Graduate Program in
Childhood Mathematics

Options for Matriculation in the Program with Requirements and Matriculation Codes
_________________________________________________________

General Matriculation Requirements  General Degree Requirements  

Options for Matriculation: 
Option A  
Option B  
Option C 
Mathematics Courses  
Core Education Courses  
Other Education Courses – Required or Elective 
Samples of Schedules to Complete the Program

This program leads to a Master of Science Degree in Education and a New York State Professional Certificate in Childhood Education with a specialization in mathematics (grades 1-6).Three options of the program will be offered, to meet the needs of the different groups of prospective graduate students it serves:

*Option A (30 credits) for Applicants who hold a New York State Initial Certificate in Childhood Education (Grades 1 -6) or its equivalent;  [matriculation code  616]

*Option; B (33 credits) for applicants who hold a New York State Initial  Certificate in Early Childhood (birth – grade 2), Middle Childhood  (grades 5-8) or Adolescence Education (grades 7-12) or their equivalents; [code 617]

*Option C (45 credits) for applicants with no initial New York State certification. [code 618]. For all options, the following matriculation and degree requirements apply.  Additional requirements are listed on the next page under each of the three options.  

General Matriculation Requirements

	Applicants must submit scores on the Liberal Arts and Science Test (L.A.S.T.).
	Applicants must have a minimum of 6 credits in mathematics.
	Applicants must have a minimum undergraduate scholastic index of 3.0.  A minimum scholastic index of 3.0 in graduate courses is required to maintain matriculation.
	International applicants for whom English is a second language are required to pass the Test of English as a Foreign Language (TOEFL) with a minimum score of 550.
	Students should note additional requirements found in the Brooklyn College Graduate Catalog at the beginning of the chapter on Education programs as well as in the chapters "Admission"  and  "Academic Standing."

General Degree Requirements

	Students must complete the following 12-credit core of  Education courses in the listed sequence:  Education 712.23T,  713.23T,  701.23T,  702.23T ( See page 9 for course titles and descriptions.)  These and other required Education courses and some elective Education courses require permission for registration as indicated in the Schedule of Classes.
	Students must complete four of the following Mathematics courses (12 credits): Mathematics 604.1T, 604.2T, 604.3, 604.4, 604.5, 604.6.  (See page 10 for course titles and descriptions.)  Other graduate mathematics courses approved by the Program Adviser can be credited towards this requirement.
	Students must complete an additional 6 to 21 credits according to the option which applies to them.

OPTION A (30 credits) [matriculation code  616] 

Additional Matriculation Requirements

Applicants must hold a New York State Initial Certificate in Childhood Education (Grades 1-6) or its equivalent.  

Additional Degree Requirements

In addition to the four Education courses and four of the six Mathematics courses listed above, the following courses are required: 

Education 784.1X,  and

            (b)  one of the following elective Education courses: Education  722.03T, 726.1X,  726.2T, 742.1X, 744T, 751.2, 763.23, 763.25, 765.1, 792.2,   (See page 5 for course titles.), or an Education course approved by the Program Adviser.

OPTION B  (33 credits) [matriculation code 617]

Additional Matriculation Requirements

Students must hold a New York State Initial Certificate in Early Childhood Education  (birth- grade 2), Middle Childhood Education (grades 5 - 8),  Adolescence Education (grades 7 -12), or their equivalents.

Additional Degree Requirements

In addition to the four core Education courses and four of six Mathematics courses listed above, the following courses are required:

Education 784.1X, 

one of the following elective Education courses: Education  722.03T, 726.1X,  726.2T, 742.1X, 744T, 751.2, 763.23, 763.25, 765.1, 792.2,   (See page 9 for course titles.), or an Education course approved by the Program Adviser. 

Education 763.23 which requires student teaching experiences in grades 1-6.

OPTION C (45  credits) [matriculation code 618]

Additional Matriculation Requirements:  

Students who do not have a New York State Initial Certificate, and have not completed courses in Education or do not have teaching experience in grades 1-6 must complete the additional degree requirements below.  Students who do not have a New York State Initial Certificate but have a few courses in Education and are currently teaching in grades 1-6 will have to be evaluated on an individual basis to prevent duplication in Education coursework. 

