Maryland Collaborative for Teacher Preparation
Methods Group
Trends assignment: Mathematics and Science Education Focus
Authors: J. Randy McGinnis (UMCP) and Tad Watanabe (TSU)
with practicing elementary teacher participation by Evelyn Nicks, N. Forestville Elementary, and written contributions from Lois Williams (UMBC)
History of Scholarship:
A subset of the MCTP Methods Group, the Trends Group, was given the following task:

i. Develop a list of resources for the topic. Encompass both math and science/technology
Note: The topics given to the Trends Group to work on were objectives 2.1, 2.2, 2.3, 2.4 and 6.1 that were generated by the Methods Group.

ii. Develop a list....of how trends are alike/different in mathematics and science
iii. Develop a bank of strategies, moves, means for conveying the information to our preservice students
The Trends Group divided task i. into mathematics and science education sections. Tad Watanabe took leadership in preparing the mathematics education section; Randy McGinnis took leadership in science education section. Evelyn Nicks provided the authors with a practicing elementary teacher's perspective. Tasks ii. and iii. were collectively worked on. A first draft of the Trends Group document was presented to the Methods Group for review on July 25, 1994. Subsequent written feedback from Lois Williams was incorporated into the revision of task i., objective 2.1.
2.1 Have knowledge of the fact that there are differences in the level of mathematics and science performance and attitudes toward these subjects by geographic region, by economic condition, by gender and by race/ethnicity.
Mathematics Education Component:
The Mathematics Education community is keenly aware of the importance of the existing gaps in student achievement. The following articles discuss many issues related to mathematics learning of those groups that have traditionally been under-represented.
The following articles can be found in Teaching and Learning Mathematics in the 1990s: 1990 NCTM Yearbook (NCTM, 1990).
"Mathematics for All Americans" by Steen (pp.130-134)

"The Challenges of a Changing World for Mathematics Education" by Secada (pp.135-143)
"Teaching Mathematics: A Feminist Perspective" by Damarin (pp.144-151)
"African-American Students and the Promise of the Curriculum and Evaluation Standards" by Stiff (pp.152-158)

"Increasing the Achievement and Participation of Language Minority Students in Mathematics Education" by Cuevas (pp.159-165)

