Examples in Math

One of the things I have to do is set a goal to work towards from a list.  I've chosen to work on giving the students ways to help them become more independent learners. Over the past nine weeks, I've realized my students are unwilling to pay careful attention to examples.

Textbook have lots of examples with detailed information explaining how it was solved.  My students prefer being passive as I discuss examples and they really don't want to write things down so beginning next week, I'm going to work with them on learning to "read" examples.

I have one student who takes time to look at his textbook when he does his assignments.  He asks questions when he doesn't understand something and is understanding way more than most who take a passive attitude towards learning.  Most examples include drawings or diagrams to provide the visual key but my students read the problem but won't draw anything so it makes it more difficult for them to understand what is being requested.

I admit, at their age, I didn't want to read my textbook.  I didn't see why I needed to and I'm sure they feel the same.  So it is going to be a bit of a struggle but I think it will be worthwhile.  Over the years of my own education, I've learned how important examples are to learning.  This is something I hope to share with my students.

One way to use examples is to begin with a completed example and having students explain the steps in the example.  This reduces anxiety and memory load so students can focus on understanding the concepts behind the process.  It allows them to explore the equations and process it more deeply because they are not just following a procedure.

There is research to indicate that students learn more accurately from worked examples because they are paying more attention when they concentrate on the examples.  However, students need to be taught to examine examples.  Researchers found there are three components when using worked examples with students.  The first is formulating a problem, the second is examine the steps used to complete the problems.  The third is sharing correct answers with the students. One way to working on the second component is to leave out some of the steps and asking students to supply them.

Research it is not the words the teacher uses to explain the examples but it's getting the students to think about the example as they examined it.  Some of the ways worked examples can be used more effectively in class is to assign a few worked examples to students as part of their homework.  In addition, the teacher should model their thinking as they solve problems.  Finally, create animated worked solutions for students to see solutions develop.  The nice thing about animation is students can rewind and review parts they don't understand.

Another layer to include is to ask students questions like "Why was this strategy used?" or "What principal was applied and why?" because these require deeper thinking.  The question is how do you get students to use worked examples.

One way is to have students explain to themselves as they go through worked examples.  Some of the things they might consider are "where did that number come from?" or "Why did they do that next?"  Another way is to used the faded examples where the first problem is fully worked out, the next example is worked out for the last step which the student fills in.  As the student works through the examples, each one has one less step until they work the complete problem from start to finish.

If you make the problems more complex, its important to show examples with the added complexity so students see how things change.  Let me know what you think, I'd love to hear.  Have a great day.