sistema universitario ana g. méndez school for ... 173 dlp... · clasificar triángulos y...

Sistema Universitario Ana G. Méndez School for Professional Studies

Florida Campuses Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo

MATH 173

PLANE GEOMETRY AND SPACE I GEOMETRÍA PLANA Y DEL ESPACIO I

© Sistema Universitario Ana G. Méndez, 2008 Derechos Reservados.

© Ana G. Méndez University System, 2008. All rights reserved

MATH 173 Plane Geometry and Space I 2

Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves

TABLA DE CONTENIDO/TABLE OF CONTENTS

Página/Page

PRONTUARIO ................................................................................................................ 3

STUDY GUIDE .............................................................................................................. 10

WORKSHOP ONE ........................................................................................................ 17

TALLER DOS ................................................................................................................ 22

WORKSHOP THREE .................................................................................................... 26

TALLER CUATRO......................................................................................................... 30

WORKSHOP FIVE/TALLER CINCO ............................................................................. 33

ANEJO A/APPENDIX A ................................................................................................ 40

ANEJO B/APPENDIX B ................................................................................................ 42

ANEJO C/APPENDIX C ................................................................................................ 47

ANEJO D/APPENDIX D ................................................................................................ 49

ANEJO E/APPENDIX E ................................................................................................ 50

ANEJO F/APPENDIX F ................................................................................................. 52

ANEJO G/APPENDIX G ................................................................................................ 54

ANEJO H/APPENDIX H ................................................................................................ 59

ANEJO I/APPENDIX I ................................................................................................... 61

ANEJO J/APPENDIX J .................................................................................................. 62

ANEJO K/APPENDIX K ................................................................................................ 63

ANEJO L/APPENDIX L ................................................................................................. 65

ANEJO M/APPENDIX M ............................................................................................... 66

ANEJO N/APPENDIX N ................................................................................................ 67

ANEJO O/APPENDIX O ................................................................................................ 68



PRONTUARIO

Título del Curso Geometría Plana y del Espacio I

Codificación MATH 173

Duración Cinco Semanas

Prerrequisitos MATH 151 – 152

Descripción

Este es un curso de geometría para estudiantes de Educación con especialidad en

Matemáticas. El propósito principal del curso es presentar los conceptos fundamentales

de la geometría Euclidiana del plano, y de la geometría del espacio con un enfoque

moderno en términos de las definiciones y notación. Se aspira a que los estudiantes

logren un dominio práctico de la materia a través de la aplicación de los conceptos en

la resolución de ejercicios.

En el curso de Matemáticas 173 se estudiarán temas que incluyen los conceptos

básicos relacionados con planos, líneas rectas, ángulos, polígonos, etc. Se desarrollará

el método deductivo para realizar demostraciones (pruebas), se discutirán los

conceptos de perpendicularidad y paralelismo, las propiedades y los teoremas

relacionados con triángulos, rectángulos y la geometría de coordenadas.

Objetivos Generales

1. Entender los términos básicos de geometría como punto, línea, plano y ángulos.

2. Distinguir entre el razonamiento inductivo y deductivo.

3. Realizar demostraciones (pruebas) geométricas.

4. Utilizar postulados para realizar demostraciones (pruebas) geométricas.

5. Clasificar triángulos y demostrar congruencia entre triángulos.

6. Demostrar y aplicar teoremas sobre rectas y planos.

7. Identificar los diferentes tipos de ángulos.

8. Identificar líneas paralelas y polígonos.

9. Entender los conceptos de perpendicularidad y paralelismo.

10. Entender el sistema de coordenadas cartesianas.

11. Localizar puntos en el plano cartesiano, hallar la distancia entre dos puntos, hallar la

pendiente de una recta y trazar la grafica de ecuaciones.



12. Resolver problemas verbales utilizando la formula de la distancia y la del punto

medio.

Texto y Recursos

Lial, M. L., Brown, B. A., Steffensen, A. R., & Murphy Johnson, L. (2004). Essentials of

Geometry for College Students. (2nd ed.). Prentice Hall.

Marin Isaacs, I. (2004). Geometry for College Students. (4th ed.). Prentice Hall.

Referencias y Material Suplementario

Baldwin, Harry L. (1993). Essential Geometry. McGraw Hill, New York.

Geiter & Peterson, Prindle. (1991). Geometry for College Students. (1st ed.). Weber &

Schmidt, Boston.

Evaluación

1. Trabajos para realizar previo a cada taller 15%

Antes de cada taller, el/la estudiante deberá completar una variedad de ejercicios y

preguntas guías que le ayudarán en el proceso de comprensión de conceptos que se

desarrollarán en la práctica de las actividades que se efectuarán en el taller. Los

mismos, constarán de una selección de ejercicios asignados por el/la facilitador/a o de

la búsqueda en la Internet de información básica conceptual. Deberán entregarse a

partir de la primera reunión. Cada trabajo tiene un valor de 20 puntos para un total de

100. No entregar éstos en el tiempo establecido conlleva un descuento de 5 puntos por

cada tardanza en la entrega.

2. Cuatro (4) Trabajos Cooperativos 15%

El/la estudiante tendrá la oportunidad de trabajar en grupo con diferentes compañeros

matriculados en el curso MATH 173. El/la facilitador/a estará a cargo de incorporar los

grupos en cada uno de los talleres. Cada grupo trabajará una situación asignada que

resolverá y presentará a la clase. La solución del trabajo se entregará al finalizar la

presentación de los mismos en cada taller con el nombre de todos los participantes por

grupo en la hoja provista por el/la facilitador/a. Habrá cuatro (4) trabajos cooperativos a

partir del primer taller, cada uno de ellos con un valor de 25 puntos para un total

agregado de 100. En la quinta reunión no se realizará esta actividad .

3. Cuatro (4) pruebas para realizar en los talleres 20%



A partir de la primera reunión y hasta el cuarto taller, una vez discutidas las tareas

realizadas previo a cada taller, el/la estudiante estará capacitado/a para contestar una

prueba corta individual. Esta constará de una selección de ejercicios prácticos que

fortalecerán las destrezas y conceptos estudiados y tendrá un valor de 25 puntos en

cada taller, para un total de 100. En la quinta reunión no se realizará esta actividad .

4. Trabajo Final: Concurso 25%

Durante el quinto taller, se llevará a cabo un trabajo final; concurso. Este, será un

trabajo colaborativo. Sin embargo, la evaluación considerará tanto variables de

desempeño individual como grupal. El/la facilitador/a seleccionará aleatoriamente a

los/las estudiantes que integrarán los grupos. Cada uno de los grupos tendrá la

oportunidad de contestar ejercicios prácticos de los temas que se han facilitado en los

talleres. Esta actividad tiene un valor de 150 puntos. El/la facilitador/a informará la

composición de los grupos en el cuarto taller.

5. Portafolio 10%

En el quinto taller, los estudiantes entregarán un portafolio. (Ver Anejo E: Portafolio).

Este trabajo tiene un valor de 100 puntos y se realizará individualmente (Ver Anejo G:

Rúbrica para la evaluación del Portafolio). El facilitador informara durante el taller uno

cuáles serán los trabajos asignados que se incluirán en el portafolio. Las actividades

efectuadas en cada uno de los talleres, brindarán las destrezas necesarias para que el

estudiante pueda desarrollar el portafolio.

