Voyages
in Mathematics and Science
October 2000 , Issue 23
Pacific Mathematics and Science Regional Consortium: An Eisenhower Consortium
Project DELTA: A National Science Foundation Program

In This Issue:


Ask an Earth Scientist Website

Do you have an Earth Science question you would like answered? Ask a real live scientist at: http://www.soest.hawaii.edu/GG/ASK/askanerd.html, a site managed by the Department of Geology and Geophysics at the University of Hawaii at Manoa. To begin, look under the appropriate subject heading to see whether someone has already asked your question that the scientists answered. If you do not know under which category your question falls, you may explore different categories, or go to the General/Other section. You may also do a search by typing key words in the search box. For example, if you want to know how your island was formed, you can go to the Volcanoes and Igneous Rocks section and look for a similar question, or you can enter the words island formation in the search box. If you do not find an answer to your question, read the criteria for questions and then return to the most appropriate section, which in this case would be Volcanoes and Igneous Rocks. Then scroll down to: Couldn’t find an answer? Ask us, and click on: Volcanoes and Igneous Rocks. You will then find boxes where you fill in your name, e-mail address, and question. You may receive an answer within a few weeks. Just remember to revisit the site often to check for the answer.

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DELTA Institutes Conducted Across the Region

DELTA cadre members from the 10 participating entities conducted local summer institutes and workshops for mathematics teachers in the middle grades. Enthusiastic feedback indicates that the institutes were successful in introducing teachers to a variety of mathematics activities and teaching strategies that will be useful in the classroom. The cadre members plan to do follow-up activities with the participating teachers. There will be classroom observations, team teaching, and after-school workshops. Some of the teams were able to offer their institutes for college credit. More future institutes may be offered for credit.

The DELTA cadre met for the 2nd Regional Institute in Guam from July 30 to August 5 and shared experiences, successes, and challenges. Members also engaged in math activities; continued planning for follow-up sessions with teachers; organized future local institutes; and continued developing toolkits for professional development. The week was packed with many sessions. The participants enjoyed working with old friends, meeting new DELTA cadre members, and made time in the early mornings and evenings for social events, such as a 6 a.m. tennis tournament.

Project staff interviewed cadre members for feedback on the project and to inform the focus of the work during the next year. As a result, preliminary plans are underway for sub-regional cadre sessions in early 2001, since the next regional cadre institute will not take place until June 2001. Project staff will also provide cadre members with mathematics resources for classroom use.

For more information about Project DELTA, please contact your local cadre members, your PREL Service Center Coordinator, Sandy Dawson at dawsons@prel.org, or visit PREL’s website at www.prel.org for further information.

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GLOBE Training Held in American Samoa

Sixteen teachers from seven elementary schools and two high schools in American Samoa participated in a Global Learning and Observations to Benefit the Environment (GLOBE) training conducted during August. GLOBE is an integrated environmental education program that involves hands-on science activities with data reporting via the Internet. The participants collected data and conducted experiments in 26 protocols in land cover and biology, soil, hydrology, and atmosphere. The workshop was conducted by staff from the Pacific Mathematics and Science Consortium at PREL and GLOBE staff from the University of Oklahoma, including GLOBE’s lead atmospheric scientist, Susan Postawko.

A set of equipment was given to each school for the students to use in collecting data. The nine schools will be registered as GLOBE schools, and their students will do some of the science activities their teachers had learned in the workshop. The students will collect data such as measurements of temperature and rainfall and then report the information online. More complex measurements such as dissolved oxygen content in stream water may also be reported. These data will be used by scientists for a more detailed picture of climate and climate change locally, regionally, and globally.

Currently, GLOBE involves more than 9,500 schools in over 90 countries. Scientists, teachers, and students in all these sites are working together to learn from one another. Images of synthesized data collected by students are available on the World Wide Web. For more information, see www.globe.gov.

