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Teach Times Tables Without Apologies

Teach times tables to children in grades K-6: this is arguably one of the most important jobs a K-6 teacher has.

Why Teach Times Tables? Surely Calculators Make Memorization Redundant?

This sounds a little plausible, but I encourage you to stop and imagine this scenario: first, you have to imagine that you’re a child, around 10 years old. You haven’t had the experiences that your future adult self will have. You’ve been told by teachers that you don’t have to learn math facts by heart. You have a calculator in your desk, and you are encouraged to use it.

Now, picture this: you are working out the perimeter of a 6 by 8 rectangle using the formula “P = 2x(L + W)”.

Imagine This: You are a Child Whose Teachers Did Not Teach Times Tables

You remember you should add the length and width first, but you don’t know what six plus eight equals, since you never learned the addition facts by heart either. You look around in your desk and find the calculator, switch it on, look at the question again, press “8”, “+”, “6”, “=” and see “14” in the display. “What does that mean?” you think. Oh yes, that’s what “L + W” equals. Somehow you figure out the next step is to multiply 2 by the number you just found. You pick up the calculator, press “2”, “x”, then ask “What do I times this by?”.

You have forgotten the answer and you didn’t write it down, so you start again: “8”, “+”, “6”, “=”. This time you take note of the answer, “14”. You look back at the formula again, and press “2”, “x”, recall the previous answer again, “1”, “4”, “=”, and see the display shows “28”. You quickly write “28” in the space for the answer and move on to the next question. Oh look, it’s another perimeter question – it will be quicker this time, because you know the sequence of steps you have to take.

This is what happens if no-one takes the time to teach times tables. Notice that not only does this imaginary child take much longer to complete this simple question than it would have been if tables were memorized, the child is repeatedly interrupted in working through the question to carry out mechanical actions, mostly the pressing of calculator buttons, with little or no thought of why he or she is carrying out the process in the first place.

I promise you this: from today onward, I will not apologize for expecting students to memorize the times tables.

I’ve had enough. Students who don’t know the multiplication facts by heart will not achieve much success, if any, in their future math studies. So why don’t we do more to get our students to memorize facts?

Teach Times Tables: A True But Sad Story

In the video: The experience I had recently watching Year 5 kids trying to do a multiplication test without knowing the times tables illustrated this perfectly for me.

Students simply had no idea of the times tables, and so most of them resorted to drawing arrays of dots and then counting the dots from 1. Of course, this was much too slow, and in addition students frequently made mistakes.

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Math in the News: Babies Can Do More Math Than We May Have Realized

Infants as young as six months recognize interesting shapes. And babies who show higher spatial reasoning skills do better in math at age four. This is good news for parents and carers who purposefully try to help their children understand the world around them in explicitly mathematical ways: developing better spatial reasoning in infancy should result in better understanding of math generally when they start school.

Watch the video for more:

 

In this study, babies between six and thirteen months were shown images on two screens, where on one screen pairs of images appeared in a symmetrical arrangement. This caught the babies’ attention, and using eye-tracking technology the researchers were able to measure how often and for how long they focused on the more interesting images, and so deduce relative levels of spatial reasoning.

The really encouraging news for parents and carers who want to give their babies a head start before they start school is that higher abilities in spatial reasoning were associated with better math results at age four.

Since spatial reasoning is not a fixed ability but can be taught, I know what I will be doing when I get the chance with my grandchildren; all parents should do the same!

What do you think?

Does trying to expand young infants’ awareness of the world around them in targeted ways really help prepare them for school success? Share a comment below.

Reference Article

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Math in the News: Is Rote Learning the Secret Behind Chinese Mathematics Success?

Education planners and commenters in the west seem to be looking enviously at Asia, especially China, Korea and Singapore, for inspiration to improve math test results in their own countries. But everything is not as it may first appear; let me explain why below the video:

Apparently, since students in developing countries did so poorly on international math tests compared to most Asian nations, we in the west should adopt Asian methods as soon as possible. This is surely a scenario that old-style communist dictators could dream of: China beats the United States (and most of the developed world), showing the superiority of the disciplined approach forced on their citizens by the central government.

I admit, that last paragraph sounds just a little over the top.

But consider this: the government of the UK is spending £41m to train teachers in 8000 English primary schools in so-called “mastery maths”, based on the approach in Shanghai, China.

So, can we deduce from this decision by Whitehall that “Shanghai Maths” is the secret to success in maths for schoolkids in the UK?

Not so fast.

The space here won’t allow for a detailed analysis of this issue, so let me instead list a few points for consideration:

  • First up, why copy Shanghai? It isn’t a country, but rather a city, albeit a very large one. Perhaps Shanghai is cited as the example to follow because out of all results in China, Shanghai’s were the pick of the bunch?
  • Do planners believe that merely training teachers and changing textbooks will provide equivalent results with today’s English schoolkids as teachers in Shanghai see?
  • Why should we assume that an educational system based on a highly-regimented repetition-based pedagogy is preferable to teaching for understanding, after abandoning rote teaching for English students in the 1960s?
  • Why should western democracies copy nations in which avoidance of failure and measuring a person’s worth is based on academic results?
  • While Shanghai did well on highly-structured math tests, statistics on the numbers of Nobel Prizes tell a very different story: the USA tops the list by a huge margin, whereas China is almost dead last.

What do you think?

How much rote learning should we allow? None? A little? As often as possible? Share a comment below.

Reference Articles

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K-6 Math in the News: Everyone CAN Succeed at Maths

What do your students believe about their abilities in mathematics? Do they say “I can do this”, or “I’ll never get this”?

Original article link: How ‘Everyone Can’ Succeed at Maths – TES UK, 6th July 2016

I’m sure all teachers know about the idea of the “self-fulfilling prophecy”: if you start off believing that you have a high achieving class, they are more likely to do well than if you believe from the star that they are a “weak” class.

This article focuses on the message that “Everyone Can” succeed at math, urging teachers and students to believe in the students’ success.

I recommend that you watch the video linked in the article, which has a really nice performance by a young girl taking the role of teacher “Miss Rose”, teaching a class of adults acting as the students:

Maths: Everyone Can from White Rose Maths Hub.

What do you think? Is simply being positive about students’ abilities and capabilities really going to make a difference to the results that they achieve? And are some people simply born “with a maths brain” and others not? Please leave a comment below; I’d love to hear what you think.

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Asian Kids Beat Out the West in Math Again

Pisa test results released:

Why do western nations like the US, Australian and the UK struggle to compete on the international stage when it comes to school mathematics?

A couple of days ago, the Programme for International Student Achievement (PISA) results from OECD countries were released. I encourage you to go over and have a look.

If you’d rather read someone else’s summary of what is shown in the results, try one of these articles. It’s fascinating to see the different interpretations put on the results in just these few media outlets:

National Rankings:

The big majority of visitors to this site are in the following five countries. Check out the position of each one on the mathematics test, out of 65 in the PISA rankings:

  • USA – 36th
  • Australia – 19th
  • UK – 26th
  • New Zealand – 22nd
  • Canada – 13th

What can educators in the West do about the relatively poor showing of their students in mathematics?