I tutor in an afterschool program that is being heavily funded by the feds for intervention in math for k-5 kids. We were specifically told not to spend time on basic facts. We are encouraged to use “rich” problems like....If I am building a neighborhood of homes and can use the numbers 3, 5, and 6 for the addresses, how many homes can I build? It is so sad to see these kids being pushed to do fractions and higher level algebra everyday when they are counting on their fingers for every addition and subtraction step and don’t know the basic steps of a multiple digit multiplication and division problems.
I’m a tutor, and thank God, I’m not bound by those regulations. I start with the basics and then move on. Sure it takes longer but I get results.
My daughter just started 5th grade. When she was in 3rd she could add subtract multiply and divide. However, she only knew the algorithms and she didn’t really have an understanding of what she was doing. She really didn’t understand our base ten system and place value.
We found an incredible math program and started over. It was very childish for her at the beginning but the program is based on an asian model of math and was very different than anything we had been exposed to before.
If she had been in public school they would have kept pushing her through and she would have been math illiterate like I was until I started to teach her this program. Now she is understanding math and doing well.
Without a strong foundation there is no hope of moving on to higher levels with understanding.
All of education today is stressing higher-order thinking. Personally, I think the two lower steps of Bloom’s Taxonomy, knowledge and comprehension, are critical and at points, actually use skills educators consider low and too often insignificant. For example, I consider summarizing, listed in comprehension, a skill that uses more higher-order thinking than it’s given credit for. Unfortunately, teachers are being taught higher-order thinking “good”, lower-order thinking “bad.” But without the foundation of knowledge and comprehension, children aren’t able to move to the higher levels which they mostly aren’t ready for until they’re older anyway.
One of my favorite quotes from Thomas Jefferson targets the result better than any words of mine could:
“There is a certain period of life, say from eight to fifteen or sixteen years of age, when the mind, like the body, is not yet firm enough for laborious and close operations. If applied to such, it falls an early victim to premature exertion; exhibiting indeed at first, in these young and tender subjects, the flattering appearance of their being men while they are yet children, but ending in reducing them to be children when they should be men.”