The Solution for Better Mathematics Isn't a Homework Overload, Not Especially During the Holidays

IgnitED

As Christmas vacation comes near, I remember a couple of stuff why "vacations" aren't vacations. The schools tend to give ridiculous schedules. For example, the unit test or the periodical test comes right after Christmas vacation. Many times, the value of rest is overlooked. It's even ironic how science teachers should say, "Nobody should be sleeping at 9 P.M.  You are in high school and you should sleep even at 10 P.M. Do your work even if it breaks your biological clock." Remembering those words, I also wrote an essay on why sleep-deprived education is one of the biggest problems. Then we wonder why students end up rebelling by doing many things like too much screen time (which I did a lot to the point I lost touch with reality) or even going out with the wrong people. I wonder if the three musketeers back in high school went home late out of rebellion? Sure, they weren't the unruly crowd but they probably did some mischief out of frustration. 

I recall getting mad on Christmas breaks because I still had to do math drills. It's the most abused solution whether the teacher is good or terrible. Math homework is often said to improve math skills. High grades may be achieved in the short run. However, the irony of grades over learning is that good grades can't be maintained in the long run. Good grades should be a product of diligence and good character, not a result of cheating. When there's learning, better grades will follow and be more consistent than just grading alone. 

Connecting mathematics to real life

How often teachers would give assignments over the weekend and the holidays. The body may have a fight-or-flight response. That may explain why some schools have a high failure rate. There are 40 students in Grade 5 but more than half failed. When people enter the first year under K+10, there's also the issue of 10 out of 30 didn't make it. Sure, it's good to raise parental concerns. It's a good thing though that some parents pulled out their children if they can't make it. In fact, I rebelled by playing video games for more than two hours. Even worse, family fights happen when I say, "I'm sick and tired of it! Just get over it! I'm stupid and I'll never be smart! What can I do? I'm stupid in math!" What's worse is that the Boomer Generation can be so proud of their academic accomplishments but their common sense has gone to zero. Today, schools tend to produce idiots more than intellectuals (read here).

The problem with teaching mathematics is always rooted in this--it's not linked to real-life scenarios. I almost thrashed out at DNews, until this video by Trace Dominguez came...

Dominguez discusses the one thing that really makes sense. In his case, there's no such thing as a math person--most people feel stupid because mathematics is taught stupidly. I cringed when he presented the sad truth that we're taught only how to do math but not to understand it. This makes me think that homework overload isn't feasible. But no, the education system tends to demonize rest and relaxation as "something evil". Even worse, parents want to get their children to be early graduates. It's almost like trying to force a plant to grow with an overdose of fertilizer. 

This information by mathematician Paul Lockart also gives an idea of how mathematics education is done wrong:

Lockhart begins with a vivid parable in which a musician has a nightmare in which music is taught to children by rote memorization of sheet music and formal rules for manipulating notes. In the nightmare, students never actually listen to music, at least not until advanced college classes or graduate school. 

The problem is that this abstract memorization and formal-method-based "music" education closely resembles the "math" education that most students receive. Formulas and algorithms are delivered with no context or motivation, with students made to simply memorize and apply them. 

Part of why many students end up disliking math, or convincing themselves that they are bad at math, comes from this emphasis on formulas and notation and methods at the expense of actually deep understanding of the naturally fascinating things mathematicians explore. It's understandable that many students (and adults) get frustrated at memorizing context-free strings of symbols and methods to manipulate them. 

This goes against what math is really about. The essence of mathematics is recognizing interesting patterns in interesting abstractions of reality and finding properties of those patterns and abstractions. This is inherently a much more creative field than the dry symbol manipulation taught conventionally. 

During the preparations for the NSAT (which were thankfully canceled), I could remember coercing one of my former enemies to recall his mathematical genius. Sure, he was known as a math wizard but even he soon suffered from stress. I wonder if some of his silly written work resulted from a flight-or-fight response.  I was good at writing and he was good at mathematics. Both of us were weak at each other's strengths. That's why we were told it'd be better if we both cooperated. 

Teaching mathematics in Chinese classes feels redundant. However, I talked with someone who graduated high school in Chinese education saying that Chinese mathematics had better reasoning. I got so curious that I researched on Chinese mathematics and wrote an essay about it (read here). I was even amazed when I found Domino Chinese discussing how Chinese mathematics is winning. The Chinese mathematics method can be learned without learning Mandarin. It can be taught in any language. We don't learn Greek to learn mathematics pioneered in ancient Greece. Isaac Newton didn't need to learn Greek before he discovered how calculus (invented by Hippharchus) could be used in his experiments. 

