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Table of Contents
by Martha B. Johnston and Donald Weinstein
Curriculum mapping is an essential tool in aligning what curriculum is taught with what is tested. Data from Curriculum maps are fueling a dynamic dialogue among mathematics teachers across grade levels and courses in the Blackhawk School Distict. In spite of the demise of the steel industry and its effect on the economy in western Pennsylvania, the school district's 171 teachers and 9 administrators are committed to keeping Blackhawk “someplace special!” One of their strategies for attaining educational excellence involves using curriculum mapping to monitor and revise the curriculum for their 2,900 students.
Blackhawk's mathematics teachers in grades 1–12 are piloting the endeavor under the sponsorship of the Curriculum Council, a 25-member committee representing teachers, administrators, school directors, parents, and students. The Mathematics Curriculum Review Committee, a subcommittee of the Curriculum Council, consists of teachers from grade 1–12 and administrators, all volunteers and novices at curriculum mapping. This Council has guided the district's mathematics faculty through the mapping project.
Curriculum mapping is based on the assumption that administrators, supervisors, and teachers need to know what is actually being taught in classes. The process of mapping curriculum is based on two beliefs—that the quantity of time teachers allocate to a task influences student achievement, and that curriculum decisions need to be based on facts, not opinions, pressure, or expedience.
The purpose of curriculum mapping is to establish agreement between curriculum guides, the actual material taught in classes, and the material covered on tests; that is, to align the curriculum. Curriculum mapping enables teachers to systematically communicate how classroom time is used to implement the written curriculum. Teachers record the time (in minutes or periods) actually allocated to a subject, topic, skill, or behavior on a map or log. This information, when summarized and reported, indicates how classroom instruction is aligned with the written curriculum. Mapping furnishes each teacher with a schematic of instructional content and emphasis. And the reports provide teachers and administrators with data to evaluate the curriculum's horizontal and vertical articulation.
Horizontal articulation reports allow teachers in the same grade to compare time on task for specific instructional objectives. These reports provide the necessary information to bring about alignment between grade level curricular guides, actual instruction, tests, and textbooks.
Vertical articulation reports provide information about specific subjects, objectives, topics, skills, and behaviors between grade levels and throughout course sequences within a school. This allows a school to verify strengths and identify weaknesses in sequence and continuity.
With the computerized curriculum mapping system used by Blackhawk, teachers take only one to two minutes per class each day to map time spent on curricular goals. Concerns that teachers may resist using this procedure were overcome in the Blackhawk schools as teachers recognized the ways in which curriculum mapping directly benefits them:
When teachers realize how curriculum mapping will benefit them and how distortions of the data could result in unwise curriculum decisions, they can more easily see the importance of reporting time honestly. To reduce pressure on teachers to “color” data, anonymity can be ensured by data codification.
In the Blackhawk schools, administrators and teachers saw positive results within the first year. With data in hand they could make necessary adjustments to establish alignment between curriculum guides and the taught curriculum. This offered the possibility for more practical, usable guides for teachers based on better estimates of the amount of time needed for specific curricular tasks. The data also enabled administrators and faculty to make sound decisions about the need for classes of different ability levels, staffing needs, and the inclusion or exclusion of material in the scope and sequence of programs. This made it possible to select appropriate textbooks and tests for the real curriculum.
When the Blackhawk School District embarked on curriculum mapping a year ago, it faced several challenges. There were no subject area supervisors. Teachers needed data in order to communicate objectively about their experiences with the written curriculum, to give each teacher a realistic picture of the curriculum throughout the school, and to link the written curriculum with the taught curriculum. The district's staff believed that the written curriculum, in many cases, included more concepts and skills than could be effectively taught within the school day and year. They needed a way to collect data that would help them fit the written curriculum into available time.
Curriculum mapping had previously been recommended during a curriculum audit conducted in the district after which a delegation of the district's teachers and administrators attended a national seminar on mapping. At that time, a curriculum management planning team decided that curriculum mapping was appropriate for the district.
Before initiating curriculum mapping, the district administrators guaranteed the faculty that the data for curriculum maps would be gathered in a manner that would provide anonymity and confidentiality and that the data would not be used in teacher evaluations or in any punitive manner with regard to faculty. The primary purpose for the data collection would be to provide substance for and to stimulate dialogue among teachers. This required the empowerment of teachers as change agents for the curriculum. The endeavor was based on the district's belief that teachers will make meaningful changes to the curriculum if they are provided with objective, relevant data justifying such changes and with a practical, easy-to-follow process to facilitate such change. The district used the Administrator's Guide to Curriculum Mapping: A Step-by-Step Manual (Weinstein 1987).
