Unlike intellectuals who usually begin at first principles and then reason towards final conclusions, my writing has always started from first-hand experiences.
There is an alarming situation in education at the moment as well. The watered down “New Math” and “Common Core” techniques have made the recent generation generally unable to teach math at a level that we assumed before. Each generation must pass the baton to the next or the knowledge and wisdom will disappear. Now we are having the incompetent struggle through math instruction leaving the current generation even more confused. And this is happening at both public and private schools as the private ones have drunk their own kool-aid and watered down even more (assuming they can coast on their records). It’s very bad and only a change of leadership could right the ship.
There are actually great mathematics curriculums out there. The issue is that teachers tend to just rely on automated websites like IXL and schools embrace "New Math" fads that filter in and out of districts every few years. They also rely way too much on technology which is the last thing these kids need. Here are some programs off the top of my head.
For K-8: "Math in Focus: Singapore Math" (2009 Edition) by Marshall Cavendish is the best. It is based on the national curriculum of Singapore developed in the 1980s and since then. It is intuitive with a reoccurring bar model and wonderful for word problems along with difficult concepts like fractions. However, instructors need to be well-trained and have some mathematical giftedness along with supplementing with extra practice. Generally, a school or school district will adopt it without sufficient staff training. Teachers will do their best and generally grade lightly for word problems, and then parents/teachers will complain and it will be dropped in 3-4 years for a new flashy "New Math" iPad/Chromebook program. (https://www.discovery.org/a/could-singapore-math-be-a-fix-for-u-s-mathematics-education/)
For High School Algebra 1 and 2: Glencoe Algebra (Common Core Edition 2014) by McGraw-Hill Education is excellent and provides sufficient practice/instruction. Alternatively, Algebra by Elaine Martin-Gay (published by Pearsons) is also excellent and probably provides better explanations.
For High School Geometry: "Geometry for Enjoyment and Challenge" by Richard Rhoad (out of print)
For High School Precalculus: "Precalculus" (9th Ed.) by Michael Sullivan
There are also extra challenging programs out there for 3-8th graders that are underutilized: "Math Contests" by mathleague.com, "Challenge Math" by Edward Zaccaro, and "Art of Problem Solving (AoPS) by Richard Ruszyk and David Patrick.
If the unwinding of competence proceeded from the center outwards, can the opposite also happen? Can the prioritization of competence at the center - or, at least, the cutting of incompetence and waste - drive broader positive trends?
I do not see how the outer rings could fix the core. An individual living whithin their means will not influence the government to balance theirs. It is a simplistic example but I think it makes the point.
There is an alarming situation in education at the moment as well. The watered down “New Math” and “Common Core” techniques have made the recent generation generally unable to teach math at a level that we assumed before. Each generation must pass the baton to the next or the knowledge and wisdom will disappear. Now we are having the incompetent struggle through math instruction leaving the current generation even more confused. And this is happening at both public and private schools as the private ones have drunk their own kool-aid and watered down even more (assuming they can coast on their records). It’s very bad and only a change of leadership could right the ship.
Can you share mathematics curriculums you think work well? Either those used historically in the United States or used in other countries today?
There are actually great mathematics curriculums out there. The issue is that teachers tend to just rely on automated websites like IXL and schools embrace "New Math" fads that filter in and out of districts every few years. They also rely way too much on technology which is the last thing these kids need. Here are some programs off the top of my head.
For K-8: "Math in Focus: Singapore Math" (2009 Edition) by Marshall Cavendish is the best. It is based on the national curriculum of Singapore developed in the 1980s and since then. It is intuitive with a reoccurring bar model and wonderful for word problems along with difficult concepts like fractions. However, instructors need to be well-trained and have some mathematical giftedness along with supplementing with extra practice. Generally, a school or school district will adopt it without sufficient staff training. Teachers will do their best and generally grade lightly for word problems, and then parents/teachers will complain and it will be dropped in 3-4 years for a new flashy "New Math" iPad/Chromebook program. (https://www.discovery.org/a/could-singapore-math-be-a-fix-for-u-s-mathematics-education/)
For High School Algebra 1 and 2: Glencoe Algebra (Common Core Edition 2014) by McGraw-Hill Education is excellent and provides sufficient practice/instruction. Alternatively, Algebra by Elaine Martin-Gay (published by Pearsons) is also excellent and probably provides better explanations.
For High School Geometry: "Geometry for Enjoyment and Challenge" by Richard Rhoad (out of print)
For High School Precalculus: "Precalculus" (9th Ed.) by Michael Sullivan
There are also extra challenging programs out there for 3-8th graders that are underutilized: "Math Contests" by mathleague.com, "Challenge Math" by Edward Zaccaro, and "Art of Problem Solving (AoPS) by Richard Ruszyk and David Patrick.
If only it was just math instruction!
Excellent article!
If the unwinding of competence proceeded from the center outwards, can the opposite also happen? Can the prioritization of competence at the center - or, at least, the cutting of incompetence and waste - drive broader positive trends?
I do not see how the outer rings could fix the core. An individual living whithin their means will not influence the government to balance theirs. It is a simplistic example but I think it makes the point.