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Project SkyMath Project SkyMath: Making Mathematical Connections Using the Science and Language of Patterns to Explore theWeather1996 University Corporation for AtmosphericResearch This Web Page is designed for middle school mathematics teachers. Itcontains all of the information needed for teachers to use the 16classroom activities of SkyMath, including the module itself. Webelieve that it is an effective and innovative way to present elements ofthe middle school mathematics curriculum. Index(Click on to move to subject and to return to Index) Introduction SkyMath: Mathematicsin Context SkyMath and the NCTMStandards Module Design SkyMath and the National Science Education Standards Education Development Center The SkyMath Module End Of Unit AssessmentInstrument Finding a Partner Class SkyMath Mailing List Field Tests Insites' External Evaluation of the Program SkyMath Pamphlets SkyMath Research Teachers References Mathemtmatics for a Blue Planet Introduction The University Corporation for Atmospheric Research (UCAR) received funding from the National Science Foundation to prepare a middle school mathematics module incorporating real-time weather data. The goal of the pilot project is to demonstrate that acquiring and using current environmental and real-time weather data in middle school classrooms, in ways that embrace the dynamic and the uncertain natures of these data, will promote the teaching and learning of significant mathematics, consistent with the standards set by the National Council ofTeachers of Mathematics. The module may be freelydownloaded from thispage and we hope that middle-school mathematics teachers will find itinteresting enough to use in their classrooms. The module can beincorporated as a replacement unit that uses connections to mathematicalconcepts in data analysis, graphing, number and number relationship,patterns and functions, and statistics and measurement. The project is led by a Design Team of mathematicians, math educators, scientists, technology experts, and teachers; this group reflects the interdisciplinary nature of the program and its emphasis on the use of technology in a science/math school environment. SkyMath's Organization Chartillustrates the contributions made by its affiliated groups. Project SkyMath has profited by the close collaboration of Dr. NancySonger, Program Director for Kids as GlobalScientists. Her research into the learning opportunities ofInternet-based weather studies has encouraged us to apply her pioneeringwork to mathematics. SkyMath: Mathematics in Context The SkyMath Module, "Using the Science and Language of Patternsto Explore Temperature", calls for the development of several mathematicalconcepts using a single central concept from weather --- temperature. The SkyMath curriculum uses real-time weather data, involvesclassrooms inhands-on mathematics, elicits higher-level thinking, engages students inpurposeful projects, and calls for reflection and communication. The SkyMath module's focus is on doing -- rather thanhearing, reading, seeing, or saying -- and is consistent with what isknown about learningretention rates associated with these different levels ofinvolvement. One overall goal of this design is to provide guidance tostudent learning while allowing increasing degrees of student independence in the development ofideas and activities. The 16 activities of the SkyMath module reflect thisdevelopment of student-initiated learning style. The students are organized in groups; they collect and analyze data,exchange data and messages electronically with distant peers, identifyand solve problems that emerge from classroom activities and that may havemany possible solutions, and present or publish information acquiredduringthe unit. The activities lead students to develop methods of representing change;how temperature changes with time and with location. Students arechallengedto measure, represent, and analyze these changes. Activities include developing symbol sets, preparing graphs for median-based analysis,predicting magnitudes of changes, and learning about the correctness oftheir work by seeing what really happens! The sixteen activities, which take at least six weeks to cover,include: Brainstorming: Temperature and Temperature Changes Be a Weather Watcher Introduction to Blue Skies Reading Celsius and Fahrenheit Make Your Own Temperature Scale Converting from One Unit of Measurement to Another Making a Rule to Convert Between Fahrenheit and Celsius Is Our Room All One Temperature? How Can We Describe Our Room Temperature? Sampling and Comparing Temperatures Line Graphs Exploring the StowAway Data What's Been Happening? Were the Predictions Correct? Answers and Questions Presentations and Reflections SkyMath and the NCTM Standards At the 5-8 level, the NCTM Curriculum and Evaluation Standards forSchool Mathematics (NCTM 1989) identifies 4 process standards (1-4) and nine content standards. These are all addressed in the SkyMathmaterials.Those standards which are given explicit conceptual development are shownin the chart below. A tenth column has been added, (use of) Technology,since this aspect of the work in SkyMath deserves to be highlighted as well. Number work is always present, and the nature of the module infusesProblem Solving into every activity. NCTM Standard #1: Mathematics as Problem Solving NCTM Standard #2: Mathematics as Communication NCTM Standard # 3: Mathematics as Reasoning NCTM Standard # 4: Mathematical Connections NCTM Standard # 5: Number and Number