By Pam Kenney
Beginning this month I will be part of a group that will review the K-12 Common Core Math Standards. The standards come from the Common Core State Standards Initiative, “a state-led effort coordinated by the National Governors Association Center for Best Practices and the Council of Chief School State Officers.” Their purpose is to delineate the knowledge and skills students should acquire to succeed in both college and workforce training programs. Rigorous content and the application of knowledge through high-order skills, international benchmarks, and an insistence on evidence- and/or research-based criteria are their hallmarks.
To prepare for my role in the review process, I have spent many hours the past three weeks reading and thinking about the K-8 math standards from several states. To date, I’ve pored over standards from Massachusetts, California, Indiana, Washington, and Maine. I chose Massachusetts because it has had the highest NAEP fourth and eighth grade math scores in the nation for the last several years, Maine because it’s my home state, and the others because they were recommended to me as examples of states with particularly strong standards. As I read the state documents, I compared the broad strands that organize their mathematical content, the concepts under each strand, and the more specific skills that guide day-to-day classroom instruction.
All the states have basically the same strands through the eighth grade, although they may be grouped in different ways. The five strands in the Massachusetts document are representative: Number Sense and Operations; Patterns, Relations, and Algebra; Geometry; Measurement; and Data Analysis, Statistics, and Probability. The concepts related to the strands are similar, too. For example, the first concept listed under the strand “Number Sense” in California’s Grade Two standards is “Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000.” All the state standards I read had a similar concept.
The final and most detailed level of the states’ K-8 standards encompasses the specific skills that students must acquire over a one- or two-year period. And it is here that significant differences among the states appear. Some states write their standards using verbs such as “count’, “identify”, “know”, and “compare”, which allow the standards to be measured objectively. Others employ “understand” and “use.” How states teach addition, subtraction, multiplication, and division facts under the “Number Sense and Operations” strand is particularly noteworthy. In Massachusetts, California, Indiana, and Washington students are required to memorize facts through 10 or 12. In Maine, fact mastery is not required by its Maine Learning Results’ standards. In Maine, students learn a variety of methods to solve addition, subtraction, multiplication, and division problems, and the use of standard algorithms is not mandated. In the other state standards I read, children must learn standard algorithms, although several methods for solving problems are taught, too.
The use of technology differs among the states, also. In Maine, for example, calculators are an integral part of elementary school math instruction, and students can use them daily to solve problems as well as on standardized tests. In other states, such as Massachusetts, students “learn how to perform thoroughly the basic arithmetic operations independent of the use of a calculator.” In addition, the fourth and sixth grade state assessments in Massachusetts do not allow the use of calculators.
Overall, I found significant differences among the state standards I read. Maine is intensely focused on its students acquiring a thorough understanding of concepts and procedures, so focused that it allows technology to compensate for the absence of basic fact mastery. Massachusetts, California, Indiana, and Washington have math standards that offer an excellent balance between understanding concepts and fluent computation. Massachusetts has the highest test scores in the nation. Maine’s math scores, though, are higher than California’s, Indiana’s, and Washington’s.
I’d love to be able to write that I’ve drawn some far-reaching conclusions from my reading of the five different state standards. I can’t do that, but I have decided that balanced standards will help our nation produce better math students in the future than we are producing today. Standards that are clear, detailed, rigorous, and measurable and that require fluency in basic computational skills, an understanding of mathematical concepts, and the acquisition of problem-solving skills that focus on reasoning, communicating, and connecting are what we should strive for. As I review the K-12 Common Core Math Standards, that’s what I’ll be looking for.