In July 1990, Donald Weinstein provided a full-day inservice program for members of Blackhawk's Mathematics Curriculum Review Committee and other members of the Curriculum Council. Scheduled in a high school computer lab, the program gave participants a hands-on orientation to CMT: FOR TEACHERS, a curriculum mapping software program designed to replace the tedious, time-consuming manual method for managing the data yielded by curriculum maps. The hardware required to operate CMT properly on a personal computer includes an IBM PC, XT, or AT, or fully IBM-compatible computer with a 640k memory; two double-sided floppy drives or a floppy drive and a hard disk: a printer and a monitor. The recommended hardware for best speed and screen display is a PC with 640K memory, a hard disk, a color monitor, and a printer.
George Trombulak, Blackhawk's computer services specialist, had no problem setting up the district's IBM XT, AT, and Model 25 computers to run the program. A transfer of format from 5¼″ to 3½″ DOS drives was easily accomplished using standard procedures.
The orientation program in Blackhawk took six hours and was divided into two sessions. During the morning, Weinstein reviewed the benefits of curriculum mapping for administrators and teachers. He spoke about program articulation and linkage between special programs and “mainstream” programs. He also provided examples of findings from curriculum projects involving elementary health education and mathematics programs, middle school English, high school mathematics, special education, and child study teams. Weinstein discussed the foundations of curriculum mapping and explained the processes for decision making about mapping and data collection and the design of matrices.
Weinstein explained to the Blackhawk faculty that curriculum mapping helps to determine:
Weinstein also described how curriculum mapping is used to determine administrative time on task, the degree of linkage between special education and mainstream programs, and the time needed by members of child study teams to complete their tasks.
The afternoon program was a hands-on session conducted in the high school computer laboratory. The twenty teachers and administrators who attended were divided into teams of two and three. Each team worked at its own computer learning and practicing with CMT.
CMT is user-friendly. The main menu contains all the computerized functions needed to run a curriculum mapping project. The functions are listed in the order one would logically follow when setting up and administering a project. The main menu includes:
The period after the workshop was demanding for the Blackhawk School District's faculty as they took the first step toward constructing maps. The construction of maps for the mathematics curriculum involved the development of a comprehensive matrix. One component of the matrix was a listing of all mathematics objectives for grades 1–12. The other component provided spaces wherein each teacher could record the class time spent daily on each of the listed objectives.
Mike Thomas, a high school assistant principal, and chairman of the Mathematics Curriculum Review Committee, states that “the preparation of items to be mapped by math teachers proved to be a complex process.” He recommends allocating one semester for map construction before teachers begin using the maps to record instructional time. This would allow time for input from teachers and for developing a vocabulary that can be understood by all.
Blackhawk's Mathematics Curriculum Review Committee developed a comprehensive, sequential list of 200 objectives for grades 1–12 after only one full day's work. Committee members benefited from reviewing another school district's list of mathematics objectives. Mathematics department chair Mary Beth Quinn states that “it was a challenge to develop a matrix that would include topics presented in the wide variety of mathematics course offerings. Once we were able to transfer the specific, individual course topics into more general mathematics topics, the matrix development went quite smoothly.”
Once the matrix was constructed, subject information had to be entered into the software. Mary Fontaine maintains the district's computerized mathematics curriculum mapping database for sixty-three teachers and twenty-six courses. She found the original entry of data identifying mathematics objectives to be time consuming because of the number of objectives and the required proofreading and checking. Figure 1 is a partial list of the mathematics matrix that was developed for the Blackhawk School District, grades 1-12.
Subject Short Name
CMP WHL #
ADD WHOLE NUMBERS
ADD WHL #
DIGITS VERTICAL FORMAT W/O REGRPG
DIGITS VERTICAL FORMAT W/ REGRPG
DIGITS HORIZ FORMAT W/O REGRPG
DIGITS HORIZ FORMAT W/ REGRPG
ADDITION FACTS TO 18
ADD TO 18
SUBTRACT WHOLE NUMBERS
SUB WHL #
2+ZEROS IN THE MINUEND
DIGITS VERT FORMAT W/O REGRPG
DIGITS VERT FORMAT W/ REGRPG
SUBTRACTION FACTS TO 18
SUB TO 18
MULTIPLY WHL NUMBERS
X WHL #
BY 1 DIGIT NUMBER
1 DGT #
BY 2 DIGIT NUMBER
2 DGT #
TIMES TABLE THROUGH TEN
X TBL TR 10
BY 3 DIGIT NUMBER
3 DGT #
DIVIDE WHL # BASIC FACTS ONLY
D WHL# BFO
DIV WHL NUMBERS
D WHL #
DIVIDE W/O REMAINDERS
D W/O REM
READING & WRITING NUMBERS
SOLVE SIMPLE EQUATIONS +,-,x,:
SEQUENTIAL NUMBER PATTERNS
SEQ # PAT
MEASUREMENT, STATISTICS, PROBABILITY
AREA, PERIMETER, CIRCUMFERENCE
GRAPHS OF DATA
CALENDAR/DAYS OF WEEK
CAL D WK
READ A RULER
FACTORS & MULTIPLIERS
Once the matrix was completed by the faculty and the information entered into the program, CMT generated the curriculum maps. Each map includes a listing of appropriate objectives on the left side. Each objective is identified by its code and abbreviated name. To the right of the list of objectives are six columns: one for each day of the week and for the week's total. Space is provided at the top of the map for identifying information to be supplied by the teacher completing the map. A row of data entry spaces is available for each objective; however, teachers record instructional time only for the objectives that they teach during the designated week. Figure 2 is a sample map for mathematics, grades 1–12, for Blackhawk.