Relationship NCTM Standard # 6: Number Systems and Number Theory NCTM Standard # 7: Computation and Estimation NCTM Standard # 8: Patterns and Functions NCTM Standard #9: Algebra NCTM Standard #10: Statistics NCTM Standard #11: Probability NCTM Standard #12: Geometry NCTM Standard #13: Measurement The Context-Matrix NCTM Standard 1 2 3 4 5 8 9 10 13 Technology Activity#1 x x x x #2 x x x x x * x x #3 x x x x x x #4 x x x #5 x x x x x x #6 x x x x x x x x #7 x x x x x x x x #8 x x x x #9 x x x x #10 x x x x x x #11 x x x x x x x x #12 x x x x x x x #13 x x x x x x x #14 x x x x x x #15 x x x x x x x x x x #16 ** xx * The work with patterns and functions is implicit ** Activity 16 will most likely include all of the areas - and perhaps others, as students reflect on their work and share results. Sincecommunicationis so central here, a xx has been placed in that column toshow that emphasis. At the beginning of each of the 16 activities, the exercises thataddress the mathematics standards identified above (mathematical goals of theactivity) are described: Students identify questions and pose problems that can be solved using mathematics. They are introduced to the Celsius and Fahrenheittemperature scales. Students review what state, national and world weather data are available and how those data are collected. They design a process for collecting data to answer local weather-related questions, and decideon a common set of data to be collected. Students learn how to read athermometer in Fahrenheit and Celsius scales and how to use aweather log, read and record temperatures, and calculate changes. Students read a max-min thermometer. They record minimum and maximum temperatures and analyze differences and use maps toidentify locations. Students look for patterns of differences across the United States. They learn to use Blue Skies to access and uploadtemperature and weather data. Students learn to read Celsius and Fahrenheit thermometers with intervals representing 1 and 2 degrees, respectively. They match Fahrenheit and Celsius temperatures. They add and subtract signednumbers (integers) and look for patterns and discuss rules. Students list statements that are measured by temperature and rankorder them. They review how Fahrenheit and Celsius created their temperature scales and make and calibrate their own temperaturescales by identifying fixed points. Students find differences and useother operations. They measure distances and divide them into equalintervals and assign temperatures to events. Students describe how units of measurement are mathematicallyrelated. They develop formulas for converting between units ofmeasurement. Students identify and describe mathematically significant patterns indata sets. They use ratios to describe the relationship between two scales. They graph number pairs on a coordinate system and discuss properties of their graph, such as slope and intercepts. Students use the slope of the line to informally develop and describe a rule forconverting Fahrenheit and Celsius scales. Students translate an informalrule into a formula using a spreadsheet. They create spreadsheets for converting between Celsius and Fahrenheit and describe the rule. Students read analog thermometers and examine the concept of calibration (equating scales so that all instruments read the same at the same location and the same time). They make conjectures about room temperature. They make bar graphs and consider maximum, minimum, and range of temperature readings in the room. Students examine the concept of "typical", or average, and explain their reasoning. They are introduced to measures of central tendency: mode, median, and mean. They discuss which measure ofcentral tendency best describes the "typical" temperature in the room and in a given situation. They explore the effects of extremedata points on the mode, median, and mean of a data set. Students discuss ways to gather data to determine the "average temperature" at a location. They report on and critique their plans. They are encouraged to consider how the choice of measure of central tendency is affected by sample size, placement of recordingdevices, timing, range, and repetition of specific readings. Students identify extremes, compute the range, and find the mean, meadian, and mode of given sets of data. They make decisions based on an analysis ofdata. Students read and interpret line graphs; they discuss scales, axes, and labels. They construct line graphs to show changes in temperatureover time and use line graphs to informally compare rates of change andthey informally discuss slope. Students interpret line graphs and discuss patterns in the data. They use the LogBook software to construct a line graph and importdata into a spreadsheet. They use the data from the StowAway to createa table of temperature highs, lows, and range. They identify patternsand trends in line graphs and tables. Students compare weather log datawith StowAway data. Students calculate the rate of change between high and lowtemperatures. They explore the meaning of a positive (or negative)rate of change and relate rate of change to the slope of a line in a linegraph. They compare rates of change. They write about datacollected outside the classroom using StowAway data, noting patterns in thedata. Students read and interpret a temperature map and discuss legend,labels, patterns, and differences between predicted and actual high temperatures. They use computers to gather data about hightemperatures in selected cities and compare the actual high temperatureswith the predicted