I think this also shows how mathematics can be used by any country:

The pedagogical approach to teaching Mathematics at schools in China is known as the Mastery Method, and there is a lot more to this approach than simply memorising times tables. 

A central concept in the Mastery Method is the development of a solid foundation in basic Mathematics ability.  This is established by focusing on a narrow set of core skills during the early years of education. Students are supported in the development of each skill to the point where they have mastered the concept. When, and only when, students have mastered each concept can they move on to the next skill.

Mathematics builds upon skills, you need to count before you start addition, you need multiplication to divide,  you need division to master fractions, and so on and so forth. An approach which affords individual students the necessary time and practice to master each skill before moving on to more advanced operations, has clear benefits.

The development of students’ foundation in Mathematics is supported by carefully designed exercises which encourage students to identify patterns. Schools which follow the Mastery Method use a wide variety of visual representations to help the students make these connections. Number lines and fraction diagrams are also deployed by teachers to support students’ mastery of fundamental concepts. 

Pretty much, everything can go with learning the four basic operations. Looking at the mastery method, it might be appealing to me. I even felt my hatred for Trigonometry dissolve when I found that it's part of life. However, higher mathematics is hardly taught with real-life examples. SOH-CAH-TOA doesn't make sense until more real-life examples are made. Just think if teachers talked about finding Trigonometry everywhere. Right now, I even find Calculus everywhere with every slope and curve in the road. However, classroom discussions tend to be forced to be boring.

Mastering every basic skill in mathematics is necessary for appreciation. It means not just memorizing formulas but their applications. Call me nuts but I believe mathematics exams also need essays, not just science exams. Students should spend less time with numbers but also understand why these formulas are needed. For example, I could now write an essay on Trigonometry. I could write about how Trigonometry starts with basic right angles but they help solve big problems. I would discuss how Trigonometry is used to measure house angles to ensure the right length is there. I could write an essay about Calculus and talk about how rates of change matter. Sadly, students aren't taught to do that. They can do SOH-CAH-TOA but need help to see its basic applications. 

How rest periods may also be beneficial to mathematics learning

Not giving homework over the weekend may actually be beneficial not just to students but also to teachers. Back then, I survived it. However, after doing an exercise program, I want to stress that exercise rest days are vital. Academics is mental exercise and the brain needs to rest. Sometimes, I take a break by watching intellectually stimulating yet it's not required to be written as a report. I do blogging like this to ease my mind. I do set a schedule but the fact that I'm not being graded over my entries relieves the pressure. 

I think about how Christmas breaks for students aren't really breaks. The only time students (and teachers) get to relax is on December 24 and December 25. However, on December 26, students are stressed out again. The same goes for the teachers. Teachers are required to start getting ready to check exams. The flight-or-fight response students will have is, "Sir/ma'am we have too much homework?" Unfortunately, teachers might be forced to say, "Shut up! You're not a student if you complain about homework over the holidays." I wonder if one of my former teachers left the teaching profession because she was forced by the school system to give homework over the holidays. 

I mentioned earlier about exercise. I tried having exercise with no rest day. The result was that after 120 days of getting 8,000 steps--I hurt my back. The muscles are bruised and torn during exercise. Sure, exercise is needed but so is rest. All work and no play makes one stupid. Having at least one rest day from exercise can help the muscles grow back. The moment I took a break from exercise having five to six days of exercise was helpful. The next thing I knew I could walk for more than an hour without much pain in the legs. 

The same concept can be done with schooling. Students should be given time to bond with their families, have time to rest over the weekend and the holidays, and the like. The students (and teachers) should have no extra work over the two weeks. Vacation during the Christmas break isn't going to be long. If machines need rest then so do humans. A computer or a calculator can blow up if it's overused. How much more the human mind will blow up from overwork. Maybe, it's time to distance exams a week or two weeks after the vacation. Make use of the next two weeks to build momentum. Maybe, the solution is to have more days of schooling so the third grading doesn't become hectic. 

If students are well-rested, they can learn mathematics better. Some students catch up with mathematics faster than the hours. A well-rested mind is going to be more ready for mathematics. Mathematics is always going to be that hard gym exercise. A body that's not well-rested isn't ready to hit the gym. The mind that's not well-rested is sure to suffer in mathematics class.