## Take Math, Take Charge

Algebra by Grade 8

Beginning with the 8th grade class in the 2010-11 school year, all students will be required to complete Algebra I by 8th grade and Algebra II in high school. In addition to biology they must also have a high school course in chemistry or physics. With the completion of mathematics at the Algebra II level, more students will have the skills for a wider range of job options and will increase the capability of Minnesota’s workforce. Clearly, algebra is a key content area of mathematics but geometry, statistics and other areas of mathematics are also critical to guarantee literacy. In addition, all content areas must be infused with the key mathematical habits of mind such as reasoning, strategic thinking, and perseverance to finding a solution.

The national standards for mathematics, delineated in Principles and Standards for School Mathematics were developed by the National Council of Teachers of Mathematics. The original standards were the first of its kind in any content area in 1990 and the revised standards in *Principles and Standards for School Mathematics in 2000 were en*dorsed by 15 professional associations that have mathematics as a critical component of their work. The national standards include standards and benchmarks that define the key components of learning in five areas: Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. Equally important are standards and benchmarks for the following five key mathematical processes: Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. “The standards outline an ambitious and comprehensive set of curriculum standards for all students. Standards are descriptions of what mathematics instruction should enable students to know and do – statements of what is valued for school mathematics education… The mathematical Content and Process Standards . . . are inextricably linked.” (*Principles and Standards for School Mathematics, p. 7). Recently the NCTM added Focal Points to complement the Principles and Standards for School Mathematics, indicating a few select concepts and skills that should be the core of instruction at each grade. (www.nctm.org).*

Other national reports have called for a comprehensive mathematics education that connects mathematical ideas and includes reasoning as a critical component of mathematics instruction. Foundations for Success, a report to determine what mathematics middle school students need, reinforces algebra as critical, but strongly cautions it must be taught in an age-appropriate way. Equally essential to middle school success is the inclusion of geometry, data and statistics, and reasoning in building a firm foundation for the study of mathematics in high school. Merely requiring algebra as taught in the past may only produce the results common in Minnesota ten to twenty years ago when only 20% of middle school students were enrolled in middle school algebra.

The Mathematical Association of America (MAA) calls for all students to have Quantitative Literacy, the ability to work with, analyze and make inferences from quantities in various ways, as essential to a well educated student and worker in this century. The American Diploma Project in its report, Ready or Not and Standards for Success, a report from the American Association of Universities both call for a high school education that includes a strong base in multiple content areas and includes reasoning and problem solving. Fundamentally, reasoning is what mathematicians do.

Foundational to all mathematical learning is the initial preparation all students receive in their beginning years of learning. The National Research Council has reviewed the main research on how children learn about mathematics and number and summarized it in two reports, Adding It Up and Helping Children Learn Mathematics (www.nap.edu). These reports found that mathematics is best learned when the following five strands, computation, concepts, reasoning, application, and strategic reasoning are integrated. In fact, they found that learning any one of the strands in isolation is harder than learning them in coordinated ways. Surprisingly, or perhaps not so surprisingly, these same five strands continue to be part of the definition of essential mathematics at the high school level.

Rather than define what students should learn by a course name, it may be more systemic to actually specify the mathematical skills students need. The above mentioned reports do this. In addition the Minnesota Standards have also defined what should be learned in the areas of 1) algebra, 2) geometry and measurement, 3) data analysis and probability, and 4) number and operation. Test specifications further define how students will be assessed in Minnesota to show the level of proficiency among Minnesota students at grades 3-8 and in high school. This year revision of these standards ought to continue specifying a comprehensive set of standards for mathematical literacy. These may be learned in individual courses or in integrated courses of study. The mathematics needed to create a stronger workface may best come from a definition of quantitative literacy that is inclusive of the multiple areas and processes of mathematics. Specifically detailing what mathematical skills and concepts are needed may make mathematical learning become more of a pump instead of a filter in increasing mathematical literacy among Minnesota students.