highs. They represent national highs as color bandson a map and construct a temperature map of the United States and compare actual to predicted highs for the day. They discuss reasonsfor differences between predicted and actual temperatures. Students consolidate knowledge and skills acquired in previoussections. They pose and solve authentic problems and apply reasoning and problem-solving skills to independent projects. Students use mathematical communication to explain the results oftheir work on a final project. They explain how they solved problems and reflect on what they have learned. They assess their own progress andachievements. (This analysis was prepared by Dr. Fernand J. Prevost. ) Module Design In an article published in the Mathematical Sciences Education Board'sOn the Shoulders of Giants, Ian Stewart discusses mathematicalconcepts related to "change." Noting that every natural phenomenon is amanifestation of change, Stewart stresses that mathematicsis the most effective tool for understanding patterns of change. Henotes that to master the concept of change, one must be able to"represent changes in a comprehensible form, to understand the fundamentaltypes of change, and to recognize these types of changes when theyoccur". The SkyMath Design Team identified the mathematics of change as the mostnatural concept to address in a module that utilizes current weatherdata. The module articulates a mathematical study of the changing weather,focusing on temperature. It leads students to develop methods ofrepresenting change; how temperature changes with time and with location.Students are challenged to measure, represent, and analyze these changes. Thinking about how the real world changes with time and recordingreal-time data to accumulate a time series are activities that willevoke student ownership of the data and will provide experiences thatretrospective data cannot. The module makes use of the KWL design, a research-based feature that is commonly used in reading instruction. K refers to the sharing of what studentsKnow (or thinkthey know) about a topic, W refers to determining some new things students Want to learn about thetopic, L refers to reflecting on what has beenLearned after studying thetopic. The 16 activities of the module reflect thisdevelopment of student-initiated learning style. The module design calls for three levels of performance assessment. Two of these (lesson-by-lesson assessment to guide instruction and summary assessment through an extended project) are internal to the module; note that KWL is also a form of imbedded assessment. The third level is an external assessment with a comprehensive test of the module's key mathematical concepts. Also included in the module design is an array of "teacher inservice" features that are intended to make the module self-standing, i.e., usable without formal inservice by outside experts. For instance, it provides initial inservice or support for teachers by providing "stories" from teachers who have used the module. Stories that anticipate problems, suggest solutions, and provide background lead to enriched classroom discussions and offer teachers tips alerting them to challenges and opportunities. Step-by-step descriptions of the use of technological tools are amplified by diagrams and screen images. Internet mail groups are established early in the module for use by teachers and students. The module is designed to employ technology as a tool in the service of the learning of mathematics. The level of technology used is appropriate to the tasks at hand. The pursuit of questions leads students through a progression of resources: newspapers, television, thermometers, graphs, max-min thermometers, an electronic device (coupled with a computer) for the organized collection/display of data over extended periods of time, e-mail, a spreadsheet, and software for displaying and exploring real-time surface and satellite weather data. The rule for the use of technology is that its form follows an identified need. A typical lesson begins with an overview page that describes the math goals, the ongoing assessment, and the necessary advanced preparation. Following this are descriptions of the student activities with associated "teacher stories". Background information and explanations of the technology used are included, followed by assessment guidelines. Examples of the kinds of mathematics addressed include theuse of scales, statistics, and data representation. One example of therichness of the mathematics involved in reading a temperature graph isgiven here in the story of Euclid's tour of theUniversity, and an assessment profileis also provided. SkyMath and the National Science Education Standards Although the modules are mathematics modules -- instructional unitsfocused on the development of mathematical concepts and procedures foundin the NCTM Curriculum and Evaluation Standards -- they are also rich inthe science content and procedures set forth in the NationalScience Education Standards. According to these guidelines, thefundamentalabilities and concepts that underlie the science standards include theability to identify questions that can be answered through scientificinvestigations: to design and conduct a scientific experiment; to use appropriate tools and techniques to gather, analyze, andinterpret data; to develop descriptions, explanations, predictions, and modelsusing evidence; to think critically and logically in order to identifyrelationships between evidence and explanations; to recognize and analyze alternative explanations