Most couples enter into marriage expecting great sex to happen naturally. After all, how can sex not be great between two loving, consenting adults in a committed relationship? However, just as great marriages do not just happen, great sex does not just happen too. There will be certain seasons when sex is naturally not as high a priority in your marriage, for example, during the early days of parenting. However, long periods of neglecting your sex life can be detrimental to the health of your marriage. While it may sound unromantic to intentionally spice up your sex life, sometimes it is a necessary thing to do in order to keep the fire burning in your marriage.
Here are some tips to make great sex happen in your marriage:
Let’s talk about sex
Many people have the misunderstanding that their spouse should naturally meet all their sexual needs. However, no two individuals are the same and rather than leaving it to be a guessing game between you and your spouse, exercise initiative by communicating with your spouse about your sexual preferences and needs.
Married couples should feel safe to talk openly and honestly about their sexual likes and dislikes. Decide with your spouse that talking about sex will not be taboo in your marriage so that an open channel of communication can be established and awkwardness or fear can be abolished in all discussions about sex.
Make love, not war
Men and women are wired differently when it comes to sex. However, couples should learn to embrace these differences rather than allow the differences to become a source of conflict. Men desire the physical connection before they can connect emotionally with their wives. Women, on the other hand, seek the emotional connection before they are willing to connect physically.
When both parties recognise that sex is a gift to their marriage and choose to put the needs of the other party before their own, they will find themselves naturally satisfying their needs in the process of satisfying their spouse’s needs.
Stop and smell the roses
Just because you are now happily married to each other, the courtship does not end. Don’t allow complacency or busyness to cause your marriage to fall into a routine and become bored with each other. Seek out ways to keep the passion alive. Be creative and enjoy your love and sexual relationship.
Prioritise spending quality time with your spouse. If you have children, ensure that you put your spouse before your children. Arrange for a babysitter and go on a date if that is possible. If not, think of ways to date each other in the comfort of your home when the kids are asleep. Remember that a strong marriage is the best gift for your children.
Sex is the greatest natural intimacy builder in your marriage. Culture might tell you to settle for less than great sex in your marriage but it is not true! As you take time to discover each other sexually, the potential for greater intimacy and joy through the sexual bond will keep increasing over the years.
In recent years, because of the popularity of Singapore math books being promoted and used in many countries, suddenly local publishers seemed to have been hit by an aha! moment. They realized that it’s timely (or simply long overdue?) that they should come up with a general or pop book on the Singapore’s model (or bar) method for the lay public, especially among those green to the problem-solving visualization strategy.
A Monograph à la Singapour
The first official title on the Singapore model method to hit the local shelves was one co-published by the Singapore’s Ministry of Education (MOE) and Panpac Education, which the MOE christened a “monograph” to the surprise of those in academia. Thank God, they didn’t call it Principia Singapura!
This wallet-unfriendly—over-promise, under-deliver— title did fairly well, considering that it was the first official publication by the MOE to feature the merits of the Singapore’s model method to a lay audience. Half of the book over-praises the achievements of the MOE in reversing the declining math performance of local students in the seventies and eighties, almost indirectly attributing Singapore’s success in TIMMS and PISA to the model method, although there has never been any research whatsoever to suggest that there is a correlation between the use of the model method and students’ performances in international comparison studies.
Busy and stressed local parents and teachers are simply not interested in reading the first part of this “monograph”; they’re looking for some practical teaching strategies that could help them coach their kids, particularly in applying the model method to solving word problems. However, to their utter disappointment, they found out that assessment (or supplementary) math books featuring challenging word problems are a better choice in helping them master the problem-solving strategy, from the numerous graded worked examples and detailed (and often alternative) solutions provided—and most of them cost a fraction of the price of the “monograph.”
A Missed Opportunity for a Better Strategy
Not long after the MOE’s publication, the Singapore public was spoilt with another local title on the bar method. Unfortunately, the editorial team working on Bar Modeling then didn’t take advantage of the lack of breadth and depth of the MOE’s “monograph” to offer a better book in meeting the needs and desires of local parents and overseas math educators, especially those not versed with the bar model method.
Based on some investigation and feedback why Dr. Yeap Ban Har didn’t seize the opportunity to publish a better book than the one co-published by the MOE, it sounds like Dr. Yap had submitted his manuscript one or two years prior to the MOE’s publication, but by the time his publisher realized that the MOE had released a [better?] book similar to theirs, they had little time to react (or maybe they just over-reacted to the untimely news?); as a result, they seemed to have only made some cosmetic changes to the original manuscript. Sounds like what we call in local educational publishing as an example of “editors sitting on the manuscript” for ages or years only to decide publishing it when a competitor has already beaten them to the finishing line.
