Monday, January 4, 2010

Comparing State Math Standards

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.


Anonymous said...

Why not look to the top performing countries and what makes their system work. They tend to have teachers who are experts in academic content. Something that's missing in the US. Look at the schools of education where content is almost absent. The focus is on pedagogy.
The state, as in CA can only do so much. They set the standards high, compared to Maine and states like NH, if the schools refuse to adopt curriculum that aligns to high standards, what else can they do? That burden falls on the individual schools who choose fautlty or reform math curricula that leaves gaps in academic knowledge.

This is a good post, however just because the individual schools in CA are not rising to the level set for them by the state, doesn't mean the standards are flawed. In fact, they are some of the best in the country as you've indicated.

In Mass. they set high standards too, however they've managed to move their schools in the direction of educating their students to meeting those high standards.

Parents need to become more involved and pressure their school boards and administrators to do more to meet those standards.

The problem is, if your child is in NH or Maine, meeting those standards is the equivalent to meeting "F" rated standards (per NH)

So we are in the position of not only needing to focus on academic excellence in the schools, but having standards that are quality instead at the low level they are at today.

Pam Kenney said...

Thanks so much for the thoughtful response. As a matter of fact, I will be reading international standards from England, China, Belgium, Japan, Korea, Chinese Taipei, and Singapore before I review the Common Core Standards later this month.

Mary said...

Hi Pam,Look at Finland's as they lead or are close to lead regularly for years. They required preschool teachers to have masters in early childhood education. Teachers have advanced degrees and are paid (in their scheme of things which is also higher than ours) better. I haven't looked recently, they had national outcomes rather than curriculum mandates. The have amazing preschool programming but do not expect reading until age 7. I do not how different their math is BUT I would assume it is similar. I think we need to look beyond curriculum for lasting change. Prenatal support, neonatal and early childhood support, cultural beliefs about school & learning and the content area are so important. (Finland pays women to stay home with their babies... (but then they don't support every war that comes along). I think real success in America in any content area needs to be look at through many lenses... culture, family, school, political expectations). Micro-managing thru just curriculum has not been very successful for students even though it has been for publishing houses. Learning is more complex and more personal than that.
Good luck. I am glad to hear that you are involved in such an endeavor.

Pam Kenney said...

As usual, Mary, your comments are right on target, and I agree with them. I've been reading lately about recent research on the readiness of preschoolers' brains to grasp math concepts, much of which contradicts what was the prevailing view only a few years ago:

In other reading I've learned that many researchers are discovering that the ability to make letter-sound connections aren't at their maximum level until children are 10 or 11. I think delaying the teaching of reading is an excellent idea, and the schools I'm familiar with that haven't started formal reading instruction until age 7 believe it's the best approach.

Anonymous said...

Pam, GREAT POST! Thanks so much for your great research!

Below are some major differences between math education in Maine & Massachusetts:

-Massachusetts has taken seriously the recommendations of the National Mathematics Advisory Panel. The state continually improves, clarifies and revises the K-12 math curriculum frameworks. The Maine DOE left the Math Standards essentially unchanged for 10 years, even after receiving a “D” rating.

-Calculators – MA doesn’t allow calculators on any section of the state exam until the 7th grade. ME gives not only a calculator, but also a “100’s chart” and “multiplication table” on two of the three math sections. Vermont reports that the students do poorest on the “non-calculator” section of the NECAP.

-Massachusetts requires that the “Standard Algorithms” (i.e. Traditional Long Division) be taught. Maine does not.

-Massachusetts has a new math requirement for teacher licensing. Only 27% of the first group of 600 taking the exam passed it. The new licensing exam tested potential teachers on their knowledge of elementary school mathematics. This requirement will ensure that future elementary education teachers in Massachusetts add more mathematics preparation to their background before becoming licensed. According to Tom Scott, executive director of the Massachusetts Association of School Superintendents, “If you look at transcripts of some applicants for elementary school teaching positions, it’s possible you could see a transcript without anything math related. Someone could have last taken a math class in high school.” As a result of this new requirement, teacher colleges across the state have beefed up math requirements for graduation. Maine needs to do the same.

-Massachusetts tests in May, with results given in June. State assessments should be given in the late spring and not the fall (NECAP is administered in October, so 3rd graders are assessed at the 2nd grade level, etc). There should be few “Open Response” items; the majority should be multiple-choice, as in the Massachusetts assessment, with results of the multiple-choice items given to the schools by the beginning of June. What are parents to do if proficiency results aren’t given until five months after the child moved up a grade? In Massachusetts, parents have the summer to address any proficiency concerns.

Another thought is that some schools in the US are testing out “Elementary Math Only” teachers. I’m not sure if other countries break out subjects at the elementary level, but it would be interesting to research the results of this set-up.

I believe that ME & MA used to have close test scores (we might have even shared the same test). I’m not positive, but Maine might have even outscored Massachusetts in the past (it would be interesting to research). MA now has the highest test scores in the nation. This was not always the case. It would be wise to take a close look at the differences. I’d also love to see some schools in Maine consider a “no calculator” policy until at least the 4th grade. Schools do have the option to administer the NECAP without a calculator and multiplication table.

Pam, thanks again for all of your efforts!

Beth - mom to three

Anonymous said...

I believe in Finland they have "true school choice". Parents can put their children in any school which drives schools to perform at a higher level.

England has a National Curriculum. I would suggest signing up up for the daily news on Education around the world. You will read about the education in England and other parts of the world in addition to the US.

Parents are pulling their kids out of the England schools. With the national curriculum comes the political agenda. Less focus on academics, more focus on political agendas.

Something to think about with these Common Core Standards. National Standards lead to a National Test which leads to National Curriculum

Anonymous said...

Sorry, the Education News I suggested singing up for is from: