MCTM Position Paper

Position Statement and Answers to Frequently Asked Questions about Standards-based Mathematics Programs

EXECUTIVE SUMMARY

POSITION STATEMENT: The Minnesota Council of Teachers of Mathematics supports efforts of Minnesota schools and districts to implement standards-based mathematics programs.

EXECUTIVE SUMMARY OF ANSWERS TO FREQUENTLY ASKED QUESTIONS ABOUT STANDARDS-BASED MATHEMATICS PROGRAMS:

Minnesota Council of Teachers of Mathematics (MCTM)

MCTM is the professional organization for teachers of mathematics in Minnesota schools. It is dedicated to helping teachers help all students learn mathematics. The Council has published a paper in support of Standards-based mathematics programs, of which this is an Executive Summary.

 

Standards-based Mathematics Programs

Standards-based mathematics programs are those with the following characteristics:

• Comprehensive. They are based on the broad content of the national standards at each grade level: Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. They also incorporate the important processes of mathematics: Problem Solving, Reasoning and Proof, Communication, Connections, and Representation.
• Coherent. They are woven together as a whole, with ideas connecting to each other. They are not repetitive, and the sequence from one grade to the next gives students the preparation they need for the next learning step.
• Depth. Important and pivotal ‘big ideas’ are developed in increasing depth as students mature.
• Sense-making . They have a goal of guiding students to learn mathematics with understanding, enabling them to remember the ideas, rather than viewing mathematics as a set of unrelated symbols, rules, formulas and definitions.
• Engaging. They provide challenge to all students intellectually and actively involve them in "doing" mathematics. This enables all students to both participate and grow in learning.
• Motivating. They teach mathematics through realistic situations and applications, giving both an understandable approach and a reason to learn the mathematics.

(Definition adapted from "Standards-Based Mathematics: A Phrase in Search of a Definition", Trafton, Reys, and Wasman, Phi Delta Kappan, November, 2001).

Need for Change

Minnesota students have learned well up to now. However, for the future, more students need to learn mathematics, and those who have been reasonably successful need to learn even more for tomorrow’s world. In other words, the reasons we need to change relate to who learns mathematics, why more students need more mathematics, and what the content of that mathematics should be.

 

Differences between Standards-based programs and non-Standards-based programs

Though non-standards-based programs are not all alike, and each has both strengths and weaknesses, generally they are different in precisely those elements that characterize standards-based programs.

• Comprehensive. Elementary programs not based on standards emphasize number skills and procedures at the expense of geometry, measurement, and introductory probability and statistics, while non-standards-based middle and high school programs emphasize rote learning of skills and procedures at the expense of conceptual understanding and problem-solving.
• Coherent. In some non-standards-based programs, there is little connection from one grade or year to the next; in others, almost everything in one grade is simply a repetition of the previous grade, with little or no increase in depth.

• Depth. Non-standards-based programs are often characterized more by superficiality than by depth and intensity, with many topics given a shallow treatment in a short period of time.
• Sense-making. Non-standards-based programs often try to induce learning based only on the authority of the teacher and the textbook, treating mathematics as a collection of unconnected ideas, rather than fostering learning as an activity that makes sense.
• Engaging. In non-standards-based programs students are passive recipients of instruction, generally uninterested in learning mathematics, since they are not actively engaged in their learning, and the mathematics is not purposefully connected to their previous learning experiences.
• Motivating. Non-standards-based programs often do not help students to want to learn mathematics, since they do not communicate practical reasons for learning mathematics or demonstrate its usefulness.

The Current Situation in Minnesota

Many Minnesota students currently perform well. But many do not. In order for all students to participate fully in tomorrow’s workplace, they will need stronger mathematics skills, not just the basics, but also the ability to solve problems using quantitative reasoning. There is ample evidence that it is possible for virtually all students to successfully learn important and challenging mathematics. More than half of the students in the state are in schools using standards-based programs in mathematics.

 

Summary

MCTM is affiliated with the National Council of Teachers of Mathematics, which published the first national standards document in 1989, and issued an updated edition, Principles and Standards for School Mathematics (PSSM), in 2000. The intent of standards-based mathematics programs is to support teachers in their efforts to implement high standards for all students.

The mathematics education community, locally and nationally, sees a standards-based approach as having the best potential for benefiting all students. These programs will vastly increase the percentage of students taking three or more years of high school mathematics and will expand the domain of mathematics studied to include probability and statistics and topics from discrete mathematics along with algebra and geometry. In addition, the teaching approaches used are more consistent with the nature of human learning, so increased levels of achievement are to be expected. Large scale student achievement data currently being collected will provide evidence of the efficacy of a standards-based approach.

For further information:

For a copy of the full paper, please contact MCTM, P. O. Box 289, Wayzata, MN 55391 or tmuchlinski@earthlink.net