Tag Archives: math
10 Tips for Easy Web Mapping in the Classroom Tomorrow
Date and Time: Wednesday, March 30, 2011 at 9pm EDT/8pm CDT (1 hour).
Webinar presented by: Esri Education Team, Esri and the National Council for Geographic Education (NCGE). NCGE will host the webinar.
About: Learn about the basics in web mapping technology and easy-to-implement strategies for the geography & science classrooms. Critical websites and power tips will be provided to teachers new to geospatial tools – designed specifically for use “tomorrow”. We’ll even show you how to create your own map-enabled presentations, suitable for use in any academic subject area.
In my last blog entry, I discussed why GIS has a natural fit with mathematics education, why the GIS education community should build partnerships with mathematics educators, and how mathematics can be taught through GIS. Let’s get more specific.
First, the use of GIS brings math to life by making math visual. Think of common problems such as: “Where and when will these trains cross paths? One departs Point A at 6:00am and heads toward Point B at 70kph, while the other departs Point B at 6:30am bound for Point A at 60kph.” Where and when will they cross paths?” GIS allows the anchoring of these and other problems in the real world: Points A and B could be Cheyenne and Casper, and students can determine and plot the course and passing point at a real point on a GIS map layer. Second, solving math problems in a GIS environment allows students to grapple with biodiversity, crime, natural hazards, climate, energy, water, and other relevant real-world issues of the 21st Century.
Third, students often do not feel that what they are learning is relevant to what they will be doing after they get out of school. Hundreds of jobs in geospatial technologies—not just surveyors and remote sensing analysts—require analytical, statistical, and computational skills that are learned in mathematics.
To build bridges with mathematics means to serve with primary, secondary, and university mathematics educators on advisory boards at all levels, to conduct professional development with them and for them, and to regularly dialog with teachers and administrators about the clear linkages between GIS and mathematics. Curricular materials that incorporate math concepts and skills are critically needed and can be best created through partnering with math teachers and professors.
These connections have deep historical roots: Willis Ernest Johnson wrote Mathematical Geography back in 1908, and Eratosthenes connected geography to mathematics in measuring the Earth’s circumference over 2,200 years ago! I encourage you to build these bridges so that mathematics teaching and learning can be enriched by GIS technology and spatial analysis.
–Joseph Kerski, ESRI Education Manager
GIS provides an excellent way to teach mathematical concepts and skills. The value of visualizing numbers is affirmed throughout the US Principles and Standards for School Mathematics, designed by the National Council of Teachers of Mathematics (NCTM). Representing numbers, understanding patterns, relationships, and function, 2-D and 3-D geometric and spatial relationships, probability, statistics, change, models, measurements, problem solving, reasoning, connections, and communications are critical concepts. Every one of these can be explored using GIS tools and methods. Comparing graphs and maps of birth and death rates over time and region, analyzing the response of a stream to a recent storm through a real-time hydrograph, and creating cross-sections of terrain are three common activities in geography instruction, easily done in a GIS environment. All of them—and thousands more geographic activities—involve analyzing numbers. One might say that GIS is visualizing numbers, since its basis is representing numbers as cells, points, lines, or polygons on a map.
NCTM’s curricular “focal points” also connect well with GIS. A focal point must pass three rigorous tests: Is it mathematically important, both in mathematics and for use in applications in and outside of school? Does it “fit” with what is known about learning mathematics? Does it connect logically with the mathematics in earlier and later grade levels? When we connect latitude and longitude to the Cartesian coordinate system, when we measure area, shape, size, and distance in different map projections, when we compare geometric to exponential growth rates of agricultural output, even when we explain the Earth’s shape, rotation, and revolution, we are applying geographic and mathematical concepts and can use GIS to teach it.
Why should we build bridges with mathematics educators? Mathematics is funded, assessed, and is strong in all levels of primary, secondary, and university education. The more that GIS is seen as indispensable to the teaching of mathematics, the more likely it will be that spatial analysis will be taught in schools and universities. In addition, our own curriculum and professional development will be enriched by what we learn from our colleagues in mathematics.
–Joseph Kerski, ESRI Education Manager
I love surprising my students with facts and trivia that will make curricular elements stick with them. Previously, I discussed using place as proof and analyzing water resources. What about breaking the stereotype that if you’re good at English then you can’t do math! The students I tutor in Algebra are always surprised that I can indeed “do math.”
A great way to incorporate a little math is a journey book or story. A great example is Journey to Jo’burg by Beverly Naidoo. A 13-year old boy and his sister must make a journey 300 kilometers from their small village to Johannesburg, South Africa to get medical help. How far is that…really? For you sharp GIS folks, it’s a quick little buffer activity in ArcGIS or AEJEE. You could use ArcGIS Explorer and measure that distance; however, if you only have the internet available to your classroom, our trusty tool Sketch-A-Map can give us some assistance here. As the teacher you will have to do some homework here to discover real distance. In the case of our story, Pietersburg, South Africa is approximately 300 kilometers from Johannesburg.
With the street map in view, students can draw a line on the map of that distance and more lines to discover where the children’s small village is. For some perspective, then we could zoom over to the USA and draw a similar line from Washington, D.C. to Newark, NJ. It’s about the same distance. Most students would realize quickly, “Hey! That’s pretty far!” Most of my students wouldn’t have considered such a journey!
Now that we can see that journey on the map, let’s appreciate what Tiro and Naledi in the story did to get help. Time to do a little math!
