THE DEPARTMENT OF MATHEMATICS
DEPARTMENT OF MATHEMATICS
1970s
INTRODUCTION
Is math confusing? Are we teaching the same content over and over rather than building on concepts learned? The 1970s mathematics community suggested that educators, consultants and the “average person” should easily interpret the research being conducted.
In turn, the U.S. public was concerned about the report on test scores called the National Assessment of Educational Progress (NAEP). Once this document was released, professional groups prepared position papers. The National Science Foundation (NSF) funded Priorities in School Mathematics (PRISM) and the National Council of Supervisors of Mathematics (NCSM) prepared a position paper stating problem solving is the most important basic skill.
The MPLS Department of Mathematics teaching faculty during the 1970s included William Bader, Joseph Hohlfeld, George Immerzeel, Dennis Kettner, Earl Ockenga, Lynn Schwandt, John Tarr and Donald Wiederanders.
TEACHING
The Junior High seventh- and eighth-grade mathematics curriculum at Price Laboratory School is designed to provide a transition from the mathematics general education of the elementary school to Math 7 and Math 8 and finally the more specialized courses in grades 9 through 12, including Analysis, Statistics, Matrix Algebra, Geometry, Investigations in Mathematics, Computer Programming and Calculus.
Math 7
The content for seventh-grade mathematics is organized in seven units. Two units focus on the computation skills for four operations for natural numbers and rational numbers. Geometric concepts are developed in two units — one a non-metric geometry unit where the focus is on a finite geometry and the other is a metric geometry unit where the focus is on direct and indirect measures associated with length, distance, area, and volume. Students’ exposure to the structure of mathematics is extended in a unit on the natural numbers and the development of the properties of the rational numbers. Students study simple proof and logic sequences that require valid arguments. A substantial unit on problem solving develops a function approach to problem analysis through the use of tables. The unit is heavily laboratory oriented. Short units on the base 2 (binary) numeration system, an introduction to computer programming, and probability complete the seventh-grade course of study.
Assignments seldom require more than twenty minutes of out-of-class work. Most seventh graders will be able to complete assignments during the class period.
Math 8
Although the study of operations with natural numbers is abbreviated in Math 8, other major units from seventh grade are extended in depth and breadth.
In metric geometry students are introduced to many new ideas including the Pythagorean theorem. The metric geometry study is complemented by problems in the field at 8th grade camp. Introduction to integers as a number system is expanded into a study of the rational numbers. An in-depth study of the ratio concept with special emphasis on applications to problem solving is a major unit in the eighth-grade course. A set of number pairs and their graphic representation in the coordinate plane is taught as an introduction to the algebra course that follows in the ninth grade. Though some work is done in problem solving, the number pair unit is primarily a pre-algebra study. Units in non-metric geometry and elementary statistics conclude the eighth-grade mathematics course.
Assignments seldom require more than twenty minutes of out-of-class work. Most eighth graders will be able to complete assignments within the class period.
The courses for both 7th and 8th grade are written by the PLS faculty. Some units help students consolidate their learning as previously studied. Other units are exploratory in nature. Laboratory and game activities are an integral part of the curriculum.
North Central Association Visitation Team Summary
To ensure the PLS Department of Mathematics was providing learning opportunities for all students, the faculty conducted a self-study and invited a team of educators to provide an external evaluation. The following comments were made in the team report:
Mathematics at N.U.H.S. may be characterized by one word: flexibility. Though basic content objectives are identified with each course, the means by which these objectives are pursued vary from year to year depending on such factors as: the ability of the students, the teaching strategy being investigated, and decisions regarding use of instructional devices and computational aids. The mathematics faculty at N.U.H.S. recognizes and enthusiastically accepts the challenge to provide a consistently high-quality mathematics program for students as they simultaneously conduct a continuous program of action research in curricular modification and pedagogical reform.
PUBLICATIONS
During the 70s, many classroom teachers were learning how to use a calculator along with their students and this tool could be intimidating. The calculator changed the way teachers taught, how students learned, and the timing of everything, including daily lessons. The PLS math faculty were in demand to help school faculty and students become proficient in the use of calculators. This increased the need for informative publications and newly funded projects.
Keys to Mathematical Ideas
John Tarr, William Bader
1975
Monroe Publications invited John Tarr and William Bader to write guides that would help teachers move into the world of technology with confidence. The authors used their classroom experience working with preservice teachers to aid in making these books a valuable resource to other professionals.
Calculator Instructional Materials
George Immerzeel and Earl Ockenga
1979
SERVICE
As faculty created new curricula field tested their lessons, then published the materials, they also were asked to make presentations and provide workshop opportunities to school districts. The hot topics were problem solving and the use of new technology.
Iowa Problem Solving Project
1976
A major Price Lab project with national distribution was the Iowa Problem Solving Project, a series of eight math instructional units for grades 5-6 and 7-8 to be used instead of the regular classroom mathematics units. While the team of George Immerzeel, John Tarr, Earl Ockenga, and Joan Duea at the Lab School were still developing the units, more than 300 Iowa teachers were using the units and they were sold in 29 states plus five Canadian provinces and England. Some of the larger orders came from Honolulu, HI; Arlington, VA; Memphis, TN; Milwaukee, WI; and Halifax, Nova Scotia.
The project, originally designed by George Immerzeel, aimed to develop certain problem solving skills not commonly taught in textbooks. John Tarr, project manager, said at the time, "The units teach students skills like how to make intelligent guesses and how to use reference books to solve problems."
Reflecting on the 70s, content expanded due to the focus on problem solving and methodology was greatly influenced due to technology. Rather than having teachers, students and parents feeling intimidated, PLS reached out to all ages to encourage changing the mindset of learners. Making guesses, exploring approaches to solutions, the whole process of identifying problems and using mathematics to reach solutions took on new meaning.
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