Department of Teaching & Learning
Course Title: Principles and Methods: K9 School Math
Course Number: MAE 4350
Credit Hours: 3 Semester Hours
Prerequisites: MAE 4310*, LAE 4353 & TSL 4080
*Note: Students majoring in ESE are required to complete 6 credits in collegelevel math, but are not required to complete MAE 4310 as a perquisite to this course.
Course Logistics:

Terms: fall, spring, summer

Hybrid/Hyflex: online/inclass/mixed mode

Class location and time: Davie, Boca, Jupiter (time not available)
Instructor: To be determined
Office Address/Office Hours: To be determined
Phone Number/Email: To be determined
TA contact information: Not applicable
Catalog Description:
A review of mathematics information and skills and a study of methods/materials related to K9 mathematics teaching in a diverse setting.
Course Connection to the College of Education (COE) Conceptual Framework:
As reflective decisionmakers students will continue to refine their abilities to make informed decisions, exhibit ethical behavior, and provide evidence of being capable professionals who have mastered the mathematics content knowledge necessary to document emerging numeracy/mathematics development, develop lessons plans that demonstrate respect for the developmental characteristics of young people and needs of ESOL students, follow the standards for mathematical practice, and demonstrate the capability to teach and respect all young people.
Required Texts/Readings:
Reys, R., Lindquist, M., Lambdin, D., Smith, N. & Suydam, M. (2015). Helping children learn mathematics (11th ed.). Boston, MA: John Wiley & Sons Publishing, Inc.
Individual Professor Required Materials on Blackboard at no charge (to be announced in class).
Special Course Requirements:

Students in this course are required to have an active LiveText account to track mastery of programs skills, competencies and critical assignments, and to meet program and college accreditation requirements. To receive a passing grade in this course, you must have a LiveText account within the first four (4) weeks of the fall or spring semester, within the first three (3) weeks of summer session, or after the first class of a fast track course. Students who do not have an active LiveText account may have an academic hold placed on their records. For information regarding account activation, please go to the COE website at: http://coe.fau.edu/livetext. For information pertaining to financial assistance, please go to: http://www.coe.fau.edu/livetext/livetextfinincialassistane.htm.

Clinical field or online observations (10 hours, using Effective Teaching Practices placement).

Triman Compass, crayons/markers, scissors, glue stick, composition notebook, binder, Texas Instruments Explorer Calculator, Explorer Plus Calculator, TI34II (any fraction calculator.)

Florida Department of Education Electronic Curriculum Planning Tool, Software for New Florida Curriculum Frameworks, Math. Florida DOE at: http://www,cpalms.org/Public/.

Math Vantage Video Series http://www.iptv.org/series.cfm/3449/math_vantage/ep:104/episodes.

Marilyn Burns Manipulative Video Series at: http://www.mathsolutions.com/.

Beacon Learning Center Website at: http://www.beaconic.org/BEACON/default2.asp.

Blackboard Webassisted Learning with FAU at: http://www.blackboard.fau.edu.
Supplementary/Recommended Readings:
Parrish, S. (2014). Number Talks: Helping children build mental math and computation strategies. Sausalito, CA: Math Solutions.
Diezmann, C. & Yelland, N. (2000). Developing Mathematical Literacy in the Early Childhood Years. In Nicola J. Yelland (Ed.) Promoting meaningful learning: innovations in educating early childhood professionals. Washington, DC: National Association for the Education of Young Children (NAEYC).
National Council of Teachers of Mathematics (2006). Curriculum focal points. NCTM: Reston, VA.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. NCTM: Reston, VA.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. NCTM: Reston, VA.
Common Core State Standards for Mathematics (CCSS) at: http://www.corestandards.org/math
Florida Department of Education Curriculum Frameworks (Mathematics) at: http://www.fldoe.org/core/fileparse.php/5390/urlt/0081015mathfs.pdf
Standards and Guidelines Used for Developing Course Objectives:
Association for Childhood Education International Elementary Education Guidelines (ACEI)
https://www.acei.org/sites/default/files/aceielementarysupportingexplanation.507.pdf
Florida Educator Accomplished Practices (EAP)
http://www.fldoe.org/teaching/professionaldev/thefleducatoraccomplishedpractices.stml
Florida Subject Area Competencies (ESOL)
http://www.fldoe.org/core/fileparse.php/7719/urlt/0071749mnellf.pdf
Florida Subject Matter Competencies (FSMCS: ELE MA)
http:///www.fldoe.org/accountability/assessments/postsecondaryassessment/ftce/tdi/comps andskills.stml
National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics (NCTM) at: www.nctm.org
Course Objectives/Student Learning Outcomes:

