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?
In the busyness of classroom teaching, do you find math lessons becoming a bit stale? Are textbook lessons getting you and your students down a bit?
I believe that students crave interesting, relevant lessons, especially in math. How can we provide such lessons?
It’s a simple idea: find real math going on in the world around you and bring it to the children’s attention.
In the video I talk a bit about the new kitchen we’re having put in. There’s a heap of math that the builders have to get right, including measurement, simple arithmetic and three-dimensional geometry.
What can you talk about with your students? Here are some ideas:
Real-Life Contexts for K-6 Math: Some Suggestions
Take photos with your smartphone, add them to PowerPoint slides, ask students “What do you notice?” or “What questions are you thinking of?”
Talk about shopping experiences where you had to figure out a best buy, someone gave you the wrong change or something cool happened
Explain how you adapted a recipe for a different number of servings
Talk about your favourite sport and how rankings work, and how many points teams have to win to come out on top this season
Talk about designing something cool, such as a garden, a craft project, a greeting card or a decorated cake
What ideas have you used to bring classroom math to life? Leave a comment below.
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.
Indigenous students in Australia typically lag two years behind other kids in math: a disappointing statistic by any measure. Dr Chris Matthews of Griffith University has come up with a new approach that shows great promise for connecting indigenous kids with mathematics.
Going further, I believe that this new method would help any kids of a non-mainstream background to understand math. Watch the video for more:
The approach recommended by Dr Matthews is explained by Prof Tom Cooper of the YuMi Deadly Centre at QUT, using the acronym RAMR:
Reality: connect first of all with students’ existing culture and interests. In the case of indigenous kids, this includes story telling and dance
Abstraction: come up with ways to turn stories and concerns into mathematical problems, equations and so on
Mathematics: invent mathematics in standard symbolic format to capture the original question or scenario
Reflect: consider the result and match the mathematical results with the original source situation and consider how well the mathematics enabled the solution for the problem, or explained a story in mathematical terms
[Click the link below to watch Prof Cooper’s explanation]
But a teacher who teaches students of non-indigenous but also non-mainstream backgrounds could adopt the same basic pedagogy, starting with those students stories, culture and questions that interest them.
Mathematics has sadly often been presented as the product of a lot of “old white males”, which for some students immediately puts them offside and makes math irrelevant and boring, in those students’ minds. This approach deals with this problem by starting with examples from the students’ own culture and background.
What do you think?
How should we teach math to students from backgrounds other than our own? Share a comment below.
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.
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.
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.
Rain gauges measure rainfall by collecting a small sample and measuring how deep the water is. The trouble is, we are interested in very small units – in the metric system, rainfall is measured in millimetres/millimeters. How can you accurately measure such small amounts?
How can we use everyday examples to teach measurement?
Watch the video: I explain how a rain gauge amplifies the depth of water collected to make it easier to measure.