"Cultural Power and Defining of School Mathematics: A Case Study" by Donovan (pp.166-173)
Additional References:
"Nurturing At-Risk Youth in Math & Science: Curriculum
and Teaching Consideration" Randolf Tobias (1992)
"Opportunities, Achievement, and Choice: Women and Minority Students in Science and Mathematics" by Oakes. In Review of Research in Education, 16, 1990.
Establishing a Research Base fir Science Education: Challenges, Trends, and Recommendations (NSF, 1986)
Science Education Component:
In general, the prominent education reform documents advocate teacher education programs to provide all prospective science teachers with knowledge and experiences that prepare them to teach children of other cultures, races, and social classes. "Science for all Americans" (Science for all Americans,) "every student, every day, every science," (Scope, Sequence, and Coordination) are slogans in the documents that acknowledge student differences but advocate success and access in science for all. Standardized testing on both the national level (in particular NAEP) and on the local level (MSPAP) report science performance by student backgrounds. These data indicate that there are differences in the level of mathematics and science performance and attitudes toward these subjects by geographic region, by economic condition, by gender and by race/ethnicity.
Selected References:
Allen, G. G., & Seumptewa, O. (1988). The need for strengthening Native American science and mathematics education. Journal of College Science Teaching, 55, 364-369.
Jacobowitz, T. (1983). Relationship of sex, achievement, and science self-concept to the science career preferences of black students. Journal of Research in Science Teaching, 27(7), 621-628.
Kahle, J. (1982). Factors affecting minority participation and success in science. In R. E. Yager (Ed.), What research says to the science teacher: (Vol. 4, pp. 80-95) Washington, DC: National Science Teachers Association.
Oakes, J. (1990). Opportunities, achievement, and choice: Women and minority students in science and mathematics. IN C. B. Cazden (Ed.), Review of research in education: Volume 16 (pp. 153-221) Washington, DC: American Education Research Association.
Rakow, S.J. (1985). Minority students in science: Perspectives from the 1980-1982 National Assessment in Science. Urban Education, 20(1), 103-113.
Additional Comments (contributed by Lois Williams, UMBC):
[International achievement comparisons]
In mathematics, among 10 countries testing 9-year-olds in the 1991 International Assessment of Educational Progress, Americans ranked ninth; among 15 countries testing 13-year-olds, 11 ranked significantly higher. U.S. students did comparatively better in science: among 9-year-olds, only one country ranked significantly higher, although among 13-year-olds, six ranked higher.
[National achievement comparisons]
Among the 41 states and the District of Columbia which participated in the NAEP 1992 Trial State Assessment, Maryland 4th graders and 8th graders performed at the average mathematics proficiency level. District of Columbia students had the lowest average proficiency at both levels.
NAEP science results are not yet available by state, but results for a national sample of 10th graders on a 1990 science test are presented by sex, with males scoring higher than females; by race/ethnicity, with Asians scoring higher than Whites and Whites scoring higher than Hispanics or Blacks; by socioeconomic status...with high socioeconomic status students scoring higher than middle or low. Virtually all achievement test scores at any grade level in mathematics and science show a similar pattern of differences among subgroups, with the exception of sex where at lower grades, females often score higher than males.
[Maryland achievement comparisons]
Within Maryland, there are three measures of mathematics achievement and one of science achievement. These measures are reported by school system (23 counties and Baltimore City) in the annual Maryland School Performance Report, and by schools in separate school system reports. The Maryland Functional Testing Program tests basic competencies in reading, mathematics, writing, and citizenship, and functional test results are reported as percentages of 9th graders and 11th graders passing at the end of the year. A norm-referenced assessment, the Comprehensive Test of Basic Skills (CTBS/4), is given in grades 3, 5 and 8, and results reported as median percentiles for reading comprehension, language and mathematics. The Maryland School Performance Assessment Program (MSPAP) is a performance-based assessment in reading, mathematics, science and social studies given in grades 3, 5, and 8, and the results reported as the percent of students scoring at Satisfactory and Excellent levels.
Regional differences within Maryland are substantial. The state-wide average Functional Mathematics Test passing rate in 1992-1993 for 9th graders was 79 percent, while the rate for Baltimore City was 48 percent and for Howard County was 87 percent. For females, the rate was 80 percent. For males, the rate was 78 percent. The rate for White (not Hispanic origin) females was 90 percent, while the rate for African American males was 64 percent. The 1992-93 8th grade CTBS/4 mathematics median percentile for Maryland students was 49, for Baltimore City students was 26, and for Howard County students was 72. A Satisfactory score on the 1992 5th grade MSPAP science test was achieved by 34 percent of the students in Maryland, 10 percent in Baltimore City, and 54 percent in Howard County. Thirty-two percent of males achieved a Satisfactory score with the rate for White males being 42 percent and the rate for African American males being 11 percent. Mathematics and science achievement is inversely related to wealth per pupil in the area. Achievement is directly related to the percentage of students who are eligible for free and reduced price meals: 28 percent of the students in Maryland, 68 percent of students in Baltimore City, and 7 percent of students in Howard County are eligible.
Digest of Education Statistics 1993, U.S. Department of Education, Office of Educational Research and Improvement, National Center for Education Statistics.
State Indicators of Science and Mathematics Education 1993, Council of Chief State School Officers, State Education Assessment Center.
Maryland School Performance Report 1993, State and School Systems, Maryland State Department of Education.
2.2 Have knowledge of the fact that there is considerable public dissatisfaction with current levels of achievement in these subject areas.
The National Assessment of Educational Progress (NAEP) and The International Evaluation Assessment (IEA) results of American students' performance on standardized tests on mathematics and science have been widely reported. These data indicate that the performance of American students on standardized tests in mathematics and science is below desired outcomes both within the United States and in comparison with students in other countries. A Nation at Risk makes the argument that these data indicate our society is in grave danger of losing its preeminence in science and technological innovation unless there is dramatic improvement in students' performance in mathematics and science.
Selected References:
A Nation at Risk (1983)
IEA and NAEP reports
National Academies of Sciences and Engineering (1982)
National Science Board (1983)
Education Summit of 1990 reports in popular press
Underachieving Curriculum: Assessing U.S. School Mathematics from an International Perspectives (McKnight et al., 1987)
Everybody Counts (NRC,1983)
A World of Differences: An International Assessment of Mathematics and Science (1989)2.3 Can describe the current societal concerns about school mathematics and science and the mathematics and science education profession's responses (e.g., NCTM Curriculum, Teaching, and Assessment Standards, NSES National Science Education Standards, NSTA's Scope, Sequence, and Coordination Project, Project 2061) in terms of recommendations about curriculum and teaching practices (e.g., impact of technology on desired outcomes, increased opportunities for more students, the rationale for integrating subjects).
Mathematics Education Component:
The most influential document in the field of mathematics education have been the NCTM Standards series. These documents have clearly illustrated what mathematics should be taught, how it should be taught, how students' learning should be assessed, and how mathematics programs should be evaluated. Other organizations, such as Mathematical Association of America, have also published recommendations. However, they are in alignment with the NCTM's recommendations. MAA's focus has been at college level.
Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989)
Professional Standards for Teaching Mathematics (NCTM, 1991)
Assessment Standards (NCTM, Working Draft, 1994)

