I had heard about this a long time ago but never bothered to investigate it much. Do I ever regret it now! Desmos Graphing Calculator is an easy-to-use online graphing calculator that takes the place of the expensive Ti-83 I used to have. What is better, it allows you to save and share your functions, a handy tool to have for many reasons. One reason that is important to us out here in the sticks: being able to email your graphs is key when many of your higher math classes are either online courses or distance learning. That aside, it’s a great tool to have for any student that finds their tablet or laptop more convenient than a calculator.
Posts tagged ‘math’
The educational world is full of great, seemingly boring software. These are usually applications that are not the prettiest or the most feature-rich but have tremendous staying power and appeal. A great example of this is Oregon Trail. Not the flashiest program, but I still use the original Apple II version of it in my classroom, and it is still as fun as it was when I was a kid.
This week, to round off a math unit on geometry, we used a program called Geometer’s Sketchpad. Sketchpad is a seemingly boring piece of software that nonetheless has nearly unlimited potential. The program resembles a drawing program that allows you to make points, rays, and lines on a plane, program them, and measure them. Simple, right? Well, after getting a crash course from a coworker, I now think it’s amazing. It does for geometry what Excel does for graphs and Word does for writing papers. It takes all the work out of measuring and drawing objects in geometry and lets you play with shapes and constructions, testing out concepts like area and formulas. Pretty soon my students were drawing dozens of triangles, stretching them out as far as they could go, but the sum of their angles never changed. The only way that you can do this in a standard classroom would be to cut out about a million triangles out of construction paper, measure their angles, and add them as a class. This program frees up so much time teaching the basics and expanding on advanced concepts. Before long, my kids were programming pool games to show the angles in bank-shots and programming the hands of a clock. It also makes a great primer for computer drafting using Alice or Sketchup.
It does have a learning curve. I recommend you check out the website’s expansive resource center, full of lesson plans, or find any one of the great instructional workbooks on the program.
I got a chance to play with a really nice set of games created by the Science Museum in England. They have developed a set of really fun games called Futurecade. Some of these games are based some of the real problems of the future. For example, removing land mines using robot drones you have to program (dealing with the real issue of mine removal) or creating strains of e-coli that can clean up oil spills. Others involve teaching genetics by having students care for, nurture, and breed ‘Things’ in the game Thingdom.
Many educational games are little more than regular arcade-style games with some math facts thrown in. These games were created to promote issues in math and science, but also to develop thinking and problem-solving. These could easily be adapted to lessons on global warming, energy, genetics, food distribution, and natural resources. What really makes them great is the optimism that science can solve these seemingly overwhelming problems, and that they allow your students to stand in the shoes of the problem solvers of tomorrow. Good thing too, since they will have to fill that role in the future.
I had a crisis of faith last week. I had been riding high for some time over the use of my recorded lessons in my classroom. Basically, I was using a screen-grabbing app to record math lessons and posting them on YouTube so that I could curate my math class. I created a “Khan Academy lite” in my classroom, geared to my student’s needs. It worked great and my students have been responding very well in math since adopting this new program.
But then something happened. I heard that several local politicians were embracing the Khan Academy and sites like it as something “new” and “innovative.” Great, I thought, I love the Khan Academy! My students use it all the time to brush up on math, or get the help that their parents don’t have time to give. But it turned out they weren’t promoting Khan Academy because it’s a great tool; they were promoting it because they felt that, with such great resources available for free online, why were they paying teachers so much money?
Here was my dilemma. If I make my lessons available for free online, am I diluting the value of my instruction a product? Are teachers who share their instruction and lesson plans online putting themselves out of a job? I had to think really hard about it and I came to this conclusion: Heck, no.
Even though I can buy the album or listen to it on the radio, I won’t stop going to concerts. Even though Shakespeare is public domain, people don’t stop paying to see his plays or think that an audiobook can replace a performance. Canned tomatoes, while handy, don’t replace the real thing—if anything, they make you appreciate the real thing more.
Khan Academy and similar sites are not the end of education as some other educator-blogs would have you believe. Khan himself writes that his site is not a curriculum; he is simply offering another way to teach children, one that is realistic and pragmatic. He does not abstractly teach ‘why.’ Instead, he focuses on the ‘how’ of actually solving math problems and succeeding in math. Frankly, many students (including myself when I was a kid) were frustrated by the constructivist approach of ‘finding a way that works for you’ and would rather just skip to practicing the method that works every time.
Many make the argument that Khan is not a teacher and is not qualified to teach children. That just rubs me the wrong way. What I do is not special; anyone can teach, just like anyone can cook, work on a car, or learn to play guitar. But not everyone is brave enough to try and willing to put the work into doing it well. To me, Khan Academy is no different than a student getting help from mom and dad, who are often not certified teachers, and educators don’t turn up our noses at that.
I will continue to post my lessons, because it helps me become a better teacher. I like to think that if more people see my teaching, it will help them see the value in what I do. I want parents at home to watch the lessons with their kids and think, “Wow, my kid get to have him in person.” Like so many other times in my life when I have felt doubt and am forced to confront it, I end up only more sure that I am in the right place, doing the right thing.
