ELED 5301: 

Assessing/Modifying/Integrating Mathematics Instruction (3G)

Dr. John A. Piel

Email:  japiel@email.uncc.edu

Office: 390 College of Education Building

Phone: 704-687-8731

Assessing/Modifying/Integrating Mathematics Instruction. Application and refinement/expansion of pedagogical knowledge gained in the introductory summer course (ELED 5201), with focus upon assessment of student learning, evaluation of effectiveness of instruction, and modification of methods and materials for diverse learners.  Closer examination of performance expectations by grade level, EOG Testing, and effective instruction for struggling learners will be the focus of this course.  Continued expectation for curriculum integration and use of models of teaching as an organizer for understanding instruction, assessment, and modifications.  Applications of technology in mathematics instruction.  design, implementation, and evaluation of math lessons and brief mathematics-centered integrated unit will be central to mathematics instruction.

COURSE PREREQUISITES: Grade of B or better in ELED 5100 and 5201

COURSE RATIONALE:  Today's elementary school teacher must be more than a curriculum manager.  Teachers in today's elementary classroom must be able to diagnose and prescribe effective instructional tactics aimed at improving students' performance.  As teachers learn instructional techniques they concurrently must be able to make adjustments to these techniques so that under-performing students begin to move closer to grade level expectations and so that gap scores between high performing groups and low performing groups are lessened.  Teachers will learn an alternative to ability or whole group classroom organization in order to focus on developmental grouping thus lessening the common practice of artificial pacing based upon amount of content exposure.

            This course builds upon the content of ELED 5201 where teachers learned instructional tactics based upon a constructivist rationale.  The content of this course allows new teachers to adjust these tactics to fit the needs of students who are performing at varied levels of proficiency as well as integrate mathematics with other subject areas.  The primary focus is to help teachers assess, modify, and integrate content as needed.

COLLEGE OF EDUCTION CONCEPTUAL FRAMEWORK AND 5301 CONNECTIONS – (See conceptual framework)

The Elementary Education program is built on a conceptual framework of principles and characteristics identified with effective teachers.  In this course, a number of activities directly reflect elements of the conceptual framework and will be formally evaluated.  These elements and their evaluation are identified below.

·        Demonstrate highly advanced knowledge of human development and of student needs

·        Demonstrate highly advanced knowledge of curriculum  and content (mathematics)

·        Make links among theory, research and practice as well as between content and pedagogy

·        Use justifiable, appropriate strategies well grounded in research and the wisdom of practice within respective discipline

·        Apply knowledge to planning, goal-setting, implementation, and continuous assessment

·        Demonstrate positive impact on student learning

·        Engage in continuous improvement of professional practice

·        Provide developmentally appropriate, age appropriate, individually appropriate, and culturally responsive instruction

·        Hold high expectations for all children and provide high levels of support for high achievement

·        Value the collective contribution of others

·        Communicate professional knowledge effectively to others

PROFESSIONAL STANDARDS -- NCDPI/ACEI

NCDPI

Elementary teachers have a broad knowledge and understanding of the major concepts in mathematics NCDPI 2

• Teachers have knowledge of number sense, numeration, and numerical operations
• Teachers have knowledge of geometry and measurement
• Teachers have knowledge of patterns, relationships, functions, symbols and models
• Teachers have knowledge of data, probability, and statistics

Elementary teachers use developmentally appropriate strategies to design and deliver instruction in all areas of the elementary curriculum NCDPI 7

• Teachers develop and implement the pacing and alignment of curriculum that is consistent with the NCSCOS, LEA standards and pacing guides, and national standards in mathematics
• Teachers promote new learning by using student’s prior knowledge, misconceptions, and interests when designing lessons
• Teachers implement a variety of teaching and communication strategies for instruction
• Teachers assist students in developing multiple learning strategies to address discipline specific content, critical thinking and problem solving skills
• Teachers develop and use a variety of formal and alternative assessment strategies as an integral part of instruction and learning appropriate for assessing individual, peer, team, and collaborative skills 