"Essential Mathematics for the 21st Century" National
Council of Supervisors of Mathematics (1988)
Core Curriculum (NCTM, 1991)
Algebra for Everyone
"Reshaping School Mathematics: A Philosophy and Framework for Curriculum" Mathematical Sciences Education Board & National Research Council (1990)
"Telecommunications as a Tool for Educational Reform: Implementing the NCTM Mathematics Standards" Report of a Conference of the Aspen Institute's Communications and Society Program (1991)
Science Education Component:
Three organizations are in the vanguard of reform in science education. They are the American Association for the Advancement of Science (Project 2061), the National Academy of Sciences, through its National Research Council (National Standards), and, to a lesser extend, the National Science Teachers Association (Scope, Sequence, and Coordination). A common goal promoted by these associations is that all students should become scientifically literate. Differences exist among the associations, however, in type and extent of the science content needed to achieve scientific literacy. A scientifically literate person is defined as being familiar with: the nature of science and how it is performed, the key components making up the body of scientific body of knowledge, the human contexts of science--including science's reciprocal development with technology. With this understanding about aspects of science, the scientifically literate person can then better participate in personal decision-making and in civic life.

Documents such as Science for All Americans, Benchmarks for Science Literacy, National Science Education Standards: An enhanced sampler, Scope, Sequence, and Coordination of Secondary School Science all advocate dramatic changes in the teaching of science. Primarily, large portions of content are suggested to be eliminated ("less is more") so that more emphasis can be placed on students' sense making, translating, and placing knowledge in a social, cultural, and historical context. Four aspects of good teaching described in the documents are:
* choosing worthwhile scientific tasks
* orchestrating classroom discourse
* placing an emphasis on the classroom environment
* recognizing a need to increase knowledge and beliefs about science
Implications for teaching science include:
*using "hands-on, minds-on" activities
*investigating a few questions in depth as opposed to "covering" vast amounts of science content in the abstract
*connecting school science with the everyday world of the student
*allowing students to share and test ideas with their classmates and beyond.

