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Posts Tagged ‘math

In 2015, we had Cheryl’s birthday to contend with. This year we have a different math question to contend with. I call it Cheryl 2: The Sequel.

There were many types of reactions from layfolk.

The mathematically-inclined came up with different solutions. Adults wondered if life was getting that much more difficult for kids. Parents pondered getting even more tuition for their children. Enrichment centres have probably added the puzzle to their brochures.

I wager that one of the most common types of reaction looks something like the one below.

Such exasperation seems reasonable given how perplexing the problem is. However, all these responses are unwarranted.

We need not worry that we seem to have forgotten how to do math. Why? We were not taught that way, so you have nothing to forget.

Being older, and by implication, more knowledgeable and wiser, does not mean you should be able to solve the math problem.

Instead consider the silo that the math problem was designed in. According to this blog entry, the problem is called a Petite Circle-Sum Walkthrough. You can solve the problem if you follow the rules of the solution.

Solution source

Now ask yourself what application this has beyond that context. How does this actually contribute to thinking and applying in a broader sense? How does a child in Primary 1 use it now and later? How do you as an adult use it now or later?

What are you worried about?

If it is about your inability to solve the problem, then worry not because this solution was a Google search away. Your ability to find a feasible solution is more important than solving the problem because information fluency and critical thinking are more useful in the short and long term.

If you are worried about the type of math being taught, you should be more worried if their teachers do not know why the question was set.

  • If the teachers say that the question was a “bonus” one that did not mark students down, why include it in an examination? Such a challenging question could have been done in class as a form of differentiated instruction.
  • If the strategy was not taught beforehand, how assessment literate are the teachers? One generally does not test what was not previously taught and learnt.
  • If the goal was to identify students with Math Olympiad potential, could there be some other strategy for doing this? Alternatives include, but are not limited to, talent-spotting, student volunteering, and special group testing.

I critique this sequel to Cheryl not to say that mathematics is unimportant. Math is critical as a universal language and it is the foundation of our sciences.

I mean to point out that the WHY and SO WHAT of math often gets lost in the WHAT and HOW. People here seem to focus on how to solve it and what the right answer is as if setting such a question is acceptable practice. Instead we should be asking why such a practice even exists. We should be wondering “so what” if students can or cannot answer this question.

 

 
Do not blame yourself if you do not “get” this Cheryl sequel. Think of Cheryl 1 and Cheryl 2 as bad movies, like Sharknado and its sequels. Those B-grade movies were fuelled by fantasy, preyed on ignorance, and fed movie studio greed.

Those in schools and enrichment centres that perpetuate content and thinking that has no contextual meaning or relevance elsewhere are doing the same. They operate in their own silos, take advantage of information you do not (and need not) understand, and feed inertia.

Cheryl 2: The Sequel is not your fault if you do not understand it. It is your fault if you fuel the hysteria and let Cheryl 3: It Returns happen.

This video is one of many where adults try to do math that, say, a 10 or 11-year-old does today.


Video source

The results are hilarious because the adults struggle. It is only funny until you realise that the adult could be you.

If you were that adult, you could react like this: I feel so stupid. To feel less dumb, you could become an armchair philosopher and say: Life is more difficult for kids now.

You need not do either.

How about realising that such odd or convoluted ways of thinking 1) exist only for the bubble that is schooling and tests, 2) are not needed later in exactly that form, and 3) do not transfer to the wider world?

Instead of having a typical allergic reaction to math, treat yourself to an a-ha moment instead.

I shared this cryptic tweet during the last #edsg fortnightly chat.

We had been focusing on the possible “game”-based changes to the Primary mathematics syllabus in Singapore.

I use “game” because what a teacher might understand as a game is not necessarily what students experience as gamers. A drill-and-practice “game” might be a welcome addition to the teacher toolbox, but it is not necessarily a game as the child understands it.

Hence, Godin’s blog entry was timely, specifically this part:

That’s why it’s so important to understand the worldview and biases of the person you seek to influence, to connect with, to delight. And why the semiotics and stories we produce matter so much more than we imagine.

Another dimension of differing world views is the focus of the activity. To a teacher, it is MATH game; to kids, it is a math GAME. For an adult, the game is for learning a math principle; for a child, the game is for racking up points, being the fastest, or topping the charts.

The students are likely to enjoy game initially because of the novelty effect. They might even participate over a longer term because of the extrinsic rewards provided by gamification tools (which are not game-based learning).

Neither a reliance on novelty and extrinsic drive are desirable because a teacher might be forced to take part in the race to hyper stimulate and entertain.

If a teacher does not get forced into the “engage them” race, it is because students soon realise that drill-and-practice is not really a game and they reject this practice.

Adults rarely get into the child’s headspace when trying to plan activities that are supposed to be good for kids. So here are three guiding and core questions (as contextualised in game-based learning):

  1. What does the child think (is a game/about gaming)?
  2. How do they think (as they game)?
  3. What can I design based on sound educational psychology principles and rigorous research?

For the good of kids, we need to focus on what is good for kids. We start with a focus on kids, not curricula, syllabi, assessments, or policy. To be learner-centred, you have to be kid-centred first.

Last week Sugata Mitra suggested this at a leadership conference in Singapore:

This is not new to thought leaders and those that follow them.

For example, in 2012 I tweeted a link on the Danish experiment on allowing Internet use during exams. Here are some other links I have been collecting in Diigo.