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The Eisenhower National Clearinghouse

The Eisenhower National Clearinghouse for Mathematics and Science Education (ENC) can help, whether you are:

  • an elementary teacher looking for a better way tohelp your students understand a science concept,
  • a parent helping your child in math,
  • a high school teacher searching for new materials for your lab classes,
  • a student wanting more resources for a class project.

Just log on to www.enc.org for the most recent information and resources in mathematics and science.

Since August 1, ENC Online has been redesigned to give everyone easier and faster navigation through ENC’s categories and thousands of K-12 math and science teaching materials, curriculum resources, innovative ideas, and professional development opportunities.

ENC works in partnership with the 10 Eisenhower regional consortia. The Pacific Regional Consortium at PREL serves the entities of American Samoa, Commonwealth of the Northern Mariana Islands, Federated States of Micronesia (Chuuk, Kosrae, Pohnpei, Yap), Guam, Hawaii, Republic of the Marshall Islands, and Republic of Palau. Visit www.prel.org/programs/ms/math-science.html for our regional ENC information.

You may apply online for a free subscription to the quarterly magazine ENC Focus: A Magazine for Classroom Innovators at www.enc.org/order or by a toll-free call to 800-621-5785. The magazine contains information on innovative and free ENC resources and services. There are articles written by readers and classroom teachers who share practical information and classroom successes related to the topic of each issue. You are also invited to contribute classroom innovations on “Partnerships with Business and the Community,” to be distributed in January 2001 and on “The Standards-Based Classroom,” in April 2001.

Recent ENC Focus topics include integrating technology in the classroom, assessment that informs practice, and mathematics and science in today’s world. Mathematics and Science in the Real World speaks to a concern that teachers have. They are constantly striving to meet the needs of students by trying to make what happens in the curriculum relevant to students’ Real World interests. This issue of ENC Focus contains several teachers’ descriptions of how they did it.

The issue, Focus on Assessment That Informs Practice, deals with the daily classroom processes that teachers use to gauge their students’ understanding of what is being taught. It is also used to measure how well they as instructors are succeeding. Twelve articles in this issue offer helpful ideas and insights for teachers.

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We Invited, They Came, We Did It!

A major effort is now in progress to review all Pathfinder curriculum learning units developed during last five years of Pathfinder workshops. The units are the work of teachers from all entities of the Region who came together for a period of three weeks each summer to participate in vigorous hands/minds-on learning and in developing standards-based instructional units. Program and education specialists from the Pacific Mathematics and Science Regional Consortium and the Hawaii Sea Grant /Pacific Program have collaborated to review and organize these units into a usable format for teachers of the Region. The three topics selected for this teacher handbook are Endangered Species, Coastal Development, and Coral Reefs.

The June issue of Voyages invited educators bound for PEC 2000 in Palau to come and check out the Pathfinder workshops during the conference. The three sessions were presented collaboratively by Juanita Rilometo, Pacific Educator in Residence (PEIR) from the Republic of the Marshall Islands, Liz Kumabe of the Hawaii Sea Grant/Pacific Program, and Martin Weirlangt of the Pacific Mathematics and Science Consortium. The presenters reviewed the Pathfinder Learning Units, how they were developed during the Pathfinder Institutes, and how they had been modified into standards-based formats. Here are several highlights of the Palau Pathfinder workshops.

More than 20 teachers and educators participated in the three workshops. The main clusters presented were: “Getting to Know the Pacific Standards Used in the Pathfinder Institutes;” “Standards and Their Application in the Classroom;” and “Resources to Support Teachers’ Pathfinder-like Activities.” In Session One, participants were introduced to the Pathfinder history and how the collaborative efforts of its main stakeholders. PREL, Hawaii Sea Grant, local institutions of higher education (IHEs), and local educational agencies (LEAs) contributed to its success. Workshop participants also examined in depth several aspects of the Pacific Standards for Excellence in Science, and some critical issues on standards, such as what, why, and whose standards. In Sessions Two and Three the focus shifted to how the standards are brought to life in the classroom and the resources available to help in that effort. To simulate a Pathfinder experience, the participants created standards-based unit plans on the topic of “Turtles as Endangered Species.”

