Is Our Math Curriculum Relevant for the Real World?

Last week, I attended a Primary 5 & Primary 6 Parents' Maths workshop. This was the first time I had attended a workshop of such nature, and Maths had never been a favourite subject, so I wasn't really looking forward to it. However, with so much changes in the primary school Maths curriculum, plus the challenging Maths questions that Big Bee occasionally asked me at home, I thought it is good to understand what Big Bee is going through in school. The real Maths whiz in our family, Hubby, came along too, much to my relief, and I was really thankful for his interest and support in his girls' education.

What ensued was a 2.5 hour of mind-boggling and muddle-headed session where parents were taught the various strategies used in the PSLE Maths curriculum, and parents were made to do 16 problem sums (gulp!).

The audience was filled with parents from all walks of life - from doctors to lawyers to journalists to parents with postgraduate qualifications. But the looks of bewilderment on most parents were truly priceless. We had to throw all our years of algebra aside, and for Hubby especially, to toss his advanced Engineering maths aside, so that we can become primary school students, learning a new curriculum from scratch again.

We grappled with new strategies like repeated identity, branching, advanced model drawing, etc. Eventually, the final problem sum that we had to solve baffled most of us, and it was so ironical that a Primary 6 girl had to come up to the main board and explained the solution to the entire audience.

After the workshop, I was really perturbed. Today's Maths curriculum does not help in fostering creativity and problem-solving skills in our children at all. Today's Maths - with its allocated strategies for respective problems - reinforces the perennial problems that most Singaporean students are facing, which is the inability to think out of the box and the lack of opportunities to think beyond what they are learning in the classroom. Having fixed strategies for individual problem sums just prove to students that there are ready-made solutions for every problem they face, when the world's problems are really made up of so many ambiguous issues with no black-and-white solutions. Thereby, this will sadly reduce our children's inspiration to think beyond the traditional boundaries of knowledge to create more unique and applicable solutions, which is what a fledging and small country like Singapore really needs.

Frankly, I emerged from the workshop disillusioned and disappointed. Despite the Ministry of Education's call for more creative teaching and a more holistic curriculum, the teaching of this core subject, Mathematics, shows that we, as a nation, are somewhat unprepared to veer away from the staid curriculum of rote-memory and examinations-based learning. Worst of all, I fear that such a curriculum will not foster a life-long love for and interest in learning, and is not practical nor intellectual.

When will we be ready to steer away from rote memory examinations, from ready-made solutions for a more liberating and intellectually stimulating curriculum that will nurture the true abilities of our children?

Some of the questions that we had to solve are below. Want to try your hand at solving? ;)

1) On Monday, Alynna has $48 more than Eunice. On Tuesday, Alynna spent 1/4 of her money and Eunice received 20% of the amount of money she had on Monday from her father. Eunice found that she had $72 more than Alynna on Tuesday. How much money did Eunice have on Monday?

2) Anne, Belle, Cecil and David each have some stickers. The number of stickers Anne ha is 2/3 of the total number of stickers Belle, Cecil and David have. The number of stickers Cecil has is 20% of the total number of stickers that Anne, Belle and David have. If Cecil has 35 stickers, find the total number of stickers that Belle and David have altogether.

Travelling Back In Time (Part 3): Medieval Towns in Germany

The Romantic Road is a marketing nomenclature for 350 km of medieval towns and countryside in Bavaria, southern Germany, and we spent 3 days exploring different towns in our journey from Frankfurt to Munich. For Hubby and me, these 3 days were the best and most enjoyable part of our holiday. We immersed deep into the small, unknown towns of medieval Germany, and revelled in the fact that we were lost in time.

I find the history of Germany fascinating. Do you know Germany only became a unified country back in the late 19th century? Before that, Germany was rarely united, and hundreds of independent states and rulers existed. I think this is part of the reason why the residents of Germany are full of pride and self-initiation in whatever they do – and it is very apparent in the excellent condition of their buildings, their processes, their work, etc – because they had never needed to rely on a central authoritative government or ruler in the past.

Solar-powered wind energy is very common in green Germany

Anyway, back to the trip. Here are some highlights of the Romantic Road trip!

Wurzburg

As we departed from urban Frankfurt, we were captivated by the gradual transition from a big, commercial city to the rolling meadows of the countryside, seeing charming villages set at the foot of little hills, and an expansive horizon of meadows and farms. 



We started off the Romantic Road trip with a brief stop in Wurzburg, a bustling town from the 4th to 5th century. The imposing Fortress Marienberg set on a hilltop, with views of a monumental bridge hailing from the Middle Ages across a broad, serene river, as well as myriad spires from the majestic architecture of the town, were most memorable for me.

Shortly after Wurzburg, we visited a historic manor house owned by a Count, with gardens resembling that of Versailles Palace's in France. It was liberating just to stroll in the gorgeous gardens, and the rich Baroque interiors of the dancing hall made a deep impression on us.