Summaries of documents:
National Science Education Standards: An enhanced sampler Draft (1993)
The National Science Education Standards project was started with funds from the U.S. Department of Education. In the spring of 1991, the President of the National Science Teachers Association wrote the Chair of the National Research Council (NRC) and requested that he convene and coordinate a process with the goal of creating science education standards, K-12. After much discussion, the NRC agreed to take the lead in this matter. In 1992, a Chair's Advisory Committee was formed, consisting of representatives of the National Science Teachers Association, The American Association for the Advancement of Science, American Association of Physics Teachers, American Chemical Society, Council of State Science Supervisors, Earth Science Education Coalition, and the National Association of Biology Teachers. This group participated in identifying and recruiting CO-Directors of the staff and volunteers to serve on an oversight committee and its three working groups, dealing with curriculum standards, teaching standards, and assessment standards. The outline for the standards is divided in three categories of grades (K-4), (5-8), and (9-12).
Project 2061: Benchmarks for Science Literacy (1993)
Benchmarks came about as a result of the success of Science For All Americans (1989). In that document, a set of adult science literacy goals were promulgated. In Benchmarks, a set of tools for meeting those goals is presented. These goals are envisioned being used to guide science educators who design K-12 curricula. Notably, Benchmarks integrates mathematics and technology with a consideration of science. The twelve categories of Benchmarks are:
* the nature of science
* the nature of mathematics
* the nature of technology
* the physical setting
* the living environment
* the human organism
* human society
* the designed world
* the mathematical world
* historical perspectives
* common themes
* habits of mind
Scope, Sequence, and Coordination (The Content Core) (1992)
This document was developed to guide science curricula designers. It was funded by both the Department of Education and the National Science Foundation. The primary innovation in curriculum design advocated in this document is to do away with the layered cake curriculum in the secondary school (defined as grades 6-12 in this document). Instead, a coherent science program that included some science from every discipline in every year is promoted.
In addition, Dimensions of Learning (Marzaw et al. 1993), has played a significant role locally.
2.4 Understand how changes in desired outcomes change the nature of assessment and how changes in assessment
impact teaching. Explain the rationale for authentic/performance assessment.

Mathematics Education Component:
The following documents address the rationales and/or needs for different types of assessment process in "reformed" mathematics classrooms. Some also include suggested assessment tasks.
NCTM Assessment Standards (Working Draft, 1994)
For Good Measure
Measuring What Counts: A Conceptual Guide for Mathematics Assessment (NRC, 1993)
Measuring Up (MSEB/NRC, 1993)
Mathematics Assessment: Myths, Models, Good Questions, and Practical Suggestions (Stenmark, 1991)
Assessment in the Mathematics Classroom: 1993 NCTM Yearbook
Science Education Component:
National Science Education Standards, Headline Summary, Feb. 1994
Assessment tasks focus on these aspects of science important for students to learn: ability to inquire, understand subject matter, use knowledge to solve problems. and communicate about scientific ideas.
Assessment is to give equal attention to the assessment of opportunity to learn as well as to student attainment. The design of the assessment process is determined by the intended use of the data obtained.
Aldridge, B. (1992). Project on Scope, Sequence, and Coordination: A new synthesis for improving science education. Journal of Science Education and Technology, 1(1), 13-21.
Advocates the use of compact-disc interactive video for individual students to be performance-assessed. System developed with a grant from the Department of Education.
Maryland State Performance Assessment Program
