State Making Big Changes in How Students Will Learn Math

While doing some recent research on the skills and knowledge students will need to succeed in the changing job market, I repeatedly encountered this fact: Good math skills are essential for most of the jobs worth having.

The state Department of Education is aware of this too, and is completely overhauling the way public schools teach mathematics.

The overhaul is based on a set of reforms recently adopted by the State Board of Education. The reforms are described in a publication titled “Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve.”

It is, in short, the curriculum bible math teachers must follow.

The state’s aim is lofty: It seeks to “change what mathematics we teach, how we teach it and to whom” by designing, from scratch, curriculum and methods of teaching and assessment.

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Here is a rundown of the major changes mandated for California schools:

First, the very stuff that is taught has been revised. This “mathematical content” now consists of eight categories of knowledge known as strands. They are: number, measurement, geometry, patterns and functions, statistics and probability, logic and language, algebra, and discrete mathematics (a rather nebulous new category that includes, among other things, set theory and game theory).

Each strand will be included in math study at all grades, from kindergarten through high school; the theory is that integrating the strands helps students see connections among them. Previously, certain strands, such as geometry and algebra, were taught in bulk in a specific grade.

Some new ways of thinking about math will also be used, or applied to areas of math where they were not often before.

Gone are the days of just “finding the sum” or “solving for x.” Now students must classify, plan, analyze, conjecture, design, evaluate, investigate, model and verify, infer, hypothesize and synthesize.

The material is also organized differently, into large chunks called “units.” This means large mathematical concepts can be taught and learned in entirety, instead of broken up into isolated bits. It also allows several similar strands to be grouped and related.

For example, a high school class might spend several weeks on a unit built around the theme of growth and decay, during which the students would calculate the half-life of various radioactive substances. The strands employed along the way would include algebra, patterns and functions, statistics and arithmetic.

The kinds of assignments suggested in the framework also differ considerably from traditional math work.

“Investigations,” for example, are larger than traditional math assignments, and present realistic problems to solve. Students may need several days or even weeks to complete an investigation.

A class, for example, might be given the task of preparing a water-rationing plan for a city. Along the way, the students would have to figure out how much water is needed for a year, how much is available, how much additional water could be anticipated under normal weather conditions, and so on.

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The curriculum also emphasizes a variety of instructional techniques--short exercises, group tasks, maintaining portfolios of work, building models and the large-scale investigations.

There will also be more communication among students about their math work. Instead of turning in written homework and moving on to the next assignment, math students will make oral presentations, write paragraphs and essays, and participate in class or small-group discussions about the material.

Math teachers will undergo some changes too.

The framework outlines a number of steps that teachers must take in order to carry out the reforms.

Teachers will need additional training in a number of areas--including math concepts themselves, since many will be teaching concepts that were not featured during their own school years.

That means that time is needed, above all; time, for example, to attend professional meetings and conferences, and meet with outside consultants to learn and share new methods.

Math departments will need time to compare, evaluate and select new strategies and materials.

And in the classroom, there will somehow have to be more time for teachers to work individually with students and review their work.

Teachers will have to make an even more sweeping change: how they operate in the classroom.

Lecturing and other monopolizing modes of instruction won’t do anymore. Teachers must now adopt a more Socratic method in which they guide and facilitate, helping students navigate thought processes and discover answers for themselves.

More tools of math learning are also needed. That includes everything from blocks and other “manipulatives,” to compasses and computers.

Better textbooks are also crucial. It is hard to guess when all of these reforms will be in place throughout California’s public schools. It depends largely on the amount of money, organizational time and other resources whose availability varies from school to school.

But the authors of the framework offer a fairly optimistic estimate: by the middle of this decade.