A simulation is the process of imitating a real situation or object with a set of mathe- matical formulas. Computer simulations can imitate weather conditions, chemical reactions, nuclear accidents, medical techniques, costs required to produce a partic- ular design, biological processes, cockpit and spacecraft systems, and product safety testing, to name just a few. Some situations or objects are more problematic to create than others, reflecting the ease with which they can be reduced to mathematical data and equations. Interaction with the situation is an integral component of a simula- tion. An important factor when creating simulations is to clearly define the situation or object and determine the most important factors. Simulations are often used to test theories of causal relationships.
How can teachers effectively incorporate simulations into the curriculum? The critical task is to coherently integrate the simulation software as a vital part of the curriculum, not as an add-on. This means students use the simulation for an ex- tended time period and should be engaged in extension activities based on the thinking skills embedded in the simulation (Henderson, Klemes, & Eshet, 2000). Computer simulations can be used to do the following (among other things):
- Visualize the invisible
- Manipulate variables, observe results, and draw conclusions
- Facilitate role playing
- Use gaming approaches
- Mimic real-world situations
- Involve multiple participants
Simulation software and data analysis activities help develop the central elements of statistics. Statistics is defined as a set of methods used to collect, analyze, present, and interpret data. Whereas a computer assists in summarizing data, statistical methods focus on the interpretation of the output in order to make inferences and predictions. Young students start off working with simple classroom census data. At this age, the teacher may elect to generate the question at first. For example, the problem of de- ciding on a breakfast menu for an elementary school could begin with the question “What do kids like to eat for breakfast?” Students collect data to answer the question. The notion of sampling is difficult to develop. However, upper elementary and mid- dle school students start to acquire an understanding about statistical inference. Be- fore students leave high school, they should know that statistical techniques are used daily in work settings to solve problems and make informed decisions (NCTM, 2000).
Software programs as well as the websites that follow may be used as resources for the creation of curriculum units, educational resources, and learning activities. Yeo and Tan (1999) recommend designing simulations to “provide dynamic prob- lem situations for learners,” which foster a “theoretical understanding of the inter- actions in the simulated environment through direct feedback from their actions” (p. 70). This can be done by encouraging three types of feedback: self, peer, and teacher. Time should be provided for students to (1) reflect and write about their simulated experience and (2) share their reactions (Tomlinson, 2000). Students need to understand that computer systems and software programs are designed to per- form specific jobs. These data analysis software programs help students acquire data literacy, which includes the skill and knowledge of selecting the best tools and methods to accomplish a task, solve a problem, and/or make a decision based on available data.
An example of a student-oriented statistics and data analysis software program is InspireData (www.inspiration.com/productinfo/inspiredata/index.cfm), which focuses on students developing data literacy. InspireData is part of the Inspira- tion family of software programs (see Chapter 2). This software program allows students to collect, organize, and analyze their own collected project data. Stu- dents discover the meaning of data collection and analysis as they explore data with the unique visual nature of InspireData. The software includes a capability to build databases and then visually analyze the data with multiple plot types, such as Venn, stack, pie, and axis plots. Students use the InspireData table view (see Figure 12.1) to enter, import, and customize data from experiments or research activities.
In the InspireData table view, the user can:
- Enter multiple data types easily, such as numbers, text, lists, series, and formulas
- Start with one of InspireData’s 50+ curriculum-based databases
- Import data from the Internet or other sources
- Use the Questionnaire tool to launch surveys and guide data collection
- Customize table properties or create multiple tables within a database
- Add notes to reference sources and provide explanations
In plot view, the user can:
- Create Venn plots with up to three loops to show similarities and differences
- Create stack plots to show distribution of values and take data analysis further using stack plot options, such as parallel stack plots
- Create pie plots to easily recognize patterns or subdivide data in multiple pie plots
- Create axis plots to investigate correlations and discover relationships
- Manipulate variables and settings to further explore data
- Easily select and change axis labels to visualize different sets of data
- Isolate data subsets to focus investigation
- View data as they change over time with animated Time Series
- Customize plots with labels, colors, and unique icons
- Combine data categories to discover larger trends
- Perform calculations and use basic statistical tools, such as mean, median, and summary counts, to support conclusions and summarize data
Students can see the meaning of data by visualizing animated data as they change over time. By indexing to time, students can create a plot and watch it change. This makes data analysis a more dynamic visual experience (see Figure 12.2), where decision making and data-based conclusions are realistic.