andpredictions; to communicate scientific procedures and explanations; to use mathematics in all aspects of scientific inquiry; to develop understandings about the scientific inquiry. The activities in the SkyMath temperature module follow this scientificmethod and develop all of the abilities described in the Science Education Standardsby applying a scientific approach to the investigation of temperature. The physical science standards for grades 5-8 focus on the characteristicproperties of substances, such as boiling and melting points; thus, theconcept of temperature must be included. The Earth and Space Science contentstandards for grades 5-8 stress the development of an understanding ofearth and the solar system as a set of closely coupled systems, theatmosphere being one of the four major interacting components of the earthsystem. SkyMath clearly incorporates elements of the quantitative studyof the temperature of the atmosphere with associated weather patterns. The Science and Technology Science standard for grades 5-8 suggests thatstudents investigate simple, familiar objects (in the case of SkyMath, itis a thermometer or temperature probe)through which students can develop powers of observation and analysis. InSkyMath, the technology is introduced only as needed to aid a specificinvestigation. The students can see the value of technology in providinginstruments, techniques, and communication capabilities that help themmaster their SkyMath projects. The history of the development of thethermometer, provided as background material for the teachers in theSkyMath module, and further developed on Web page About Temperature, serves as a specificexample of the History and Nature of Science standard for grades 5-8. Thepedagogy of the SkyMath module is consistent with the Science TeachingStandards that call for inquiry-based science programs. Education Development CenterThe SkyMath educational strategies and materials have been prepared bytheEducation Development Center,Inc. (EDC)of Newton, MA, a nonprofitresearch and development organization (see their Skymath page), in a flexiblecurriculum modulethat includes guidance and tools for exploration plus a collection ofresources and activities that use weather and real-time data to teachmath concepts. The SkyMath Module The second draft of the module,which was used in our April 96 field tests, can be downloaded from this page. These filesare in pdf format and you will need to first download a copy of the Adobe Acrobat, which can be accessed here freeof charge. You also may need (for a Mac) to download a Stuffit Expander program to decompress the Acrobat file. Once you have installed this reader on your computer (read the text read mefile for help in this), then click on the files listed below to download the module. Instruct your browser to save the files to your harddrive or to floppy disks. You can then open them with your Acrobat reader and find the SkyMath module. When youopen the SkyMath files in the Acroread program, you will find that the hand cursor will change to a hand withindex finger extended if there is a link to somewhere else. A solid red border opens up the WWW link to which the text inside it refers, but you will need another program to do this. Acrobat requires Plug-Ins to link to the WWW. They can be accessedhere. Bookmarks have been added that allow easy navigation within the documents. The Bookmarks must be turned on (a button that allows bookmarks to be turned on appears second from left in the toolbar of the reader). They appear on the left-hand side of the screen and are titled. Clicking on a bookmark takes the reader to the position described. The module is copyright 1996 University Corporation for AtmosphericResearch; permission for limited reproduction of the module or portions ofit for educational purposes but not for sale may be obtained upon requestfrom UCAR. Contact blynds@unidata.ucar.edu. The entire module can bedownloadedin the following sections: Cover (713K) Table of Contents (62K) Overview (62K) Section 1 (341K) Getting Started Activity 1: Brainstorming: Temperature and Temperature Changes E-mail your partner Activity 2: Be a Weather Watcher Activity 3: Introduction to Blue Skies Section 2 (341K) Matters of Scale Activity 4: Reading Celsius and Fahrenheit Activity 5: Make Your Own Temperature Scale Exchange Personal Scales with your Partner Class Activity 6: Converting from One Unit of Measurement to Another Activity 7: Making a Rule to Convert Between Fahrenheit and Centigrade Section 3 (217K)Central Tendency Activity 8: Is Our Room All One Temperature? Activity 9: How Can We Describe Our Room Temprature? Sharing Our Room Temperatures with Our Partner Class Activity 10: Sampling and Comparing Temperatures Section 4 (341K)Data Representation and Change Activity 11: Line Graphs Activity 12: Exploring the StowAway Data Activity 13: What's Been Happening? Exchanging StowAway Data with Partner Class Activity 14: Were the Predictions Correct? Section 5 (124K) Pulling It Together Activity 15: Answers and Questions Activity 16: Presentations and Reflections Sharing Our Projects with Our Partner Class Reproducible Masters (651K). Reproducible Masters in Spanish Con nuestrasmascumplidas gracias a Carmen Wildman por ésta traduccion alEspañol. We suggest that you send a letter (or in Spanish) to theparents of the children explaining the activities of the module. To do SkyMath in its entirety, you will need the following materials andequipment: at least one computer with Internet access and BlueSkies installed an e-mail account