Hermann, J. L., Aschbacher, P.R., & Winters, L. (1992). A practical guide to alternative assessment. ASCD Publication.6.1 Know of professional organizations (NCTM, NSTA, MCTM, MAST), benefits of membership, use of professional
Mathematics Education Component:
Professional Science Education Organizations:
National Council of Teachers of Mathematics (NCTM)
Benefits of membership:
Annual national convention and several regional conventions.
Newsletter (NCTM News Bulletin, Student Math Notes)
Teaching Children Mathematics (9 issues, September - May, for pre-K and elementary grades)
Mathematics Teaching in the Middle School (4 issues, Sept., Nov., Feb., Apr., for middle grades)
Mathematics Teacher (9 issues, September - May, for secondary grades)
Journal for Research in Mathematics Education (5 issues, Nov., Jan., Mar., May, July)
Membership and dues (as of August 1994):
Students, $22.50.
Regular, $45.
Dues include subscription to one journal. Additional subscriptions are $15 each.
National Council of Teachers of Mathematics
1906 Association Drive
Reston, VA 22091-1593
Maryland Council of Teachers of Mathematics (MCTM)
Benefits of membership:
Annual meeting (usually held in October)
The Banneker Banner (3 issues - Fall, Winter, and Spring)
Membership and dues (as of August 1994)
Student, $5
Regular, $10
Maryland Council of Teachers of Mathematics
405 East Lake Avenue
Baltimore, MD 21212
School Science and Mathematics Association
Benefits of membership
Annual meeting
School Science and Mathematics (8 issues, Oct. - May)
Membership and dues:
Regular, $30.
School Science and Mathematics Association
Curriculum and Foundation
Bloomsburg University
400 East Second St.
Bloomsburg, PA 17815-1301
Women and Mathematics Education
Benefits of membership:
Resource Bibliography
Newsletter (3 issues: Fall, Winter, and Summer)
Membership and dues:
Students: $5
Regular: $10
Dues are due in April of each year.
Women and Mathematics Education
c/o SummerMath
Mt. Holyoke College
302 Shatuck Hall
South Hadley, MA 01075
Association for Women in Mathematics
Benefits of membership:
The Association was founded in 1971 in Boston, MA. The purpose of the association is to encourage women to study and to have active careers in the mathematical sciences. Equal opportunity and the equal treatment of women in the mathematical sciences are promoted.
Newsletter (bi-monthly)
Membership and dues:
Student: $8
Regular: $40
Dawn V. Wheeler
4114 Computer & Space Sciences Building
University of Maryland
College Park, MD 20742-2461
Science Education Component:
Professional Science Education Organizations:
National Science Teachers Association (NSTA)
Benefits of membership:
One national convention and three regional conventions
Newsletter (NSTA Reports!)
Journals (eleven issues per year)
Elementary Level: Science and Children
Middle School Level: Science Scope
Secondary: The Science Teacher
College: The Journal of College Science Teaching
Membership and dues (as of July 1994):
Student, $22 per year (one journal)
Regular, $52 per year (one journal)
Member Services Department
National Science Teachers Association
1840 Wilson Blvd.
Arlington, VA 22201-3000
Maryland Association of Science Teachers (MAST)
Benefits of membership:
Two conferences each year in Maryland (Fall and Spring; Spring conference is only for K - 8)
Four issues of the journal
The MAST Rapper
Membership and dues (as of July 1994):
Student rate: $3 per year
Regular: $10 per year (October 1 to September 30)
Karen Gurley
40 Trout Brook Circle
Reistertown, MD 21136
National Association for Research in Science Teaching (NARST)
Benefits of membership:
One national conference held each year (Alternates between meeting with AERA and NSTA).
Ten issues of the journal per year
The Journal of Research in Science Teaching
Membership and dues (as of July 1994):
Student (sponsored by member), $14 (no journal), $30 with journal
Regular, $74 per year
Dr. John Staver
Executive Secretary, NARST
Center for Science Education
Kansas State University
219 Bluemont Hall
Manhattan, KS 66506-5313
Association for Multicultural Science Education (AMSE)
Benefits of membership:
Meets annually with NSTA
Occasional Newsletter
The AMSE Newsletter
Membership and dues (as of July 1994):
$20 per year

