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Kentucky: Council on Postsecondary Education

How To Reduce the Need For Postsecondary Remediation in Mathematics

The Mathematics Alignment Team endorses the competencies outlined in the Kentucky Department of Education Program of Studies in mathematics, the KDE Grade 11 Mathematics Core Content, and the recommendations of the KDE Algebra II Task Force (9K PDF) as an initial list of required competencies.

For P-12 Educators
  1. Prepare all students to begin studying Algebra I no later than ninth grade.
  2. Require all students to take a rigorous mathematics course every year they are in high school. Taking mathematics every year of high school reinforces and helps students remember what they have learned. For many students, it is better to spread the current three years of mathematics over four years to learn concepts more thoroughly. New courses are needed.
  3. Distribute to high school teachers the description of Algebra II, part of the Pre-College Curriculum, prepared by the KDE Algebra II Task Force (9K PDF). Include it in the KDE Program of Studies. High school teachers need to know what they are expected to teach, high school students need to know what they are expected to learn, and postsecondary faculty need to know what competencies courses listed on a high school transcript indicate.
  4. Use the Kentucky Early Mathematics Testing Program before grade twelve (and ideally before grade eleven) to identify and remedy deficiencies before college entrance.
  5. Provide ongoing mathematics-based professional development for teachers. Support it through the Teachers' Professional Growth Fund.
  6. Teach mathematics using a variety of techniques to reach students with different learning styles and to develop a deep level of understanding. Use real problems to highlight the relevance of mathematics.
For Postsecondary Institutions
  1. Offer a range of general education mathematics courses, including alternatives to the calculus preparatory sequence, to address the needs of all students, regardless of majors.
  2. Teach mathematics using a variety of techniques to reach students with different learning styles and to develop a deep level of understanding. Use real problems to highlight the relevance of mathematics.
  3. Provide courses and other ongoing mathematics-based professional development opportunities for P-12 teachers, at times and in places and ways that ensure access.
  4. Provide incentives to mathematics faculty and faculty in mathematics-related fields to encourage an active role in P-12 teacher preparation and professional development.
  5. Provide incentives and recognition to mathematics faculty for professional development that includes content and teaching. Mathematics faculty should participate in professional development that teaches multiple methods for teaching mathematics to diverse learners.
For Teachers of Mathematics at All Levels
  1. Form local alliances within disciplines. Mathematics faculty at two-year and four-year institutions and P-12 mathematics teachers should work together to address diverse student learning needs. Increased disciplinary collegiality can improve developmental learning opportunities for students. Local disciplinary alliances can raise awareness among students of study and career opportunities requiring mathematics. They can also improve P-12 and postsecondary teaching.
  2. Form groups as needed to implement these recommendations. The P-16 Council should continue to call on mathematics faculty, faculty in mathematics-related fields, and K-12 educators to improve the teaching and learning of mathematics.
  3. Establish a mathematics alignment Web site for instructors and students. The P-16 Council should form a task force to develop a mathematics Web site, available through both the Council on Postsecondary Education and the Department of Education Web sites. A teacher link could provide course offerings at K-12 and postsecondary levels, lesson plans, and teaching modules for addressing a variety of student needs. The student link would offer sample problems, information on careers requiring mathematics, and postsecondary placement policies.
Background

The Mathematics Alignment Team reviewed the following:

  • Postsecondary admissions standards and placement policies and mechanisms. (12K PDF)
  • P-12 curriculum and assessment standards (Program of Studies and Core Content for Assessment in the four sub-groups of mathematics taught from P-12: number and computation, geometry and measurement, algebraic ideas, and probability and statistics. The Program of Studies outlines the minimum content required for all students to graduate from Kentucky schools. The Core Content for Assessment is the content identified as essential for all students to know. It is included in the Commonwealth Accountability Testing System (CATS) by which schools and districts are evaluated.
  • Kentucky Department of Education released questions and scoring guides for assessing competency levels in algebraic ideas and geometry.
  • Descriptions of skills and competencies indicated by ACT test scores in mathematics (ACT Standards for Transition).
  • Skills and competency standards published by other states (Oregon and Colorado).
  • Annotated student work (elementary, middle, and high school) in algebraic ideas and geometry/measurement using the Kentucky Mathematics Problem Solving Rubric.
  • Sample first-year postsecondary placement tests.
  • High school mathematics diagnostic tests (including the test offered by Northern Kentucky University and one offered by North Carolina through East Carolina University).
  • High school graduation requirements and the Pre-College Curriculum.
  • SCANS (Secretary's Commission for Achieving Necessary Skills) competencies and skills summarized in the Partnership for Kentucky Schools' Ready for Work: Essential Skills for Kentucky Jobs.