spreadsheet software an overhead projector and the ability to make transparencies at least one StowAwaytemperature data logger with a six-foot probe and Logbook software. Thisdevice continuously records the temperature and its data can be downloadedinto the computer and displayed in graphical form. at least 12 indoor thermometers at least one min-max thermometerThe last three items cost about $200 in 1996.One good source for theStowAway and for less expensive dataloggers may be found at theScience Education Solutions web page. If you have no StowAway datalogger (the most expensive of the last three items), limited or no accessto computers, orno connection to the Internet, you can do a scaled down version ofSkyMath as follows: no StowAway data logger: Omit Activities 11 and 12 no computer: You can still do most of SkyMath by omitting activitiesinvolving the StowAway data logger, e-mail, Blue Skies and other Internetsites. This means you must omit Activity 3 and all of Section 4 with theexception of Activity 10. if you have at least one computer but no telecommunicationsfunctionality: Omit Activity 3, Activity 13 and the e-mail activities. SkyMath utilizes software and data dissemination methods of theUniversity of Michigan'sBlue Skies program, anendeavor developed under a National Science Foundation grant. Blue Skies software, which can be downloaded from its homepage, offers anextraordinarily simple interface so thatusers with a minimal computer experience can easily and quickly obtain needed information. Access is provided to hundreds of real-time weather and environmental images by using the client-server protocol developed fortheUniversity of Minnesota's "gopher" system (though Michigan dubs theinformation-providing components "groundhog" servers). If a teacherregisters with Blue Skies, the classroom students can upload their data tohis/her site. End of Unit Assessment Instrument The SkyMath Assessment Team, headed by Dominic Peressini, University of Colorado at Boulder, has prepared a two-part assessment instrument thatcan be used at the end of the unit as a tool to evaluate studentachievements in mathematical skills, abilities, and understanding. TheTeam refined a set of assessment items that map directly back to the goalsand objectives of the SkyMath curriculum. The Assessment Instrument isdesigned around three primary constructs: (1) National Assessment ofEducational Progress (NAEP) items, (2) SkyMath short-response items, and(3) performance-based items. The short-response items are based on theSkyMath curriculum, classroom observations, collections of student work,and teacher and student interviews. The performance-based items are based on the SkyMath curriculum and havebeen developed using the same process as was used for the short-responseitems. These tasks allow students to demonstrate their ability to applymathematics in meaningful problem situations. They ask students todemonstrate their problem solving, reasoning, and communication abilitiesas well as their ability to make connections within the discipline ofmathematics and across content areas. Dominic's team has also prepared aGeneral Scoring Rubric for the open-ended items and a Scoring ProfileSheets foreach of the open-ended problems. These performance-based items are available in .pdf files here: SkyMath Test1 SkyMath Test2 SkyMath Scoring Profile General Scoring Rubric Finding a Partner Class One of the SkyMath activities most popular with the students iscorresponding via e-mail with a partner class. Teachers wanting to use themodule will have to pair up with another classroom and coordinate thetiming of the activities so that students can effectively share theirweather studies with each other. In order to find a partner class, pleaseregister here.Review the list and contact a possible teacher for collaboration. Whenthe two of you have agreed to be partner classes, remove your names fromthe list by scrolling down the form to the"remove your name from the list" form (you have to remember yourpassword!). It is important that the paired classes coordinate thescheduling of activities so that students will be corresponding whileparticipating in the same SkyMath activities. SkyMath gives special thanks to Matt Hicks of Unidata for preparingthis SkyMath form for us! SkyMath Mailing List We have established a mailing list for all educators interested in orusingSkyMath. We hope that teachers will share their experiences with othersand that any helpful supplementary materials can be referenced here. To subscribe, go to the Unidatamailing listregistration and scroll down to skymath in the "select list" option.Then register and participate in the SkyMath correspondence! This mailing list is not for students; to set up an e-mail exchange forstudents, teachers must find a partner class using the "Finding a Partner Class" procedure. Field Tests The schools that took part in the Spring 96 Field Test were Hanscom Middle School, Bedford MA; Centennial Middle School, Boulder CO; Gilbert School, Gilbert IA; Long Middle School, Atlanta GA; Sherman IndianHighSchool, Riverside CA; John Muir Middle School, San Jose CA; Gilroy School, Gilroy CA. Centennial Middleschool was assisted by University of Colorado at Boulder.Long Middle school was assisted by ClarkAtlanta University Earth System Sciences Program; Gilbert School was assisted by Iowa State University; the Gilroy and San Jose schools are assisted by San Jose State University. The fall 1996 field test was conducted at Blackstone Elementary School in Gunnison CO assisted by Western StateCollege Cetennial