 

Rothenburg ob der Tauber

We spent a night in Rothenburg - and oh, what a fabulous 24 hours that was! Rotherburg is the epitome of German romance and chivalry, and the moment we entered the walled medieval town, I could immediately tell why.

Nestled in resplendent, exquisite, rolling countryside, with majestic guard towers, lordly gateways and magnificant historical city walls, the antiquated town is the most well preserved of all the small towns in southern Germany. The ubiquitous half-timbled fachwerk cottages and houses dot the entire cobblestoned, walled town which is redolent of gallant knights and regal ladies.

We wandered in the dreamy countryside with little vineyards, aqueducts and manor houses.

We explored country lanes in the surrounding woods, blowing gigantic dandelions, peering up at ancient trees that the girls claimed were Enid Blyton's Faraway Tree, peered into an empty but pretty bird's nest, daydreamed at miniature, growing grapes in the vineyard. What a heavenly afternoon!

 

We browsed in quaint, dark little shops that sell the most amazing merchandise, from a whole shop full of the most beautiful Christmas accessories to resplendent chess sets with fantastical pieces (which Hubby could not resist buying!).

 

 

One of the chess sets that we bought, and the Bees with their father had been busy playing with them since then!

 

A multitude of exquisite Christmas decor items!

 

 

Sausages and frankfurters galore!

Schneeballen, a Bavarian delicacy that is very sweet and crunchy!

We dined alfresco under the ambrosial sunlight and ambled along cobblestoned streets in the tangerine golden rays of a 8pm sun.

In the evening, we set out to join the historic Night Watchman's Tour, where a night watchman related tales of this medieval town from eons back.

Unfortunately, jetlagged Little Bee fell asleep in our arms midway through the tour, and we had to return to the hotel.

Our hotel was an absolute charmer - it was a lovely guesthouse run by a very friendly woman called Marian, whom we had many amiable conversations with.

The Bees love her big French sheepdog, and breakfast was spent playing incessantly with it.

We stayed in a spacious room with 2 queen-sized beds up on the highest floor (3rd floor!) of her guesthouse, and loved the quaintness of it all. We had to lug our heavy luggages up all 3 levels of her spiral staircase, and we slept without air-conditioning, with the windows opened to the fresh, beautiful air of the Rothenburg countryside - and we revelled in this country living! I remember waking up in the middle of the night to absolute silence...no sound of moving cars or late-night party-goers. This is truly the sound of the real planet earth - the sweet silence of nature in slumber.

The next morning, we woke up bright and early for breakfast. The breakfast was the best we had in this whole trip! It was a homely breakfast set in the cosy and heartwarming dining room of her beautiful guesthouse, and we loved all the personal touches of her country-styled breakfast! It was a truly memorable stay here.

 

What I love about German breakfasts - an abundance of fresh vegetables and fruits!

We then spent more time exploring the rest of Rothenburg - once again, we wandered into quiet historical courtyards, and eventually ambled to the ancient walls of the town, much to our delight. The scenery around us was so picturesque that everything was heartachingly beautiful - the charming outline of the town from outside the walls, alluring courtyards with little flowers blooming, an archaic dark brown bridge spanning the inner and outer city walls on which I could just visualise ancient knights galloping into town.

We even had the amazing opportunity to stroll on the grassy patch of the now-defunct moat and chanced upon a big, dark loft with a huge cannon room within the walls. It was somewhat creepy and the Bees were a little spooked, but Hubby and I were thrilled with our discovery!

We also spent some time wandering about the surrounding woods that resembled something straight out of the Lord of the Rings - damp forest grounds full of busy ants, emerald-green foliage and dim surroundings. We strolled for a while in the outer areas of the woods but did not venture deeper because the Bees felt pretty uneasy in the dark, lonely woods where not a soul was to be found!

After a sumptuous lunch set in the most picture-perfect restaurant where we had a bird's eye view of the surrounding countryside and the beautiful outline of the town's buildings, we set off finally from this gorgeous little town, much to our melancholy.

On that day alone, we stopped by several thousands-year-old medieval towns like Dinkelsbühl, Nördlingen and Ausburg, where each town has its own distinctive flavour and specialty.

Dinkelsbühl

Dinkelsbühl is somewhat similar to Rothenburg, but much quieter, with beautifully preserved buildings dating back from the Middle Ages. Their cobblestoned streets are broader, and thus a little more impersonal to me. Their houses are a lot wider and bigger, and there are blackletter labellings of every single house which really captivated me!

We stopped here for a little ice-cream set in an alfresco cafe beside a man playing a fiddle - how relaxing! But most of all, we were struck by the majestic cathedral of Dinkelsbühl, with magnificant interiors!

