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?

Are you getting a little tired of other people interfering in how you teach in your classroom?

I see around the world teachers being put under greater and greater pressure to perform, as if they were mere employees or servants of the state. And I’m over it!

Most politicians have never taught a day in their lives, from what I can tell. How dare they act like teachers should somehow get more motivated to achieve higher results, for the good of the nation?

Now, of course the curriculum is important, as I say in the video. But bureaucrats and nit-pickers seem to think that teachers need to stop being so opinionated, and just accept that they are there to do the will of their masters. Arrggghhhh!!! What doctor, engineer or lawyer would accept such treatment?

So let’s stand up for professional autonomy in our classrooms, go out and do an outstandingly excellent job, for our students, their families, and of course our nations.

Do you use technology as much as you’d like to help your K-6 students understand math? How do students respond to tech? Would they actually prefer old school resources?

Have you started using Snapchat yet? Would you like daily K-6 math videos to start conversations? Follow me: petes_classroom

Let me know what you think in the comments below!

The big message in the video is this: it’s not about the technology. A great teacher can use any resources, or none at all, to effectively teach students what they are ready to learn.

That said, we should test new technologies to see how they can help our students to learn. No technology is capable, in itself, of “revolutionizing learning” (how often do we hear that phrase?). But in the hands of a competent teacher, technologies open up new possibilities and new opportunities to present content to students in new ways.

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.

Teachers recently told us, of all the K-6 math topics in the curriculum, which one they would most like help with.
Care to guess which topic came to the top of the list?

Most Challenging K-6 Math Topic

The “winner”: Place value. Close behind? Operations, followed by Number facts.

Since these three broad topics form the bulk of the mathematics curriculum, especially if you include fractions, perhaps this isn’t a big surprise. But another perspective is that, while these three form the backbone of the math curriculum, they are possibly the most abstract and the most difficult for children to understand.

Most Requested Resources

The followup question we asked was “If support for the above K-6 math topic were available, which of the following components would you like included?” The following possible components were listed:

Teacher information about recommendations for teaching the topic

Pretest to assess students’ learning prior to starting the topic

Video to set the scene / prompt discussion / show math in real life contexts

Video for teacher on recommended teaching

Instructional video for students

Hands-on learning activities

Worksheets

Differentiation activities for various levels of ability

Homework sheets

Parents information to explain homework

Posttest to assess students’ learning after learning the topic

The results? The top request, made by 85% of respondents, was “Hands-on learning activities”, followed by “Differentiation activities for various levels of ability”, and then “Video to set the scene / prompt discussion / show math in real life contexts“.

I am encouraged to see that teachers we have contacted want their students to have experiences with hands-on activities to help them learn math. As we all know, math is a highly abstract discipline, and traditionally it was taught around the symbols, which themselves are linked abstractly to the numbers which they represent. So to provide children with physical, hands-on ways to represent and play around with numbers is the way to help them to understand the subject, in my view.

What Next?

We are now starting development of a new package of resources to support teachers in their teaching of K-6 math. We will start with a small beta product, and put it out to a small group of our best supporters. All being well, this will then become available to others, via this website.

If you would like to be notified of when the package is publicly available, click the box 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.

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?

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!