Describe the Curriculum and Evaluation Standards for School Mathematics (NCTM, the Florida Sunshine state focus, and the Common Core Standards) and explain their significance to teachers and children in designing lessons exemplifying their focus.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 8.1, 8.2, 10.1, 10.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4

NCTM: 5.1, 5.2, 5.3, 8.1 8.9, 16.1, 16.2, 16.3
2. Describe and demonstrate methods of instruction that provide well balanced instructional lessons including the experience of informal experiences in introducing concepts, identifying steps in a classroom lesson, and describing ways to facilitate mathematical investigation for all while creating a positive classroom management plan that is conducive to learning and motivating for all students.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 8.1, 8.2, 10.1, 10.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4

NCTM: 5.1, 5.2, 5.3, 8.1 8.9, 16.1, 16.2, 16.3
3. Explain the role of manipulatives in the teaching of mathematics and describe some commonly used commercial and teachermade manipulatives for modeling.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4,4.0, 5.1, 5.2

EAP: 10.1, 10.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4

NCTM: 5.1, 5.2, 5.3, 8.1 8.9
4. Demonstrate the use of technology in the teaching of mathematics.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 12.1, 12.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4

NCTM: 6.1
5. Describe the role of collaboration, mentors, cooperation, and drill in the teaching of math.

ACEI: 5.1, 5.2, 12.1

EAP: 11.1

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4

NCTM: 2.1, 2.2, 2.3, 2.4, 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 5.1, 5.2, 5.3, 8.1 8.9
6. Describe the role of verbal and written communication (literature) in the teaching of math.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 2.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4
7. Explain alternative assessment forms that provide insight into individual unique learning styles.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 1.1, 5.1, 5.2, 9.1

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4
8. Explain the role of integration, family involvement, and resources that provide meaningful math lessons to all children and involve the cultural characteristics of Florida’s LEP population including culture/diversity/equity issues/special needs/ESOL.

ACEI: 2.3, 3.1, 3,2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 5.1, 5.2, 10.1, 10.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4

NCTM: 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 5.1, 5.2, 5.3, 7.1 7.6, 8.1 8.9
9. Describe and demonstrate the current NCTM/SSS/Common Core view of problem solving and
describe the problem solving strategies.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 4.1, 4.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 12.1, 12.2, 12.3, 12.4

NCTM: 1.1, 1.2, 1.3, 1.4, 2.1
10. Describe and demonstrate the current NCTM/SSS/Common Core view of number sense/
estimation/mental calculation and describe lessons and assessment techniques that encourage
number sense as well as fractions, decimals, ratios, percents, proportions, and number theory.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 1.1, 8.1, 8.2, 10.1, 10.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 7.1 7.9, 12.1, 12.2, 12.3, 12.4

NCTM: 3.4, 8.1 8.9, 9.1 9.8
11. Describe and demonstrate the current NCTM/SSS/Common Core view of geometry and spatial
sense and measurement in the curriculum.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 1.1, 8.1, 8.2, 10.1, 10.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 8.1, 8.2, 8.3, 8.4, 8.5, 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 12.1, 12.2, 12.3, 12.4

NCTM: 3.4, 8.1 8.9, 9.1 9.8, 11.111.7, 13.1, 13.2, 13.3, 15.1, 15.2, 15.3, 15.4, 15.5
12. Describe and demonstrate the current NCTM/SSS/Common Core view of data analysis and
probability in today’s world and describe activities that encourage students to collect and
analyze data as well as predict outcomes.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 1.1, 8.1, 8.2, 10.1, 10.2

ESOL: 5.4, 6.10. 14.3, 17.5

FSMCS: 11.1 11.6, 12.1, 12.2, 12.3, 12.4

NCTM: 3.4, 8.1 8.9, 14.1 14.6
13. Describe and demonstrate the current NCTM/SSS/Common Core view of math as the science
of patterns and order and describe lessons that involve patterns that lead to algebraic thinking.