Middle School in Boulder assisted by the University ofColorado Crawford W. Long Middle School in Atlanta GA assisted by Clark AtlantaUniversity Gilbert School in Gilbert IA assisted by Iowa State University Hanscom Middle School in Bedford MA assisted by EDC, Inc. Lincoln Middle School in el Paso assisted by University of Texas at ElPaso Pleasanton Middle School in Pleasanton CA assisted by San Jose StateUniversity Talawanda Middle School in Oxford OH assisted by Miami UniversityThe final field test in the Spring of 1997 added the following sites: Schools in Bronx, New York Wakefield (PS 16) Castle Hill (MS 127) Donald Hertz (PS 83) Helen Keller (PS 153) Cetennial Middle School in Boulder Colorado's Finest Alternative High School, Englewood, CO Elizabeth City Middle School in Elizabeth City NC assisted by ElizabethCity State University Hanscom Middle School, Bedford MA Middle schools affiliated with NASA Langley Research Center, Hampton VA Yorktown Middle School, York County, VA Poquoson Middle School, Poquoson, VA, Hines Middle School, Newport News, VA Syms Middle, Hampton, VA Sherman Indian High School, Riverside, CA Schools affiliated with University of Texas at El Paso Lincoln Middle School Wigg Middle School San Elizario School We have prepared a questionnaire that wewould like to have all teachers whohave used the module to complete and send their answers to Beverly T. Lynds Unidata P.O. Box 3000 Boulder CO 80307-300 The SkyMath module is now complete. The materials are available on the Internet so that anyone wishing to use the module can do so with Internet access. All feedback is welcomed and should be sent to the Program Director, Beverly Lynds (blynds@unidata.ucar.edu). Insites' ExternalEvaluation of the Program We began classroom evaluations during the 95/96 school year and continued through 1997. Initial results indicated that the students learned the mathematical concepts featured and that they and theirteachers liked the activities. Insites' final report focused chiefly oninstructional design and development considerations for learning,teaching, and technology. Findings in these areas provided evidence thatSkyMath is a viable method for teaching and learning mathematics in themiddle grades, and that technology supports the integration of weatherdata and mathematics. Together, weather data, mathematics, and technologyare appealing to students. We quote here the summary of their report: SUMMARY OF EVALUATION FINDINGS "Over the course of development and field testing, the SkyMath module hasproven to be a highly effective tool for teaching and learning middleschool level mathematics. Some key contributing features are: linkage of the SkyMath learning goals to mathematics standards connection of mathematical learning to real-time scientific data ofhigh interest and the integration of other subject areas ease of use of the module and inclusion of supporting resources forteachers use of hands-on learning strategies and application of learning inclusion of unit quizzes and the end-of-unit assessment test integration of technology that supports the mathematics curriculum andlearning goals in a meaningful way Some key findings that emerged from the evaluation of SkyMath are: Students are learning mathematics through SkyMath. The unitstrengthens basic math skills, deepens understanding of mathematicalconcepts, and improves communication about mathematics. SkyMath is aligned with national standards for the content, teaching,and assessment of mathematics and science in grades five through eight. SkyMath can be aligned well with state and district mathematicsstandards and district mathematics curricula that build on NCTM Standards. SkyMath works effectively as an integrated math and science unit.Students learn mathematical skills in the course of scientificexploration. The module can be used successfully with 5th through 8th gradestudents under a variety of formats and schedules. It can be used as astand-alone unit or integrated into a school's math curriculum. Teachers can adapt the SkyMath materials to accommodate thelearning needs of students with a range of math abilities and experiences.Students at all performance levels, including special education, benefitfrom the SkyMath activities. SkyMath is relatively easy for teachers to use - teachinginstructions, background information, teacher stories, and resources areall included in the cost-free materials. SkyMath offers a non-threatening way for teachers to try newhands-on pedagogy to enrich their teaching repertoire. Teachers and students enjoy using the SkyMath module. The study ofreal-time weather data and the use of technology motivates students tolearn mathematics. The use of technology and real-time data in the module supportsmathematical learning. Challenges to implementing the SkyMath module are: Many teachers are not able to complete the entire module withinthe estimated six-week time frame due to schedule constraints. Longerblocks of time and schedule flexibility are more conducive to usingSkyMath than short class periods. Teachers and students need a basic level of computer know-how touse the technology in the module. Schools need a basic level of computerhardware and an Internet connection to support using SkyMath. The technology components of SkyMath do not always run smoothlyand this causes frustration. Some classes have had difficulty logging ontoBlue Skies and the Internet. In some schools, SkyMath stands alone as the only hands-on,integrated mathematics unit, unconnected to previous and subsequentmathematics instruction. This