This is really a missed opportunity, not to say, a pity that the editorial team failed to leverage on the weaknesses or inadequacies of the MOE title to deliver a better book to a mathematically hungry audience, at an affordable price.
Is Another Bar Model Method Book Needed?
Early this year, we’re blessed with another title on the bar method, and this time round, it’s reasonably affordable, considering that the contents are familiar to most local teachers, tutors, and educated parents. This 96-page publication—no re-hashed Dr. Kho articles and authors’ detailed mathematical achievements—comprises four topics to showcase the use of the model method: Whole Numbers, Fractions, Ratio, and Percentage.
As in Dr. Yeap book, the questions unfortunately offer only one model drawing, which may give novices the impression that no alternative bar or model drawings are possible for a given question. The relatively easy questions would help local students gain confidence in solving routine word problems that lend themselves to the model method; however, self-motivated problem solvers would find themselves ill-equipped to solve non-routine questions that favor the visualization strategy.
In the preface, the authors emphasized some pedagogical or conceptual points about the model method, which are arguably debatable. For example, on page three, they wrote:
“In the teaching of algebra, teachers are encouraged to build on the Bar Model Method to help students and formulate equations when solving algebraic equations.”
Are we not supposed to wean students off the model method, as they start taking algebraic food for their mathematical diet? Of course, we want a smooth transition, or seamless process, that bridges the intuitive visual model method to the abstract algebraic method.
Who Invented the Model method?
Because one of the authors had previously worked with Dr. Kho Tek Hong, they mentioned that he was a “pioneer of the model method.” True, he was heading the team that made up of household names like Hector Chee and Sin Kwai Meng, among others, who helped promote the model method to teachers in the mid-eighties, but to claim that Dr. Kho was the originator or inventor of the bar method sounds like stretching the truth. Understandably, it’s not well-known that the so-called model method was already used by Russian or American math educators, decades before it was first unveiled among local math teachers.
I’ll elaborate more on this “acknowledgement” or “credit” matter in a future post—why the bar model method is “math baked in Singapore,” mixing recipes from China, US, Japan, Russia, and probably from a few others like Israel and UK.
Mr. Aden Gan‘s No-Frills Two-Book Series
Let me end with two local titles which I believe offer a more comprehensive treatment of the Singapore model method to laypersons, who just want to grasp the main concepts, and to start applying the visual strategy to solving word problems. I personally don’t know the author, nor do I have any vested interest in promoting these two books, but I think they’re so far the best value-for-money titles in the local market, which could empower both parents and teachers new to the model method to appreciate how powerful the problem-solving visualization strategy is in solving non-routine word problems.
A number of locals may feel uneasy in purchasing these two math books published by EPH, the publishing arm of Popular outlets, because EPH’s assessment math books are notoriously known to be editorially half-baked, and EPH every now and then churns out reprinted or rehashed titles whose contents are out of syllabus. However, my choice is still on these two wallet-friendly local books if you seriously want to learn some basics or mechanics on the Singapore model (or bar) method—and if editorial and artistic concerns are secondary to your elementary math education.
Curriculum Planning & Development Division Ministry of Education, Singapore (2009). The Singapore model method. Singapore: EPB Pan Pacific.
Gan, A. (2014). More model methods and advanced strategies for P5 and P6. Singapore: Educational Publishing House Pte. Ltd.
One Singapore’s problem-solving strategy that is gaining currency among more and more local teachers in Singapore is the Stack Model Method, which has proved to be conceptually more advantageous—a more intuitive and creative strategy—than the bar model method. On a lighter note, let’s look at a dozen benefits one could derive should one fearlessly embrace this visualization problem-solving strategy to solve word problems.
1. As a Form of Therapy
Like bar modeling, getting involved in stack modeling may act as a form of visual therapy, especially among visual learners, and for those who need a diagram or model to make sense of a problem-situation. Indeed, a model drawing is often worth more than a dozen lines of algebraic symbols.
2. A Possible Cure to Dementia
Like Sudoku and crossword puzzles, practicing the science and art of stack modeling may help arrest one’s schizophrenia or dementia, particularly those who fear that their grey matter might play tricks on them in their golden years.
3. Prevention of Visual or Spatial Atrophy
For folks wishing to enhance their visualization skills, stack modeling could potentially turn their worry of short-term visual apathy and long-term visual atrophy into aha! moments of advanced visual literacy.
