Addressing Challenges in the Common Core: Mathematics Specialists in Elementary and Middle Schools Patricia F. Campbell Center for Mathematics Education Department of Curriculum and Instruction University of Maryland College Park, MD 20742 This work was developed through the support of grants from the National Science Foundation. Any opinions, findings and conclusions or recommendations expressed are those of the author and do not necessarily reflect the views of the National Science Foundation.
Current state sanctions and district policies have led administrators to emphasize only that mathematics content which is assessed and to de-emphasize or ignore what is not assessed. The result in K-8 mathematics has been a narrowing of delivered curricula, or the redefining of a test-driven curriculum, in each state that: Has clarity and specificity (expectations defined with sufficient detail to communicate intent and applicability), Lacks coherence (expectations for mathematics content and processes are marked by logical disconnections and inappropriate trajectories), and Lacks focus (insufficient time available to learn concepts and skills critical for understanding the expected content, in part due to re-teaching of (un)learned content).
Common Core State Standards for Mathematics offer potential for improvement situated within challenge. With few exceptions, the standards for mathematical content are clear, specific, and focused. Their coherence, in particular their grade-level placement and their learning trajectories, represent a marked shift that cannot be implemented successfully by edict and should not be implemented without concurrent review/evaluation. Teachers will require focused and recurring professional development to advance their own knowledge: of the meaning of and expectations for content and practice standards, about teaching those standards, and about how students learn those standards.
Why not simply implement by edict? Marylands State Standards (Grade 3) Read, write and represent fractions as parts of a single region using symbols, words and models (only proper fractions with denominators of 2, 3 and 4) Read, write and represent fractions as parts of a set using symbols, words and models (only proper fractions with denominators of 2, 3 and 4) Represent fractions on a number line (only proper fractions with denominators of 2, 3 and 4) Common Core Standards (Grade 3) Understand a/b as the quantity formed by a parts when a whole is partitioned into b equal parts Represent a/b (a 1) on the number line by marking off a lengths of 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. Understand two fractions are equivalent (equal) if they are the same size or represented by the same point on the number line. Recognize and generate simple equivalent fractions; explain why they are equivalent. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Compare two fractions with the same denominator or same numerator by reasoning about their size. Recognize valid only if same whole.
Why not simply implement by edict? Marylands State Standards (Grade 3) Read, write and represent fractions as parts of a single region using symbols, words and models (only proper fractions with denominators of 2, 3 and 4) Read, write and represent fractions as parts of a set using symbols, words and models (only proper fractions with denominators of 2, 3 and 4) Represent fractions on a number line (only proper fractions with denominators of 2, 3 and 4) Common Core Standards (Grade 4) Explain why a/b is equivalent to (n x a)/(n x b). Use this principle to recognize and generate equivalent fractions. Compare two fractions with the different numerators and different denominators. Understand a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators; solve word problems involving addition and subtraction of fractions with the same whole and like denominators. Understand a fraction a/b as a multiple of 1/b. Multiply a fraction by a whole number; solve word problems involving multiplication of a fraction by a whole number.
Simply teaching more mathematics content to teachers is not the answer. Teachers not only need to know the content they teach (including notation, language and definitions), they also need to know what mathematics to access and how use it when they: Pose mathematical questions, Evaluate students mathematical explanations, Use or choose ways of representing the mathematics, Choose, sequence and design math tasks and examples, Determine whether and how to provide mathematical explanations, Analyze and address student errors, and .
Elementary Mathematics Specialists (Coaches) Sporadic teacher workshops have no sustained impact. Instructional change requires schools to become places where teachers can learn through sustained, job- embedded professional development. School districts are implementing a variety of coaching models to advance school-wide change and increased student achievement. Intent is a for a knowledgeable colleague who has a deep understanding of mathematics and of how students learn, as well as teaching expertise, to serve as an on-site mathematics resource in a school and as a leader for teachers. (community organizer for mathematics)
Research Project Virginia Commonwealth University, in partnership with the University of Virginia, Norfolk State University, and the University of Maryland, received a grant from the National Science Foundation to develop two cohorts of mathematics specialist/coaches and to investigate their impact in Virginia in a control-treatment design. Five school districts (36 schools) were involved in a 3- year implementation (preceded by 4 semesters of coursework to prepare the specialists). Comparable schools were randomly identified to serve as control sites or to receive specialists who completed 5 prior math courses and 2 leadership/coaching courses. (efficacy study)
Masters Program Number and Operations Geometry and Measurement Probability and Statistics Algebra and Functions Rational Numbers and Proportional Reasoning Coaching/Leadership I, II & III Implications of Mathematics Education Research Mathematics for Diverse Populations Externship (Masters Project)
Impact on Student Achievement Grades 3, 4, and 5 Overall, students in schools with elementary mathematics specialists for 3 years had statistically significant higher scores on Virginias state assessment. This difference in achievement was NOT evident in the first year of placement of a specialist at any grade (in either cohort). The pattern of achievement was: An increase in scores in Year 1, Followed by a greater increase in scores in Year 2, Followed by an even greater increase in scores in Year 3. The size of the increases in Years 2 and 3 drive the statistically significant effect.
Cautions The specialist/coaches in this study engaged in a high degree of professional coursework addressing math content, pedagogy, and coaching prior to and during at least their first year of placement. Do not generalize these results to anointed coaches. The significant positive effects of specialist/coaches on student achievement did not occur simply with the placement of a coach in a school. This impact emerged as the coaches gained experience -- as a knowledgeable specialist/coach and a schools instructional and administrative staffs learned and worked together.
Cautions (continued) There is no evidence that the specialists/coaches in this study impacted the mathematics achievement discrepancies frequently associated with race or poverty. These specialist/coaches had differing responsibilities than that discussed for math specialists as specialized teachers in the National Mathematics Advisory Panel report.
Are mathematics specialists/coaches a feasible way of addressing the demands that the implementation of the Common Core Standards will place on schools and teachers? They can play a key role, but they cannot serve as the individuals responsible for introducing the Common Core Standards to teachers, for designing instructional materials, or for prioritizing potentially conflicting expectations in their schools. Specialists/coaches can play a significant role in advancing a school mathematics program, but administrators must convey expectations and support efforts for change. Specialists could also serve as a liaison for improving the Common Core, communicating need for change or clarification.
Feasibility (continued) Specialist/coaches can be expected to design and support ongoing, intentional opportunities for teacher learning in their schools, utilizing grade-level (course-focused) team and individual interaction. Specialists/coaches will need professional development addressing the changed learning trajectories, especially the increased formalization of mathematics in the elementary school and the major shifts expected within middle school. The more time that specialists/coaches spend on non- coaching, programmatic demands (e.g., interpreting benchmark data, creating unit assessments, producing sample lesson plans, tutoring students, and communicating with parents), the less impact they will have on teachers, instruction, and student achievement.
Implications for mathematicians and mathematics educators working together to develop mathematics courses for K-8 teachers The mathematics courses for the specialist/coaches were designed and taught collaboratively by mathematicians, mathematics educators, and school district mathematics supervisors. Bill Haver (mathematician, VCU) hypothesizes that the school district mathematics supervisor kept all focused on the needs of the teachers and students, rather than the egos and favorite topics of the mathematicians/mathematics educators. The key is to focus efforts on connecting mathematical content to teaching practice, drawing on the expertise of each collaborator, and to model the intended teaching practice during delivery of the courses for teachers.