Additional Degree Requirements

Prior to taking the core Education courses required for the degree, students must complete Education 718.22T, 794X, 763.25T, 763.26, 763.23T and 764.2T.   Students must obtain departmental permission to register for these courses.

Mathematics Courses 

The program requires four of the follow mathematics courses:

MATH 604.1T   Number Systems and Algebra for Childhood and Middle Childhood Teachers

MATH 604.2T   Geometry for Childhood and Middle Childhood Teachers  (Sp-3; Sp-4) 

MATH 604.3T   Probability and Statistics for Childhood and Middle Childhood Teachers  (F-2,  F-3)

MATH 604.4T   History of Mathematics for Childhood and Middle Childhood Teachers  (Sp-3, Sp-4) [Prereq: Math 604.1 or 604.2]

MATH 604.5T   Discrete Mathematics for Childhood and Middle Childhood Teachers  (Su-3,   Su-4) 

MATH 604.6T   Introduction to Functions for Childhood and Middle Childhood Teachers (Sp-3,  Sp-4)

All courses except Math 604.4 may be taken in any order.

Core Education Courses 

ED 712.23T   Childhood Mathematics Education: Advanced Methodology and Practice (F-3, F-4) 

ED 713.23T   Middle Childhood Mathematics Education: Advanced Methodology and Interdisciplinary Approaches (Sp-3, Sp-4)

ED 701.23T   Seminar in Applied Theory and Research in Mathematics Education: I  (F-3, F-4)

ED 702.23T   Seminar in Applied Theory and Research in Mathematics Education: II (Sp-3, Sp-4)  

These four courses must be taken in the sequence listed.   Two mathematics courses, and ED 784.1  with approval of the Program Adviser, ED 784.2) or an elective education course should be taken prior  to the first course in the sequence.  Three mathematics courses and one elective should be taken prior to ED 701.23.

Other Education Courses – Required or Elective

ED 784.1 Introduction to Technology in Childhood Education  (F-3, Sp-3, F-4, Sp-4)

ED 784.2X  Integrating Technology and Media in Middle Childhood and Adolescence Education (F-2, Sp-3, F-3, Sp-4) (Su-3, Su-4)

D 722.03T Teaching Mathematics in Adolescence Education  (Sp-3; Sp-4)

ED 726.1X  Children and Youth with Special Needs

ED 726.2T Teaching in the Least Restrictive Environments

ED 742.1X Multicultural Education

ED 744T Moral Development, Moral Education and the Ethics of Teaching

ED 763.23T Mathematics and Special Education  (UFT Course: F-2, Sp-3, Su-3, F-4, Sp-4, Su-4)

ED 763.25T Literacy and Special Education (UFT Course: F-2, Sp-3, Su-3, F-3, Sp-4, Su-4)

ED 792.2X   Writing Across the Curriculum

 Some of these courses or other possible electives are offered through the UFT, and may be taken  in the program with the approval of the Program Adviser.

Prerequisite Courses for 45-credit Childhood Mathematics program (Each course requires field experiences.)

ED 718.22T   Social Discourses in Education:  Integrating Social Sciences in Childhood Education

ED 794X Literacy:  Issues and Analysis

ED 763.25T   Teaching Mathematics in Childhood Education

ED 763.26T   Teaching and Learning Science in Childhood Education

ED 763.23T Childhood Education:  Student Teaching in Grades 1-6

ED 764.2T Childhood Education:  Student Teaching Practica 

Samples of Schedules to Complete the Program

The program can be completed in as short a time as two academic years and a summer session, or over a longer period of time (e.g., 5 or 6 semesters, and a summer)  which accommodates a student’s teaching and personal commitments. 

Schedules A and B are recommended for new teachers who generally want to take only one course in the fall term when they need to devote more time to getting started teaching.