When using simulations and other problem-solving programs, remember never to rely on the software to teach higher-order thinking skills. Students need teachers to help them make connections. Encourage students to explain their thinking frequently when working collaboratively. Brainstorming tools such as Inspiration (see Chapter 2) and InspireData help students structure a strategy needed to solve a problem by flowcharting, or explore the problem domain by creating concept maps. Building data literacy, analytical skills, and higher-order critical thinking are an integral part of this problem-solving approach to student learning.
|SIMULATION WEBSITES AND DATA RESOURCES|
- BioLab Frog: www.biolabsoftware.com/bls/frog.html
- Capitalism: www.enlight.com/capitalism2/
- Catlab: www.emescience.com/bio-software-catlab.html
Purpose: to become familiar with genetic research and the laws of genetics. Learner chooses parents’ characteristics and kittens arrive in a few seconds. Many generations of kittens are produced to demonstrate how genetic laws work.
- Chemistry Simulations: http://ir.chem.cmu.edu/irProject
The IrbYdium Project at Carnegie Mellon University, funded by the National Sci- ence Foundation, creates simulation-based chemistry learning environments.
- Computer Traffic Simulation: Graphical Version: www.math.toronto.edu/mathnet/carcompet/simulation.html Provides a simple model of traffic flow.
- Exploring Data: http://exploringdata.cqu.edu.au
- Website provides curriculum support materials for teachers of introductory statistics.
- Future Lab: Circuits for Physical Science: www.superkids.com/aweb/pages/reviews/science/10/circuits/merge.shtml
- Microsoft Flight Simulator: www.microsoft.com/games/flightsimulator
- Physics Java Applets: www.walter-fendt.de/ph11e
- Many applets are available for download covering buoyancy, optics, and the theory of relativity, to name just a few.
- SimCity Classic http://simcity.ea.com/play/simcity_classic.php Builds cities of various sizes.
- SimScience: www.simscience.org
- Devoted to areas of science in which computer simulations are at the forefront of discovery; provides access to four simulations: membranes, fluid flow, cracking dams, and crackling noise.
- SimEarth: http://en.wikipedia.org/wiki/SimEarth
- Activity: design planets and analyze effects on populations.
- SimFarm http://compsimgames.about.com/od/simfarm Business simulation
- SimSurface: http://storm.shodor.org/simsurf/simsurfinfo.html
- A simulation designed to solve the problem of minimization of potential energy, this uses the computational technique of simulated annealing and the relaxation method.
- Statistics: www.ruf.rice.edu/~lane/rvls.html
- This virtual site includes simulations and demonstrations on various topics and formulas on statistics.
- ThinkQuest: www.thinkquest.org/library
- This is the archived site of student-generated ThinkQuest Contest entries. Enter “simulation” in the search box to locate simulation entries.
- United Nations Simulation—The Electronic United Nations: www.simulations.com/cont1.htm
- In this United Nations simulation, classrooms become classroom-countries and interact with other classroom-countries.
- Chaos Game: http://math.bu.edu./DYSYS/applets/chaos-game.html
- This online game is designed to improve students’ geometric intuition and algorithmic thinking.
- Easy Fibonacci puzzles www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpuzzles.html This provides puzzles that have Fibonacci numbers as their answers.
- NCTM electronic example of using data sets available on the Internet: http://standards.nctm.org/document/eexamples/chap5/5.4
- NCTM simulation example: http://standards.nctm.org/document/eexamples/chap5/5.2
- Grades 3–5 understanding distance, speed, and time relationships using simula- tion software
- Statiscope, by Mikael Bonnier: www.df.lth.se/~mikaelb/statiscope/statiscope-enu.shtml
- This is an interactive environment (Java applet) for summarizing data and de- scriptive statistical charts.
- Statistical Teaching Activities: www.statcan.ca/english/kits/teach.htm
- Categorized by grade bands, this provides interactive exercises focusing on data analysis and survey skills. It is maintained and developed by Statistics Canada.
- WebWinds: http://asds.stsci.edu/packages/graphics/WebWinds.html
- This is an interactive data system for collecting, representing, and analyzing data, and statistical decision making.
Other Online Resources and Data Sets
Bureau of Census data—Population data set http://factfinder.census.gov/servlet/BasicFactsServlet www.census.gov/main/www/access.html
These are comprehensive sites to locate population, housing, economic, and geographic data.
- Forbes.com: http://www.forbes.com
- This is a source for business data; for example, a comparison of health benefits and 401(k) plans.
- Liberty Library of Constitutional Classics: www.constitution.org/liberlib.htm
- This online collection of classic books and other works on constitutional govern- ments ranges from antiquity to the present.
