It is our objective that these standards be implemented in such a manner that assures high student achievement thereby enabling Connecticut students to enter the ranks of the highest performing U.S. states and ultimately be competitive with their international peers in the A+ countries.

 CT Coalition Policy Briefing

Developing World Class Students through World Class Mathematics Standards:  Do Connecticut’s Standards, Students, and Teaching Measure Up?

Introduction             Students who graduate from Connecticut high schools need to be well grounded in the mathematics that will elevate them to being among the best in the United States and eventually to being among the best in the world—a goal we have not yet reached.

·         Connecticut needs world class standards to support the state economy and prepare future citizens

·         Knowing and understanding mathematics is a key competency for a highly qualified workforce and citizenry

·         To be effective, standards must be part of a world class system, which also includes textbooks and other learning materials, instruction, assessments, preparation of teachers, and ongoing professional development for practicing teachers—all aligned with higher standards

Connecticut needs world class standards in mathematics if the state is to prepare today’s students to be tomorrow’s skilled workers in a global economy.

To be world class, standards must:

•       Include important mathematics critical to a 21st Century economy

•       Integrate skills, concepts, and applications

•       Be focused and coherent with a small number of attainable topics for each grade

•       Be taught well by knowledgeable and effective teachers

•       Be embedded in a world class system that aligns assessment,

instruction, textbooks and other learning materials

It is the position of CT Coalition⁴ World Class Math that every student should study rigorous, internationally benchmarked mathematics throughout K-12.

How can we               There is no international definition of high quality mathematics
define world              standards for students. However, it makes sense to examine the

class                          goals for learning and the system for delivery of that learning in those

mathematics              countries whose students demonstrate outstanding performance on

standards?                             international assessments, especially those countries that have been consistently high-performing over time.  Such countries include Singapore, Japan, Korea, Finland, the Netherlands, and the Czech Republic.

                                  Based on this examination, we can say that world class standards meet the following set of criteria:

•       Are focused, coherent progression of mathematics learning

•       Specify a small number of attainable topics at each grade with topics that can be taught effectively at that grade

•       Reflect guidelines such as the Final Report of the National Mathematics Advisory Panel, Critical Foundations of Algebra and Benchmarks for the Critical Foundations and the National Council of Teachers of Mathematics’ document, and the Curriculum Focal Points, which outlines 3 big ideas at each grade, PK-8

•       Are specific enough to guide development of rich assessments, selection of textbooks, preparation of pre-service teachers, and ongoing renewal of licensed teachers

•       Provide a carefully sequenced progression of learning for students K-12, to help all to reach the required level of attainment, in particular algebra by the end of 8^th grade, and at least 3 credits of high school level mathematics including algebra II, geometry, statistics and probability

•       Incorporate a balance of skills, processes, and concepts, leading to understanding, retention, and the ability to apply learning

How can we tell         Currently Connecticut students are not performing as well as they could or

if we currently                       should be.  A look at the evidence supports this view.

have world

class standards?        Our existing state mathematics standards enable many students to achieve just slightly above the national average for students in most other states. When we compare Connecticut students scoring at or above proficient on NAEP with those deemed proficient on state tests such as CMT and CAPTS, a much lower proficiency standard is revealed. (Achieve, American Diploma Project)  Furthermore, the overall performance of state students as a whole disguises the fact that some groups of Connecticut students perform well below the rest, on many measures. Students of color and low-income students take fewer high school mathematics courses; perform less well on assessments, complete high school at lower rates, and complete college at lower rates (National Assessment of Educational Progress, 2007).

                                  Out of 30 industrialized countries participating in the OECD’s Programme for International Student Assessment (PISA) in 2006, the U.S. ranked 25^th in math and 21^st in science achievement.  The performance gap between the United States and top-performing nations is vast:  American students lag about a full year behind peers in the countries that perform best in mathematics.  Even our “best and brightest” cannot compete with excellent students elsewhere.  According to the OECD, “the United States does not just have more students performing badly—it also has many fewer students performing well.”  Our best math students performed worse than the best math students in 22 other OECD nations.

                                  When the performance of American students is compared with more developed nations considered our economic competitors, the U.S. performance on the Trends in International Mathematics and Science Study (TIMSS) is similar to our performance on PISA- disappointing.  In an analysis by the American Institutes for Research of a group of industrialized nations participating in both TIMSS and PISA, U.S. students consistently performed below average across international assessments. 

“U.S. performance is below the 12-country average at both low- and high-skill levels and low and high-levels of item difficulty.”

To summarize where Connecticut is now:

•       NAEP – slightly above the national average*see "information and links", 2008 NAEP graph

•       ACT – slightly above the national average

•       SAT – slightly above the national average

•       Achievement data masks large gaps between segments of student population

•       Lower performing students are in segments of the Connecticut population that are growing fastest

•       These same students – students of color and low income students –complete high school at lower rates than other students, and complete college at very low rates

American education has not adequately responded to these new challenges.  The United States is falling behind other countries in a resource that matters most in the new global economy:  human capital.  By 2012, 85% of Connecticut’s fastest growing jobs will require some college or training beyond high school, including a projected 25,000 jobs in the health care field.  Such statistics point to a future shortage of the types of workers needed for a strong Connecticut economy, one in which our competition is not workers in Massachusetts or New York, but workers in Singapore or Korea.

Why do we                              World class standards are necessary for preparing Connecticut

need world                              students for the 21^st Century workplace and citizenship.  Student

class standards                        data from the U.S. Department of Education repeatedly

in                                             indicates that the single strongest predictor of completion of a

mathematics?                          bachelor’s degree is the highest level of mathematics completed in high school. Completing a course beyond advanced algebra, such as pre-calculus or statistics, more than doubles the chance that a student entering college will complete a degree (Adelman, 1999).  Furthermore, the number of college and university mathematics courses taken is the single greatest predictor of lifetime earning potential, cutting across gender and other demographic groups (Adelman, 1994).