Schedule A:  6 semesters and a summer session

Year 1  
Fall  Math 604.1 
Spring     Math 604.2, ED 784.1
Summer:  Math 604.5 

Year 2
Fall  ED 712.23
Spring ED  713.23, Math 604.3,  ED  elective or in Summer 

Year 3  
Fall  ED 701.23
Spring  ED  702.23

Or

Schedule B:  6 semesters and two summer sessions

Year 1
Fall  Math 604.1
Spring     Math 604.2 
Summer:  Math 604.5, ED 784.1

Year 2
Fall  ED 712.23
Spring  ED  713.23, Math 604.4          
Summer:  ED elective or Math 604.6

Year 3   
Fall  ED 701.23
Spring ED  702.23

Some students who have ample time complete the Program in five semesters, three courses at the start and then doubling up for two semesters afterwards.  For example:

Schedule C:  Five semesters and two summer sessions

Year 1     
Fall  - 
Spring      Math 604.2, ED 784.1
Summer:  Math 604.5

Year 2
Fall  ED 712.23, Math 604.1
Spring  ED  713.23 Math 604.4  or Math 604.6
Summer:  ED elective  or taken in Fall of Year 3

Year 3     
Fall  ED 701.23             
Spring  ED  702.23, ED Elective

Students who have a strong background in mathematics, experience teaching, and adequate time during the academic year complete the program in two years and a summer session.

Course Descriptions

Core Mathematics Education and Educational Technology Courses

Education 712.23T  Advanced Methodology and Practice in Childhood and Middle Childhood Mathematics:

30 hours lecture;  30 hours laboratory; 3 credits. Fall  term Mon. or Wed.  6:05 – 9:30 pm

Development, application, and implementation of methodology and materials, and related research and theoretical perspectives.  Principles and standards for mathematics curriculum, instruction, and assessment.  Emphasis on teaching and learning in the whole number and operations,  algebra, and data interpretation in the preK-6 curriculum. Organization for instruction.  Planning, tryout and reflective evaluation of worthwhile mathematical tasks.  Literacy and mathematics:  writing as a tool for learning,  word problems and the writing process, connections to children’s literature.   Thematic instruction.  Use of technology in teaching and learning mathematics.  

Prerequisite of Education 712.23:  Two of the following mathematics courses:  604.1T, 604.2T, 604.3T, 604.4T, 605.5T, 605.6T, or mathematics courses approved by the program adviser of Childhood Mathematics and one education elective course.

Education 713.23T  Advanced Methodology and Practice in Childhood and Middle Childhood Mathematics: II
30 hours lecture;  30 hours laboratory; 3 credits. Spring term    Mon. or Wed. 6:05 – 9:30 pm

Continuation of Education 712.23T.  Emphasis on teaching and learning involving rational numbers and operations,  ratio and percent,  measurement and geometry, and  probability.   Interdisciplinary approaches involving mathematics and  science, social studies, and literacy.  Diagnostic-prescriptive instruction:  analysis of error patterns,  strategies for remediation and prevention.   Adaptations of  materials and methods for special needs learners.   Introduction to research paradigms in mathematics education; overview of types of research in mathematics education and clusters of research by students in the MS mathematics education program.  Prerequisite:  Education 712.23T

Education 701.23T    Seminar in Applied Theory and Research in Mathematics Education: I

30 hours lecture;  30 hours laboratory;  3 credits.  Fall term Mon or  Wed  6:05 –9:30

Educational research as applied to the analysis teaching and learning of mathematics. Qualitative and quantitative  research. Use of educational research techniques to analyze curricular resources,  teaching,  learning of mathematics in urban schools  Reading and writing in mathematics, and the special needs and English-language learner.  Types of assessments; alignment of assessment and instruction;  design. scoring, and use of teacher-made and high-stakes tests.  Design of  “action research.”  Selection of a research topic, initial review of literature, and design of research project.

Prerequisite:  Education 713.23;  four mathematics courses and two education elective courses required for the program,  or permission of the Program Head.

Education 702.23T   Seminar in Applied Theory and Research in Mathematics Education: II

30 hours lecture;  30 hours laboratory;  3 credits Spring term 

Continuation of Education 701.23T.  Techniques for analyzing qualitative and quantitative data. 