ACEI: 2.3, 3.1, 3.2, 3.3, 3.4, 4.0, 5.1, 5.2

EAP: 1.1, 8.1, 8.2, 10.1, 10.2

ESOL: 5.4, 6.10, 14.3, 17.5

FSMCS: 10.1, 10.2, 10.3, 12.1, 12.2, 12.3, 12.4

NCTM: 3.4, 8.1 8.9, 10.1 10.6
Please note on the Content Topical Outline (below), the specific dates that readings are due to be discussed in class. Prior to class, you are required to read all chapters and have summaries, reflections, and discussion question completed and in your journals. Be prepared to share all of this information with the class, as well as, your math journal problem solving.
Content Topical Outline: Reys text  Helping Children Learn Mathematics (citation page 1).
Week

Topics

#1

Introduction and course overview.

#2

Problem Solving, the National Council of Teachers of Mathematics (NCTM) and the Florida Math Standards:
Assignments  Reys: Chapter 1 Math Education, Overview, 5 Problem Solving and Geometry Beginnings.

#3

Geometry Terms, Tessellation, Less/Unit Plans, Learning Theory:
Assignments – Reys: Chapter 2 Math Learning Theory and Chapter 3 Math Lesson Planning.

#4

Geometry, 3D Geometry, Measurement, Lesson Planning, NCTM Standards:
Assignments  Reys: Chapter 15 Geometry and Chapter 16 Measurement.

#5

Geometry, Coordinate Geometry and Algebra:
Assignments  Reys: Chapter 14 Algebra.

#6

Lecture/Notes: Numeration Systems:
Assignments  Reys: Chapter 7 Prenumber Sense.
Assessment #1: Completed inclass

#7

Whole Numbers and Operations:
Assignments  Reys: Chapter 8 Numbers and Chapter 9 Operation Strategies.

#8
Offsite

Clinical Week:
Meeting in Schools, Observations, Teaching and Research.

#9

Money/Time and Math Assessments:
Assignments  Reys: Chapter 4 Estimation & Review and Chapter 16 Measurement.
Distribute takehome examinations for Assessment #2, due inclass week #10

#10

Integers/Number Theory and Cooperative Learning:
Assignments  Reys: Chapter 10 Computations/Operations, Chapter11 Alternative Computational Algorithms,
and Chapter 18 Number Theory.
Assessment #2: Due inclass (see week #9)

#11
Offsite

Clinical Week:
Meeting in Schools, Observations, Teaching and Research.

#12

Fractions, Decimals, Percents and Technology/ Fractions, Calculators:
Assignments  Reys: Chapter 12 Fractions and Chapter 12 Decimals, Percents, and Ratios.

#13
Offsite

Clinical Week:
Meeting in Schools, Observations, Teaching and Research.

#14

Statistics/Data Analysis and Probability:
Assignments  Reys: Chapter 17 Data Analysis and Probability.
Turn in 3 questions for Assessment #3 and turn in all work due for grading (to be returned week #16).

#15

Assessment #3: Oral Final Examination
Review and study tips for Assessment #4

#16

Assessment #4 (Subject Matter Content Test) and Return Work

Course Assignments/Requirements:
Assignments will include, but will not be limited to, the following: class work, homework, tests and quizzes, computer/calculator activities, clinical experiences, journal problems, research position paper/case study, and projects (both group and individual). All assignments turned in for a grade must be wordprocessed, turned in with an attached rubricgrading sheet on the date that appears in the syllabus (no assignments will be accepted after the due date), and handedin on LiveText, if it is a critical assignment (with the exception of the ABC Math Book). Please see the professor for special needs.
MAE students are required to apply the ESOL/Accommodation teaching practices, as discussed in class, in unit/lesson plans, journal problemsolving, and clinical field (teaching) experiences.
As requested by university administration, all students should use their FAU MYFAU Email for the course when communicating with the instructor.

