So recently Dan Meyer posted this question on his blog…
March 10th, 2014 by Dan Meyer
An ongoing question in this “fake world” series has been, “What is real anyway, man?”
Are hexagons less real-world to an eighth-grader than health insurance, for example? Certainly most eighth graders have spent more time thinking about hexagons than they have about health insurance. On the other hand, you’re more likely to encounter health insurance outside the walls of a classroom than inside them. Does that make health insurance more real?
I don’t know of anyone more qualified to answer these questions than our colleagues at Mathalicious who produce “real-world lessons” that are loved by educators I love.
To which I posted the following comment:
These examples are what I have been questioning for the past few years. Looking at our state standards, the buzzwords of “real world” are overused and can trap educators. Intriguing is also a word that I don’t want to throw out casually. Motivating seems to be the real key with students, what will get students to work on a problem and persevere even though they may come along obstacles? I can’t say intriguing in this case because it implies student interest in the content, not just working on a problem to completion. With my students today, the candy examples are the most effective example that would illicit work.
None of these are practical real world, the fencing one is the closest, but then again farmers will go to any lengths to create straight-edged enclosures because you do not want to waste land area and creating circles do just that.
All in all, my question would be which of these examples will get students to struggle to find an answer, and make a strong enough connection that students will remember the process if a similar problem was posed to them.
And other than the frustration from posting from my phone, getting typos and errors- this question has been in the forefront of my mind. There are a lot of good responses to Real World and Intriguing questions for students and I really recommend you to check out the blog.
So let’s look at Real World and Intriguing…
Real World: noun
the realm of practical or actual experience, as opposed to the abstract, theoretical, or idealized sphere of the classroom, laboratory, etc.: recent college graduates looking for jobs in the real world of rising unemployment.
By looking at this definition, it already raises questions to what many students believe real world means. To them, real world means a situation where they will actually grab a pen and paper, write out an algebraic equation and solve it. We all know that there are very few “real world” scenarios where this happens, but that there are many situations where student mathematical thinking is doing just that. I did a lot of research in the Cognitively Guided Instructional model and the words that jump out to me in this definition are actual experience. I try to use student’s actual experiences in my classroom, allowing them to discover the mathematics that I intend to present for the day. Many of my students are well versed in Algebra, they just have not labeled their thinking or work in that way as of yet- which is another issue I plan to write about later.
to arouse the curiosity or interest of by unusual, new, or otherwise fascinating or compelling qualities; appeal strongly to; captivate: The plan intrigues me, but I wonder if it will work.
Once again, the definition falls short of what my students would define mathematics in the classroom. Most of my students have no curiosity or interest in math, they do it because they have to sit in my class for an hour a day and receive a grade. Granted it is my job to try and instill this into all my students, and hopefully I do to some degree, but this is the point at which they come to me in 8th grade. I can catch curiosity with a topic or story, but when you present them with the math there is a switch that turns off and they immediately retreat into “defensive mode”. Storytelling is a very powerful tool with students, and initially keeping the mathematics verbal and mental will allow students to work harder on a problem than going right for the pen, paper and equations. That is one of the reasons I have found reflection to be such a powerful tool, you can review the events of the class period and show students the connections between their Algebraic thinking and the formal Algebraic notation. Allowing students to write about how they view those connections will drive your instruction and give you the best assessment on where those students are mathematically and where you need to go.
to provide someone with motive- so we look at motive
1. something that causes a person to act in a certain way, do a certain thing, etc.; incentive.
2. the goal or object of a person’s actions: Her motive was revenge.
This is the happy medium that many educators find. Most of the “fun” projects labeled by students fall into this category, you found the “zone” for students to do mathematics while allowing them to feel good about themselves or providing a reward that they enjoy. Doing an activity where you have students supply information about themselves and their interests is a good way to find this, as well as using current students in story problems. One activity that normally catches my student’s interest is when we start graphing, I will read them a story or tell them a scenario that they have to graph. Having students race again me is always a hit, and students normally go above and beyond on these graphs with labels, added details to the race and even pictures of their teacher after he loses. Once again, the biggest challenge is when to introduce the formal math without turning the students off. I finally had one class admit today that when they say math sucks, they do not really mean they feel that way about math rather than they do not want to expend their energy working on a problem they conceive as difficult. They are not confident enough in their skills to take leaps, so I am now finding ways to scaffold learning so that the gap does not appear as large to them.
So when I look at what types of problems are real world, I think about what problems will draw on student’s reserve of math experiences, motivate students to work on challenging concepts, and strengthen connections so that they can use their mathematical thinking more efficiently on similar problems presented to them.