4. A Disruptive Methodology and Pedagogy
When most Singapore coaches and teachers are no longer excited or thrilled about the Singapore’s model method, what they need is a more powerful and intuitive problem-solving strategy like the stack model method to give them that competitive edge over their peers, all of whom are involved in the business of Singapore math—from training and coaching to consulting and ghostwriting.
5. A Platform for Creative Thinking in Mathematics
Getting acquainted to the stack model method would not only help one to hone one’s visualization skills, but it’ll also refine one’s problem-solving and creative thinking skills. Being mindful that competing stack models could be designed to figure out the answer, the challenge is to come up with the most elegant stack model that could vow even the mathophobics!
6. Look-See Proofs for Kids
Stalk modeling could help remove any “mathematical cataract” from one’s mind’s eye to better “see” how the parts relate to the whole. The way stack models are drawn (up-and-down and sideways) often allows one to see numerical relationships that would otherwise be difficult to visualize if bar models were used instead.
7. The Beauty and Power of Model Diagrams
Even those who are agnostic to the Singapore math curriculum, a “Stack Modeling” lesson could help enliven the beauty and power of model diagrams in creative problem solving. The stack model method could act as a catalyst to “seeing” the connection between parts and whole—normally, the same result would be tediously or boringly derived by analytic or algebraic means, understood only by students in higher grades.
8. A Simple but Not Simplistic Strategy
Like Trial and Error, or Guess and Check, the stack model method shows that Draw a Diagram is a simple, but not simplistic, problem-solving strategy. The stack model reinforces the idea that often “less is more.” The simplicity of a stack model can reveal much hidden information that is often lost in an algebraic argument.
9. A Branded Problem-Solving Strategy
For math educators who might think that Singapore math, or the bar model method, in particular, is a mere fad in mathematics education, the stack model method further disproves that myth. Like bar modeling, stack modeling shows that a simple problem-solving strategy like the “draw a diagram” has what it takes to attaining brand status, especially when we consider the types of challenging word problems that lend themselves to both bar and stack models, and which could also be assigned to a younger audience.
10. Stack Modeling as a Creative Art
To the novice problem solver, stack modeling is a science; to the seasoned problem solver, stack modeling is an art— the challenge is to come up with more than one stack model to arrive at the answer. Remember: Not all stack models are created equal!
11. Earn as You Learn
If you are a mathepreneur, you can easily steal the ideas in The Stack Model Method: An Intuitive and Creative Approach to Solving Word Problems to write a more expensive Singapore math book on the subject. There are dozens of ethically challenged ghost writers and cash-strapped undergrads from China, India, and the Philippines, who can help you professionally plagiarize any types of editable contents! You earn as you learn! Of course, you need to mail them your copy, or buy a new copy for them to do the “creative work” at a fractional cost! Make sure you don’t get caught, though!
12. Green Math à la Singapour
Ecologically speaking, stack modeling, which generally uses less space than bar modeling, could help math educators save millions of ink and square miles of paper [aka trees]. In economic terms, millions of dollars could be saved by the right choice of model drawing. In other words, stack modeling could act as a catalyst to help one play one’s part in reducing one’s carbon footprints!
From Bar to Stack Modeling
With a bit of imagination, I bet you could come up with another dozen benefits of stack modeling. The stack model method is no longer an option, nor should it be treated as a mere visualization strategy to be discussed only during an enrichment math lesson.
The stack method is going to be a problem-solving strategy of choice, as more math educators worldwide invest the time to learn and apply it to solve non-routine questions in elementary math. Be among the first creative problem solvers to embrace the stack model method, as you gain that methodological or pedagogical edge over your fellow math educators!
Estimation (or guesstimation as it is more commonly known in the U.S.) is a creative mathematical activity that is seldom given enough curriculum attention and time in Singapore. For the lay public, and probably for a disturbingly large proportion of local math teachers, tutors, and parents, estimation is often confused with approximation (or rounding off numbers).
Like swimming, cycling, and driving, estimating ought to be a life skill that is indispensable for all responsible citizens aiming to be numerate in our quantitative world of bloated data.
A PSLE Estimation Routine
In this year Singapore’s PSLE (grade 6) math paper, a routine guesstimation MCQ question has irked some parents, who “blamed” the Ministry of Education for posing an “unfair” question.
Ghostly Math from @MathPlus
How to Fermi-ize
Current Singapore math textbooks are often too Puritan, not to say, boring, to contain fertile exercises that could hone students’ estimation skills. A dose of humor, without insulting or shocking the readers, will go some way in nurturing some Fermi disciples. Let’s look at eleven non-drill-and-kill guesstimation questions, which could be posed to above-average math students bored by school math.