P-12 teachers were familiar with KDE curriculum and assessment; postsecondary representatives were generally unfamiliar with the P-12 system. P-12 teachers were generally unaware of postsecondary entrance-level placement processes. Postsecondary representatives were familiar with the admissions and placement policies of their own institutions, but some were not aware of how they compared with those of others.

The mathematics alignment team divided the problem of postsecondary remediation into three chief categories: 1) The misalignment of mathematics curriculum, instruction, and assessment between the P-12 and postsecondary systems; 2) the preparation, professional development, and reward system for teachers at all levels; and 3) communication among educators, students, parents, and others.
  1. Misalignment of mathematics curriculum, instruction, and assessment between the P-12 and postsecondary systems.
    • P-12 Mathematics Core Content comprises four broad categories, one of which is algebraic ideas; postsecondary faculty in mathematics and in mathematics-related fields focus on competency in algebra in particular as prerequisite for college-level work.
    • The topics, concepts, and applications covered in the mathematics courses of the Pre-College Curriculum (Algebra I, Geometry, and Algebra II) are not uniformly taught in secondary schools.
    • Postsecondary faculty assume that entering students, who have completed the PCC, will possess certain skills and knowledge. Often, they do not.
    • Some postsecondary institutions lack general education mathematics courses that are not heavily algebra-based and primarily designed to prepare students for calculus.
    • P-12 assessments and postsecondary placement tests differ fundamentally in scope. P-12 state assessments focus on open-response, performance-based tasks, on problem-solving, and on conceptual understanding. Postsecondary placement tests stress fundamental skills and concepts.
    • P-12 assessments and postsecondary placement tests differ fundamentally in purpose. Placement tests in mathematics are neither final exams nor diagnostic tests. Their purpose is to determine whether a student has minimal mathematical skills needed for entry-level courses.
    • The ACT mathematics test has a greater proportion of non-algebra questions than do college placement tests. (The ACT serves as the chief postsecondary admissions device and a trigger for remedial placement assessment.) The CPE's mandatory minimum ACT cut-off score of 18 does not necessarily indicate the kind and level of critical skills required for college-level mathematics. But raising the minimum ACT score will raise the number of students identified as needing remediation.
  2. Preparation, professional development, and reward system of teachers of mathematics at all levels of the P-16 system.
    • Some elementary, middle, and secondary school mathematics teachers do not know enough mathematics to teach what students need to learn.
    • There are not enough mathematics content-based professional development opportunities offered by some postsecondary institutions to practicing P-12 teachers and inadequate incentives by the P-12 system for mathematics content-based professional development.
    • Some P-16 teachers and faculty do not use enough variety of teaching methods to meet the needs of their students.
    • The postsecondary reward system does not consistently put highest priority on effective teaching.
  3. Communication among educators, students, parents, and others.
    • College-bound students get rusty if they skip mathematics their senior year. College-level mathematical competency is best guaranteed by continuous and recent mathematics study, but only three years-not four-of mathematics are required in high school, even in the Pre-College Curriculum.
    • Too few students understand that college success in mathematics (and in other subjects) requires discipline, persistence, and a willingness to work both outside and in class.
    • P-12 and postsecondary educators do not know enough about the curriculum and assessment policies of each other's system. There is insufficient formal connection between these two groups of educators.

Mathematics alignment team members acknowledged the different roles and responsibilities of the P-12 and postsecondary education systems: the P-12 system is expected to educate all students, whereas (four-year) postsecondary institutions may set admissions as well as placement standards. Many agreed that postsecondary faculty will need to serve a broader spectrum of educational needs as greater numbers of high school graduates pursue postsecondary education and are admitted into postsecondary institutions, and teaching at the postsecondary level will need to respond creatively to these circumstances.

Whether Kentucky high schools should offer any curriculum other than one that prepares all students for postsecondary work or study is an important policy question that the P-16 Council will address elsewhere. The task of this alignment team, however, is to reduce the need for postsecondary remediation of those students who have taken the courses they believed would prepare them for postsecondary study. The mathematics alignment team's recommendations are premised on the notion that students graduating from a Kentucky high school who have satisfactorily completed the Pre-College Curriculum with adequate mastery have the right to assume that they are ready to undertake credit-bearing coursework if they are admitted to a Kentucky postsecondary institution.

 

Last Updated 6/16/2005
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