Elementary teachers understand and use the processes of problem solving, reasoning and proof, communication, connection, and representation as the foundation for the teaching and learning of mathematics NCDPI 9

• Elementary teachers develop instruction in problem solving that enable all students to:

1.      build new mathematical knowledge through problem solving

2.      solve problems that arise in mathematics and in other contexts

3.      apply and adapt a variety of appropriate strategies to solve problems

4.      monitor and reflect on the process of mathematical problem solving

• Teachers develop instruction in reasoning that enablers all students to

1. recognize reasoning and proof as fundamental aspects of mathematics
2. make and investigate mathematical conjectures
3. develop and evaluate mathematical arguments and proofs
4. select and use various types of reasoning and methods of proof

• Teachers develop instruction in communication that enable all students to
  1. organize and consolidate their mathematical thinking through communication
  2. communicate their mathematical thinking coherently and clearly to peers, teachers, and others
  3. analyze and evaluate the mathematical thinking and strategies of others
  4. use the language of mathematics to express mathematical ideas precisely

• Teachers develop instruction in representation that enables all students to
  1. create and use representations to organize, record, and communicate mathematical ideas
  2. select, apply, and translate among mathematical representations to solve problems
  3. use representations to model and interpret physical, social, and mathematical phenomena

Elementary teachers encourage underrepresented groups to engage in the schooling process, especially math and science

• Teachers use a variety of strategies to encourage underrepresented groups to engage in the math process
  1. They utilize community resources
  2. They give personal attention and encouragement to underrepresented groups of students
  3. They give relevant and real-world applications that interest a diverse population
  4. They encourage underrepresented groups to assume leadership roles

Effective Teachers are successful in teaching a Diverse Population NCDPI Diversity Standards

• Teachers understand the central concepts, tools of inquiry, and structures of the discipline they teach and can create classroom environments and learning experiences that makes these aspects of subject matter accessible, meaningful, and culturally relevant for diverse learners -- Standard 1

1. teachers select, evaluate and incorporate unbiased instructional materials
2. teachers use multiple strategies to address the needs of individual learners
3. teachers create a safe, inclusive and caring environment in which all students can learn
4. teachers use a variety of assessment procedures/instruments

• Teachers understand how students’ cognitive, physical, socio-cultural, linguistic, emotional, and moral development influences learning and address these factors when making instructional decisions – Standard 2

1. teachers seek and apply good matches among instructional goals, methods, and materials, and students’ skills and abilities
2. teachers assist students in developing multiple learning strategies to address discipline specific content, communication, critical thinking, and problem solving skills
3. teachers modify instruction and assessment to meet the needs of individual students

Teachers plan and design effective learning environments and experiences supported by technology NCDPI Technology Standards

• Teachers demonstrate knowledge, skills and understanding of concepts related to technology
• Teachers demonstrate continual growth in technology knowledge and skills to stay abreast of current and emerging technology
• Teachers design developmentally appropriate learning opportunities that apply technology-enhanced instructional strategies to support the diverse needs of learners
• Teachers identify and locate technology resources and evaluate them for accuracy and suitability
• Teachers use technology to support learner-centered strategies that address the diverse needs of students
• Teachers use technology to support learner-centered strategies that address the diverse needs of students

ACEI 

Standard 2.3  Mathematics: Candidates know, understand, and use the major concepts, procedures, and reasoning processes of mathematics that define number systems and number sense, Geometry, measurement, statistics and probability, and algebra in order to foster student understanding and use of patterns, quantities, and spatial relationships that can represent phenomena, solve problems, and manage data.

Standard 2.8 Connections across the curriculum:  Candidates know, understand, and use the connections among concepts procedures, and applications from content areas to motivate elementary students, build understanding, and encourage the application of knowledge, skills, and ideas to real world issues.

Standard 3.1 Integrating and applying knowledge for instruction:  Candidates plan and implement instruction based on knowledge of students, learning theory, subject matter, curricular goals, and community.

