A Healthy Approach to Math
Technology for Learning
by Bob Coulter
Class projects promoting physical health offer many chances to improve the vitality of your students data analysis skills in the process. From counting calories to monitoring personal exercise regimens, opportunities for individual and class investigations abound. One particular area worth considering is working with the data your students can collect with simple pedometers. Whether you share a small number of units, or invest in a class set (available for under a hundred dollars in a recent Google search), pedometers can help you generate data sets that provide days of productive investigations. If your budget is particularly tight, it is likely that parents or colleagues will have units you could borrow for a while.
Through a well-focused series of explorations, many of your curriculum goals can be met. Aside from meeting the National Educational Technology Standards relating to using technology for productivity and research, your students will be developing skills in several areas addressed by the national Principles and Standards for School Mathematics including algebra, measurement, data analysis, communication, connections, and representation. The examples here are just a couple of the possibilities that will arise as you and your students mine the data collected.
The simple act of counting paces over the course of a day gives students a chance to develop skills in collecting, recording, and organizing data into tables and graphs. Opportunities will also present themselves to deepen students understanding of measures of central tendency such as mean and median. For any one person, the number of steps taken in a given day will vary depending on what he or she does. Over a five-day period recently, I recorded a range of steps, from a low of 8,334 to a high of 13,001. The low day was spent mostly in my office; the high day was spent at a technology conference held at Arizona State University, which entailed considerable walking around a large university campus as well as trips through the St. Louis and Phoenix airports.
Projects like this help students to see that collecting real data usually results in a range of values, and that what is presented as typical doesnt occur every day, if ever. Hence, the need for developing an understanding of measures of central tendency such as mean and median. The opportunities to build this understanding get even better if you have a class set of data, since each student can compare their personal data with class norms. Class averages will also show the effects of larger sample sizes, since individual highs and lows will effectively cancel each other out in means and medians. The superjock and the couch potato may define the extremes, but the class average will fall somewhere in between.
Not to be missed in this messing about with the data is the opportunity to compare individual data with established standards. Just as calorie counting can help to monitor for an appropriate level of eating and heart rates can help in gauging the aerobic effects of exercise, tracking the number of steps taken can help in evaluating the amount of exercise each person is getting. (Your own data shared publicly, of course, sets an important example for the class.) Many experts recommend 10,000 steps per day, a level that I missed slightly in my five-day trial run. (My average for the five-day trial run was 9,795 steps per day, though it should be noted that not all steps in a day will be recorded unless you wake up and go to bed with the pedometer.)
How far did you go?
Aside from basic counting of paces, pedometers can be used to determine how far you walked. Many pedometers will attempt to tell you how far you walked in a given day, but that number is dependent on how long each stride is. An average-sized first grader and a teen who has experienced a growth spurt will inevitably have different stride lengths, which will lead to dramatic differences in the total distance traveled while taking the same number of steps. Viewed another way, the first grader would need to take more steps to cover the same distance.
To investigate these relationships, a spreadsheet can be quite useful. The example here uses ThinkFree Calc, but a number of others such as Microsoft Excel and OpenOffice could be used. The key is to be able to establish formulas expressing the relationships between cells in the table. Depending on the sophistication of your students, you may want to have them generate the formulas involved or simply show them how the calculations are being done. In the figure shown here, data for two boys from the same family are listed, along with my data. For each, our stride length is recorded (in inches) and the distance (in miles) covered in 10,000 steps is calculated by the spreadsheet. Your students may be surprised to see how many miles they walk in a day.
In addition, data is calculated for how many steps would be needed to match the distance that would be covered in the 10,000 steps taken by each of the other 2 people listed. As you can see in the table, Turner and William provide surprising results. Even though Turner is taller, his stride length (as it was measured that day) is a bit shorter. This anomaly is likely to occur with at least some of your students, which gives you a wonderful opportunity to extend everyones learning. The curiosity engendered by an unexpected event like this can provide a springboard to more experience with measures of central tendency. Students determining class averages for stride will learn about correlation as they create a graph comparing each persons height and stride length. Of course, authentic uses of fractions and ratios will abound here, helping to counter the ever-present math refrain of, When are we ever going to use this?
As these examples show, a simple tool like a pedometer can lead to a rich array of data investigations. Authentic opportunities emerge for students to experience the power of mathematics and technology to address real needs. Too often, schools teach computer skills in a just in case mode, with the premise of learning tools just in case they are needed some day. Instead, through investigations like the ones here, students can develop skills just in time for their use. Portable data collection devices are used to collect interesting data, which is then organized, analyzed, and presented using powerful tools to answer real questions. Along the way, their understanding of healthy exercise will improve and they will develop important math skills. Stepping back a bit, these projects show how schoolwork can be meaningful and intellectually rich while not neglecting academic standards.
©2006 by Synergy Learning International, Inc. All rights reserved.
- Bob Coulter is director of Mapping the Environment, a program at the Missouri Botanical Garden's Litzsinger Road Ecology Center that supports teachers' efforts to enhance their science curriculum through the use of the Internet and geographic information system (GIS) software. Previously, Bob taught elementary grades for 12 years.