Through the efforts of the Connecticut Department of Education, Connecticut is ratcheting up the expectations for course-taking in mathematics, particularly for higher levels of mathematics in high school. However, just taking courses, and even passing them, does not necessarily insure understanding. Consider the following.  Results for the 2008 ACT college admission test show that many Connecticut high school seniors are “appallingly” unprepared for college-level work. Thus the further challenge is to prepare the system of K-12 education to offer all students not just the challenge, but also the support needed to accomplish the new requirements, and to meet the goals of the standards with understanding.

What                                        Every student, by no later than eighth grade, should be prepared to  mathematics is                      succeed in an authentic algebra course as identified in the
included in                              National Mathematics Advisory Panel’s March 13, 2008, report.
world class                              Robert Moses, former civil rights worker and Director of The
standards?                               Algebra Project, declares that algebra is the new civil right, stating, “I

believe that the absence of math literacy in urban and rural communities throughout this country is an issue as urgent as the lack of registered Black voters in Mississippi was in 1961” (Moses, 2001).

Algebra is critically important since it is the gateway to the areas of mathematics most needed for understanding our quantitative world. With a solid foundation in algebra, students can—and should—study topics such as geometry (the mathematics of shape), statistics (the mathematics of data), discrete mathematics (the mathematics of computers), and operations research (the mathematics of business and industry).

But mathematical education is not only about topics, it also is about reasoning. The mathematics needed for a technological workplace usually involves using a broad set of mathematical tools, in messy and often ill-defined applications. This requires strong reasoning ability, as well as problem solving and critical thinking skills.

The challenge is immense. We are adding to, not subtracting from, the list of skills our students and teachers must have. Algebra is important, not as an end, but as a means. Our students must be ready to use mathematics in their careers. To do so, they must have both the foundational skills and the desire and ability to apply mathematics to the questions around them.

What kind of                            In addition to making changes in standards and course-taking
teaching is                               expectations for all students, teachers must teach effective
necessary for                           mathematics from the earliest grades. At present instruction is
students to                               sometimes characterized by endless repetition through spiraling, which
meet world                              is often no more effective the sixth time than it was the first.
class                                       

standards?                               All students deserve high quality instruction. Elementary teachers are giving students the foundation to be ready for middle school algebra and challenging high school courses. It may be time to reconsider our expectations that elementary teachers be generalists and teach multiple subjects, leaving little time for preparing to teach new ideas in mathematics or other areas. Several presidents of the National Council of Teachers of Mathematics have called for serious consideration of having elementary and middle grade teachers specialize in teaching mathematics (NCTM, 2006, 2003). Intermediate and middle grade teachers who show interest and ability in teaching mathematics might focus on teaching mathematics to multiple classes, either at one grade, or over several grades or serve as coaches to teachers.

Nationally, most elementary teachers have minimal preparation in mathematics at the college/university level; in fact, nationally only 7% of elementary teachers majored or minored in mathematics education (NCTM, 2000). Requirements for licensure are usually one or two courses in mathematics. In addition, since we expect most elementary teachers to teach classes in many subjects each day, they do not have sufficient time to prepare for the demands required to give all students the necessary foundation for algebra in eighth grade. Models that allow specialization, where fewer teachers are responsible for multiple classes in mathematics, show promise. In addition they are pragmatic in focusing professional development dollars on a smaller number of teachers rather than attempting to train all elementary teachers in all academic subjects over multiple years.   

Connecticut elementary teacher education programs and licensure tests should cover the topics in the Critical Foundations of Algebra; and for middle school teachers, the Critical Foundations of Algebra and all of the Major Topics of School Algebra as identified in the National Mathematics Advisory Panel’s March 13^th, 2008 report.

What does a                            The primary component for a system of effective learning is a
world class                              guaranteed and viable curriculum. This means having a K-12
system look                              course of study that gives all students the opportunity to learn
like?                                        mathematics that prepares them for college and career with a focused                                                       number of cohesive and effectively taught topics each year.          

Such a system requires all its parts to be in alignment. This means that the standards be supported by instructional practices that enable all students to achieve the standards. This in turn requires that all teachers understand and be prepared to deliver such instruction. It also requires that all instructional materials, including textbooks, support and align with the standards. In a world class system, assessment must also be aligned with the standards, not only in terms of topics, but by having a balance of

skills, concepts, and applications, demanding that students demonstrate reasoning, problem solving, and critical thinking. Assessments must be objective measures that are internationally benchmarked.  Finally, teachers at all levels in a world class system must participate in ongoing reflection and renewal in order to prepare them to support powerful learning for all students.

Conclusion

With all these components in place – standards that are focused, coherent, with a small number of attainable topics at each grade, teachers who are well prepared and effective in their instructional practices, and an entire system of standards, textbooks, tests, teacher preparation, and ongoing professional development that is aligned – Connecticut will produce students who have embarked on a path to rise to world class status and achievement and graduates who will be ready to compete in a global economy.

Many questions remain.  Among them:

·         Will Connecticut’s mathematics standards contain the focus and content needed to produce world class achievement in mathematics?

·         Since standards alone are not enough, will ongoing professional development that helps instruction deepen and guarantee that all students achieve the standards be provided for all teachers?

·         If algebra is a means and not an end to world class achievement, will we provide students with a K-12 and beyond education in mathematics that imposes greater rigor and preparation for career and college?

The challenge ahead is certainly one that Connecticut can meet, with the collaboration of state education agencies, PreK-20 educational systems, parents and other stakeholders.  The Connecticut Coalition⁴ World Class Math stands ready to help meet this challenge.

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