Math - long term thinking

[bethben]

My 6th grader is currently in Saxon algebra and having no problems with it. Saxon fits his learning style with the constant review and incremental steps. He makes computational errors in his work which show he knows the material, but is just a silly mistake. Just to make sure his word problem solving is good, he is also doing AOPS alcumus. His problem solving skills are doing just fine. He really likes math, but I can't see him joyously spending an hour on a problem just so he could get the right answer, KWIM? He likes the straight computation but can't see himself just doing word problems exclusively.

 

Here's the question. At the rate he's going, he will be hitting calculus in 10th grade. Do I just let him continue through all the levels without slowing? I talked with my math professor neighbor across the street who by the end of high school, had finished linear Algebra (a class or two after Calculus). Or, do I switch to a more challenging program like AOPS? My dilemma is that he really does better with constant review.

 

I'm hitting unknown territory here. Any help would be appreciated!

 

Thanks!

 

Beth

[Belacqua]

It's been a while since I looked, but CTY used to offer linear algebra, multivariable calc, and differential equations among their online courses. That could be something for you to consider.

[regentrude]

A few thoughts.

 

First: careless computational errors in a student with conceptual understanding are often an issue of maturity. Both my students went through phases like this, in the beginning of algebra in 6th/7th grade, and we took the time to work on the issues by using graph paper and color for signs. Patience and perseverance made the errors go away, but it took time. So, don't gloss over it, but work on the issue.

 

Second: straight computation will become less and less important, because math is needed as a tool to solve problems - so a solid mastery of word problems is a must. It is in doing word problems that true understanding is demonstrated, not it straight computation. Supplementing Saxon which is lacking in creative word problems with Alcumus sounds like a good idea.

 

Third: If your student is advanced, beware of the race to calculus See here:.

http://www.artofprob...alculusTrap.pdf

Instead, take the time to study some topics in discrete math like number theory and probability theory for which the traditional sequence does not have enough time. We have used AoPS Counting and Probability for a one semester break from algebra, and I can highly recommend it.

 

Fourth: I would consider switching to AoPS. A student who is mastering a traditional algebra course in 6th grade will benefit from the different approach and the different way to think about math. It may not work for your student, but I would definitely investigate this option. Both my kids are accelerated and using AoPS with great success.

 

Lastly: If the student has indeed thoroughly mastered algebra 1 and 2, geometry and precalculus, there is no problem in taking calculus in 10th grade. My 15 year old who would be in 10th grade in ps took calc 1 over the summer. It prepared her well enough to ace a weed-out calculus based physics course at a STEM university this fall semester. She is doing calc 2 over winter break so that she can take the second semester calc based physics in the spring. For next school year, we are planning multi-variable calculus and differential equations. There is plenty of math after high school calculus, no danger of "running out of math".