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I have been talking about homework and practice. How much practice is necessary for a student to really understand how to do something? I have seen research that says 20-30 repetitions will generally store something in permanent memory. Many have posted on the forum/discussion site that they assign 5-10 problems. Is this enough? Is it only once or is it 5-10 related problems for more than one day? I have students that require several days of practice before they get some topics - and even then it is a struggle. Thoughts??

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Comment by Ryan LP Coenen on January 28, 2010 at 4:37pm
I like to think of it in terms of think time instead of # of problems. If you remember back to your proofs classes in college, very rarely were you assigned more than 8 or 10 proofs to for homework in an entire week's problem set. However, each proof would take me upwards to a couple of hours to complete. I didn't have to do 30 to remember how to do them. I had just spent a very large portion of my free time thinking about math. That's how I believe concepts stick in terms of memory and retention. If you are a concepts/connections teacher, you probably worry more about think time or Time On Math. If you are a skills teacher, you probably worry about more # of repetitions ~ they might not know why they are doing something, but they have done it enough that it is engrained in the backs of their heads. Saxon math and our military prove that this can be a successful regimen. However, a lot of teachers would argue that there is very little actual thinking being done when working with Saxon material ~ very little creativity ~ very little problem-solving awareness.
Comment by Kari on January 31, 2010 at 10:00pm
So I think math should consist of both (few questions and many questions) depending on what you are teaching that day. Sometimes your content for the day is just a basic skill - required so that the student can solve a a word problem - or something that involves a higher order of thinking. The basic skills do require much repetition. They should (like playing a sport or an instrument) become "muscle memory", automatic, no thinking involved. Lots of practice required. When your content for the day involves problem solving I would give less problems. They take longer, require more thinking, and not all word problems, etc. are the same - so the "muscle memory" doesn't really happen. I think math is a mix of both and the homework should follow suit.
Comment by Paula Larsen on February 1, 2010 at 12:44am
Kari,
Thanks for your input. Maybe I wasn't as clear as I should have been. I agree that a mix is required. Of the problems that I assign, the first day of the lesson is generally the basic skill - solving proportions. The second day entails mainly application/word problems - how to set up a proportion in order to solve. If we require a third day, it generally involves both the basic, application, and review problems from previously. I truly believe that repetition is what helps with retention. Just because they can do the process 10 times doesn't mean they understand the concept or can retain the information long term.
Comment by Kari on February 1, 2010 at 7:25am
I definitely agree with you. Just because a student can answer a basic skills question doesnt' mean they understand what they are doing. Once the skill is part of their permanent memory I think that more repetition is overkill and doesn't add understanding. So I guess the real question is how can we get a student to really understand the concept behind the skill? And what kind and amount of homework will lead to this.

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