Teacher Code: 29
Teacher Name: Richards
XTBL TR 10
After subject information is entered into CMT, teacher data can be entered. CMT can also be used to map time for administrators, members of child study teams such as psychologists and social workers, and special education students. The limitations of the software require that teachers be associated with a single grade. Middle, junior, and senior high school teachers need to be assigned a different code for each separate course mapped. Participants who are not specifically assigned to a grade can be assigned a different code in lieu of a grade, for example, psychologists can be placed in a grade identified as “PS” and social workers' grade can be identified as “SW.”
The sixty-three teachers involved in Blackhawk's mathematics project began mapping data for ninety-one separate classes during the second week of school. Shortly after they began mapping, they realized that their subject matrix needed to be modified. Although the original data was retained, only data from weeks ten on were used to generate horizontal and vertical reports. During the period from week 10 to week 32, 5,340 time records were put into the program. With regard to the regular entry of data from weekly maps, Fontaine states that “the most time-consuming part of the entry is looking up the teacher code. Nothing about the code can indicate who the teacher is for reasons of anonymity and confidentiality. Gaining familiarity with the information and the program led to a decrease in data entry time; but for the first two or three months, weekly data entries took about four hours.”
Once time data are entered into CMT: FOR TEACHERS it is possible to generate individual teacher reports and horizontal and vertical articulation reports. In Blackhawk, these reports indicate the amount of time teachers spent in each of the 91 mathematics classes on each of the 204 subjects/topics/skills/behaviors listed in the subject matrix. By March, Fontaine had entered more than 7,000 time records into the program.
All reports produced from September through February were vertical maps including summary data for mathematics courses in grades 1–12. Horizontal maps detailing data for all teachers of each course were not produced until March. The first computer printout of the horizontal maps for all twenty-six courses required approximately ten hours of printing time.
Horizontal maps include information about ranges and percentages that can be used to compare data for individual teachers. For example, a teacher's allocation of units of time and of percentages of total course time for specific objectives can be compared to the totals for all teachers and to minimum, maximum, and average allocations.
Report generation is simple. The CMT software allows you to display or print three different types of reports each with three options for periods covered: Individual Teacher Reports, Horizontal Articulation Reports, and Vertical Articulation Reports.
A Daily Individual Teacher report can be produced to indicate the:
A Weekly Individual Teacher Report can be produced to indicate:
An Individual Teacher Report for total time for all weeks can be run at the end of each week to reflect the project to date. It is a good way to verify progress. This report is most useful when you have completed the project, as it is then that it gives a composite picture. Figure 3 is an Individual Teacher Report for all weeks.
Horizontal Articulation Reports compare time on task spent by teachers in the same grade, level, or ability group. CMT generates two types of Horizontal Articulation Reports for each selection—one in time units, the other in percentages of total time.
The first Horizontal Articulation Report displays the total time on task, in minutes, for each teacher in a grade. It shows total time on task for the entire grade level; minimum, average, and maximum amount of time on task for each objective for individual classes within the grade level; and the range of time on task for each item in the study. Appendix A is a copy of the Blackhawk School District's 4th grade report for all eight 4th grade teachers by total times for ten weeks.
The second Horizontal Articulation Report converts this time into percentages. This enables educators to identify instructional priorities in common units for teachers in each grade. This information allows them to compare and contrast different teachers in the same grade. It can help to determine whether a textbook or test is suitable and appropriate for a grade level or ability group. Educators can use this information to determine whether there is linkage between the percentage of time allocated to a subject, topic, skill, or behavior and the percentage of the text dedicated to it. Appendix B is a copy of the percentage report for all eight 4th grade teachers for ten weeks.
