No Kill and Drill

  Unfortunately, there is a segment of the population who still believe the old ways are the best.  Lecture on something new every day and have them practice tons of problems within a short time before moving on.

Unfortunately, this does not mean that students will truly learn the material.  I discovered the other night that some people feel we should not integrate technology into the classroom to the extent of making students more independent because these same students could easily find the answers on the internet.

Yes, they could but they don't know what they are doing if you throw in a quiz here and there or if you require them to explain each and every steps and require justification for each step.  In addition, it is felt that if I as a teacher are not requiring 20 to 30 problems per day, I am not doing my job.

Current research indicates that we should not be assigning tons of the same type of problems to the students each day.  What we should be doing is assigning several problems arranged in such a way that no two problems in a row are solved in the same manner. For instance, you might have them find the area of a circle, solving a multi-step equation, finding the answer to 6^3, graphing a linear equation, identifying the transformation then start again.

Then this is done, it forces students to choose a strategy based on the problem itself rather than knowing that is the strategy being used in the section.  It creates a more real life situation such as you might find in a job.  It allows them to learn what they need to know.

Most schools have textbooks are still set up to introduce new material complete with lots of problems that all use that strategy to solve.  Because the problems are not mixed students do not get to practice selecting a strategy and the solution to that problem is found by choosing the correct strategy.  In addition, many problems are similar but require different strategies to solve.  Understanding this, helps students read problems more carefully.

With most textbooks, students know they have to use a certain strategy to solve all the problems in that group so they do not have to read the problem.  Furthermore, this type of practice means students believe they have learned to solve the problems when in fact they do not because they have not had the opportunity to select a strategy.  Even in mixed review sections, the publishers have grouped several problems of the same type together.  In other words, students are trained to just do the problems all the same way so when they get a test where the problem types are mixed up, they do not do well.

One way around this is to make a copy the mixed review problems or several problems from different sections of the text book, cut them into individual problems, tape them on a new paper and make copies, if you are still doing things the old fashioned way.  If not, take the problems and create a quiz with no two problems requiring the same strategy next to each other.

Another way is to just assign a bunch of different problems from different pages such as page 32 #5, page 45 # 10, page 61 # 12, etc. No matter which way you choose to do it, you are helping students to really look at the problems to choose a strategy rather than just blindly doing problem after problem as is normal.

So should all their practice be done this way?  No, it is recommended that one third of the problems be interleaved but the first few problems should all be the same so they get practice in the strategy.  When giving interleaved problems, students should be given immediate feedback so they can make corrections and ask questions for clarification.

Interleaved practice does raise scores on tests which contain a bunch of different problems much in the same way as a cumulative test is set up.  It helps students learn to both choose and use a strategy which is something they need for most high stake tests.

Let me know what you think, I'd love to hear.