Three sample beginning units are included which, because of time limitations, are not finished products. The participants agreed to take their work home, complete it, and attempt to implement the units. The presenters and participants promised to stay in touch and keep each other updated on the progress of their units. They agreed to seek ongoing support. During the closing minutes of the sessions, the participants discussed the different electronic and print resources available to them and received a packet of materials.

There is good news for all teachers. The Pathfinder materials will be available and disseminated in print and via the Internet in early 2001.

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Turtles As an Endangered Species
Unit Drafts

 

Authors: Lynett Villagomez, Lucy Barnes, Theodosia Kurtei, Rihner Elias, and Ella Raiall
Grade Level: Lower Elementary
Context Setting/Situation Sea turtles are an endangered species in our ocean and are in danger of becoming extinct due to poaching for consumption and commerce.
Pacific Science Standards and Benchmarks Addressed.

Science as Inquiry

Students will . . .

  • Ask good questions about the world around them.
  • Make careful observations and seek logical explanations.

Habits of Mind

Students will . . .

  • Demonstrate behavior that reflects caring and respect for living things and their environment.
  • Use thinking skills to make informed decisions and choices in their everyday lives.

Living Environment

Students will . . .

  • Respect and take responsibility for all living things.

Human Society

Students will . . .

  • Participate meaningfully in local practices that encourage conservation of island resources.

Scientific Connection

Students will . . .

  • Integrate ideas in science and build personal understanding through connections.
Driving Question and Other Related Questions

WHAT DO WE DO TO TAKE CARE OF OUR TURTLES?

What do we feed our turtles?

How can we help take care of sea turtles so that they do not become extinct?

Parts of a Standards-based Unit drafted by the participants to the Pathfinder in Practice workshop at the PEC 2000.

 

Authors: David Hadley, Cyril Leonardia, and Centry Paul
Grade Level: Middle Elementary
Context Setting/Situation The number of sea turtles is decreasing so rapidly that they are being placed on the endangered species list. There are several reasons for this. As islanders we have the responsibility to take care of the turtles, so that their population will once again increase.
Pacific Science Standards and Benchmarks Addressed.

Science as Inquiry

Students will . . .

  • Research the life cycle of sea turtles.
  • Research the population of sea turtles.
  • Name several reasons for the declining sea turtle population.

Habits of Mind

Students will . . .

  • Educate and encourage the community to refrain from or limit the harvesting of sea turtles.

Living Environment

Students will . . .

  • Classify different species of turtles.
  • Explain the life cycle and the food chain/food web for turtles.
  • Discuss the habitats of sea turtles.

Human Society

Students will . . .

  • Participate in local conservation efforts.
  • Identify the cultural and economic values of sea turtles.

Technology and Society

Students will . . .

  • Learn about effective breeding of turtles in captivity.
  • Examine local methods and tools for making turtle shell ornaments.

Scientific Connection

Students will . . .

  • Use scientific inquiry to investigate the problems regarding the decrease in sea turtle population.
Driving Question and Other Related Questions What can we do to help increase the population of our sea turtles?


Authors: Moegalafo Faumuina, Faaeseina Stevenson, and Susan Burger
Grade Level: Upper Elementary
Context Setting/Situation Sea turtles have provided Pacific Islanders rich cultural and economic resources for hundreds of years. The current endangered species status of sea turtles makes it essential to find ways to protect and increase their number while respecting human interests, so that this resource is not lost forever.
Pacific Science Standards and Benchmarks Addressed.

Students will:

  1. Ask good questions about the cultural roles and habitat of the sea turtle, as well as reasons why it has become endangered.
  2. Design and conduct valid investigations to find answers to their questions concerning the habitat, life cycle, and roles of sea turtles.
  3. Care about and value science as a means to know the importance of the sea turtle.
  4. Be curious, creative, and open-minded.
Driving Question and Other Related Questions

How do we engage in a dialogue that promotes protection of sea turtles?

How can we educate the fishermen and community to stop destroying turtles?