limits impact and viability. If teachers do not closely coordinate implementation of the modulewith partner schools, e-mail messages between students are not meaningfuland do not meet the communication goals of the unit. The SkyMath approach appeals to teachers with a hands-on teachingstyle. More traditional mathematics teachers may not be as interested intrying the module or in team teaching."Insites has provided us with some anecdotal data they obtained. One teacher conducted the Skymath pilot with a group of students whohave low math skills. She said that the value of Skymath for this groupis that they are getting math from a completely different angle. "Theyhave all struggled with math in the past. With Skymath, they don't realizeit's math they're learning because they're not struggling." She wasimpressed that some of the students in her group said that learning themean, median, and mode was easy. She thinks these are generally difficultconcepts for 6th graders to master. Skymath fits well with one school's strong overall focus on developingwriting skills. "With the old way of teaching mathematics, kids could do the mechanics,but theydidn't know what it meant. With Skymath they really understand theconcept." "When using Skymath I am covering the curriculum and doing it better." Two teachers comment that they are able to fit in all of the required 6thgrade curriculum and Skymath because they are complementary. One very positive aspect of the module is its flexibility. Teachersadjust use of the module to their context and schedule and gearinstruction to their students' levels of experience and skill. Oneteacher has her kids working in mixed ability groups. She sees evidence that all are learning math because, "I give very little directives tostudents and they take what I say and know what to do with it." "I amamazed the groups have worked and have had very little trouble." "Skymath is very motivational. The kids get excited." "Kids will work with numbers where they never would before becausethey have a reason for doing it." "Skymath has been very enjoyable for my students and for myself. Wehave become collectors of information and have learned how to recorditems in a useful manner. My students have become more aware of theirenvironment and the changes that take place in and around school." SkyMath Pamphlets Building on their experiences with teachers, administrators, students, andparents, Insites, Inc. has prepared four pamphlets for SkyMath to use inpublicizing its program. These pamphlets target select groups who shouldbe informed about the program if it is to be incorporated into a schoolcurriculum. For School and District Administrators, SchoolBoard Members, and Parents For elementary and Middle School Teachers ofMathematics, Science, and Technology Spreading the Word about SkyMath Information for Parents About SkyMath SkyMath Research Teachers During the course of the development of the module, we have been assistedby a group of very talented and dedicated teachers, without whoseparticipation the project would not have succeeded. We have designatedthese educators as SkyMath Research Teachers. They have agreed to serveas resources for other teachers interested in using the SkyMath module. Duane Habecker, Pleasanton Middle School, Pleasanton CAdhabecker@pleasanton.k12.ca.us Paige Larson, Centennial Middle School, Boulder CO plarson@bvsd.k12.co.us Barbara Mullins, Blackstock Elementary, Gunnison CO,bmullins@tomichi.ghs.gunnison.k12.co.us Jane Thomas, Hanscom Middle School, Beford MAthomasj@mail.hanscom.lincoln.k12.ma.us Becky Thornburg, Blackstock elementary, Gunnison CObthornburg@tomichi.ghs.gunnison.k12.co.us Wewould like to hear from any teachers interestedin trying out this module in math classrooms. Internet connectivity is necessary for certain of the SkyMath activities. Please contact blynds@unidata.ucar.edu if interested. References A tutorial, About Temperature, has been prepared for the use of the SkyMath (and other) teachers. It covers the basic physical concept of temperature, temperature scales, thermometers, thermodynamics, kinetic theory, and radiation temperature. There are many sites on the World Wide Web that hold -- or will route youto -- useful resources in mathematics education. Here's a starter set. NCTM This is the home page of theNational Council ofTeachers of Mathematics. Its features include membership info,dates/places of NCTM meetings, the NCTM products catalog, the entire textof a year's worth of NCTM newsletters, and the content outlines (and fulltext to selected articles) of a year's worth of NCTM journals. SAMI.This is a subsiteof the site operated by the Annenberg/Corporation for Public BroadcastingMath and Science Project (http://www.learner.org). SAMI (Science AndMathematics Initiatives) is a clearinghouse of lesson plans and projects,free software and services, funding opportunities, and curriculummaterialsfor mathematics and science teachers. Swarthmore MathForum. The Swarthmore Math Forum is anNSF-funded project that was to create a one-stop shopping web site formathematics educators. In short, it is a link to many other web sites ofinterest. Some routings are categorized (resources in K-12 mathematics;info on specific topic in education (e.g., block scheduling,constructivism); organizations; conferences; curriculum materials). Therealso is a general (uncategorized) router to mathematics education websitesof interest (Steve's Dump). NCRS. This site, located atthe National Centerfor Educational Statistics, is the primary site for information about theThird