Design, implementation, and reporting a research project.  Current issues in mathematics education. Professional leadership in mathematics education.

Prerequisite:  Education 701.23 

Education 784.1X  Introduction to Computers in Childhood and Middle Childhood  Education

30 hours; 30 hours laboratory;  3 credits 

Introduction to educational uses of computers. Definition and development of computer literacy.   Evaluation of software in reading, writing, mathematics, science, and social studies. Calculators and  CBL as instructional tools.  The  internet as a resource for teaching and learning.  Project-based instruction.   Examination of the roles of  technology in classrooms and in relation to school curricula, and the consequent new roles for teachers.  Survey of relevant education research.  Prerequisite:  12 credits in education and permission of  program adviser of Childhood Mathematics.

Education 784.2X  Integrating Technology and Media  in Middle Childhood and Adolescence  Education. 30 hours; 30 hours laboratory; 3 credits 

Examination of instructional applications of technology and media in middle and secondary school classrooms; consequent new roles for teachers and changes in classroom organization.   Implications of technology on curriculum.  Computer literacy. Analysis and evaluation of selected software designed for teaching subject areas in grades 7-12. The Internet as a resource for teaching and learning.  Survey of relevant educational research

(Not  open to students who have completed Education 784.1T)

Prerequisite:  12 credits in education or permission of the program adviser of Adolescence Education.

Mathematics Courses for Childhood and Middle Childhood Teachers

The program requirement is any four of the following six courses.

Mathematics 604.1T Number Systems and Algebra in for Childhood and Middle Childhood  Teachers  (45 hours; 3 credits) 

The real number system and some of its subsystems.  Introduction to group and field structures, solutions to equations.   Number theory.    Sequences and patterns, and  problem solving.  Technology as a tool for investigating algebra. Connections to curriculum and pedagogy.

Mathematics 604.2T Geometry for Childhood and Middle Childhood Teachers  (45 hours;  3 credits) Investigation of  two-and three-dimensional objects and their properties, Congruence and Similarity.  Coordinate geometry. Transformations in the plane, and their geometric and algebraic properties. Measurement of length, area, volume, surface area, Inductive and deductive proof in geometry.  Connections of geometry to the arts and everyday applications.  Technology as a tool for investigating geometry. Connections to curriculum and pedagogy.

Mathematics 604.3 Probability and Statistics for Childhood and Middle Childhood Teachers. (45 hours;   3 credits). Set and graphical representations, counting principle, sample spaces and probability.  Measures of central tendency and variability,  binomial and normal distributions, applications to sampling theory and testing of hypotheses; introduction to correlation and regression., applications to research in education.   Use of the graphing calculator and the data bases on the internet  for exploring  probability and statistics.  Connections to curriculum and pedagogy

Mathematics 604.4T  History of Mathematics for Childhood and Middle Childhood (45 hours; 3 credits). A study of  historical and cultural perspectives of mathematics.  Mathematical problem solving. Origins of number systems and number theory, algebra and topics in geometry, probability, and calculus. Famous men and women in mathematics.  Video and internet  resources for exploring the history of mathematics.  Connections to curriculum and pedagogy.

Requirement:  Math 604.1 or 604.2, or permission of the Program Head

Mathematics 604.5  Discrete Mathematics  for Childhood and Middle Childhood Teachers (45 hours; 3 credits). Selected mathematical topics and modeling in the social  sciences. Networks,  Euler paths;  Sets, classification, and the counting principle; Linear and exponential functions and their graphs;  Linear programming;  Matrices.   Mathematics of voting.  Technology as a tool for investigating discrete mathematics.   Connections to curriculum and pedagogy.

Mathematics 604.6  Introduction to Functions and Applications for Childhood and Middle Childhood Teachers (45 hours;  3 credits).      Analysis of the function concept and its unifying role in mathematics.  Elementary algebraic and transcendental functions.  Functions as mathematical models in the physical and social sciences.  Use of the technology to investigate functions, their properties.    Connections to curriculum and pedagogy.