Parts of a Standards-based Unit drafted by the participants to the Pathfinder in Practice workshop at the PEC 2000.

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New Website Developed for Mathematics and Science

The Pacific Mathematics and Science Regional Consortium is developing a more extensive website to provide mathematics and science resources for educators. These resources include:

  • Information about mathematics and science organizations and programs in the Pacific region, including but not limited to those at PREL,
  • Lesson plans,
  • Research and reports,
  • Online journals,
  • Curriculum projects,
  • Professional organizations,
  • Standards and frameworks,
  • Informal education,
  • Network of mathematics and science service providers in the Pacific region,
  • Educational organizations,
  • Other resources for mathematics and science educators.

This is a work-in-progress, which will be up and running in the near future. The site will eventually become a searchable database. The consortium is soliciting information about mathematics and science contact people, organizations, and projects operating in the Pacific region. Please help us make this site a truly useful database for Pacific educators by sending information, updates, corrections, and comments to askmathsci@prel.org. Check out the site at www.prel.org.

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MATH: Mastering the Art of Thinking How
How Should Mathematics Be Taught?

by Alpha C. Espina
F.B. Leon Guerrero Middle School, Guam
7th Grade Mathematics Teacher and Guam DELTA Institute 2000 Member

“Miss, I don’t get it!” seems to be a comment that middle school teachers often hear from confused math students. It is actually better for students to express their frustrations rather than remain silent and pretend that they understand the lesson. If a teacher perceives mathematics as the science to master thinking how and believes it, then the teacher must be able to communicate that concept to the students. Traditional mathematics instructors asked, “What is the answer?” However, today’s teachers ought to teach their students to focus on how they got their answers.

In the middle school classroom, math teachers should explore the different possibilities and strategies to facilitate learning. A philosopher once said, “If you give a man a fish, he eats for a day; if you teach a man how to fish, he eats for a lifetime.” The same concept can be applied to teaching mathematics. For example, in a lesson on simple interest (I = P X R X T), the students are asked to discover how the lesson can be applied in everyday situations or how the formula can be validated. The students may bring a newspaper to class and show how simple interest is used in the news and advertisements. The class may also formulate ideas on how principal, rate, and time become factors in finding the simple interest. When students are encouraged to think about how to get the answer more than getting the answer itself, their perspective of mathematics will become broader and uninhibited.

As a seventh grade math teacher, I have found that students become motivated and eager to learn when games and movement are part of the lesson. Every year, I hold a math tournament called “24-Game” (the “I Got It!” game). For two quarters every Friday, each class prepares for the tournament by forming class teams to play the game. The game involves four numbers on a card that is held up for everyone to see (i.e., 5-7-2-7). The students know that the answer is always 24. Each team makes up a story problem that uses all the numbers once in the basic operations (add, subtract, multiply, divide) to show how the four numbers equal 24 (i.e., 5x2=10; 7+7=14; 10+14=24). The game involves speed, accuracy, and team cooperation. The first team to answer another team’s word problem accurately wins and is awarded a prize. Each team member is also given a teacher-made No Homework ticket to take the place of one homework grade. All the classes compete against each other until there are two top winners who reach the finals.

  • This game seems to be enjoyed by both high level thinkers and academically challenged students. The winning class last year consisted mostly of LOTE (languages other than English), at-risk, and general math students. They competed in the finals against the pre-algebra class. All the other students were amazed at the skills shown by the winning group. Through this experience, the students look forward to math class and know that mathematics can be challenging and fun.
    Another math assignment that students turn in on Fridays is called Newspaper Math. This writing exercise requires students to:
  • Cut out a newspaper article published that week.
  • Paste it on a sheet of paper.
  • Formulate a word problem based on the news article written in complete sentences. Extra points are given for problem questions related to the week’s math lessons.
  • Show the step-by-step solution to the problem, and
  • Give the correct answer.