6. Asistencia y Participación 15%

La asistencia a todos los talleres es necesaria e indispensable. En caso de ausencia,

el/la estudiante debe realizar todas las gestiones necesarias para comunicarse con el/la

facilitador/a de manera que pueda prepararse adecuadamente para la próxima reunión.

Todas las actividades realizadas en el taller ausente, sujetas a evaluación, serán

consideradas y ponderadas de acuerdo con los parámetros específicos. Es decir, es

vigente la pérdida de puntuación por cada trabajo del cual no fue partícipe el/la

estudiante por causa de la ausencia. (Ver Anejo A: Parámetros Específicos para

Evaluar Asistencia y Participación)

7. Escala de evaluación



La evaluación final se calculará a base de promedios ponderados, pero considerando la

escala estándar de por cientos.

Nota A B C D F

Por ciento 90 – 100 80 – 89 79 – 70 69 – 60 59 – 0

NOTA:

Es de suma importancia que el estudiante tenga una calculadora científica , ya que es

una de las herramientas principales para poder realizar eficientemente las tareas y

actividades provistas para cada taller. También deberá tener regla y papel

cuadriculado.

Descripción de las Normas del Curso

1. Este curso sigue el programa “Discipline-Based Dual Language Immersion

Model®” del Sistema Universitario Ana G. Méndez, el mismo esta diseñado para

promover el desarrollo de cada estudiante como un profesional bilingüe. Cada

taller será facilitado en inglés y español, utilizando el modelo 50/50. Esto

significa que cada taller deberá ser conducido enteramente en el lenguaje

especificado. Los lenguajes serán alternados en cada taller para asegurar que

el curso se ofrece 50% en inglés y 50% en español. Para mantener un balance,

el módulo debe especificar que se utilizarán ambos idiomas en el quinto taller,

dividiendo el tiempo y las actividades equitativamente entre ambos idiomas. Si

un estudiante tiene dificultad en hacer una pregunta en el idioma especificado,

bien puede escoger el idioma de preferencia para hacer la pregunta. Sin

embargo, el facilitador deberá contestar la misma en el idioma designado para

ese taller. Esto deberá ser una excepción a las reglas pues es importante que

los estudiantes utilicen el idioma designado. Esto no aplica a los cursos de

lenguaje que deben ser desarrollados en el idioma propio todo en inglés o todo

en español según aplique.

2. El curso es conducido en formato acelerado, eso requiere que los estudiantes se

preparen antes de cada taller de acuerdo al módulo. Cada taller requiere un

promedio de diez (10) horas de preparación y en ocasiones requiere más.

3. La asistencia a todos los talleres es obligatoria. El estudiante que se ausente al

taller deberá presentar una excusa razonable al facilitador. El facilitador



evaluará si la ausencia es justificada y decidirá como el estudiante repondrá el

trabajo perdido, de ser necesario. El facilitador decidirá uno de los siguientes:

permitirle al estudiante reponer el trabajo o asignarle trabajo adicional en

adición al trabajo a ser repuesto.

Toda tarea a ser completada antes del taller deberá ser entregada en la fecha

asignada. El facilitador ajustará la nota de las tareas repuestas.

4. Si un estudiante se ausenta a más de un taller el facilitador tendrá las siguientes

opciones:

a. Si es a dos talleres, el facilitador reducirá una nota por debajo basado en

la nota existente.

b. Si el estudiante se ausenta a tres talleres, el facilitador reducirá la nota a

dos por debajo de la nota existente.

5. La asistencia y participación en clase de actividades y presentaciones orales es

extremadamente importante pues no se pueden reponer. Si el estudiante provee

una excusa válida y verificable, el facilitador determinará una actividad

equivalente a evaluar que sustituya la misma. Esta actividad deberá incluir el

mismo contenido y componentes del lenguaje como la presentación oral o

actividad a ser repuesta.

6. En actividades de grupo el grupo será evaluado por su trabajo final. Sin

embargo, cada miembro de grupo deberá participar y cooperar para lograr un

trabajo de excelencia, pero recibirán una calificación individual.

7. Se espera que todo trabajo escrito sea de la autoría de cada estudiante y no

plagiado. Se debe entender que todo trabajo sometido esta citado

apropiadamente o parafraseado y citado dando atención al autor. Todo

estudiante debe ser el autor de su propio trabajo. Todo trabajo que sea plagiado,

copiado o presente trazos de otro será calificado con cero (vea la política de

honestidad académica).

8. Si el facilitador hace cambios al módulo o guía de estudio, deberá discutirlos y

entregar copia a los estudiantes por escrito al principio del primer taller.

9. El facilitador establecerá los medios para contactar a los estudiantes proveyendo

su correo electrónico, teléfonos, y el horario disponibles.



10. EL uso de celulares esta prohibido durante las sesiones de clase; de haber una

necesidad, deberá permanecer en vibración o en silencio.

11. La visita de niños y familiares no registrados en el curso no está permitida en el

salón de clases.

12. Todo estudiante esta sujeto a las políticas y normas de conducta y

comportamiento que rigen al SUAGM y el curso.

Nota: Si por alguna razón no puede acceder las dire cciones electrónicas

ofrecidas en el módulo, no se limite a ellas. Exis ten otros motores de búsqueda y

sitios Web que podrá utilizar para la búsqueda de l a información deseada. Entre

ellas están:

• www.google.com

• www.altavista.com

• www.ask.com

• www.excite.com

• www.pregunta.com

• www.findarticles.com

• www.telemundo.yahoo.com

• www.bibliotecavirtualut.suagm.edu

• www.eric.ed.gov/

• www.flelibrary.org/

El/la facilitador(a) puede realizar cambios a las d irecciones electrónicas y/o

añadir algunas de ser necesario.

Filosofía y Metodología Educativa

Este curso está basado en la teoría educativa del Constructivismo.

Constructivismo es una filosofía de aprendizaje fundamentada en la premisa, de que,

reflexionando a través de nuestras experiencias, podemos construir nuestro propio

conocimiento sobre el mundo en el que vivimos.

Cada uno de nosotros genera nuestras propias “reglas “y “métodos mentales”

que utilizamos para darle sentido a nuestras experiencias. Aprender, por lo tanto, es

simplemente el proceso de ajustar nuestros modelos mentales para poder acomodar



nuevas experiencias. Como facilitadores, nuestro enfoque es el mantener una

conexión entre los hechos y fomentar un nuevo entendimiento en los estudiantes.

También, intentamos adaptar nuestras estrategias de enseñanza a las respuestas de

nuestros estudiantes y motivar a los mismos a analizar, interpretar y predecir

información.

Existen varios principios para el constructivismo, entre los cuales están:

1. El aprendizaje es una búsqueda de significados. Por lo tanto, el aprendizaje debe

comenzar con situaciones en las cuales los estudiantes estén buscando

activamente construir un significado.

2. Significado requiere comprender todas las partes. Y, las partes deben entenderse

en el contexto del todo. Por lo tanto, el proceso de aprendizaje se enfoca en los

conceptos primarios, no en hechos aislados.

3. Para enseñar bien, debemos entender los modelos mentales que los estudiantes

utilizan para percibir el mundo y las presunciones que ellos hacen para apoyar

dichos modelos.

4. El propósito del aprendizaje, es para un individuo, el construir su propio significado,

no sólo memorizar las contestaciones “correctas” y repetir el significado de otra

persona. Como la educación es intrínsicamente interdisciplinaria, la única forma

válida para asegurar el aprendizaje es hacer del avalúo parte esencial de dicho

proceso, asegurando que el mismo provea a los estudiantes con la información

sobre la calidad de su aprendizaje.

5. La evaluación debe servir como una herramienta de auto-análisis.

6. Proveer herramientas y ambientes que ayuden a los estudiantes a interpretar las

múltiples perspectivas que existen en el mundo.

7. El aprendizaje debe ser controlado internamente y analizado por el estudiante.



STUDY GUIDE

Course Title Plane Geometry and Space I

Code MATH 173

Time Length Five Weeks

Prerequisites MATH 151 – 152

Description

This is a course in geometry for students specializing in Mathematic Education. The

main purpose of this class is to present the fundamental geometric concepts including

Euclidean geometry of the plane and geometry of the space providing a modern focus

in terms of the definitions and notation. It is expected for the students to obtain a

practical knowledge of the subject by applying the concepts in the solution of exercises.

MATH 173 will cover the basic concepts of geometry including the plane, straight

lines, angles, polygons, etc. This course will develop the deductive method to formalize

geometric proofs; will discuss the concepts of perpendicularity and parallelism, the

properties and theorems related to triangles, rectangles and the geometry of

coordinates.

General Objectives

1. Understand the basic concepts in geometry such as point, line, plane and angles.

2. Distinguish between inductive and deductive reasoning.

3. Formalize geometric proofs.

4. Use postulates to formalize geometric proofs.

5. Classified triangles and demonstrate congruent triangles.

6. Demonstrate and apply theorems on straight lines and planes.

7. Identify the different types of angles.

8. Identify parallel lines and polygons.

9. Understand the concepts of perpendicularity and parallelism.

10. Understand the Cartesian Coordinate System.

11. Find points in the Cartesian plane, find the distance between two points,

calculate the slope of a straight line and construct the graph of an equation.

12. Solve verbal problems using the formula for distance and for the middle point.



Texts and Resources

Lial, M. L., Brown, B. A., Steffensen, A. R., & Murphy Johnson, L. (2004). Essentials of

Geometry for College Students. (2nd ed.). Prentice Hall.

Marin Isaacs, I. (2004). Geometry for College Students. (4th ed.). Prentice Hall.

References and Supplementary Materials

Baldwin, Harry L. (1993). Essential Geometry. McGraw Hill, New York.

Geiter & Peterson, Prindle. (1991). Geometry for College Students. (1st ed.). Weber &

Schmidt, Boston.

Evaluation

1. Assignment previous to each workshop 15%

Previous to each workshop students must finish certain assignments that will include

exercises and questions that will help them understand the concepts and prepare for

the activities in the workshop. The assignments will be selected by the facilitator from

problems in the textbook and/or Internet sites research related with the current topic.

The assignments must be submitted starting at the first meeting. Each assignment will

be worth twenty (20) points for an accumulated score of one hundred (100) points. Each

late assignment will be penalized with five (5) points.

2. Collaborative Exercises (4) 15%

Collaborative exercises will be given from meeting one until meeting fourth. The student

will have the opportunity to work in groups with different classmates registered in the

course. The facilitator will select randomly the student distribution in each group. Each

group will have assigned a situation or problems that they will develop, solve and

present to the class. The group solution to the exercise will be given to the facilitator at

the end of the class and will include the participants name on each group. It will be four

(4) collaborative exercises starting on workshop I. Each of these exercises will be worth

twenty-five (25) points for an accumulated score of one hundred (100) points. This

activity will not be done during workshop five.

3. Workshop tests (4) 20%

Starting on meeting one until meeting fourth, after the group assignments has been

completed and the assignments to do previous to each workshop have been discussed,

the students will be able to take an in-class test. The test will include several practice



exercises that will help the students to strengthen their skills obtained in the workshop.

Each test will be worth twenty-five (25) points for an accumulated score of one hundred

(100) points. This activity will not be done during workshop five.

4. Final Work (Contest) 25%

During workshop five, there will be a Final Work; Contest. This will be a collaborative

exercise; however, the evaluation will consider both aspects, individual and group

evaluation. The facilitator will select at random the student for each group. Each group

will have the opportunity to solve several practical exercises related to the topics

discussed during the course in the different workshops. This activity will be worth 150

points. The facilitator may select the groups during workshop four.

5. Portfolio 10%

I workshop five, the students will turn in a portfolio. (See Appendix E: Portfolio). This

activity will be done individually and will be worth one hundred (100) points (See

Appendix H: Rubric for Portfolio evaluation). During workshop one the facilitator will

inform the students the assigned work to be included in the portfolio. The activities

conducted in each workshop will provide the students the skill and knowledge

necessary to do the portfolio.

6. Attendance and participation 15%

Attendance is mandatory in all the workshops. In case of absence, the student will

contact the facilitator, in order to be preparing for the following meeting. All the activities

sustained in his absence will be subject to an evaluation based upon specific

parameters. In other words, the student will be penalized for each assignment that

he/she did not participate due to his/her absence (Annex A).

7. Grade scale

The final grading will be calculated base on average grades within the standard

percentages scale.

Grade A B C D F

Percentage 90 – 100 80 – 89 79 – 70 69 – 60 59 – 0

NOTE:



It is important that each student bring a scientific calculator . The calculator will be an

important tool to management effectively the task and activities listed in each workshop.

Also, a ruler and graph paper are required.

Description of Course Policies

1. This course follows the Sistema Universitario Ana G. Méndez Discipline-Based Dual

Language Immersion Model® designed to promote each student’s development as a

Dual Language Professional. Workshops will be facilitated in English and Spanish,

strictly using the 50/50 model. This means that each workshop will be conducted

entirely in the language specified. The language used in the workshops will

alternate to insure that 50% of the course will be conducted in English and 50% in

Spanish. To maintain this balance, the course module may specify that both

languages will be used during the fifth workshop, dividing that workshop’s time and

activities between the two languages. If students have difficulty with asking a

question in the target language in which the activity is being conducted, students

may choose to use their preferred language for that particular question. However,

the facilitator must answer in the language assigned for that particular day. This

should only be an exception as it is important for students to use the assigned

language. The 50/50 model does not apply to language courses where the delivery

of instruction must be conducted in the language taught (Spanish or English only).

2. The course is conducted in an accelerated format and requires that students prepare

in advance for each workshop according to the course module. Each workshop

requires an average ten hours of preparation but could require more.

3. Attendance at all class sessions is mandatory. A student that is absent to a

workshop must present the facilitator a reasonable excuse. The facilitator will

evaluate if the absence is justified and decide how the student will make up the

missing work, if applicable. The facilitator will decide on the following: allow the

student to make up the work, or allow the student to make up the work and assign

extra work to compensate for the missing class time.

Assignments required prior to the workshop must be completed and turned in on the

assigned date. The facilitator may decide to adjust the grade given for late

assignments and make-up work.



4. If a student is absent to more than one workshop the facilitator will have the

following options:

a. If a student misses two workshops, the facilitator may lower one grade based

on the students existing grade.

b. If the student misses three workshops, the facilitator may lower two grades

based on the students existing grade.

5. Student attendance and participation in oral presentations and special class

activities are extremely important as it is not possible to assure that they can be

made up. If the student provides a valid and verifiable excuse, the facilitator may

determine a substitute evaluation activity if he/she understands that an equivalent

activity is possible. This activity must include the same content and language

components as the oral presentation or special activity that was missed.

6. In cooperative activities the group will be assessed for their final work. However,

each member will have to collaborate to assure the success of the group and the

assessment will be done collectively as well as individually.

7. It is expected that all written work will be solely that of the student and should not be

plagiarized. That is, the student must be the author of all work submitted. All quoted

or paraphrased material must be properly cited, with credit given to its author or

publisher. It should be noted that plagiarized writings are easily detectable and

students should not risk losing credit for material that is clearly not their own (see

Academic Honesty Policy).

8. If the Facilitator makes changes to the study guide, such changes should be

discussed with and given to students in writing at the beginning of the first workshop.

9. The facilitator will establish a means of contacting students by providing an email

address, phone number, hours to be contacted and days.

10. The use of cellular phones is prohibited during sessions; if there is a need to have

one, it must be on vibrate or silent mode during class session.

11. Children or family members that are not registered in the course are not allowed to

the classrooms.

12. All students are subject to the policies regarding behavior in the university

community established by the institution and in this course.



Note: If for any reason you cannot access the URL’s presented in the module, do

not stop your investigation. There are many search engines and other links you

can use to search for information. These are some examples:

• www.google.com

• www.altavista.com

• www.ask.com

• www.excite.com

• www.pregunta.com

• www.findarticles.com

• www.telemundo.yahoo.com

• www.bibliotecavirtualut.suagm.edu

• www.eric.ed.gov/

• www.flelibrary.org/

The facilitator may make changes or add additional web resources if deemed

necessary.



Teaching Philosophy and Methodology

This course is grounded in the learning theory of Constructivism. Constructivism

is a philosophy of learning founded on the premise that, by reflecting on our

experiences, we construct our own understanding of the world in which we live.

Each of us generates our own “rules” and “mental models,” which we use to make

sense of our experiences. Learning, therefore, is simply the process of adjusting our

mental models to accommodate new experiences. As teachers, our focus is on making

connections between facts and fostering new understanding in students. We will also

attempt to tailor our teaching strategies to student responses and encourage students to

analyze, interpret and predict information.

There are several guiding principles of constructivism:

1. Learning is a search for meaning. Therefore, learning must start with the issues

around which students are actively trying to construct meaning.

2. Meaning requires understanding wholes as well as parts. And parts must be

understood in the context of wholes. Therefore, the learning process focuses on

primary concepts, not isolated facts.

3. In order to teach well, we must understand the mental models that students use to

perceive the world and the assumptions they make to support those models.

4. The purpose of learning is for an individual to construct his or her own meaning, not

just memorize the "right" answers and regurgitate someone else's meaning. Since

education is inherently interdisciplinary, the only valuable way to measure learning is

to make the assessment part of the learning process, ensuring it provides students

with information on the quality of their learning.

5. Evaluation should serve as a self-analysis tool.

6. Provide tools and environments that help learners interpret the multiple perspectives

of the world.

7. Learning should be internally controlled and mediated by the learner.



Workshop One

Specific Objectives:

At the end of this workshop, the student will be able to:

1. Distinguish between deductive and inductive reasoning examples.

2. Identify the points, lines, planes and real numbers postulates.

3. Define a line segment, ray and angles.

4. Identify the adjacent, supplementary, complementary, and special angles.

5. Measure, build and classify angles according to its measure.

6. Write assertions of the form "If…then".

7. Determine if an assertion "If…then" is true.

8. Give examples to illustrate that an assertion is true or false.

9. Rewrite direct and indirect tests.

Language Objectives

1. Demonstrate a command of standard English (vocabulary used, syntax and flow

of ideas)

2. Uses grammar appropriately and correctly.

3. Manages and uses verbs appropriately and correctly.

Electronic Links (URLs):

Inductive and Deductive Reasoning

http://ai.eecs.umich.edu/cogarch0/common/capa/reason.html

http://www.math.toronto.edu/mathnet/questionCorner/deductive.html

http://mathforum.org/library/drmath/view/55695.html

http://www.sparknotes.com/math/geometry3/inductiveanddeductivereasoning/sectio

n1.html

Angles

http://www.regentsprep.org/Regents/math/angles/LAngles.htm

http://www.homeschoolmath.net/teaching/g/angles.php

Points, Lines, Segments and Rays

http://www.learningwave.com/lwonline/geometry_section1/lessons/lines1.html

http://www.math.com/school/subject3/lessons/S3U1L2GL.html

Conditional Assertions



http://www.regentsprep.org/regents/math/tables/ifthen.htm

http://hubpages.com/hub/Geometry-Tutor

Assignments before Workshop One:

1. Take a look at the module. Pay close attention to the rubrics since they will be

used to assess your knowledge, language skills and class participation.

2. The student will search the internet links provided for the first workshop to find

the concepts that will be covered during the first meeting. Also, the student will

use the suggested textbook and/or the references indicated in the bibliography,

to study those chapters that cover the topics of deductive and inductive

reasoning, points, lines, planes, real numbers, angles, assertions, and geometric

tests. The student will turn it the homework properly identifying its name, course,

section and day.

3. Find information and examples on the following terms. If some of these concepts

are defined and denoted with symbols, the student should include them in the

homework:

• Inductive Reasoning

• Deductive Reasoning

• Points, lines, planes and real numbers

• Angles

• Classification of angles (i.e. Complementary, supplementary, adjacent)

• Geometric Assertions

• Geometric Tests

If the student has access to computer programs such as MS Office or Lotus

SmartSuite, he/she will be able to use them for the homework. This must be an

individual work; copies from the internet or from the URLs used will not be

accepted. (See Appendix A: Academic Honesty Policy).

Note: The facilitator can assign a selection of exercises that cover the topics of the

workshop. The student will solve the exercises and turn them in to the facilitator.

4. After searching the terms in part two above, the students will answer the

following questions as part of the assignment. Again, this must be an individual



work; copies from the internet or from the URLs used will not be accepted. (See

Appendix A: Academic Honesty Policy).

A. Answer the following questions in brief form:

• What is the difference between a postulate and a definition?

• What is the difference between a postulate and a theorem?

• How many lines can be built between two points?

• Can two supplementary angles be both obtuse?

B. Answer true or false using the following figure:

• Point B is in AC

• Point C is in AB

• If AC = 15 cm and CB = 10 cm, then AB = 150 cm

• ACD is another name for 2

• 1 and 2 are adjacent angles

• 1 is supplementary to DCB

C. Answer the following questions using the following figure:

2 1

D

B C A

45° 7 6

5 4

3

2

1 30°



• How much does 1 measures?




5. This assignment shall be turn in to the facilitator and shall be properly identified

with the student name, date and workshop. This assignment is worth 100 points;

the evaluation of this assignment will be 70% for content and 30% for language

objectives. (See Appendix B: Rubrics to evaluate assignments p rior to the

workshops).

Activities :

1. The facilitator will present and explain the objectives, the teaching methodology,

and the evaluation criteria for MATH 173. During this process, the facilitator will

verify that every student in the class has been registered in order to take this

course. Furthermore, the facilitator will review that every student has the module

and the textbook. Also, the facilitator will provide his/her contact information in

case of students need to contact him/her. The facilitator will establish the

schedule and days of contact.

2. The facilitator may conduct an ice breaking exercise to have the students

introduce them self. After all the students have been presented, a Student

Representative will be selected. Also, the facilitator will inform about other issues

or announcements such as new coming courses, holidays, and dates of the

Student Representative meeting.

3. The facilitator will discuss what should be included in a portfolio and what should

be included in it. The facilitator will provide specific information about the work to

be included in the portfolio and the rubrics for the portfolio evaluation. The

facilitator will answer any questions the students may have related to the

portfolio.

4. Assignment to be completed before workshop one: The student will submit the

assignments to the facilitator. The facilitator will clarify any doubts and will

answer any questions the student’s may have regarding the assignment.



5. The facilitator will discuss the material related to the objectives in workshop one

and may provide and discuss some practice problems during the workshop. The

facilitator will discuss the terms and provide examples that will help the learning

process and the application of these terms.

6. The facilitator will provide additional problems for the students to practice the

procedures associated with the solution of application problems. These problems

will allow the students to clarify any questions and to improve their skills and

knowledge in the workshop material.

7. Collaborative Exercise (see Appendix G ): After completion of the previous

activities the facilitator will divide the class in groups of three to five students.

Each group will work the following collaborative exercise. A speaker will be

selected in each group. The facilitator will let the students know how much time

they have to solve the problem. The solution will be turn in to the facilitator on a

piece of paper with the name of all the members of the group. (See appendix C:

Rubric to evaluate group work).

8. The facilitator will select one group and will ask them to solve and present results

of the collaborative exercise. Each group will have the opportunity to discuss

their solution if different from the solution presented by the first group.

9. Short Test : At the end of the workshop the students will take a short test that will

include the material covered during workshop one.

10. The facilitator will discuss the assignment to be completed before workshop two.

Also, the facilitator will provide a list of problems to be included as part of the

assignment before workshop two.

Assessment:

Short Test: The students will answer a short test at the end of the workshop about the

material discussed during workshop.

The students must also complete the Reflexive Diary found in Appendix F. These

activities must be included in the student portfolio to be submitted in Workshop Five.



Taller Dos

Objetivos Específicos:

Al finalizar el Taller, el estudiante:

1. Clasificará triángulos, identificará las partes del triángulo, y definirá ángulos

internos y externos de un triángulo.

2. Definirá segmentos congruentes, ángulos y triángulos.

3. Utilizará los postulados de congruencia para determinar si dos triángulos son

congruentes.

4. Demostrará y aplicará los teoremas de perpendicularidad.

5. Probará algunas propiedades de triángulos isósceles.

6. Definirá y demostrará líneas concurrentes, mediana, altura y ángulos bisectores

de un triangulo.

7. Definirá y probará la congruencia del triangulo recto.

8. Construirá diferentes tipos de triángulos.

Objetivos de Lenguaje:

1. Demostrar dominio del idioma Español (vocabulario, sintaxis, presentación de

ideas).

2. Utilización apropiada y correcta de gramática.

3. Aplicación y utilización correcta y apropiada de los verbos.

Enlaces Electrónicos:

Triángulos

http://www.aaamath.com/geo318-triangle-angles.html

http://www.aaamath.com/geo318-triangle-sides.html

http://www.math.clemson.edu/~rsimms/triangle/

http://home.blarg.net/~math/triangles.html

http://patricia91ej.wiki.zoho.com/Resoluci%C3%B3n-de-tri%C3%A1ngulos.html

Líneas y Planos

http://www.bymath.com/studyguide/geo/sec/geo14a.htm

http://tutormatematicas.com/GEO/Introduccion_puntos_lineas_segmentos_planos.html



Asignaciones antes del Taller Dos:

1. El/la estudiante leerá y buscará información relacionadas a los objetivos del taller

dos en los libros de texto recomendados o en direcciones electrónicas o cualquier

otra referencia bibliográfica.

2. Una vez realice la lectura, los estudiantes contestarán las siguientes preguntas.

Este es un trabajo individual; no se aceptarán copias del Internet o de las

direcciones electrónicas utilizadas. (Ver Anejo A: Política de Honestidad

Académica).

• Triángulos

• Diferente tipos de triángulo

• Segmentos congruentes, ángulos y triángulos.

• Postulados de congruencia

• Teoremas de perpendicularidad

3. El facilitador asignará problemas adicionales del libro de texto como parte de esta

tarea para entregar. Estos problemas ayudarán a los estudiantes a entender los

objetivos del taller. Este es un trabajo individual; no se aceptarán copias del Internet

o de las direcciones electrónicas utilizadas. (Ver Anejo A: Política de Honestidad

Académica).

4. Esta tarea deberá entregarla al facilitador debidamente identificada con su nombre,

fecha y taller. La misma tiene un valor de 100 puntos. La evaluación de esta tarea

estará dividida en 70% por contenido y 30% por objetivos de lenguaje. (Ver anejo

B: Matriz valorativa para evaluar tareas previas a los talleres).

Actividades:

1. El facilitador devolverá los trabajos completados por los estudiantes durante el taller

uno (Tarea y Trabajo Cooperativo). Estos trabajos estarán evaluados de acuerdo

con las matrices valorativas incluidas en el módulo. El facilitador discutirá la

puntuación obtenida con los estudiantes según sea necesario. El facilitador

contestará cualquier pregunta que los estudiantes tengan en relación a los trabajos

del taller uno. Estos trabajos serán incluidos en el Portafolio el cual será entregado

en el taller cinco.



2. Trabajo para realizar previo al Taller Dos : El/la estudiante entregará la tarea

asignada. El facilitador contestará preguntas relacionadas a la tarea y aclarará

todas las dudas que los estudiantes tengan.

3. El facilitador discutirá en la clase el material relacionado a los objetivos del taller y

podrá asignar o hacer algunos problemas de práctica durante el taller. Estos

problemas ayudarán a los estudiantes a aclarar dudas y contestar cualquier

pregunta que tengan lo cual los ayudará a mejorar su conocimiento y destrezas

referentes al material de la clase.

4. El facilitador dará problemas adicionales para que los estudiantes los resuelvan en

clase para practicar los procedimientos asociados con la solución de los mismos.

Estos problemas ayudarán a los estudiantes a clarificar cualquier duda o pregunta

que tengan, también los ayudará a mejorar el conocimiento sobre el material

discutido en el taller.

5. Trabajo cooperativo (ver Anejo G) : Luego de terminadas las actividades

anteriores, el facilitador dividirá la clase en grupos de tres a cinco estudiantes

dependiendo del tamaño de la clase. Cada grupo trabajará el siguiente ejercicio. El

facilitador les dirá a los estudiantes cuanto tiempo tienen para resolver el problema.

La solución será entregada en una hoja de papel con los nombres de los miembros

del grupo. (Ver anejo C: Matriz valorativa para evaluar trabaj o en grupo).

(Nota : El facilitador puede asignar otro trabajo cooperativo diferente al que esta en el

mádulo. Si el trabajo cooperativo es cambiado, el facilitador debe notificar al los

estudiantes del cambio en el taller anterior)

6. Prueba corta: Al final del taller los estudiantes tomarán una prueba corta sobre el

material discutido en el taller.

7. El facilitador discutirá la tarea que los estudiantes deben completar antes del

próximo taller. En adición, el facilitador proveerá una lista de los problemas a

resolver como parte de la tarea a entregar en el taller tres.

Avalúo

Prueba corta : Los estudiantes tomarán una prueba corta al final del taller sobre el

material del taller.



También redactará el Diario Reflexivo hallado en Anejo F. Estas actividades serán

incluidas en el Portafolio del estudiante que será entregado en el Taller Cinco.



Workshop Three Specific Objectives:

At the end of this workshop, the student will be able to:

1. Define parallel lines.

2. Determine if two lines are parallel using parallelism theorems and postulates.

3. Demonstrate and apply the transverse line theorem.

4. Define the angles formed by parallel lines.

5. Define and identify different types of polygons.

6. Determine if a figure is a polygon and if it is convex.

7. Find the sum of internal angles of a polygon.

8. Construct parallel lines and polygon

Language Objectives:


of ideas)




http://www.terragon.com/tkobrien/algebra/topics/parallellines/parallellines.html

http://www.math.psu.edu/geom/koltsova/section3.html

http://www.mathleague.com/help/geometry/polygons.htm


http://www.aaamath.com/geo318-polygons-numbers.html

http://www.math.com/tables/geometry/polygons.htm

http://www.mathsisfun.com/geometry/parallel-lines.html

http://mathforum.org/~sarah/hamilton/ham.lines.html

http://regentsprep.org/regents/math/angles/Lparallel.htm

http://library.thinkquest.org/2647/geometry/angle/parallel.htm

Assignments before Workshop Three:

1. The student will search the internet links provided for the third workshop to find








section and day.

2. Find information and examples on the following terms. If some of these concepts

are defined and denoted with symbols, the student should include them in the

homework:

• Parallel Lines

• Parallelism Postulates and Theorems

• Transverse lines Theorem

• Polygons (Types of polygons)





Watch the following video regarding parallel lines:

http://www.youtube.com/watch?v=1_3anRenfwA&feature=user

3. The facilitator will assign additional problems from the textbook as part of this

assignment. These problems will help students understand the terms and

objectives of this workshop. This must be an individual work; copies from the

internet or from the URLs used will not be accepted. (See Appendix A:





objectives. (See Appendix B: Rubrics to evaluate assignments pr ior to the

workshops).

5. You should be working with your portfolio.

Activities:



1. The facilitator will return the work completed by the students during workshop

two (Assignment, Short Test and Collaborative Exercise). The work completed

would be assessed based on the rubrics included in the module. The facilitator

will discuss the points obtained with the students as necessary. The facilitator will

answer any questions the students may have related to the workshop one. The

assessed work from workshop one will be included in the Portfolio that will be

turn in during workshop five.

2. The students will submit the assignments to the facilitator. The facilitator will

clarify any doubts and will answer any questions the student’s may have

regarding the assignment.

3. The facilitator will discuss the material related to the objectives in workshop three

and may provide and discuss some practice problems during the workshop.

These problems will allow the students to clarify any questions and to improve

their skills and knowledge in the workshop material.

4. Collaborative Exercise (see Appendix G): After completion of the previous

activities the facilitator will divide the class in groups of three to five students.

Each group will work the following collaborative exercise. A speaker will be

selected in each group. The facilitator will let the students know how much time

they have to solve the problem. The solution will be turn in to the facilitator on a

piece of paper with the name of all the members of the group. (See appendix C:

Rubric to evaluate group work). (Note : The facilitator can assign another

collaborative exercise different from the one in the module. If the collaborative

exercise is changed, the facilitator should notify the students about the change in

the previous workshop).

5. The facilitator will select one group and will ask them to solve and present results

of the collaborative exercise. Each group will have the opportunity to discuss

their solution if different from the solution presented by the first group.

6. Short Test : At the end of the workshop the students will take a short test that will

include the material covered during the workshop.



7. The facilitator will discuss the assignments to be completed before workshop

four. Also, the facilitator will provide a list of problems to be included as part of

the assignment before workshop four.

Assessment:


material discussed during the workshop.

The students must also complete the Reflexive Diary found in Appendix F. These

activities must be included in the student portfolio to be submitted in Workshop Five.



Taller Cuatro

Objetivos Específicos:

Al finalizar el Taller, el estudiante:

1. Definirá paralelogramos.

2. Demostrará las propiedades de un paralelogramo.

3. Definirá un rombo.

4. Demostrará las propiedades de un rombo.

5. Definirá un rectángulo y un cuadrado.

6. Demostrará las propiedades de un rectángulo y un cuadrado.

7. Definirá un trapezoide y un trapezoide isósceles.

8. Demostrará las propiedades de un trapezoide.

9. Construirá diferente tipos de figuras.

Objetivos de Lenguaje:

1. Demostrar dominio del idioma Español (vocabulario, sintaxis, presentación de

ideas).

2. Utilización apropiada y correcta de gramática.

3. Aplicación y utilización correcta y apropiada de los verbos.

Enlaces Electrónicos:

http://www.ies.co.jp/math/products/geo1/applets/para/para.html

http://deaver.barry.edu/bankef/P-GRAM.HTM

http://www.mathleague.com/help/geometry/polygons.htm


http://id.mind.net/~zona/mmts/geometrySection/commonShapes/trapezoid/trapezoid.

html

http://argyll.epsb.ca/jreed/math9/strand3/trapezoid_area_per.htm

http://www.escolar.com/geometr/06cuadrila.htm

http://roble.pntic.mec.es/jarran2/cabriweb/Poligonos.htm

http://www.educacionplastica.net/poligonos.htm

http://www.enchantedlearning.com/math/geometry/shapes/



Asignaciones antes del Taller:

1. El/la estudiante leerá y buscará información relacionadas a los objetivos del taller

cuatro en los libros de texto recomendados o en direcciones electrónicas o cualquier

otra referencia bibliográfica.

2. Una vez realice la lectura, los estudiantes contestarán las siguientes preguntas.

Este es un trabajo individual; no se aceptarán copias del Internet o de las

direcciones electrónicas utilizadas. (Ver Anejo A: Política de Honestidad

Académica).

• Cuadriláteros

• Paralelogramos

• Rombo

• Rectángulos

• Cuadrados

• Trapezoides

3. El facilitador asignará problemas adicionales del libro de texto como parte de esta

tarea para entregar. Estos problemas ayudarán a los estudiantes a entender los

objetivos del taller. Este es un trabajo individual; no se aceptarán copias del Internet

o de las direcciones electrónicas utilizadas. (Ver Anejo A: Política de Honestidad

Académica).

4. Esta tarea deberá entregarla al facilitador debidamente identificada con su nombre,

fecha y taller. La misma tiene un valor de 100 puntos. La evaluación de esta tarea

estará dividida en 70% por contenido y 30% por objetivos de lenguaje. (Ver anejo

B: Matriz valorativa para evaluar tareas previas a los talleres).

Actividades:

1. El facilitador comenzará la clase con un breve repaso.

2. El facilitador devolverá los trabajos completados por los estudiantes durante el taller

tres (Tarea y Trabajo Cooperativo). Estos trabajos estarán evaluados de acuerdo

con las rubricas incluidas en el modulo. El facilitador discutirá la puntuación

obtenida con los estudiantes según sea necesario. El facilitador contestará cualquier

pregunta que los estudiantes tengan en relación a los trabajos del taller uno. Estos

trabajos serán incluidos en el Portafolio el cual será entregado en el taller cinco.