For each of the two types of Horizontal Articulation Reports there are three sub-reports: Weekly, Average Time Per Week, and Total Time for All Weeks. The three reports provide data in minutes and percentages. Each includes minimum, average, maximum, and the range. The minimum time equals zero if time is not recorded or the smallest amount recorded by a teacher in that grade. The maximum time is the greatest amount of time recorded by any teacher in that grade. The average time is equal to the total time divided by the number of teachers in the grade. Range is the difference between the maximum and minimum amounts of time recorded, by teachers, for a subject, topic, skill, or behavior.
The Weekly Horizontal Articulation Report shows:
The Average Time Per Week Horizontal Articulation report determines the average times per week that each teacher and all teachers in a grade level spend on a topic, skill, or behavior. These reports are necessary for curriculum alignment.
The data can be used to determine:
The All Weeks (Total) Horizontal Articulation report provides the total time for each and all teachers in a chosen grade for the year.
Blackhawk's faculty also needed data on curriculum linkage between grades and courses within a school or schools within the district. The Vertical Articulation Reports provide time on task for a topic or activity through the grade and course sequence. The Vertical Articulation Reports give schematics for each subject, topic, skill, and behavior. From this, educators can determine whether time distribution trends for subjects, topics, skills, and behaviors are desirable.
The first Vertical Articulation Report displays the total time on task, in minutes, for each grade. It calculates total time on task for each grade, as well as minimum, average, and maximum amount of time on task and range for each item in the study. Appendix C is a portion of the vertical articulation report for Blackhawk's 26 courses, grades 1–12, by time.
The second Vertical Articulation Report converts this time into percentages. This enables the Mathematics Committee and mathematics teachers to identify instructional priorities for each grade level and course within a sequence. They could, for example, determine the emphasis placed on subtraction of whole numbers, fractions, and trigonometry properties in the mathematics program at each grade level. Appendix D is a portion of the vertical articulation report for Blackhawk's 26 courses, grades 1–12, by percentage.
Curriculum mapping data allow educators to determine whether a topic is completed in line with standards set by research and curricular guides. This triggers questions and provides the data to evaluate such critical factors as the realism of course expectations and whether time spent on a skill in earlier grades improves the performance on related tasks in later grades.
Similar to Horizontal Articulation Reports, there are three Vertical Articulation Reports: Weekly, Average Time Per Week, and Total Time for All Weeks. The three reports provide data in minutes and percentages. Each includes the minimum, average, maximum, and range for time on task. The minimum time equals zero if time is not recorded or the smallest amount recorded in every grade. The maximum time is the greatest amount of time recorded by any grade. The average time is equal to the total time recorded divided by the number of grades. The range is the difference between the minimum and maximum times recorded.
On the left side of the screen for the Weekly Vertical Articulation Report are the subject codes followed by subject names. Across the top of the screen are the grade levels. There are total, minimum, average, and maximum times for each topic, skill, and behavior.
These reports are useful for administrators and teachers and are used in a formative fashion because they show the:
The Average Time Per Week Vertical Articulation Report shows the average times per week all teachers in a grade level spend on a topic, skill, or behavior. These reports are necessary for curriculum alignment.
This data can be used to determine:
The All Weeks (Total) Vertical Articulation Report provides the total time spent on each task by all teachers.
Three-fourths of the way through its pilot year in the Blackhawk School District, curriculum mapping is receiving rave reviews from faculty. As a whole, the maps proved their potential for gauging the effectiveness of the written curriculum in focusing instruction. Horizontal articulation reports are demonstrating the degree of conformity and variance on objectives and topics among teachers of the same course. Vertical articulation reports are revealing duplications and gaps in instruction across grade levels.
Helen Arbutina and Mary Lou Cox, elementary teachers and members of the Mathematics Curriculum Review Committee, praise the effectiveness of curriculum mapping for enhancing the awareness of teachers about the written curriculum and about consistency in its delivery: “The daily mapping results have been returned to the committee members in an efficient, professional manner. We have been able to share these results with our peers. Teachers are beginning to become more aware of the amount of time devoted to specific content areas of the mathematics curriculum.”
Another elementary teacher and committee member, Jane Hetche, supports this assessment: “It has been a real learning experience to compare the various concepts that are important to each grade level. Weekly mapping increases our awareness of time and emphasis placed on all aspects of the math curriculum.”
For administrators Thomas and Hink, the primary benefit of mapping is its ability to enable professional educators to participate in meaningful discussions about the curriculum across grade levels and courses: “The primary benefit associated with the curriculum mapping project is the opportunity for professional staff members to create a dialogue that leads to an understanding and appreciation of what teachers at the various organizational levels are doing in a particular academic discipline. In simple terms, the staff talks the same language as they articulate the curriculum from grade to grade.”
[Note: Appendices A-D are not available for electronic dissemination.]
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