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Vlog Ep #09: Fake Math and Pseudocontexts

 

What are pseudocontexts, and should K-6 math teachers be concerned about them?

I came across the term in Dan Meyer’s excellent blog, in which he explores better ways of engaging students in learning math, and calls out “fake math” and poor teaching. You should go check out Dan’s work, I find it really challenging and encouraging.

 

As a publisher of educational content for K-6 math, I am deeply concerned about students’ recognition of the importance and the usefulness, the utility of the math they learn.

This means that I am always looking for ways to show students examples of math in real life. But does that mean I have to restrict my examples to ones where someone is asking a specific math question that matches the topic students are learning, or can I ask questions which someone might ask, but probably didn’t?

What do you think? Leave a comment below if you’d like to share your thoughts.

Recent examples of “math in real life contexts” are found in my Where’s the Math? video series, which you can see here. Am I guilty of introducing pseudocontexts?

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Links to other pseudocontexts:

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Math is Important, REALLY Important

Who knew? Math is important. Like, really, really important.

We shouldn’t even need to say this, surely? Our kids need to grow up being good at math.

Watch the video:

 

Western Nations Spend More on Math, and Get Lower Results

And yet, despite most ordinary folks agreeing that math is a vital part of kids’ schooling, in western democratic nations we seem to be spending less time on math teaching, and getting lower results.

If you’re a teacher I’m confident that you believe in the value of a good mathematical education. But at the same time, you’re far from being alone if you find students seem to be less engaged and less proficient at math as time goes on.

Do you need ammunition to make math excellence a priority for your students?

Think on this: in 2016, terrorists are as likely to carry a laptop as a bomb. And they are probably in a basement somewhere, not risking being found out in the open.
Want to try that line “We don’t really need to be all that good at math, now we all have smartphones” again? I thought not.

Math is Important: We Should Spend More Time on Math in School, Not Less

Lastly, it distresses me to hear people say that modern technology has taken the place of people good at math, and that we can cut back on hours spent in school learning math, to make room for more trendy subjects such as coding and technology. I believe that educators as a group should spread the message that math is important; and if anything, it’s more important than it was in the past, given the spread of technology into nearly every part of our lives.

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K-6 Math in the News: Censuses, Counting People and Math

The Australian Federal Government recently conducted a survey; have you completed your form yet? Or are you waiting to see whether the Australian Bureau of Statistics website gets attacked again?

The recent national census really caught the attention of the Australian populace, mostly for all the wrong reasons. The official website couldn’t cope with the traffic to the site on “census night”, which was entirely predictable, and at the same time it was subjected to several “Denial of Service” (DOS) attacks.

But apart from that, what can we teach children about censuses? Here are a few ideas:

  • Governments use censuses to find out how and where to spend money on schools, hospitals, rail lines and highways
  • School math includes taking surveys, collecting data and analysing the results, just like in a census
  • Jesus was born in Bethlehem partly as a result of a census conducted by the Romans
  • People expect survey-takers and governments conducting censuses to protect their privacy

 

What do you think?

Do you have favourite activities for teaching children about statistics? Share a comment below.

Reference Articles

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K-6 Math in the News: Supermarket Math Fails

Do your students believe that math is irrelevant to their lives? Sadly, all too many of them do, especially as they reach high school.

The article I discuss this week lists 10 occasions in which major Australian supermarkets got the mathematics behind their special offers totally wrong. Sometimes the “offer” was worse than the standard price, sometimes it was exactly the same. And occasionally the offer was better than the staff member who put up the marketing ticket realised.

I love this article for its immediate relevance to students. Very few people don’t enjoy finding a bargain, but no-one wants to be ripped off. The examples here provide lots of examples for students to figure out what each offer is, what it’s really worth, and suggest a better, more honest offer.

Buyer beware! Even though stores are using computers to create special ticket offers, human beings are required to think up the actual numbers in each offer. And sadly, some staff members don’t recognize their own mistakes before letting customers find out about the specials.

What do you think?

Do you do “shopping math” in your classroom? Share a comment below.

Reference Article

10 Times Aussie Supermarkets Failed at Math

► Worksheets connected with this week’s video:

 

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Teaching a Great Math Lesson Part 1: Capture Students’ Attention!

Great Math Lesson Series:

Phase I Phase II Phase III Phase IV Phase V
Introduce Stimulus Whole-class Activity Problem Solving Synthesis & Reinforcement Revision & Recap

This is the first of a five-part series on how to teach a great mathematics lesson, using a simple, purposeful template that can be adapted for any math topic and any age level.

First Phase: Introduce a Stimulus

Lots of math lessons fall down in the first ten seconds: “Who can tell me what ‘ratios’ are?” Seriously, which kid or teenager is going to want to answer such a question? Later in the lesson, there will be time for lots of questions. But ask such a question in the first few seconds? Never.

You know what they say about first impressions? You don’t get a second chance to make one. Well, it’s the same with teaching. I remember starting a lesson when I was a student teacher, saying “I’m now going to teach you about ‘protecting the environment’”, or some such thing. The children were polite enough not to groan out loud, but I could see the reactions immediately on their faces: Who wants to learn about THAT?

Measurement lesson

So, what should a teacher do?

Start with something interesting, exciting, unusual, unexpected, surprising, creative or enticing – which is connected with today’s math topic. Such as:

  • Fractions – dress as a chef, bring in a chocolate cake, cut it into halves, then quarters, then eighths, and so on
  • Subtraction – sing “Ten Green Bottles” while animating green bottles on a PowerPoint slide
  • Percents – bring out a 25% off sale flyer for a department store, tell the children you’re going to buy a new outfit, but you’re not sure if you have enough money.
  • Linear equations – dress as a plumber, carry a plunger or wrench. Tell students you have a tank to fill with water. It already holds 50 liters (/litres), and water is being added from a tap at 3.6 L per minute. How can we tell how much water there will be in the tank after an hour? How long will it take to reach 250 L? Could we graph the amount of water in the tank over time?

The actual idea isn’t that important; the main thing is to grab students’ interest, connect it with the math topic, and then while they’re paying attention, start teaching. It will require some time and effort put into preparation, but the payoff should be students who look forward to their next math lesson!

Next phase: #2 Whole Class Teaching

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