International Mathematics and Science Study (TIMSS). Results of theGrade 8 testing are available now; Grade four results will be added inSummer 1997; Grade 11 results will appear in Fall 1998. There are dozens of fine Web pages that provide weather and climate information. Some that may be useful to SkyMath teachers are: Clickable Map of US States Climate Page. This web site provides easy access toclimatologies for cities throughout the US and its possessions. Simply click on the state you are interested in and then click on the city name (or the bullet that indicates the city's location). You will then get a plot of the daily average climate for that city including maximum and minimum temperature, precipitation and snowfall. The Weather Visualizer: By simply pointing and clicking, select which features you want to see on your own customized weather map. Embedded helper sections provide useful details and information to provide you with the background necessary to correctly interpret these images. Another COVIS page that is excellent is the Online Guide to Meteorology. Encyclopedia ofAtmospheric environment, a source for a range ofatmospheric issues, including weather, climate, airpollution, acid rain, global warming and ozone depletion. NorthEast Media ofAtmospheric Sciences an excellent, instructive summary of weather andclimate data with many links. SoutheastRegional Climate Center - Educational Resources page: CIRRUS is an educational medium that provides economically and environmentally important climatic information in a timely and easily accessible manner for the Southeastern states. The system gives students the opportunity to observe and analyze the weather on a daily basis which enhances their understanding and awareness of their environment. Weather Here and There: One example of a set of lessons based on weather.This one is for 6th grade and is an integrated weather unit which incorporatesinteraction with the Internet and hands-on collaborative, problem solving activities for students in grades four through six. This unit is divided into six lessons. The lessons integrate math, science, geography, and language arts in the process of teaching and learning about weather phenomena.Students will become involved in collaborative problem solving using e-mail as well as through joining projects offered via the Internet. The Global Education Project will help students see the relevance of science by interacting with scientists and other students across the world, as theycollaborate in the study of weather in their environment. The Weather Eye is an excellentresource for K12 activities. It is created by Scott Hall of KGAN NewsChannel 2. DougYarger's Home Page for Meteorology 206: This site has several interesting links to a fine cloud study, a forecasting game, and other valuable web sites. The Weather Lab: Accurateweatherforecasts for 2000 cities around the world, satellite and radar imagery,ski reports, airport delays, weather articles and tutorials. The virtual weathermap room offers a collection of many graphical and text weatherproducts. Also, the author of this page, Dr. Jon Kahl, has written aseries of weather books geared toward middle school kids. A fine educational site involving schoolparticipation is produced by NBC4 in Washington DC. If students want to find out more about where their city is compared totheir e-mail partner, thislocation provides a database of world cities and offers the latitude andlongitude of two places, and then calculates the distance between them (asthe crow flies). It also provides a map showing the two places, using theXerox PARC Map Server. If students want more information on the city,county, or state, it can be found in the the USCensus County and City Data Books Students may want to compare their current temperature maps with climate maps in order to seehow'typical' their weather is. For students in Hawaii, a good source for weather and climate data is Universityof Hawaii Meteorology and H4 Weather (nicegraphic of current conditions). If students would like to look at a weather page produced in Australia, here is one. Climate data can be accessed from The Western Regional ClimateCenter. The WorldWatcheris a COVIS program that supports the scientific visualization environmentfor the investigation of scientific data and is a superb resource fordeveloping mathematical activities relating to climate studies.Here is one example. Mathematics for a Blue Planet The first SkyMath module introduces students to the measurement oftemperature, to its representation on a map (eitherby color, contours, or numbers) and to the analysis of temperature changeas shown graphically. The module focuses ontemperature measurements closely associated with students' nearbyenvironments. The mathematical techniques masteredby the students in the SkyMath module provide students with the ability tocontinue investigating the phenomenon of theworld climate and its change. We believe that learning is enhanced ifskills previously developed are revisited bystudents. Thus we have prepared a series of additional modelingactivities to be used in subsequent middleschool years. These activities serve as the context within which mathteachers can reinforce and extend their students' learning ofmathematics as they model the earth system. We have called theseactivitiesMathematicsforaBlue Planet. Funded by NSF Grant ESI-9450248 to the University Corporation for Atmospheric Research SkyMath contact: blynds@unidata.ucar.edu 1996 University Corporation for AtmosphericResearch Chosen by BBCEducationWeb Guide