3. Trabajo para realizar previo al Taller Cuatro : El/la estudiante entregará la tarea

asignada. El facilitador contestará preguntas relacionadas a la tarea y aclarará

todas las dudas que los estudiantes tengan.

4. El facilitador discutirá en la clase el material relacionado a los objetivos del taller y

podrá asignar o hacer algunos problemas de práctica durante el taller. Estos

problemas ayudarán a los estudiantes a aclarar dudas y contestar cualquier

pregunta que tengan lo cual los ayudará a mejorar su conocimiento y destrezas

referentes al material de la clase.

5. El facilitador dará problemas adicionales para que los estudiantes los resuelvan en

clase para practicar los procedimientos asociados con la solución de los mismos.

Estos problemas ayudarán a los estudiantes a clarificar cualquier duda o pregunta

que tengan, también los ayudará a mejorar el conocimiento sobre el material

discutido en el taller.

6. Trabajo cooperativo (ver Anejo G) : Luego de terminadas las actividades

anteriores, el facilitador dividirá la clase en grupos de tres a cinco estudiantes

dependiendo del tamaño de la clase. Cada grupo trabajará el siguiente ejercicio. El

facilitador les dirá a los estudiantes cuanto tiempo tienen para resolver el problema.

La solución será entregada en una hoja de papel con los nombres de los miembros

del grupo. (Ver anejo C: Matriz valorativa para evaluar trabaj o en grupo).

7. Prueba corta: Al comienzo del taller los estudiantes tomaran una prueba corta

sobre el material discutido en el taller.

8. El facilitador discutirá la tarea que los estudiantes deben completar antes del

próximo taller. En adición, el facilitador proveerá una lista de los problemas a

resolver como parte de la tarea a entregar en el taller tres.

Avalúo

Prueba corta : Los estudiantes tomarán una prueba corta al final del taller sobre el

material del taller. También redactará el Diario Reflexivo hallado en Anejo F. Estas

actividades serán incluidas en el Portafolio del estudiante que será entregado en el

Taller Cinco.



Workshop Five/Taller Cinco

NOTA: Este taller es bilingüe. Tanto,

el Facilitador como los estudiantes,

deberán utilizar el idioma asignado

para cada tarea y actividad.

NOTE: This is a bilingual workshop.

Both the facilitator and student

should use the language assigned

for each homework and activity.

Specific Objectives:

At the end of this workshop, the student:

1. Recognize the Cartesian Coordinate System.

2. Find different points in a Cartesian Coordinate System.

3. Construct lines using tables and using x & y intercepts.

4. Solve problems requiring the use of the distance formula and the midpoint

formula.

5. Find the slope of a line using two points or its equation.

Language Objectives:


of ideas)




Cartesian Coordinate System

http://www.blc.edu/fac/rbuelow/CAL/nt1-3.htm

http://www.onlineconverters.com/cartesianexp.html

http://www.math.utah.edu/online/1010/coord/

Slope

http://www.purplemath.com/modules/slope.htm

http://id.mind.net/%7Ezona/mmts/functionInstitute/linearFunctions/lsif.html

http://math.about.com/library/weekly/aa120502a.htm

http://cs.selu.edu/~rbyrd/math/slope/

http://www.math.com/school/subject2/lessons/S2U4L2DP.html



Distance Formula

http://www.purplemath.com/modules/distform.htm

Midpoint Formula

http://www.purplemath.com/modules/midpoint.htm

http://www.regentsprep.org/Regents/Math/midpoint/Lmidpoint.htm

Assignments before Workshop Five:

1. The student will search the internet links provided for the third workshop to find






section and day.

2. Find information and examples on the following terms in English. If some of

these concepts are defined and denoted with symbols, the student should

include them in the homework:

• Cartesian Coordinate System

• Distance formula

• Midpoint formula

• Slope of a line





3. The facilitator will assign additional problems as part of this assignment. These

problems will help the students understand the terms and objectives of this

workshop. This must be an individual work written in English and Spanish; copies

from the internet or from the URLs used will not be accepted. (See Appendix A:







objectives. (See Appendix B: Rubrics to evaluate assignments pr ior to the

workshops).

5. The students will review and study ALL the material presented in the previous

workshops. It is very important to review the collaborative exercises solved

already in the other workshops. In addition the students should review the

practice problems and the exercises included in the assignments. This will help

them get prepared to participate and solve the problems to be included in the

final collaborative exercise (debate-contest).

6. Give the final touches to the portfolio and bring it to the classroom.

Activities:

1. The facilitator will start the class with a short review (English).

2. The facilitator will return the work completed by the students during workshop

four (Assignment, Short Test and Collaborative Exercise). The work completed

would be assessed based on the rubrics included in the module. The facilitator

will discuss in English the points obtained with the students as necessary. The

facilitator will answer any questions the students may have related to the

workshop one completed work. The assessed work from workshop one will be

included in the Portfolio that will be turn in during workshop five

3. The students will include the assignment in the Portfolio. The facilitator will clarify

any doubts and will answer any questions the student’s may have regarding the

assignment (in English).

4. Short Test: At the beginning of the workshop the students will answer the short test

in Spanish about the material discussed during the workshop.

5. Portfolio: The students will finalize the Portfolio in accordance with the guidance

previously provided by the facilitator. They will ensure that all the work is included

and everything is in order. The students then will turn in the Portfolio to the facilitator

(English and Spanish).

6. Final Collaborative Exercise (Debate-Contest): During this workshop the students

will participate in a final collaborative exercise (Debate-Contest). This will be a team

work, however, the assessment will consider both, individual and group performance



appraisal. Based upon the number of students registered in this course, the

facilitator will select at random a maximum of six (6) groups with no more of five (5)

students in each group. Each group will have the opportunity to answer applications

and practical exercises related to the concepts that were presented in ALL the

previous workshops. (See Appendix D: Rubric for evaluation of the final

collaborative work). The rules for this final collaborative exercise are as follows:

a. The collaborative exercise will consist of five (5) application problems that will

cover the objectives learned in the course workshops. Half of these exercises will

be in English and the other half will be in Spanish.

b. The application problems will cover the objectives, concepts and procedures

learned in class. Each problem will have a time limit of no more than 30 minutes

to be solved by each group.

c. After the facilitator divide the class in groups, the member of each group will seat

together in order to discuss and solve the problems.

d. The facilitator will provide the final instructions and rules to complete the

collaborative exercise. Any questions regarding the exercise or the rules will be

answer by the facilitator.

e. The applications problems will be solve one at a time; each group will work the

same exercise at the same time in the time allowed by the facilitator. The

facilitator has the option to let the students use the book and class notes as

reference.

f. The facilitator will give a copy of the first problem to each group; at that time the

facilitator will tell the students the amount of time the have to solve the problem

and then they will start. The solution of the problems will be in the language the

problem was written.

g. The groups will work quietly and without interruptions. If a student do not follow

the rules and disrupt the other groups, his/her group will have a penalty

(deduction) of five (5) points from that problem.

h. The first group to finish the problem before the time allowed, will obtained a

bonus of five (5) points and will present their solution in front of the class.



i. If none of the groups finish the problem before the time allowed, the facilitator will

provide an additional five (5) minutes to finish the problem and there won’t be a

bonus of five (5) points.

j. When the time allowed is finished, the facilitator will collect the solution from all

the groups. Then the facilitator will select a person from one of the groups to

present their solution in front of the class.

k. After one of the groups present their solution in front of the class, the other

groups will have the opportunity to agree or disagree with the solution presented.

