mixing solved and unsolved problems.


Consider the following math lesson:  A teacher is starting a lesson by teaching a new concept to their students.  They go over the concept and illustrate it with several examples they walk through.  Then they put an example on the board and have a student come up and work through the answer with help from their classmates.  Then there are a few examples to try with a partner and finally, a homework assignment that reinforces the concept that students will do on their own that night.  This is a prime example of gradual release or “I do, we do, you do,” that many teachers are taught in school. Unfortunately, the technique may not be the best way to teach through new problems.


In another classroom, an English teacher goes through the process of teaching a lesson on the use of commas.  In this classroom, there was a lesson that taught the basic rules of comma usage. Then the teacher gave the class an example sentence where the comma was circled.  Students were then given a sentence with no commas and asked to put them in the right place.  They do so, go over the answer, and then the teacher shows another sentence with a correctly placed comma.  They go over and through this pattern for the rest of the lesson.  When their homework is distributed that night, the page has several sentences where the student needs to place the comma interspersed with examples of sentences with correctly placed commas.


The second illustration is an example of the IES-recommended practice of interweaving solved and unsolved problems.  In this method, after every few problems, the students see an example of a correctly solved problem.  This example should have very little explanation of what makes their technique correct, encouraging students to look at them closely and think deeply about the differences between what they did and the example.  Students should start by seeing a solved example every other problem, but as they gain mastery, fewer and fewer examples are needed.  Teachers need to carefully monitor student progress in order to balance solved and unsolved problems correctly.


This is a simple change but it can be a powerful one.  Several studies have proven the ability of students to perform better on post-tests after using this technique.  One study showed dramatic acceleration of learning where students using this technique learned three years’ worth of material in only two!



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