I used to think that Google was a little scary. Perhaps I’ve watched too many science fiction movies, but the idea that you can ask a computer anything and it gives you an answer seems a little … frightening. But I could at least take solace that a search engine does not understand what it is looking up.
Last week I discovered Wolfram Alpha, and I am convinced that it is the name of the coming metal overlord. Wolfram Alpha does not search for websites to answer your questions, it simply answers them, putting out simple, concrete facts. Search for 2+2 and it gives you 4, ask it what is the 23rd most populous nation, and it finds that too. Not a website that answers it, not a Wikipedia entry—an actual answer.
I started by searching for Franklin Roosevelt. It gave me a single photo, dates, and places of birth and death, a timeline and half a dozen of his most notable accomplishments. Not enough to write a report, but enough to put him into context at a glance.
But the real fun occurs when you type in math and science based questions, or statistical data. Type in your name and it tells you how common it is, and when it peaked in popularity. Ask it what the 23rd most populous country is, and it will tell you it is Italy. When I use this website I feel like I am amazed and terrified at the same time, like riding a roller coaster.
Some fun searches could include:
- How old was George Washington when he died?
- Who was the 5th king of Spain?
If your imagination limits you, try going here.
The workhorse of good upper math courses (the kind that I never got to take since I went into physics and not calculus) is the graphing calculator, the blocky grey machine that can solve any problem, graph any equation, and can be programmed to play Tetris.
I always wondered why, in the age of smartphones and computers, the Ti-83 had never really changed. But now even the good people of Texas Instruments have been cloud-sourced.
For a long time now, if you entered a math problem into Google’s search bar, you get the answer via a calculator. Go ahead, Google 2 + 2, or even ask for a conversion like 5 gallons to liters; you will get an answer. Now Google has expanded that to functions. Try entering sin(x) into Google (or just click here). You end up getting a pretty little graph.
Will this replace the Ti? It’s hard to say. Will it work in pinch if you are without one? Probably. Math teachers (of which I am not one), test this out for me and tell me how this works!
Winter has come to Wisconsin late, but I could not be happier that it is finally here. This last weekend we got hit with a few good inches of heavy, wet powder. The snow has clung to everything like thick sugar icing; the trees, barns, and houses all look like some picturesque postcard of the great white north. For one day, we had perfect packing snow at the school and I used it to create a … ahem … math lesson. We built the first igloo of the year.
Using a 6-foot ceiling as a radius, we figured out that it would need to be 12 feet in diameter. Using pi we figured out how many rows of 8-inch bricks it would take to clear the arch — 21 rows. Then the building began. We managed to get the walls five and a half feet up before a few weak bricks (which I suspect were packed by another class, less dedicated to the cause) resulted in wall failure. The next day, the temperature dropped to 14 degrees at noon, and our bricks were as hard as glass. There would be no new bricks.
We re-used them to build 2 smaller igloos, going around in circles and eventually walling a student up inside (hopefully one who is not claustrophobic) and digging out a door. Add a little water to the walls and they become incredibly strong. Other teachers might play football at recess or take kids out to the pond for skating. I build.
There are a lot great educational websites out there for math. Then there are “educational” websites that throw a few math problems in there but at the end of the day are just unimaginative flash games designed to get children to click on banner ads. Creating a good list of educational websites is time consuming because so much of it involves first finding good sites that are relevant to your math content then organizing them. Every teacher who makes technology a priority keeps a list of links to their favorite websites for their students, because Google can’t tell the difference between good math sites and exploitative sites that just happen to have some math.
Richard Byrne’s fantastic blog, www.freetech4teachers.com, pointed me to a great little site with a fun name: MathChimp.com. MathChimp is a collection of math games from various sites, categorized and reviewed by other users. While it does have a few banner ads here and there, they are not the variety designed to separate parents from their credit cards or collect information. All of the games are broken drown by grade and by subject.
If you have a great site that you know of that helps teach math, please feel free to post it in a comment!
This is an example where a simple idea can truly change the world. In 2004, a man from Louisiana named Salaman Khan took the math lessons he had been giving to his cousin and began hosting them on YouTube. The lessons are simple. Most are 10 minutes long and consist of a person drawing or writing the lesson while conversing with the listener. The overall effect is like looking over someone’s shoulder while they do a math problem. This expanded into a massive collection of online lessons in science and technology and has grown into the Khan Academy, a website where thousands of lessons are available for viewing. There are also self-directed assessments. Funded by such notables as Google and Bill Gates, the website contains lessons in everything from adding to advanced calculus, all of it available for free. Teachers are even able to set up online “classrooms” where they can assign these virtual lessons to students and monitor progress.
Currently there are 2,100 mini-lectures and over 100 exercises that have been viewed by over 46 million people, providing educational lessons from first grade through college. As part of the effort to make it available to everyone, the lessons have been downloaded onto disks and distributed to impoverished nations without internet access.
I see using this for my advanced math students who need something extra. This site, along with a loose framework of assessment should give them plenty to do. Go ahead and give it a look, its great stuff.