Boys tend to be better at math. That’s been the stereotype, but a new study (Kane and Mertz, 2011) published in the Notices of the American Mathematical Society provides evidence that, at all levels, it’s only because society and culture tend to support, and advance the stereotype.
… we conclude that gender equity and other sociocultural factors, not national income, school type, or religion per se, are the primary determinants of mathematics performance at all levels for both boys and girls. … It is fully consistent with socioeconomic status of the home environment being a primary determinant for success of children in school.
Kane and Mertz compared math achievement in a number of countries. If there were some genetic reason for different math abilities then boys should be better than girls everywhere. This is not the case. In more wealthy countries where there is more equality between the genders, the mathematics performance gap disappears.
In poorer countries like Tunisia boys tend to do better at math, while in rich ones like Barhrain girls do better. However, in places with greater equity between the genders, like the Czeck Republic, boys and girls do equally well. Figure from Kane and Mertz (2011).
The Missouri Council of Teachers of Mathematics (MoCTM) has a Math & Art Contest that focuses on Geometry. It has fairly simple expectations, and it’s aimed at Middle School students and lower. The tie between the math and the art does not require much depth, but that’s probably appropriate for students who are still developing abstract thinking.
A tessellation. Image via Wikipedia.
I’m usually a bit cautious about the utility of contests. Their primary benefit is in the work that they motivate, not the reward (or hope of a reward) at the end; although, students do need to learn to win or lose with equanimity.
Animation showing the widening and shrinking of the parabola.
So I put together this interactive parabola program using VPython (code here) for students encountering these curves in Algebra.
Simple Excel program to graph a parabola.
It’s a more interactive version of the Excel parabola program in that you can move the curve by dragging on some control points, rather than just having to enter the coefficients of the equation. The program is still in development, but it is at a useful stage right now, so I thought I’d make it available for anyone who wanted to try it.
The program is fairly straightforward to use. You can move the curve (translate it) up and down, and expand or tighten the area within the parabola.
The program also displays the equation of the curve in standard form:
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What the buttons do.
Next Steps
I’m also working making the standard equation editable by clicking on it and typing, and am considering showing the x-axis intercepts, which will give algebra students a nice, visual way to of checking their factoring.
There was a neat little conference today, organized by LEGO’s Education division. I’ve been trying to figure out a way to include robotics in my math and science classes, but since I haven’t had the time to delve into it, I was wondering if the LEGO Robotics sets would be an easy way to get started. It turns out that they have a lot of lesson plans and curricula available that are geared for kids all the way from elementary to high school, so I’m seriously considering giving it a try.
Pedagogically, there are a lot of good reasons to integrate robotics into our classes, particularly as the cornerstone of a project-based-learning curriculum.
The act of building robots increases engagement in learning. Just like assembling Ikea furniture makes people like it better, when students build something the accomplishment means more to them.
Working on projects builds grit, because no good project can succeed without some obstacles that need to be overcome. Success comes through perseverance. Good projects build character.
The process of building robots provides a sequence of potential “figure it out” moments because of the all steps that go into it, especially when students get ambitious about their projects. And students learn a whole lot more when they discover things on their own.
Projects don’t instill the same stress to perform as do tests. Students learn that learning is a process where you use your strengths and supplement your weaknesses to achieve a goal. They learn that their worth is more than the value of an exam.
Projects promote creativity, not kill it like a lot of traditional education.
In terms of the curriculum, Physics and Math applications are the most obvious: think about combining electronics and simple machines, and moving robots around the room for geometry. A number of the presenters, Matthew Collier and Don Mugan for example, advocate for using it across the curriculum. Mugan calls it transdisciplinary education, where the engineering project is central to all the subjects (in English class students do research and write reports about their projects).
I’ve always favored this type of learning (Somewhat in the Air is a great example), but one has to watch out to make sure that you’re covering all the required topics for a particular subject. Going into one thing in depth usually means you have to sacrifice, for the moment at least, some width. The more you can get free of the strictures of traditional schooling the better, because then you don’t have to make sure you hit all the topics on the physics curriculum in the seemingly short year that you officially teach physics.
The key rules about implementation that I gleaned from presentations and conversations with teachers who use the LEGO robotics are that:
Journaling is essential. Students are going to learn a lot more if they have to plan out what they want to do, and how to do it, in a journal instead of just using trial-and-error playing with the robots.
Promote peer-teaching. I advocate peer teaching every chance I get; teaching is the best way to learn something yourself.
2 kids per kit. I heard this over and over again. There are ways of making larger groups work, but none are ideal.
A Plan of Action
So I’m going to try to start with the MINDSTORM educational kit, but this requires getting the standard programming software separately. One alternative would be to go with the retail kit, which is the same price and has the software (although I don’t know if anything else is missing).
I think, however, I’ll try to get the more advanced LabVIEW software that seems to be used usually for the high school projects that use the more sophisticated TETRIX parts but the same microcontroller brick as the MINDSTORM sets. LabVIEW might be a little trickier to learn, but it’s based on the program used by engineers on the job. Middle and high students should be able to handle it. But we’ll see.
Since LabVIEW is more powerful, it should ease the transition when I do upgrade to the TETRIX robots.
The one potential problem that came up, that actually affects both software packages, is that they work great for linear learners, but students with a more random access memory will likely have a harder time.
At any rate, not I have to find a MINDSTORM set to play with. Since I’m cheap I’ll start by asking around the school. Rumor has it that there was once a robotics club, so maybe someone has a set sitting around that I can burrow. We’ll see.
visual.ly posts and hosts some excellent graphics. The one below, calculates the nearly infinitesimal probability of just being born. There’s hardly a better argument for appreciating life.
It’s also a good example of working with probabilities [and] exponents. Very large exponents.
The answer: maybe. There are just a lot of assumptions that have to be made. Is falling bird poop spherical? What’s its density? How does the bird poop deform on impact? What is the compressive strength of automobile glass?
This is however an excellent real-life application of back-of-the-envelope physics and algebra. It required calculating:
the volume of the poop – extrapolated from the diameter of the residue on the windshield;
the terminal velocity of the poop – the velocity where gravity’s force is exactly counterbalanced by wind resistance so the poop is at its maximum speed;
the force of impact – calculated using the work done as the poop splatters;
Take what you find interesting and turn it into something challenging, something provocative for someone else.
–Dan Meyer (2011): [anyqs] Hurricane Irene Edition
I’m looking for a good reference for project-based math. Where students face the real-life problems, and learn math as they try to solve them, yet covers the entire curriculum in a complete way.
What I’m considering right now is to swap in some of the real-life questions for some of the sections in the text that consist of rather pedantic word problems, things like: the sum of two numbers is three times less than the square root of the second plus the reciprocal of the first.
Instead, I’d rather do problems like determining the height of a tsunami, which can be treated in different ways depending on which math class you’re teaching, and tie into the science classes (like Physics) as well.
Dan Meyer is a proponent of the project based approach, and he has a lot of interesting problems on his blog.