While there are many good reasons for allowing the use of the Internet for tests and exams, there is common approach among thought and action leaders. If Google can help answer questions, then we should also (only?) test 1) learners’ ability to search, analyze, evaluate, and synthesize, and 2) the unGoogleable.

I illustrate with two recent examples.

A Singapore Math question went viral locally and has gained traction elsewhere. It claims to be about logic and there is apparently more than one solution [1] [2].

I question the logic of such questions, but that is not what this reflection is about. The fact of the matter is that the solutions, the rationales, and their critiques can all be found online.

You do not need to know how to get the answer traditionally. You need only know how to search online for information and people, and decide which return is best. If that is not a 21st century competency, I do not know what is.

Next example. Last week, my wife, an English teacher, received a message containing an English problem supposedly pitched at the Primary 1 level.

It went something like this:

I am a word of five letters and people eat me. If you remove the first letter I become a form of energy. Remove the first two and I am needed to live. Scramble the last three and you can drink me. What word am I?

There are many other variations of this. There are also several reactions that kids and parents can have.

One is panic, as the messenger did. After he calmed down, he reached out to a teacher (my wife) but not his child’s teacher because the latter caused the panic in the first place.

Another reaction was to learn the “logic” of the artificial problem and use either thought finesse or brute force to crack it open.

As much as I might enjoy a puzzle, I do not appreciate fake ones, particularly ones given late at night and not meaningful to me. My reaction was to Google it.

I had barely typed “I am a word of…” and Google’s suggested search phrases appeared. And links. And answers. And variations. And discussions galore!

Is there a need to test? Certainly.

Is there a need to test what we can Google? I think not.

What does a test for the unGoogleable look like? It is difficult to say for sure, but it is NOT a just test.

As challenging as good tests are to create, they are relatively easy to grade because answers fit into as few categories as possible. Preferably two categories: Right and wrong. If you take into consideration different perspectives, answers, or talents, then tests become inadequate.

A look at what happens in online social spaces gives clues as to what assessing the unGoogleable might look like. There are discussion forums where the best answers float to the top by popular vote. There are blogs with explanations and reflections on such problems.

Expand this natural “testing” island to a broader universe and the possibilities are endless. Twitter debates, Facebook critiques, YouTube video challenges, Instagram or Pinterest collections, Vine impressions.

All these and more are already part of digital databases that capture our identities. The Googles of the world use it for research, marketing, and advertising. I say we tame, manage, and organize these data in an online portfolio to showcase what we learn. Then we might stumble on ways to assess the unGoogleable.


Video source

In this 3.5 minute video, my son and I illustrate how Minecraft might be used to practice arithmetic and put a plan to action.

This video is probably the shortest in our series so far on informal learning with Minecraft. But I think the exchanges of when I teach him and when he teaches me is the most obvious in this video.

Viewers might note that my view of Minecraft sports a different look. I apply the Sphax texture pack to make things look a bit less blocky.

I shot the time-lapse sequences with an iOS app called OSnap. My “camera” view of Minecraft was screencaptured with Quicktime and all videos were processed in iMovie (OS Maverick).

Not everyone thinks that Salman Khan and his Academy are the future of teaching. I doubt very much that Khan himself would make that claim.

At least one blogger has taken issue with Khan’s approach and claims in an entry titled, You Khan’t Ignore How Students Learn. The blogger has a lot to say in a thrust and parry reflection, but I think the crux is:

Khan (along with most of the general public, in my opinion) has this naive notion that teaching is really just explaining. And that the way to be a better teacher is to improve your explanations. Not so! Teaching is really about creating experiences that allow students to construct meaning.

When I asked @intmath what he thought of Khan and his academy, he essentially said the same thing. To paraphrase: “That’s teaching old math the same old way, isn’t it?”

I would add that you also can’t ignore how teachers teach. They teach the way they do because 1) they know no other way, and 2) they teach to the test.

I think that people like Khan provide a way (the flipped classroom) so that you meet the test requirements while challenging the way teachers teach in small but significant ways.

Do we need research to verify that this approach works? Of course. But if you refer to Hattie’s meta analysis of meta analyses, one could argue that the elements with high effect size, like feedback, direct instruction and prior knowledge, are part of Khan’s strategy.

In other words, do whatever works. We can work out why it works later!

I posted this Math question at my son’s blog about three weeks ago. It turned into an English lesson (I had a discussion with my 6-year-old about the word ambiguous) and a lesson on an aspect of critical thinking.

This was one of his easier Math questions that his teacher assigned him, but it was ambiguous thanks to the use of English in the question.

Math teachers will insist that the 8th boy is on the 7th boy’s right. From the reader’s perspective, it is.

But consider this from the 7th boy’s perpective, i.e., the right side of that boy. If he extended his right arm to put it around someone, he would get pally with the 6th boy. The 7th boy’s right is to your left. The “apostrophe s” makes the perspective the boy’s, not yours!

To make the question less ambiguous (and to reinforce Math logic), it could have simply rephrased, The ____ boy is on the right of the 7th boy.

When my son did this worksheet at home, he got stuck with it and consulted me on it. I illustrated the Math logic and we role played the language logic. He came to the same conclusion as I did but he was marked wrong.

I guessed that he would be told that he had the wrong answer, but I think he learnt more than just Math. Now he knows not to follow rules blindly.

In fact, he spots and corrects the occasional errors in grammar, punctuation or logic in his worksheets. But we tell him not to be too blatant about it. After all, not all teachers want to learn from their students. It’s a sad lesson in life…


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