0. Zero Toilet Paper
If all the toilet paper used in Singapore in an entire year were rolled out, how far would it stretch?
Assuming an average human heart of 72 beats per minute, estimate that most folks would breathe their last breath around their billionth heartbeat, or by their near-666 weeks of life on this side of eternity.
2. Pools of Eyeballs
About how many Olympic-sized swimming pools would all the world’s human eyeballs fill?
A medical association claims that a cigarette smoker shortens the length of his life by 9 minutes for each cigarette smoked. A student smokes three-quarters of a pack of 20 cigarettes every day for 30 years. Excluding leap years, by how many months or years has this student cut short his life to?
4. To Pee or Not to Pee
How much urine is in a typical public swimming pool? Or, how much pee in a pool would kill you?
5. Length of Intestine
If you were to pull your small intestine out and laid it in a straight line, how long would that be? Is it shorter than the distance from Earth to Moon?
6. A Nation of Vampires—Human Blood Aplenty
If you were to take all the human blood from all the living people in Singapore and pour it into the Singapore Indoor Stadium, how deep would it be?
Estimate how much zoo poo is collected every week at the Singapore Zoological Gardens. How much of it could be used as fertilizers?
8. The Host with the Most
How many (unfriendly and not-s0-friendly) bacteria are living on and inside you right now?
9. Cash in on the Trash
Show that, on average, every square mile of sea on the planet contains 46,000 pieces of rubbish. How much cash could be generated annually by an entrepreneur involved in the trash business? [1 mile is about 8/5 kilometers.]
Thanks to Indonesia’s mostly incompetent politicians and corrupt businessmen, its neighbors Malaysia, Singapore, and Thailand, have unhealthily been affected by the annual haze visiting them, as a result of illegal forest burning by local farmers to save costs for their bosses.
Guesstimate the number of people inside and outside Indonesia, who have been affected in the last two decades from this man-made pollution. How many natives, Mohammedans, and “infidels” will die prematurely because of near-zero political will from oft-corrupt Indonesian politicians?
Estimation Skills via Gross, Illegal, or Murderous Math
Be it via “Gross Math,” “Murderous Math,” or “Illicit Math,” creative or fertile questions on the “shit,” “death,” or “illegal” business, could be posed to enhance students’ guesstimating skills.
Indeed, gross Singapore math could serve as a catalyst to imparting real-life estimation skills to students, and to reducing more complaints from kiasuSingapore parents, whose children will be sitting for the PSLE oft-dreaded math paper in coming years.
Math educators, especially stressed [often self-inflicted] local teachers in Singapore, are always on the look-out for something funny or humorous to spice up their oft-boring math lessons. At least, this is the general feeling I get when I meet up with fellow teachers, who seem to be short of fertile resources; however, most are dead serious to do whatever it takes to make their teaching lessons fun and memorable.
It’s often said that local Singapore math teachers are the world’s most hardworking (and arguably the world’s “most qualified” as well)—apparently, they teach the most number of hours, as compared with their peers in other countries—but for the majority of them, their drill-and-kill lessons are boring like a piece of wood. It’s as if the part of their brain responsible for creativity and fun had long been atrophied. A large number of them look like their enthusiasm for the subject have extinguished decades ago, and teaching math until their last paycheck seems like a decent job to paying the mortgages and to pampering themselves with one or two dear overseas trips every other year with their loved ones.
Indeed, Singapore math has never been known to be interesting, fun, or creative, at least this is the canned perception of thousands of local math teachers and tutors—they just want to over-prepare their students to be exam-smart and to score well. The task of educating their students to love or appreciate the beauty and power of the subject is often relegated to outsiders (enrichment and olympiad math trainers), who supposedly have more time to enrich their students with their extra-mathematical activities.
Singapore Math via Humor
A prisoner of war in World War II, Sidney Harris is one of the few artists who seems to have got a good grasp of math and science. While school math may not be funny, math needn’t be serious for the rest of us, who may not tell the difference between mathematical writing and mathematics writing, or between ratio and proportion. Let Sidney Harris show you why a lot of things about serious math are dead funny. Mathematicians tend to take themselves very seriously, which is itself a funny thing, but S. Harris shows us through his cartoons how these symbol-minded men and women are a funny awful lot.
Angel: “I’m beginning to understand eternity, but infinity is still beyond me.”
Mathematical humor is a serious (and dangerous) business, which few want to invest their time in, because it often requires an indecent number of man- or woman-hours to put their grey matter to work in order to produce something even half-decently original or creative. The choice is yours: mediocrity or creativity?