Nördlingen

I was most enthralled by the history of Nördlingen, a 1,115-year-old walled ancient town set in a crater of a meteorite impact, with its impressive tower built with the rock formed from that impact! Again, its plazas and market squares were a lot wider than of Rothenburg as well, and I did not quite grasp the small quaint town feel here.

Ausburg

Ausburg is the third oldest city in Germany (older than all the historic towns we visited), so it has this bustling large town feel with trams, modern shops, and rich, large patriarchal buildings which I did not really like. There were some beggars around, and we felt like lost kids in a big city!

In all, we felt like we were literally lost in another time, another age - and truly revelled being part of this historical journey of medieval Germany!

Travelling Back In Time (Part 2): Frankfurt, Germany

FRANKFURT

This post will be about our experiences in Frankfurt. This was my first trip to Germany (other than the stopover in Frankfurt Airport on the way to the United States last year), and I did not have any expectations nor impressions about Germany, except for my deep interest in the holocaust and Nazi Germany's destructive forces. Thus, when we touched down in Frankfurt on a bright, sunny and crisply cool day on 6 June, I had zero expectations and minimal anticipation.

But, after a week spent in Germany, I was impressed and fascinated. The Germans I met are highly efficient and adept, take immense pride in whatever they do, friendly but not probing, soft-spoken, very clean and polite, and process-driven. In fact, the entire country reminded me very much of Japan, and I wondered many times during the trip if these are the potent characteristics that propelled these 2 countries to be the aggressive and ambitious superpowers in World War II!

Another thing I love about Europe during summer is their languidly long summer nights. It made travelling so much easier, and we are able to extend our daily experiences to indulge in the ethereal sunlight.

In addition, Germany has one of the better and more efficient transportation systems in the world. Their cab fares are reasonable, and all the cabs are Mercedes taxis! Their subway is clean and punctual, with an excellent network across the city, and their buses are so comfortable and spotless too! It was so easy to travel all around on our own.



Taking the subway in Frankfurt



Impactful and eye-catching designs at the subway stations

Such self-initiated creativity at subway stations!



I love the quirky personalities of trams!

Some key highlights of our Frankfurt segment of the trip are listed below.

1) The Main River
The first morning of our trip was spent languorously ambling beside the River Main. Our trip coincided with major floods happening in southern Germany, which affected most of the river systems in the country, so River Main was very swollen, with fast-flowing waters overflowing to the banks.

 

It was such a delightful early morning walk in the cool air, with minimal people around us. We were literally able to smell and admire the blossoming summer flowers around us, as well as the abundance of foliage all around.

2) Heaven for musicians - Session Music
We spent the rest of the morning indulging in Hubby's favourite hobby - browsing for music keyboards in Frankfurt's suburbs. The Bees were suitably excited by the amazing array of pianos, keyboards and guitars that adorned the vast 2-storey shop, and all 3 (except for musical idiot, me!) tinkered with the pianos and keyboards.

3) The Römerberg
The historic heart of Frankfurt was breathtaking and charming. We were captivated by alluring ancient statues around the square, and browsed in quaint shops selling the most enchanting merchandise. The Bees were drawn to an antiquated water fountain, and loved chasing the pigeons around the old plaza.

The fascinating cuckoo clocks that originate mainly from Black Forest

We had alfresco lunch at a winsome German restaurant, and indulged in typical German cuisine like bratwurst (hot dogs) and sauerkraut (sour cabbages), etc. I must say I am not a big fan of German food, as there is too much meat in their cuisine! We took a lovely long lunch under the mild sunrays of a rejuvenatingly cool summer day!

4) The cathedrals
What is a visit to the historic town centre without taking a peek at the town's cathedrals? We visited 2 cathedrals that dated back to the 12th to 14th centuries (the modest Alte Nikolaikirche and the glorious Dom St. Bartholomaus).



Little Bee doing some colouring in an ethereal cathedral

We were awed by the brilliant architecture and our frazzled urban souls were soothed by the pervasive peace within these cathedrals.

 

Splendid organ pipes

5) The Naturmuseum Senckenberg (Natural History Museum)
The highlight for the Bees was the natural history museum. I had always wanted to visit a natural history museum before, but never had the opportunity to, so I was as excited as the Bees.

And we were not disappointed. We marvelled at the splendid display of colossal dinosaur skeletons, and most of them are originals from eons ago! Simply mind-boggling and amazing.

Venturing deeper into the museum, we were able to experience interactive displays on the solar system and earthquakes. There were also highly educational displays about deep sea creatures, huge exhibits of exotic stuffed animals and the evolution of the human species. Fascinating stuff indeed. Needless to say, the kids loved this museum, albeit Little Bee was a little spooked in some deeper, darker and lonelier parts of the museum. I also found it remarkable that the museum was hardly populated with visitors! We were usually the only visitors in some parts of the museum, and this was so refreshing after having arrived from over-crowded Singapore!

 

We ended the day, jetlagged, with a cosy and relaxing room service dinner, while looking forward to what the next day might bring!