1 mile = 1.609344 kilometers. How many miles is 300 kilometers? What city is that distance from your town?
A person could walk about 2.5 miles per hour. If you made the journey, how long would it take you to get there?
If you’re just a little creative, you can continue to cover your required content and give students important connections to their curriculum! As an added bonus, the math teacher will be happy too!
- Barbaree A. Duke, Language Arts Educator
How’s the winter been so far? I know that many folks have had some seriously cold weather. As a native Minnesotan, I grew up with a clear sense of weather. And because I travel a bit, I have heard people complain when “it’s been colder than ever, for days.” It has been both humorous and frightening when folks have interpreted wintery weather to mean “global warming is a farce.”
Strangely, I have heard few say it this winter. Maybe I’ve just been preoccupied. But I hope that people have seen and heard enough analyses to appreciate the difference between long-range trends and short term fluctuations, and to understand that climate modeling is an imperfect science.
Snowfall accumulation from Dec 18-21 2009 storm (Credit: NOAA)
I rode out the storm shown above without incident (made me feel right at home!), though I know others suffered, just as some are struggling now with extended cold. Still, I think many were spared much agony simply because more and more scientists, media, and citizens are using maps better — analyzing more data, studying models, interpreting patterns, and communicating meaning.
Maps help give meaning to science. If people will seek out that association between maps and science (even though there are good and bad examples of each!), we’ll all be better off. GIS helps scientists analyze disparate data and convert complex patterns and interactions into something that has meaning to lay people. Even “simple maps” like the one above may represent vast volumes of both data and person-hours. Think science, see maps, and vice versa.
My last two blogs have been about GIS as a “powertool for STEM [Science, Technology, Engineering, Mathematics] education” or GIS as an analytical tool for STEM. As exciting as it is to work with powerful tools and skilled users, it’s even more enjoyable to watch a good teacher in action, and see how students dive in when given a good opportunity. For GIS Day, I have had the privilege of visiting some classes participating in the Virginia Geospatial Semester. I watched one teacher work with two different classes. (I’ll call the teacher “Jane.”)
Jane’s task for the students was pretty straight-forward: “You’re trying to help a doctor who is moving into a nearby state (Pennsylvania), working with two age groups: 5-17 and 65 and over. You need to find the counties with the ‘optimal number’ of potential patients. You need to make two maps that engage ratios, make your decisions, generate a layout, post it electronically, and write a paragraph explaining your choices and selection.” That was about as much instruction as Jane gave.
It was fabulous! The students had enough just skills to tackle each part of this, on their own, but it was still a stretch. In making the maps and doing the analyses, they wrestled with different combinations of fields. They employed different strategies for evaluating “optimal” — queries, manual selection and comparison, and swiping to seek most glaring color schemes.
Working in pairs — and being 12th graders — they talked, and posed questions, to each other and to Jane. Jane, in turn, asked them questions, luring them to explore, explain, analyze, and synthesize. She listened, sometimes providing a bit of info, sometimes asking a specific question. At the end, a handful of teams got up to present their selections and strategies.
Almost everyone was intensely engaged throughout. (With seniors, there’s often “that 5-10%.”) They wrestled with the content, a raft of skills, and some pretty compelling math, then communicated their findings. And all the way thru, the simple questions led them further, step by step, different questions for different students.
Good tools like GIS are fun to work with. Good teachers can take even basic ideas, present them enticingly like a jungle gym or ropes course, give some general guidance, and let the students wrestle with the content. This affords individual attention and customized assistance. But it tests a teacher’s ability to “cope with divergence.” And, since the tools, skills, and content are truly infinite in scope, the questions never end, so it provides a chance to model the lifelong learner. It doesn’t have to be rocket science, either … it’s just incredibly powerful, in the right hands.
- Charlie Fitzpatrick, Co-Manager, ESRI Schools Program
At a recent conference, some teachers asked how they could address some math concepts using ArcExplorer Java Edition for Education (AEJEE), ESRI’s free, downloadable, dual platform (WinXP/MacOSX), lightweight GIS tool. This was a fun challenge!
The opening project of the AEJEE Tutorial (10grid_hd.axl) and a companion project (10gridpn_hd.axl) provide two handy 10×10 grids for mathematical playgrounds. The two projects use “Cartesian space”, with the first strictly in “positive space” and the second covering both positive and negative portions of the X and Y axes. Creative explorers will find interesting options just playing with coordinate systems. If the 10×10 space actually represented a 100×100 unit space on the school playground, could you map the distribution of ant colonies (etc) just with a simple X,Y table?
Of course, any analysis that gets into selection and queries opens the floodgates for math work. For instance, the opening lesson of the Tutorial asks the user to do a complex query, which is good old-fashioned set theory. Coming up with an answer to any query, the user can scroll through the results table to see what appears, click the “Statistics” button below, and generate stats about a particular field using either the whole universe or just the query results, finding count, max, min, mean, standard deviation, and total.
An earlier blog entry dealt complex math queries to identify ratios, while another explored population change by doing “math-embedded queries” to find those counties in the US which had a 5-year population decrease exceeding 1% per year. And one of the earliest blog entries covered the use of buffers to determine changing impact from alternative selections. And who could resist exploring some of the simple calculations that are possible in an exercise dealing with baseball parks — Just how far is it if a batter smacks one “out of the park”?
These are just some of the innumerable possibilities for seeing how AEJEE is a great tool for demonstrating a variety of math concepts in everyday life experience!
- Charlie Fitzpatrick, ESRI Education Manager