A rubric is used for evaluating the students’ work. This assignment integrates reading, writing, social studies, science (if applicable to the article), and math. This assignment also encourages students to be innovative and unique. By reading their selection of articles and formulation of word problems, a teacher can learn about the students’ background, experiences, and interests. The students develop the process of thinking by finding how to formulate questions and solve for answers.

Teaching students M.A.T.H. means that each student is given an opportunity to explore and go beyond the concept, computation, and application involved in mathematics. Many teachers devote much time in teaching computation and application without instilling the concepts of numbers and patterns. Some do not realize that through the conceptualization of numbers and patterns, students can better understand and evaluate how a particular math problem can have various solutions. Problems can even have different correct answers depending on how one interprets and conceptualizes the problem.

For example, I posed a story problem to the class and placed them into groups. I gave them the task of discussing, analyzing, visualizing, and orally presenting their solution to the problem. As I walked among the groups, I observed that students were questioning each other and verifying one another’s solution to the problem. This exercise demonstrates that when students are given the opportunity to conceptualize a situation, the possibilities are endless. Students can be helped to create their own perceptions in problem solving. Deciding how to get the answers becomes more important than the answer itself. When students are able to think how, that is learning.

Here is a sample story problem. A family consisting of a father, mother, brother, sister, and a dog is stranded on a deserted island. From the island, the family can see a strip of land that might lead to civilization and home. After many attempts to leave the island and be rescued, the children see a boat. To their dismay, they see printed on the side of the boat instructions for the proper use and capacity of the boat. The maximum capacity is 180 pounds and not an ounce more. The father weighs 150 pounds, the mother 110, the brother 90, the sister 80, and the dog 15. How can the whole family leave the island? Do you have the solution? (If anyone wants to discuss this with me, you may email me at masterpeace@kuentos.guam.net.)

Mathematics should be taught systematically and creatively. With today’s multimedia and technology, students are always looking for the “easy” way. Instead, media and technology can be used productively in teaching mathematics, so that students will master the art of thinking how through gaming, riddles, and innovative strategies. Teachers ought to ensure that mathematics become a way of life for their students, who then can confidently say - “Miss, I GOT IT!”

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Surfing the Information Superhighway

http://www.nctm.org/about/met/ – The Mathematics Education Trust (MET) was established by the National Council of Teachers of Mathematics (NCTM) to fund special projects that enhance the teaching and learning of mathematics. Visit the site to see what awards, grants, and scholarships are available. Most 2001-2002 applications must be postmarked no later than December 5, 2000. The Dale Seymour Scholarships for Grades K-12 Teachers awards a maximum of $2000 to teachers interested in extending their mathematics background to improve their teaching.

http://www.ups.edu/community/tofu/ – Tools for Understanding is for middle and secondary school mathematics teachers who want to integrate common technologies into their daily instruction and move away from rote learning. The technologies range from calculators, paper, and pencils to spreadsheets and word processors. The site includes a strand on how to use math journals with the simple paper and pencil technologies. The target audience is intermediate and middle-grade teachers, particularly those who teach remedial math classes and secondary level special education groups.

http://www.nytimes.com/learning/teachers/lessons/mathematics.html – Daily Lesson Plan, from the New York Times Learning Network, offers lessons in Grade 6-12 mathematics integrated with other subject content. In Prize Numbers: A Novel Approach to Math, students explore what a proof is, learn how and why mathematicians create them, and then write essays on how reason and logic are used in the workplace.

http://math.com – Math.com, The World of Math Online offers mathematics-oriented resources for students and parents, as well as lesson plans and professional development resources for teachers.

http://www.siemens-foundation.org – Educators are encouraged to get their students with exceptional talent and dedication in science, mathematics and technology involved in the award programs of the Siemens Foundation. The Siemens Awards for Advanced Placement involve annual scholarship awards to outstanding AP students in math and science. The Siemens Westinghouse Science & Technology Competition is held each year in December, when independent research projects are judged by panels of prominent scientists and faculty from a network of distinguished universities. More than $1 million in scholarships and awards are given every year. High school students from the 50 states and the U.S. Territories may compete in the region of one of six prestigious universities in the United States. Application forms can be downloaded from this site.

