Course Number: mae 4350 Credit Hours: 3 Semester Hours Prerequisites



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Department of Teaching & Learning
Course Title: Principles and Methods: K-9 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 college-level math, but are not required to complete MAE 4310 as a perquisite to this course.

Course Logistics:

  • Terms: fall, spring, summer

  • Hybrid/Hyflex: online/in-class/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 K-9 mathematics teaching in a diverse setting.


Course Connection to the College of Education (COE) Conceptual Framework:

As reflective decision-makers 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, TI-34II (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 Web-assisted 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/0081015-mathfs.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/professional-dev/the-fl-educator-accomplished-practices.stml

Florida Subject Area Competencies (ESOL)

http://www.fldoe.org/core/fileparse.php/7719/urlt/0071749-mnellf.pdf

Florida Subject Matter Competencies (FSMCS: ELE MA)

http:///www.fldoe.org/accountability/assessments/postsecondary-assessment/ftce/tdi/comps- and-skills.stml

National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics (NCTM) at: www.nctm.org



Course Objectives/Student Learning Outcomes:

  1. 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 teacher-made 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

  • NCTM: 3.1, 3.2, 3.3, 3.4

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

  • NCTM: 3.4, 7.5, 8.1- 8.9

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, 11.1-11.7, 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, 3-D 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 in-class

#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 take-home examinations for Assessment #2, due in-class 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 in-class (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 word-processed, turned in with an attached rubric-grading sheet on the date that appears in the syllabus (no assignments will be accepted after the due date), and handed-in 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 problem-solving, and clinical field (teaching) experiences.
As requested by university administration, all students should use their FAU MYFAU E-mail for the course when communicating with the instructor.


  1. Journal

Keep a Math Problem-Solving 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, problem-solving process/strategies used, and especially your problem-solving 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 3-Point 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 Problem-Solving

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: Problem-Solving and Content Knowledge Exercises
Objective(s): Solves math problems using the problem-solving process and applies problem-solving 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: Problem-Solving 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 higher-order 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 4-Mat 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 4-Mat

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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