|Yes, we need real-world problems, but they also need|
to memorize times tables, understand formulae.
The bright photos and busy drawings, distracted kids.
If Tom Lehrer can write a song in the 70s about it, it is old math.
What it is: is Enquiry Math or Investigation math.
I heard an interview with Dr. Joel Westheimer, uOttawa (my alumni!) and he spoke of this very eloquently.
Regrouping is best taught early on, with hands-on materials, by the time kids enter middle school grades, kids who skipped the lessons simply used a calculator. They missed the entire concept, however.
Our school is going on a field trip. If 62 kids are bringing lunch, how many kids will be buying it in the restaurant?
What if 65 kids bring their lunch?
Originally too complex for families to solve at home, parents complained. For adults who suffered in math classes, it brought the suffering home with homework.
Used with gifted kids, this strategy it works well for those who have mastered arithmetic.
For those with any disabilities, or gaps in their learning, for kids with ADHD, or kids who have missed school for health reasons, it doesn't work.
The text books changed in the 90s. The problems became complex, which challenged kids capable of such, but totally overwhelmed kids incapable and they gave up.
As a special education teacher, I used the older texts, with sample questions, sample answers, and broke down the skills clearly and carefully, providing a road map for students.
For those trying to solve a complex mathematical problem, using higher level thinking skills, if they have not mastered the basics of arithmetic then they will fail to understand how to solve the problem.
|This is a complex problem,|
broken down for students.
|We worked out the problems, on the board, together.|
Several times. A lawyer/father, with poor English skills, told me
during parent-teacher interviews
that I didn't know how to teach his gr. 8 son.
How do you learn to solve problems? By practicing solving them. Kids need guidance. They need to understand the process, if they cannot determine it by themselves.
From Wiki: Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students' ordinary experience and was not worth taking time away from more traditional topics, such as arithmetic. The material also put new demands on teachers, many of whom were required to teach material they did not fully understand. Parents were concerned that they did not understand what their children were learning and could not help them with their studies. Many of the parents took time out to try to understand the new math by attending their children's classes. In the end it was concluded that the experiment was not working, and New Math fell out of favor before the end of the decade, though it continued to be taught for years thereafter in some school districts. New Math found some later success in the form of enrichment programs for gifted students from the 1980s onward in Project MEGSSS.
In 1973, Morris Kline published his critical book Why Johnny Can't Add: the Failure of the New Math.