Journal
Keep a Math ProblemSolving Journal in a composition notebook. You will receive 10 Problem Solving worksheets throughout the semester (approximately one each week). Do each of the assignments in your notebook describing all steps, problemsolving process/strategies used, and especially your problemsolving thinking processes written in detail for full credit. You will be graded on your effort, completion of the problems, and thinking processes. Please feel free to write about feelings and anything else you confront as you do the problems. Also, read each chapter in your textbook and include a short one paragraph summary/reflection in your notebook. Your grade will be determined by the evidence you show in your journal for completing these tasks. Please document all work/readings. Please show evidence of completing the readings and journal problems and include a grade sheet (next page) when turning in your work to be graded. MAE Students must pass this critical assignment with at least "Meets Expectations" for their program based on the 3Point rubric for the assignment. You will be allowed a chance for feedback and remediation if you "Do Not Meet Expectations." Revisions can be made to improve the critical assignment. You will be given sufficient support and guidance to successfully meet expectations for the critical assignment.
Journal Grade Sheet
Criteria

Possible Points

Points Earned

All 10 Problems Tried & Detailed ProblemSolving

40


Problem Solving Strategies Included/Written Out

20


ESOL Strategies for Teaching Written Out

20


Thinking Processes in Solving problems Written Out

30


All Chapters Read w/Paragraph Summaries/Reflections

60


Active Participation in Class Sharing/Neatness

20


Turned in with Grade Sheet

10


Total

200


Critical Assignment Title: ProblemSolving and Content Knowledge Exercises
Objective(s): Solves math problems using the problemsolving process and applies problemsolving strategies showing reflection and critical thought in solving the problems and teaching/providing methodology for teaching the mathematics problem in class and displaying content knowledge of the material.
Assessment: ProblemSolving in math journal with suggestions for teaching the problem.
Rubric for Journal
Performance

Criteria for Exceeds Expectations
(E)

Criteria for Meets Expectations
(M)

Criteria for Does Not Meet Expectations (D)

Rating

Demonstrates accuracy of subject matter knowledge in the problem solving process.
Demonstrates and models the use of higherorder thinking abilities, processes, and strategies.
Uses ESOL, technology, and other strategies/tools in solving/teaching problem solving and critical thought.
Modifies and adapts math concepts with increased attention to the learners’ creative thinking abilities/ thought process.

Complete accuracy demonstrated in the problem solving process.
Chooses and applies a correct strategy and follows a clear thought process.
Clearly identifies ESOL, technology and other strategies/tools used in teaching problem solving.
Clear and sensible modifications of problem for the learner to understand thought process. State math standard covered.

Partial arithmetic error, but shows good problem solving process.
Uses a correct strategy but may lack process and/or explanation to solve.
Shares some ESOL, technology and strategies/ tools used for teaching problem solving.
Teaches/provides methods for teaching problem solving with some class support. Lacks math standard

Incorrect arithmetic and problem solving process.
Incorrect thinking process and strategies employed.
Provides no ESOL, tech or other strategies/ tools used for teaching problem solving.
Does not teach/provide methods for teaching the math problem or problem solving. Math standard not used.


Overall Rating/Pts Earned:





Improvements Needed:





First Attempt Date:





Second Attempt Date:





Third Attempt Date:





(2) Create a Lesson Plan/Currculum Project using Common Course State Standards in Math
Please see the sample lesson plan in the classroom or at the beaconlearningcenter.com. Incorporate Best Practices, grade level expectations from the Common Core State Standards (CCSS), and cite all sources in APA. Include several websites for internet field trips with a guide/activity sheet for students, manipulatives, Cooperative Learning, ESOL strategies, a children’s literature book, etc. (all components of the sample lesson plan). Use the FAU Lesson Plan Format. Incorporate the 4Mat System in the Instructional Procedures section of the lesson.
Grade Sheet for Lesson Plan
Criteria

Possible Points

Points Earned

Name, title, typed, post on Blackboard/LiveText

20


Best Practices, activity, manipulative, tech, ESOL, etc.

40


1 Lesson Plan covering FL math standards/assessments

80


FAU Long Lesson Plan Format used with 4Mat

60


Websites, technology, manipulatives, Children’s Literature

60


Detail appropriate for a substitute teacher (handouts)

40


Overall quality/thought involved in curriculum/lesson

40


Shares curriculum project and highlights with classmates

40


Above and beyond effort/quality shown

20


Total

400


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