Dr. Vallie Guthrie
North Carolina A&T University
Mathematics and Science Education Center
217 Marteena Hall
Greensboro, NC 27411
Science Association for Persons with Disabilities
Benefits of membership:
Newsletter (Good Newsletter)
Journal (one per year)
Journal of Science for Persons With Disabilities
Membership and dues (as of July 1994):
$10 per year
Science Association for Persons with Disabilities
P.O. Box 17411
Boulder, CO 80308-0411


1. More people are expected to enroll in more courses and achieve more in both fields.
2. More technology is expected to be used in both subjects
3. Instruction in both subjects should commence after teachers and students reflect on the student's prior knowledge. Both fields acknowledge that what students take away from an experience is heavily influenced by students' existing understandings, from formal and informal education. Studies of students' naive conceptions are a growing body of literature in both fields.
4. It is generally advocated that teachers in both fields should decrease time spent in telling their students facts while increasing the time for their students to investigate meaningful issues relevant to their contexts. Understanding and reasoning are stressed over rote memorization.
5. In both fields, American student achievement as evidenced on national and international tests has been viewed as less than desirable. There is a call to improve education to ensure the success of America in foreign business/trade competition.
6. In both fields, there is concern that underrepresented people (minorities and females) do less well than white males. The lack of underrepresented people as teachers in these fields is also a concern.
7. There is a concern that multiple choice, one and only one right answer tests convey an incorrect impression about learning. Thus alternative means of assessment, including performance-based assessments are gaining momentum.
8. It is perceived as acceptable by many in this culture to not do well in mathematics or science. It is less acceptable to admit to poor command in other disciplines, language or reading, for example.
9. There are influential new documents in both fields that define what ought to be taught, how it should be taught, and how it should be assessed.
10. The current reform is characterized by the notion that one can investigate and solve interesting problems in both fields prior to knowing the basic facts.
11. In both fields, the role of student motivation in learning as imperative is increasingly being acknowledged.
12. Technology has changed what is important in both fields as well as how some mathematics and science are done.
13. In both fields, there is acknowledgment that what is learned is inseparable from how it is learned.
14. In both fields, the importance of communication(writing, reading, listening, and talking) is stressed.
1. Science education reform primarily focuses on the notion of science literacy (consisting of a body of knowledge, processes, and personal decision-making) while mathematics education places more emphasis on problem solving and modeling.
2. Mathematics education consists of different topics defined in a logical system of thought; science education consists of competing fully developed disciplines that are somewhat connected by the process of doing science;
3. Science education places much emphasis on "hands-on, minds-on" experiences; mathematics education, while promoting "hands-on, minds-on" experiences, increasingly also places emphasis on discourse in the classroom as a vehicle for encouraging reasoning.
4. Mathematics is perceived as a basic subject in the elementary school; science is oftentimes relegated to a less prominent role.
5. Although both fields emphasize the importance of technology in instruction, mathematics educators may have to overcome a more substantial myth about the role of calculators in classroom.
6. "Less is more" is more often used in science education documents than in mathematics education documents.TASK III. BANK OF STRATEGIES, MOVES, MEANS TO PRESENT/TEACH THESE DATA TO OUR PROSPECTIVE MATHEMATICS/SCIENCE SPECIALIST TEACHERS.

Sample Formatted Lesson:
Title: Teacher Candidate Analysis of Reform Initiatives in Mathematics and Science Education
The purpose of this activity is to have MCTP teacher candidates analyze the reform initiatives in mathematics and science education by using selected portions of the original documents. Students should identify the central themes of each reform document and be able to contrast/compare themes within discipline (mathematics and science) and between disciplines. This activity is related to MCTP objectives: 2.2, 2.3, 2.4
MCTP teacher candidates will need access to copies of the major reform documents in mathematics and science education. These include: NCTM Curriculum, Teaching, and Assessment Standards, NSES National Science Education Standards, NSTA's Scope, Sequence, and Coordination Project, and Project 2061's Benchmarks. Students can read these documents (or selected portions of them) out of class before participating in cooperative learning groups in class to compare and contrast the documents. Students may report their analysis orally from informal notes or in a written essay.
Activities: Prospective teachers read portions of the major reform documents in mathematics and science education. In small groups they identify specific reform themes in each. They then discuss similarities/differences in the documents within and between disciplines in a large group discussion facilitated by the professor. In their portfolios each student is responsible for including a matrix that shows this analysis.
Key Questions: Ask the prospective teachers to envision how these reform documents provide insight into how mathematics and science education are perceived by a significant number of lay people. What implications do they see on how their mathematics and science instruction will be impacted by these documents?

Additional Ideas:
2. Prospective teachers pick a science topic and, as a field based assignment, interview diverse elementary/middle school students to see if they hold different views/interests of the topic that can be correlated with their different backgrounds (ethnic, gender, race, class). The professor facilitates a symposium in which the prospective teachers discuss their findings and grapple with the notions of stereotyping (to be avoided) and individualized instruction (to be the ideal). This activity is related to MCTP objective: 2.1
3. Prospective teachers select a science activity published prior to 1980 and teach it as directed to a small group of peers. They then deconstruct the activity in a small group activity to identify key components missing or not emphasized according to today's norms. They then re-teach the activity to another small group after they have edited it to be in harmony with today's norms. They then reflect on the experience by comparing/contrasting the teaching/learning aspects of each version. Variations of this activity is to do it as a text or achievement test comparison/contrast activity. Prospective teachers look at a science textbook, science activity, or standardized achievement test published prior to 1980 and then compare/contrast it with a post-1990 science text (TIMS or AIMS are good ones) or an achievement test. This activity is related to MCTP objective: 2.3
4. Compare and contrast different "reform" documents, e.g. NCSM "essential math" and NCTM Standards.
5. What would "Essential Mathematics for the 20th Century" have looked like? How would it be different from/similar to NCSM document?
6. Compare and contrast textbooks (pre-Standards vs. post-Standard).