Standard 3.2 Adaptation to diverse learners:  Candidates understand how elementary students differ in their development and approaches to learning, create instructional opportunities that are adapted to diverse students

Standard 3.3 Development of critical thinking, problem solving, performance skills:  Candidates understand and use a variety of teaching strategies that encourage elementary students’ development of critical thinking, problem solving, and performance skills.

Standard 3.4 Active engagement in learning:  Candidates use their knowledge and understanding of individual and group motivation and behavior among students at the K-6 level to foster active engagement in learning, self motivation, and positive social interaction to create supportive learning environments.

Standard 3.5 Communication to foster collaboration:  Candidates use their knowledge and understanding of effective verbal, nonverbal, and media communication techniques to foster active inquiry, collaboration and supportive interaction in the elementary classroom.

Standard 4 Assessment for instruction:  Candidates know, understand, and use formal and informal assessment strategies to plan, evaluate, and strengthen instruction that will promote continuous intellectual, social, emotional, and physical development in each elementary student.   

ACADEMIC INTEGRITY

Students have the responsibility to know and observe the requirements of The UNCC Code of Student Academic Integrity.  This code forbids both cheating and complicity in academic dishonesty.  Academic evaluations in this course assume that student work is free from academic dishonesty of any type, and grades will therefore be adversely affected by academic dishonesty.  In addition students who violate the Code can be expelled from UNCC. 

Exams in this course will be carefully monitored to create a climate in which cheating does not occur.  Students will cover their answer sheets with the examination.  Students caught cheating (including looking at another's answer sheet) will be given a "0" for the exam.  In addition, the regularly computed course grade will be reduced one letter grade for the course. 

Field assignments must represent each student's own work and must be free of plagiarism of any kind (see definition in UNCC Catalog).  While discussion with the instructor and class mates is an appropriate form of preparing one's assignment, the work turned in must be the student's own composition, except that appropriate citations must be clearly noted.  Students caught plagiarizing will be given a "0" for the assignment, and their regularly computed course grade will be reduced one letter grade for the course.

CELEBRATION OF DIVERSITY

UNC Charlotte strives to create an academic climate in which the dignity of all individuals is respected and maintained.  This diversity includes, but is not limited to:  ability/disability, age culture, ethnicity, gender, language, race, religion, sexual orientation, and socio-economic status. 

ELED 5301 SPECIFIC COURSE OBJECTIVES:

1.      Utilize knowledge of cognitive, social, affective and psychomotor development in planning instruction

2.      Identify cognitive processes that affect pupil performance in achieving instructional objectives

3.      Identify motivational techniques that influence pupil performance in achieving instructional objectives

4.      Describe multi-cultural implications to be considered in planning instruction

5.      Utilize knowledge of the characteristics of pupils with special learning needs in adapting curriculum and planning instruction

6.      Generate a sequence of instruction based on an analysis of pupil performance

7.      Classify instructional objectives according to a recognized taxonomy

8.      State essential conditions of learning associated with categories of learning specified by a selected taxonomy

9.      Generate pupil performance objectives in precise and measurable terms

10.  Generate pupil performance objectives that address different levels of thinking

11.  Generate a task analysis of pupil performance objectives

12.  Generate alternative strategies for attaining a particular objective

13.  Describe the purposes of formal and informal diagnosis in planning instruction

14.  Differentiate among diagnostic measures that are compatible with various instructional objectives.

15.  Select appropriate instructional materials, media, and software that are compatible with pupil learning styles and instructional objectives

16.  Work effectively with other professional and para-professionals for planning to meet pupil needs

17.  Demonstrate a command of subject matter necessary to carry out the objectives of the instructional program in the areas of specialization

18.  Utilize instructional methods and techniques that are consistent with sound practice and research findings on teacher effectiveness