- Mathematics Archives: http://archives.math.utk.edu/software.html
- This is a collection of software, abstracts, and reviews.
- National Center for Education Statistics (NCES): http://nces.ed.gov
The National Center for Education Statistics (NCES) is the primary federal entity for collecting, analyzing, and reporting data related to education in the United States and other nations. It fulfills a congressional mandate to collect, collate, ana- lyze, and report full and complete statistics on the condition of education in the United States; conduct and publish reports and specialized analyses of the mean- ing and significance of such statistics; assist state and local education agencies in improving their statistical systems; and review and report on education activities in foreign countries. Through the National Cooperative Education Statistics Sys- tem, NCES supports the activities of the National Forum on Education Statistics and the publication of resources such as this.
National Center for Health Statistics: www.cdc.gov/nchs
This federal government agency provides statistical information to guide actions and policies for the purpose of improving the health of the American people; see its data warehouse at www.cdc.gov/nchs/datawh.htm.
National Forum on Education Statistics (Forum): http://nces.ed.gov/forum
The National Forum on Education Statistics (Forum) is comprised of represen- tatives of state and local education agencies, offices of the U.S. Department of Education, other federal agencies, and national associations with an interest in education data. It is sponsored by the National Center for Education Statistics. Its mission is to develop and recommend strategies for building an education data system that will support local, state, and national efforts to improve pub- lic and private education throughout the United States. The Forum is commit- ted to improving the quality, comparability, and usefulness of elementary and secondary education data, while remaining sensitive to data burden concerns.
U.S. Federal Election Commission: www.fec.gov
This provides comprehensive information on the voting process.
Problem Activity 1: Business
This activity gives students experience in real-world business operations. Students develop decision-making skills by scaling up a simulated business. Have students use the Lemonade Stand simulation at www.coolmath4kids.com/lemonade or use a search engine (e.g., Google, Yahoo!, Lycos, etc.) and search on lemonade stand sim- ulation for alternative versions. Provide students sufficient time to interact with the simulation and reflect on their experiences. Then ask them to conceptualize and de- fine a problem resulting from the experience that they would like to analyze. Help them, if necessary, to formulate a question based on their problem spaces. Have them explore the solution by increasing the size and scope of their lemonade busi- nesses. Challenge students to increase business profits and incorporate standard business operations, including inventory, sales, marketing, taxes, payroll, employee benefits, and personnel issues such as training. Have students explore purchasing and labor expenditures, and analyze consumer behavior and economic trends to as- sist their decision making about operational procedures and policies. Compare re- sults and discuss their solution strategies. Determine which practices result in higher profits, and why. Challenge students to form corporations and stage hostile takeovers. Have students work in small groups (perhaps the corporate groups they formed) through a stock market simulation. Have them use a search engine to find a stock market simulation that interests them. Challenge student corporations to of- fer stock options to their employees. Have them appoint board members and hold board meetings to discuss business operations. Plan a field trip to visit a local hos- pital’s or utility holding company’s board meeting. Have students create a profit- and-loss statement as a culminating activity. For closure, discuss their responses to the experience.
Problem Activity 2: Politics
This activity gives students experience in real-world sampling and polling situations. Students develop skills in techniques of sampling and predicting from a sample, as well as developing strategies for organizing and managing the data.
Create an election simulation based on Kids Voting results based on either the last general election or any current issue before the U.S. Senate or other legislative body. Have students do an Internet search (e.g., Google, Yahoo!, Lycos, etc.) on kids voting results for ideas. Have pairs of students use the simulation for a designated period of time. Students should reflect on their experience and identify a problem to investigate—for instance, voter irregularity. They formulate questions such as “Does ballot design affect voting patterns?” Students divide according to the cur- rent U.S. registration ratios between the two major parties and any third-party wannabes. Students campaign for their candidates and/or issues for a specified pe- riod of time and create supporting propaganda, which will be displayed in the class- room. Throughout the specified period, selected students in support of each candidate or issue will make speeches and hold press conferences. At the end of the selected time, an election will occur. If students are voting for candidates only, stu- dents will vote only to elect “electors,” who will then gather later to actually elect the candidates of their choice. Students create their own ballot box and secure the ballots. Students create a program to automate the voting process on a computer. Following the voting students will compare, contrast, and critique results and pro- cedures. The teacher or elected committee will rule on challenges to any requested procedure. Students learn about issues relevant to any modern election, the effect of third-party vote dilution, as well as the need for coalitions to further their parties’ interests.