http://www.hhmi.org/coolscience/index.html – The Howard Hughes Medical Institute sponsors this site for kindergarten through grade 3 students and invites curious kids to explore biology on screen, off screen, and in between. The site provides fun projects designed to teach kids about the importance of closely observing and testing things around them. Parents are encouraged to participate and are given helpful suggestions in “Science Suggestions to Parents.”

http://www.tryscience.org – The TryScience site is a gateway to interactive excitement with contemporary science centers and museums worldwide. The “Adventure” link offers thematic interactive experiences. The “Experiments” link provides offline hands-on activities with online components. The content changes regularly.

http://ousd.k12.ca.us/~codypren/CSEZ_Home.htm – Cody’s Science Education Zone is maintained by Anthony Cody, a middle school science teacher in Oakland, California. Cody updates the site frequently and maintains archived links to previous hot issues. He offers many lesson plans, good practical teaching ideas, articles that teachers would enjoy reading, and other valuable information. A recent special topic was national certification for teachers.

http://stills.nap.edu/books/0309070333/html/ – The report, Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium, is available online from this National Academy Press website. The report provides a new vision for preparing teachers of mathematics and science. In a report released August 16, the National Research Council called current teacher-preparation and professional development efforts “disjointed and inadequate” at a time when standards for student learning are being raised. The report calls on colleges and universities to take the lead in providing effective professional development programs.

http://www.pbs.org/teachersource – This site searches and matches standards to 1,400 lessons and activities in mathematics, science, and other content areas. There are video lessons, printed lesson guides, and online discussions facilitated by experienced classroom teachers. Additional activities are updated on the web monthly.

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Pacific Algebra Network

P(a)n , the Pacific Algebra Network, is a collaborative effort involving the Pacific Consortium, the PRELStar distance learning project at PREL, and the University of Hawaii’s Curriculum Research and Development Group (CRDG). CRDG’s “Algebra I, A Process Approach,” provides the curriculum base for the project. The mission of P(a)nis to create a learning community to help teachers and students develop problem-solving processes as they learn algebra. The key to achieving the mission and objectives of P(a)n is to develop a cadre of master teachers throughout the Region who have in-depth content and pedagogical knowledge to teach Algebra I effectively through a problem-solving process approach.

Algebra is a key component of mathematical literacy. P(a)n provides mathematics educators with intensive professional development focused on the integration of problem-solving processes in the classroom. This is carried out through intensive face-to-face professional development and follow-up and support through a variety of distance-learning tools including videotaped programming and online forums.

P(a)n has just completed its first year in Pacific region schools. Teachers implementing the program seem to be pleased with the progress being made in their classes. During April the departments and ministries of education of the Pacific entities had selected another cadre of P(a)n participants. Nineteen middle and high school algebra teachers were chosen to attend the second P(a)n Summer Institute in July in Honolulu. In learning both content and pedagogy, the participants discovered how to use the Hawaii algebra materials and developed lessons in problem-solving processes. Each participant received an e-mail account, Internet access, and learned ways to use these resources to communicate throughout the school year. The dialogue among peers and mentors will support the teachers as they teach and develop professionally. All participating teachers will receive videotapes of actual classroom sessions in algebra to help in their professional growth. Teachers are anticipating much mathematical excitement in their P(a)n classes this school year.

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The Voyages in Mathematics and Science production team welcomes comments about this publication and suggestions for the next issue. The team is interested in articles about successful mathematics and science programs, practices, activities, games, and puzzles. Please submit them to Paul Dumas, Pacific Mathematics and Science Regional Consortium, Pacific Resources for Education and Learning, 1099 Alakea Street, 25th Floor, Honolulu, Hawaii 96813.

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Voyages in Mathematics and Science is produced with funds from the Office of Educational Research and Improvement (OERI), U.S. Department of Education, under grant number R168R50023. The content does not necessarily reflect the views of OERI, the Department, or any other U.S. government agency.