I subscribe to the mastery method of education when it comes to The Three “R’s”. If you don’t know a concept, I see no point in “pushing on”. Once you understand the theory, however, is it okay to cut some corners?
Arithmetic is probably the most obvious area where this applies. We teach a new lesson and have our children do multiple practice work, showing they have command of the concept. We watch them proceed with fluency and then perhaps reduce their work slightly as they progress.
Once mastery is achieved, is it okay to let them use helps; mainly, a calculator? Am I going to somehow damage the work already done and undo necessary wrinkles if I let them cheat and use a device to help them reach their answers faster? Is using a calculator even cheating?
Honestly, I don’t have an answer for you. (Sad; isn’t it?) However, I do have some thoughts and perhaps some ideas.
I think letting our children use “helps” on a regular basis will retard their learning. Meaning: they will slowly begin to lose the knowledge of how to work without the aid of helps. So, using them all the time would be harmful. I also think never letting them use helps might be a concern, especially when it comes to higher maths. (Sheesh; one problem could take hours.) Therefore, I suggest balance.
Therein lies the tricky part. When do we allow the use of helps and when should we not? Again, I have no straightforward answers. (I really am troublesome today, aren’t I?) Each family must decide for themselves the correct method.
I do not believe helps are a good idea for the littlest youngsters; again, they need to first master the concepts. So, helps are not an option for them. Sorry, guys!
For the middle-aged kiddos, it gets a little trickier. Here is where the balance comes in. For our family, daily work must be done by hand. I want to see the work and the path which got them to the end result. (Method is just as important as finding the right answer.) During test times and the occasional quiz, this is where a calculator might be made available. I find that allowing them the use of helps keeps them moving quickly and keeps them from being frustrated with a four page test.
High school kids are pretty much free to choose, as far as I am concerned. At this point in their learning, they are doing advanced math with graphing calculators and extensive theorems; I would hate for them not to use helps, the poor things. I would still give an occasional pop quiz, to make sure the fundamentals are good to go, but, overall, helps are acceptable.
Honestly, I don’t think this idea would have ever popped up for us if it hadn’t been for SAT testing (standardized testing, not college) with our PSP last year. I fully intended for “T” to use a scratch paper and pencil during the arithmetic section of her test. The school suggested a calculator though, for the exact reasons listed above. This opened up whole new avenues of thought for me and I’m glad we had the opportunity to reflect. “T” was more relaxed and able to focus knowing her only concern was method and not spending so much time doing the calculations.
Thus far, our plan is working. The kids are progressing nicely in their learning and we are appreciating the compromise. Now; if I could only get over the nagging feeling that this is somehow cheating….
How about your family? Do you allow “helps” during your learning day?