19.  Implement instruction that is appropriate to meet student needs and achieve learning objectives

20.  Modify instruction in ways appropriate for pupils with special learning needs

21.  Demonstrate motivational techniques appropriate to student needs and instructional objectives

22.  Demonstrate use of referral services and community resources in meeting the educational needs of pupils

23.  Demonstrate evaluation techniques appropriate to program goals

24.  Utilize evaluation findings to modify instructional practice and in planning program revisions

25.  Demonstrate appropriate procedures for reporting evaluation results to parents and others to whom federal an state statutes grant access to such information

ELED 5301 COURSE CONTENT

1.      Within a relationship with ELED 5100 Intensive Orientation to Teaching, review of literature, and research in mathematics education this course relates to student performance and evaluation and teacher planning within the field of mathematics.

2.      Developmental differences and student mathematics performance and evaluation

3.      Impact of cultural diversity upon numeracy learning and instruction

4.      Evaluation procedures matched directly to instructional tactics

5.      Critical examination of a wide variety of text and other printed material designed to foster mathematics learning

6.      Critical examination of a wide variety of mathematics software and its appropriateness in a constructivist mathematics program

7.      Development and use of the Developmental Mathematics Inventory to develop instructional groups

8.      Use of a centers approach for managing a mathematics classroom whereby fluid groups are established

9.      Development of performance based assessment techniques

10.  Use of a summative and formative record keeping system to help develop effective Pupil Education Plans for those students functioning below expected level

11.  Development of problem solving modules

12.  Development of integrated curriculum units where mathematics is a key component

ILLUSTRATIVE ELED 5301 COURSE ACTIVITIES

·        Presentations by course instructor as to relevance of a constructivist mathematics model.  See ELED 5100

·        Discussions regarding effective evaluation procedures tied to instructional tactics

·        Effective usage of Developmental Mathematics Inventory to determine instructional level

·        Hands on practice with instructional and evaluation procedures for appropriate usage of manipulatives from a variety of levels (concrete, representational, symbolic, alternative algorithms)

·        Problem solving activities as a focus of mathematics modules

·        Field based activities whereby teachers learn how to use a performance and portfolio approach to evaluation

ASSIGNMENTS AND GRADING

·        Student Diagnostic/Prescriptive Project      200 points                    A = 360 - 400

·        Integrated Problem solving module for       100 points                     B = 320 - 359

       Integrated Unit                                                                              C = 280 - 319            

·        Observation/Evaluation of Math Lesson      P/F

·        Exam                                                        100 points

Total                                                   400 points

REQUIRED TEXTS

Piel, J. A., & Green, M.  (2010).  Construction number sense in the elementary and middle grades classroom.  Dubuque. Kendal Hunt.  .

SELECTED PRIMARY REFERENCES

Achieve.  (1999).  Preliminary results of the analysis of state standards and assessments.  East Lansing, MI: TIMSS Center.

Black, A.  (1989).  Developmental teacher education. Preparing teachers to apply developmental principles across the curriculum.  The Genetic Epistemologist.  17 (4), 5-14.

Committee on Mathematical Education of Teachers. (1991). A call for change.  Recommendations for the mathematical preparation of teachers of mathematics.  Washington, DC.  The Mathematical Association of America.

National Center for Educational Statistics.  (1997).  The 1996 mathematics report card for the nation and the states.  Washington, DC: Author.

National Council of Teachers of Mathematics. (1989).  Curriculum and evaluation standards for school mathematics.  Reston, VA: Author.

National Council of Teachers of Mathematics. (1991).  Professional  standards for teaching mathematics.  Reston, VA: Author.

National Council of Teachers of Mathematics. (1995).  Assessment standards for school mathematics.  Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.  Reston, VA: Author.

National Research Council. (1989).  Everybody counts: A report to the nation on the future of mathematics education.  Washington, DC: National Academy Press.

Piaget, J. (1954.  The construction of  reality in the child.  New York: Basic Books.

Vygotsky, L. S. (1962) Thought and language.  Cambridge, MA: M.I.T. Press.