Addressing Challenges in the Common Core: Mathematics Specialists in Elementary and Middle Schools

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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 - PowerPoint PPT Presentation


  • Addressing Challenges in the Common Core: Mathematics Specialists in Elementary and Middle Schools

    Patricia F. CampbellCenter for Mathematics EducationDepartment of Curriculum and Instruction University of MarylandCollege 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), andLacks 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, andabout 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 partsRepresent 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 ProjectVirginia 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 ProgramNumber and Operations Geometry and MeasurementProbability and StatisticsAlgebra and FunctionsRational Numbers and Proportional ReasoningCoaching/Leadership I, II & IIIImplications of Mathematics Education ResearchMathematics for Diverse PopulationsExternship (Masters Project)

  • Impact on Student AchievementGrades 3, 4, and 5Overall, 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.

  • CautionsThe 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 teachersThe 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.

    Presented at the Joint Mathematics Meetings, New Orleans, LA (January 6-9, 2011)*Principals have a number of not-so-subtle ways of conveying to teachers the expectation that their role is first and foremost to teach the math content that is tested. These include benchmark or practice tests encompassing the entire corpus of tested content for a given grade or course, expectations that daily lesson objectives keyed to assessment standards will be posted daily in the classroom (or identified in each daily lesson plan), providing scripted lesson plans to teachers, and curriculum pacing guides that might be useful (giving a sense of sequence for objectives, focus and duration, as well as availability of resources) or troubling (e.g., every fifth-grade teacher should be teaching pages 34-36 in the textbook on the third Tuesday in September) .

    Because no test, and in particular no multiple-choice test with only a limited number of supplemental brief constructed response items, can measure all aspects of conceptual understanding, reasoning and problem solving, the result of emphasizing only the tested mathematics content is to limit the mathematics curriculum that is presented in classrooms (the delivered curriculum) to automating skillful use of isolated procedures and recall of factual information.

    A test-driven curriculum is well-defined in terms of conveying what will be tested, but that does not mean that is sufficient for instruction. (Address lack of coherence and focus) For too many teachers, the result of a test-driven curriculum is the following perspective. While mathematics can make sense and can be understood by some students, the first priority is that all students be taught ways to remember the mathematics that is tested. The danger is that for many students, mathematics then becomes simply a collection of arbitrary rules, definitions and procedures. *There are two types of Common Core Standards for Mathematics the Standards for Mathematical Content and the Standards for Mathematical Practice.

    The Standards for Mathematical Content are listed by grade level and, for the most part, are clear, specific and focused.

    But the seemingly theoretical coherence of the content standards needs to examined via phased implementation in the reality of US classrooms.

    The Standards for Mathematical Practice are critical. It may be that this is what implementation and the design of new assessments should emphasize first, although in practice it will be easier to focus first on shifting some content objectives. (reference NCTM conference in August 2010) Without implementation of the Standards for Mathematical Practice, the danger is that there is simply a longer and more difficult listing of math rules, procedures and definitions to be remembered, So professional development (addressing both content and practice standards) is critical. *There is a massive shift in content placement and definition.

    For example, the formal definition of fraction as a rational number (Common Core) is never stated in any of Marylands State Standards. In Grade 3, the focus is on fraction of a region or fraction of a set. For regions, fractions are a way to identify a share of congruent portions (when a whole region such as a cookie or a pizza is separated into congruent parts) or a share of distinct parts in a collection (such as when baggies of Gorp are examined 12 pieces of food such as peanuts, raisins and M & Ms in each baggie, but some baggies have 4 peanuts [1/3 of the Gorp] and some have 6 peanuts [1/2 of the Gorp]). In either the case, the instruction is switching from answering, How many? to answering, How much? about regions or sets. This is not the formal definition of fraction nor is it the number line model.

    The number line interpretation of fractions is a measurement standard in Maryland in Grade 4 (4ths and halves only) and Grade 5 (up to 8ths). Fraction equivalence is introduced in Grade 4 in Maryland, not in Grade 3, as is the connection between whole numbers and fraction. In Grade 3, fractions are primarily answering the question, How much? for regions and sets.So not only must instructional materials change, but teachers will also to enlarge their repertoire for teaching new content. (Teachers do identify as being a Grade 3 or Grade 6 teacher. This seems more prevalent as testing is emphasized. Teachers become expert in teaching to the test of a particular grade.) *Even more critically, the prior standards simply are not adequate in terms of addressing prerequisite content for the next grades new Common Core standards.

    There needs to be some organized way of transitioning from current standards to the Common Core that does not take 12 years.There are three parts to this. One is the development of curriculum materials. The second is the development of aligned assessments. The third is developing the knowledge of teachers.


    The knowledge that teachers will need to acquire is not simply mathematics content knowledge.

    All of these aspects of what teachers need to know are in fact mathematical the term now being used to encompass these and other aspects is mathematical knowledge for teaching. (Hyman Bass, Deborah Ball, Heather Hill, etc. at U of Michigan).

    The issue is: How to support teachers efforts to develop accessible and usable knowledge of mathematics content and mathematics teaching and learning that teachers can call upon when they teach?*In part, that is why school districts are now turning to mathematics specialists or coaches, in both elementary and middle schools.*Efficacy study Essentially this study was designed to investigate the impact of an intended model for specialists or coaches. This was not a case of identifying matched schools, randomly assigning one school in each match to receive a math specialist/coach position that would be filled by whomever was identified by a district or principal to serve that role, and then comparing student achievement across schools.

    Rather, as an efficacy study, individual teachers first completed courses to prepare them to be specialist/coaches. Comparable schools (no prior coach or specialist in place) in the same school district were matched (based on prior student math achievement and student demographics such as free/reduced meals or ESOL) and one school was randomly selected to receive a specialist/coach. The achievement of students in these schools were compared to those of students in the comparable schools without specialist/coaches. ***

    About half of the specialists already had a masters degree. But all took the courses listed in Black Font. Those without a masters degree had support to complete four more courses to yield the degree. The specialists/coaches were placed in schools after completing the 5 math courses and one of the coaching/leadership courses. They completed the second coaching/leadership course while in their first year of placement as a coach.*Statistical analysis was completed with Hierarchical Linear Modeling. Essentially, students are nested in classrooms, each with a teacher, and classrooms/teachers are nested in schools. The schools were randomly assigned to have a coach or not. The analysis looked at individual student achievement data linked to individual classroom teachers who were clustered in schools. Longitudinal study analyzing data over 3 years of placement (cohort 1) or 1 year of placement (cohort 2). *As an efficacy study, we are not saying that simply naming someone to be a math specialist/coach and then positioning them in a school will yield this result.As a longitudinal study, we found that it took time for the specialists/coaches to impact a schools student achievement. *Discrepancies in student achievement associated with race and poverty, particularly in urban settings marked by teacher turnover and varying teacher knowledge, may require school-wide professional development in the summer prior to the placement of a specialist/coach.

    District and school administrators, not specialists/coaches, have the responsibility for identifying what will be district curriculum, for determining how the introduction and phasing in of the Common Core will accomplished, and for communicating/addressing expectations for change. Those are policy decisions. Also, specialist/coaches are not curriculum developers or textbook authors aligned instructional materials will need to be acquired. *Teachers are relatively autonomous individuals. There will be no change and no improvement in student achievement without their understanding and action.

    Specialist/coaches provide a mechanism for supporting teachers knowledge of mathematics content and pedagogy.Specialist/coaches provide a mechanism for supporting teachers efforts to work together to define and implement change in practice in meaningful ways within their schools.But this can only happen if specialist/coaches have time to work with teachers.



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