a survey of secondary mathematics education in wisconsin

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A Survey of Secondary MathematicsEducation in Wisconsin

Bruce Williamson

Mathematics Education has beenunder scrutiny both from within theprofession and from outside organi-zations for the last quarter century.Numerous conferences have beenheld, committee reports printed andrecommendations drafted coveringissues ranging from behavioral ob-jectives to the use of the new tech-nology. One area of concern wherevery little data seems to be availableis information on what is happeningin the classroom. The National Ad-visory Committee on MathematicsEducation (NACOME) report from1975 lists as one of its recommenda-tions: "Extensive and detailed in-formation about classroom practice. . . /’ The National Council ofTeachers of Mathematics (NCTM)designed a national survey on cur-rent beliefs and reactions to possiblemathematics curriculum changesduring the 1980s. Their report, Pri-orities in School Mathematics Proj-

ect (PRISM) was used as a complement to the NCTM publication, AnAgenda for Action: Recommendations for School Mathematics of the1980s. The PRISM report emphasized preference and priorities but didnot deal with current practice.

School Science and MathematicsVolume 85 (1) January 1985

Mathematics Education in Wisconsin 21

The information gathered from a survey of all schools (7-12) in thestate of Wisconsin is an attempt to focus on current practice relative toseveral major issues in Mathematics Education. The data was collectedearly in 1983 through a questionnaire mailed to every secondary school(7-12) listed in the computerized mailing file, University of Wisconsin-River Falls. A second mailing was sent about six weeks later and thus areturn of 351 high schools (74%) and 201 junior high schools was real-ized. (Percentage of return is not available for junior high schools, duelargely to the variety of school organizational structures). An added fea-ture to this study is longitudinal information available because of itemswhich replicated questions used in a similar study in 1975. (The responsein 1975 was similar with 339 high schools (72%) and 277 junior highschools responding).

"Some questions will include a short discussion reflectingthe rationale for the question or suggesting a possible trendsupported by the data"

Some questions will include a short discussion reflecting the rationalefor the question or suggesting a possible trend supported by the data.The primary intent of the survey is to gain information on current prac-tice in mathematics education for use by teachers, supervisors andteacher educators.The questions which match the 1975 study will be reported first. All re-

sponses will be listed as percentages for ease of comparison. The percent-ages may not add to 100 because of rounding errors or no answer.The Agenda for Action recommends at least three years of mathema-

tics in Grades 9 through 12. Wisconsin schools are far from this ideal,but the trend is in the right direction.

Q: Graduation requirements in mathematics in your high school (beyond7th and 8th grade). (Include ninth grade for this question.)

1975 198372% 41% lyear23% 47% 2 years1% 3% 3 years4% 7% other


22 Mathematics Education in Wisconsin

In addition, 16% of the schools indicated they were planning a change,with 9% changing to two years and 2% changing to three years.

"Curriculum conferences and study committees have beenrecommending more emphasis on probability and statis-tics , . :’_____________________________

The most discouraging item in the survey was the response to theteaching of probability and statistics. Curriculum conferences and studycommittees have been recommending more emphasis on probability andstatistics in the secondary schools for the last 30 years. This emphasis hasnot become the standard in Wisconsin. Perhaps the stress on probabilityand statistics in the undergraduate program for prospective secondaryteachers will aid in increasing the amount of instructional time devotedto these two areas.

Q: Time allotted for probability and statistics in total junior high schoolprogram.

Probability Statistics1975 1983 1975 198315% 16% 17% 19% None70% 71% 61% 61% Less than 3 weeks13% 10% 12% 13% 3-6 weeks0% 1% 1% 2% More than 6 weeks

Q: Time allotted for probability and statistics in total senior high schoolprogram.

Probability Statistics1975 1983 1975 198311% 12% 20% 28% None45% 52% 38% 45% Less than 3 weeks30% 22% 15% 12% 3-6 weeks13% 12% 11% 11% More than 6 weeks

The survey of the nature of geometry classes reflects the status quoexcept for a modest increase in time spent on coordinate and vectorgeometry. These increases, along with very small increases in most of theother topics, suggest a positive trend in the teaching of geometry. Insteadof the narrow deductive development of Euclidean geometry, perhapsmore teachers are including a wider range of topics in their geometryclasses.



Q: Describe nature of geometry class(es). Check more than one if appropri-ate (at least two weeks instruction time for each entry.)

1975 198391 % 97% Euclidean58% 73% Coordinate14% 19% Transformational (motion)47% 49% Solid (space)6% 15% Vector8% 7% FiniteNot 5% Non-Euclidean/

sampled

The metric system is making very slow inroads in both junior and sen-ior high school despite the lack of a national commitment.

Q: Integration of metric system in:Junior High School Senior High School1975 1983 1975 198347% 39% 60% 41% Traditional system dominant8% 15% 3% 6% Metric system dominant44% 44% 36% 51% Balance between two systems

The dramatic changes in student involvement with the computer willnot be surprising. The information from this question becomes outdatedbefore it can be published.

Q: Percent of students involved with computing (interactive with hard/soft-ware at least 5 hours per school year.)Junior High School Senior High School1975 1983 1975 198389% 21% 62% 3% None6% 33% 27% 45% Less than 201% 22% 7% 41% 20-501% 23% 1% 9% More than 50

The rest of the survey results are from 1983. The first four questionsdeal with information solicited at the request of the Wisconsin Depart-ment of Public Instruction Mathematics Supervisor.

