The Wisconsin Mathematics Academic Standards (content and performance) have been developed by a team of Wisconsin citizens including classroom teachers, professional educators, parents, business persons, and school board members. The team used various resource documents in its deliberations, including the Curriculum and Evaluation Standards for School Mathematics of the National Council of Teachers of Mathematics (NCTM), A Guide to Curriculum Planning in Mathematics of the Wisconsin Department of Public Instruction (DPI), and state standards and guidelines developed by other entities such as the New Standards Project, the National Institute for Educational Research in Japan, and the states of California, Colorado, Michigan, Oregon, and Virginia.
The Wisconsin Mathematics Standards are designed to be general guidelines which may be adopted or adapted by local school districts with cooperation and input from parents and other concerned citizens. They are not meant to be a full curriculum nor a prescription for instructional practice carried out from week-to-week in classrooms. They are important goals for ALL students from which individual schools can build a complete curriculum specific to their district's and children's needs.
The content of these standards reflects the shift in mathematical emphasis necessitated by technological advances in an information society. Some topics in mathematics (i.e., estimation, place value) have become more important and several new areas in mathematics (i.e., fractals, predictive statistics) have developed. The understanding of mathematical concepts has become imperative for every citizen as everyday functions become more mathematically complex and as low-skill jobs become nonexistent.
Mathematics instruction must, therefore, be made accessible, understandable, and meaningful for all students. Access includes:
- learning experiences that enable students to acquire and build knowledge and skills
- different instructor roles that use a variety of teaching techniques, adapting them as appropriate for different purposes of instruction and students' needs
- adaptive learning environments so that all students achieve success, and
- servicing all students, including populations previously sometimes under-served, i.e., special education, limited English proficient (LEP), etc.
Likewise, mathematics assessment must address the understanding of all students (as assessed with accommodations which match instructional methodologies) so that mathematics instruction can be evaluated and improved for all students.
Not all students in secondary school elect to pursue "college preparatory" courses. Therefore, the following content and performance standards do not reflect the content of those higher level courses. Rather, they reflect the content of a core mathematical experience that ALL students should encounter, regardless of what mathematics courses they choose.
These standards are intended as points of reference, not limitations. Some students will accomplish much more than these standards envision; yet the standards set the targets for what all students should be challenged, encouraged, and expected to achieve.
Goals and Instructional Practice
Classroom practice geared to the attainment of the Wisconsin Standards should be aimed at creating a community of learners and scholars, a place where the teachers and students actively investigate and discuss mathematical ideas, using a wide variety of tools, materials, and technology. Classes should engage students in more high-level mathematical thought and emphasize conceptual understanding, more so than in the past.
Important goals for students are:
- to develop a deep conceptual understanding in order to make sense of mathematics (Students need to know not only how to apply skills and knowledge, but also when to apply them and why they are being applied.)
- to master specific knowledge necessary for its application to real problems, for the study of related subject matter, and for continued study in mathematics
- to learn and view mathematics as a way of thinking about and interpreting the world around them
- to recognize that mathematics is a creative part of human culture in much the same way as music or fine art
Mathematics should be viewed as a unified whole made up of connected, big ideas rather than as a disjointed collection of meaningless, abstract ideas and skills. Learning is easier when students see the connections between various concepts and procedures, and between the various branches of mathematics. Students should also be aware of the connections between, and applications of, mathematics and other disciplines, such as the sciences, art, music, business, medicine, and government.
Mathematics is important because its concepts and procedures can be applied to the solution of problems of varying kinds and complexity. Solving problems challenges students to apply their conceptual understanding in a new or complex situation, to exercise their basic skills, and to see mathematics as a way of finding answers to many of the problems they encounter both within and outside the classroom. Students grow in their ability and persistence in problem solving through extensive classroom experience in posing, formulating, and solving problems at a variety of levels of difficulty and at every level in their mathematical development.
The ability to reason is such a vital part of mathematical behavior that it is safe to assert that mathematics cannot be done without it. At all levels, students should be able to provide a reason why they have chosen to apply a particular skill or concept, or why that skill works the way it does. Further, students should habitually check their results and conclusions for their reasonableness; that is, "does this make sense?" Proportional and spatial reasoning are specific kinds of reasoning that all students should have at their disposal. And, finally, it is important that all students should be able to apply the logical reasoning skills of induction and deduction to make, test, and evaluate mathematical conjectures, to justify steps in mathematical procedures, and to determine whether conclusions are valid by analyzing an argument.
Whether working alone, or as part of a team, students must be able to communicate their thinking to others. Students must learn not only the signs, symbols and specialized terms of mathematics, but also how to use this mathematical language in oral, symbolic, and written communication. These communication skills become even more relevant when students leave their classroom world for the world of work.
Calculators, computers, spreadsheets, graphing utilities and other forms of electronic information technology are now standard tools for mathematical problem solving in science, engineering, business, medicine, government, and finance. Thus, the use of technology must be an integral part of teaching and learning mathematics. Such use should aim at enhancing conceptual understanding and problem solving skills. However, the tools of technology are not a substitute for proficiency in basic computational skills.
In the text that follows, terms with an asterisk (*) are defined
and/or exemplified in the Glossary of Terms.