Jonathan Bartlett, an ID theorist who blogs here, is also, wearing another hat, well respected as a calculus teacher. See, for example, “The needless complexity of modern calculus. Meanwhile:

Intuition, he says, relies on skill, not the other way around:

In other words, students are frustrated because they are being asked to learn formulas and equations for things that have no connection to their present or future, whose sole purpose seems to be jumping through an arbitrary hoop set up to make them fail.

What Common Core is supposed to bring to the table is a deeper understanding of mathematics, so that students recognize how mathematical thinking is part of thinking in general. While this is a worthwhile goal, common core radically misfires on several accounts.

First of all, Common Core tries to teach the concepts first, and to incorrectly-aged students.

Jonathan Bartlett, “The Fundamental Problem with Common Core Math” atMind Matters News

His takehome point: “Common Core is not as radical as the New Math of the 1950s, but both make the fatal error of prioritizing the thoughts of adults over those of students.”

I agree with Jonathan, and I like the line “the fatal error of prioritizing the thoughts of adults over those of students.”

Motivating kids to understand math, especially calculus and the like, is a difficult task. Although math is part of almost everything we do, most people never have the need to consciously apply things like calculus in their every day lives or careers. Even though we subconsciously apply it every time we throw a ball or drive a car.

Ask most people if they can work out the calculations necessary to throw a basketball from the three-point line into the basketball and they will tell you to take a hike. Yet almost all of us, after a few practice throws, can get the ball to get close to dropping through the hoop.

I enjoyed getting kids to like calc, more or less, to gain satisfaction from their competence, and to get the big ideas. But Johnny’s points above are an important part of doing that. You have to build sophisticated understanding from the ground up, not expect to start with it from the top down.

People are visual. The more visual examples that can be used, the better. It is also about making it fun.

The best teacher I had was a math teacher. Not because I was particularly interested in math at that time, but because he was able to make it fun while teaching.

News,

JB argues:

I think, a gap here, is the point that thousands of years of civilisation tell us that there are accessible facts of Math that feed a body of lore that can be concretely, empirically explored and then put into a framework pivoting on recognising self-evident truths. In such a context, we can move from concrete to pictorial to abstract, building up a fund of Math experiences and facts tied in with at least a highlights and survey level history of Math. The tie-in to key technologies and domains of practice from accountancy [money] to carpentry [fractions!] to masonry — tiling floors — to trigonometry and surveying, to engineering, science, medicine, digital technology, statistics and finance can give a rich integration to real life. But there is an infamous gulch between the arts and the sciences.

The obvious technique is rich video and multimedia presentation, with discussion, to win this strategic hilltop, relevance. The Dorling Kindersley approach has always seemed helpful.

In that context, we build up a fund of facts, known core truths, key results, procedures and skills. This then frames the shift to the axiomatic approach. For which, Euclid’s synthesis, the issue of change and accumulation [calculus] and non Euclidean geometry are a gateway. Introductory familiarisation at first level, then exploration later. A challenging fact is the Russian practice, whereby every high school child was expected to do years of Calculus based math and also physics.

It seems to me some rethinking is in order.

KF

Common Core took away multiplication tables. I think those, although monotonous, allow students to see patterns and provide a solid foundation for basic mathematics.

ET, that was a mistake. Certain core facts, properly learned make a difference. I guess the educrats would run away screaming if they were to learn that Gen Rommel memorised log tables, enabling truly powerful stuff done in the head. I suspect that may have been curriculum at Imperial Germany’s service academies c 1910. KF