Q: The district has a permanent Mathematics Coordinating Committee, K-12, meeting at least three times a year.

Yes 22%No 75%

Q: The district has a K-12 computer plan for instructional use.Yes 13%No 28%

Being developed 53 %



Q: There is a Mathematics Department policy on the use of the hand calcu-lators in mathematics classes.

Junior High School Senior High School36% 25% Yes63% 74% No

Q: Status of competency exams in mathematics.75% None13% Requirement for graduation11 % Information for student/parent use only

The NCTM has advocated the use of hand calculators throughout sec-ondary school mathematics programs. The emphasis in the Agenda forAction is on school-provided calculators. The next question shows that astrong majority of the students either own a calculator or have access toone in the family.

Q: Percent of students who own a hand calculator or have one in the familyavailable for their use.

Junior High School Senior High School16% 11% Less than 50%31% 36% 50-70%36% 32% 70-90%13% 16% More than 90%

The final set of questions refers to computer access and the nature ofthe computer course(s).

Q: Computer Access_____ None_____ We have __ microcomputers in the junior high school

(senior high school)._____ We have time sharing with __________. (There are

__ terminals for the junior (senior) high school.

In junior high school, 83% of the schools had access to a computer.Seventy-eight percent of the schools had microcomputers with the num-ber of microcomputers available to each school as follows:

Number of Microcomputers Number of schools reporting1-2 683-4 435-6 177-8 15

greater than 8 11(17 was themaximum)

In senior high school, 97% of the schools had access to a computer.



Ninety-five percent of the schools had microcomputers with the numeri-cal breakdown as follows:

Number of Microcomputers Number of schools reportingI-2 463-4 835-6 587-8 259-10 35II-12 2313-14 11

greater than 14 28 (39 was themaximum)

Q. Identify the nature of your computer course(s)’in the Mathematics De-partment.

The instructions accompanying this question asked for the number ofhours per course since computer instruction has such a wide variety offormats. Some courses meet several times a week while others are con-centrated short courses. The following table reports the number ofschools rather than percentages. The time divisions at the top reflect a180 hour school year, 90 hour semester.

Computer literacyComputer architectureBASICFORTRANPascalOther Languages

1-15 20-45 50-85 90 95-180TOTAL

75 49 8 24 518126 2 2 2 13628 48 62 84 44293123721806153221535017

* Totals are larger than the sum of the rows because of missing or unusable informationrelated to hours.

Classroom practice dealing with problem solving in one major limita-tion of this survey. Several mathematics educators, including one au-thority on problem solving, requested survey information on this topicbut were not able to develop items which would yield unambiguous in-formation,

This survey was completed with the support of the Committee on Re-search and Studies under Institutional Grant No. 0285-9-82. State ofWisconsin.



References

CBMS, National Advisory Committee on Mathematics Education�Overview and Analysisof School Mathematics, Grades K-12 Washington, D.C.: CBMS, 1975.National Council of Teachers of Mathematics, An Agenda For Action: Recommendationsfor School Mathematics of the 1980s. Reston, Virginia: NCTM, 1980.National Council of Teachers of Mathematics: Priorities in School Mathematics. Reston,Virginia: NCTM, 1981.

Bruce WilliamsonDepartment of Mathematics/Computer SystemsUniversity of Wisconsin-River FallsRiver Falls, Wisconsin 54022

POAM INSTRUMENT

Nine earth-orbiting telescopes soon will provide University of Wyoming scien-tists with a rich harvest of information about large-scale atmospheric motionsand their effect on global climate and weather patterns.The miniature telescopes form a scanning array at the heart of POAM�the

Polar Ozone and Aerosol Measurement system�designed and built by a team inthe UW Department of Physics and Astronomy as a fourth generation space-borne research tool to be orbited within the next three months.Theodore J. Pepin, associate professor of physics and astronomy, heads the

UW team that developed POAM and its three forerunners, SAM I (StratosphericAerosol Measurement I), SAM II and PAM II (Preliminary Aerosol Measure-ment II) that have performed yeoman service in stratospheric research since1975.POAM will do more than trace dust concentrations and contribute to the

growing data base on their fluctuations. The detector array will also provide newunderstanding of the sources and sinks (collection points) of atmospheric pollu-tants and of the microphysics and microchemistry of trace components that havean effect on world climate patterns.

Pepin says earlier experiments first detected the wintertime formation of sul-furic acid clouds and their subsequent removal from the atmosphere by "veryefficient" natural processes over both polar regions. POAM will continue theseobservations and conduct others of great potential value toward a more completeunderstanding of the physical and chemical behavior of the upper atmosphere.POAM’s telescope array will be aimed at the sun during each orbital "sun-

rise" and "sunset" event, tracking it either up or down between the horizon andthe upper limit of the atmospheric envelope. Orbital characteristics will insurethat the sightings will profile the atmosphere over the polar regions.

Detectors behind each telescope will operate on selected wavelengths from thenear-ultraviolet through the visible spectrum and into the near-infrared to pro-vide data on several atmospheric characteristics. These include atmosphericdensity, temperature, the presence of nitrogen dioxide, ozone, oxygen, watervapor, the size and density of aerosols (microscopic solid or liquid particles) andthe factor by which their presence reduces the passage of sunlight through theatmosphere.


a survey of secondary mathematics education in wisconsin

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