In case of a disagreement a group can challenge the first group, the second

group will present their solution in front of the class. If the second group is

correct, they will receive a bonus of five (5) points. In case that none of the

groups obtained the correct answer, the facilitator will provide and discuss the

correct solution.

l. If the solution from a group is incorrect but the procedure used is correct, the

group will get partial credit for the problem.

m. After completing the discussion on the first problem, the facilitator will provide a

copy of the next problem to each group. The process will be repeated until all the

problems in the collaborative exercise are completed and their solution has been

presented.

n. All the students should have an active participation in the discussion and solution

of the problems to earn individual points. The individual points will be between 5

and 10 points per problem depending on the type of exercise.

o. The facilitator can grant additional points to a group depending on the number of

correct solutions and the participation of the group members.

7. After completion of the final collaborative exercise, the students will write two or

three paragraphs in Spanish were they will provide feedback to the facilitator about

the course and his/her teaching techniques. The students should include if their

expectations about the course were met. These activities must be included in the

student portfolio to be submitted in Workshop Five.

8. The students will complete the class evaluation. The student representative will

return the course evaluation to the front office.



9. Closing activity – to be determined by the facilitator. Assessment:


material discussed during the workshop.



Anejos/Appendixes



Anejo A/Appendix A

Plagiarism

Dear Student:

The internet, although a very resourceful tool in today’s world has become a tool where

students and other professionals can find what others have done in seconds; thus

promoting or developing the temptation to use what others have done without giving

them the appropriate credit for their work. In an article published by Indiana University, it

was stated that using the ideas of others without giving proper credit to the source of

that information is considered plagiarism .

Whenever we use information from other sources it is extremely important that you:

1. Give credit to the person’s ideas, theories or opinions.

2. Give credit to a person if we use a chart, graph, drawing or any other type of

knowledge needed to support a paper.

3. Give credit to a person or source if we use a quotation or paraphrase ideas that

belong to them.

For more information go to http://www.indiana.edu/~wts/pamphlets/plagiarism.shtml

or simply search for the topic of plagiarism under: www.plagiarism.org.

Important Note: Plagiarism is a serious issue and i t is considered an offense that has

serious consequences; which in turn may affect your academic success and

professional career. There are workshops offered to help you when writing papers to

avoid falling into this serious matter. You can che ck for time and dates of these

workshops in the Learning Resources Center. Our fa cilitators can also provide you with

help when writing papers and/or assignments.

Sincerely, Ricardo Ortolaza, Ed.D. Chief Learning Officer



Plagio

Apreciado (a) Estudiante:

La red cibernética (Internet) se considera una herramienta efectiva en el mundo actual.

La misma se ha convertido en un recurso donde los estudiantes y los profesionales

pueden encontrar, rápidamente información e investigaciones que otros han realizado.

Esto puede propiciar la tentación de utilizar lo que otros han hecho o investigado sin

darles el debido crédito por su trabajo. En un artículo publicado por la Universidad de

Indiana, se indica que utilizar ideas de otras personas sin darle crédito al recurso que lo

produjo se considera plagio.

Siempre que se utilice información de otras fuentes o recursos, es de suma

importancia:

1. Dar crédito a las ideas, teorías y opiniones de otras personas o recursos.

2. Dar crédito a la persona o recurso de donde obtuvo tablas, gráficas, dibujos u

otro tipo de información o conocimiento para apoyar las ideas que expone en su

trabajo.

3. Dar crédito si utiliza citas o parafrasea ideas que pertenecen a otras personas o

recursos.

Para más información visite la página:

http://www.indiana.edu/~wts/pamphlets/plagiarism.shtml

o simplemente busque información sobre plagio en: www.plagiarism.org.

Nota Importante: El plagio es un asunto serio y se considera una ofensa que tiene

consecuencias serias; que a su vez puede afectar su éxito académico y carrera

profesional. Existen talleres que le pueden ayudar a la creación de documentos y evitar

cometer plagio. Puede obtener información de las fe chas y horas de dichos talleres en el

Centro de Recursos Educativos. Nuestros facilitador es también le pueden proveer

información sobre cómo hacer sus trabajos evitando el plagio.

Sinceramente, Ricardo Ortolaza, Ed.D. Chief Learning Officer



Anejo B/Appendix B

Matriz Valorativa para Tareas Previas al Taller

Assignment Before Workshop One

Student Name: ______________________ Date: _______________

Criteria Value Points Student Score

Content Part 2 – The definitions are complete, clear and well stated. The proper information and examples are provided for each term. The sentences are cohesive and have a proper flow.

20

Part 3 (a) – The answer is correct for each of the equations. 5

Part 3 (b) – The answer is clear and well stated. The addition and multiplication properties are clearly explained. The sentences are cohesive and have a proper flow.

10

Part 3 (c) – The answer is clear and well stated. The explanation is complete and provides enough information. The sentences are cohesive and have a proper flow.

10

Part 3 (d) – The answer is clear and well stated. It provides the necessary details to explain what a slope is. The sentences are cohesive and have a proper flow.

5

Part 3 (e) – The answer is clear and well stated. It provides the necessary details to explain how to determine if a graph is a function. The sentences are cohesive and have a proper flow.

5

Part 3 (f) – The answer is clear and well stated. The explanation provides enough information to establish the relationship between functions and equations. The sentences are cohesive and have a proper flow.

5

Part 3 (g) – The answer is clear and well stated. The general steps are provided and clearly explained. The sentences are cohesive and have a proper flow.

10

Language Demonstrate a command of standard English (vocabulary used, syntax and flow of ideas)

10

Uses grammar appropriately and correctly 10 Manages and uses verbs appropriately and correctly 10

Total Points 100 (70% content and

30% language )

Student’s total Score:

_______

Facilitator’s Signature: _________________________

Student’s Signature: __________________________



Tarea Previa al Taller Dos

Nombre Estudiante: ______________________ Fecha: _______________

Criterio Puntuación Puntuación Estudiante Cont enido

Parte 2 – Las definiciones están completas, son claras y bien establecidas. Se provee información correcta y se dan ejemplos según necesario. La respuesta se provee en oraciones claras y concisas.

20

Parte 3 – Se contestan todos los problemas, las contestaciones son correctas y se provee el procedimiento por el cual se obtuvo la respuesta (según sea necesario). El procedimiento y las formulas utilizadas son correctas. Los problemas se resuelven y se entrega en forma organizada y limpia.

50

Lenguaje Demostrar dominio del idioma Español (vocabulario, syntax, presentación de ideas)

10

Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos

10

Total de Puntos 100 (70% contenido y

30% lenguaje)

Puntuación total Estudiante: _______

Firma de Facilitador: _________________________

Firma de Estudiante: __________________________



Assignment Before Workshop Three

Student Name: ______________________ Date: _______________

Criteria Value Points Student Score Content

Part 2 – The definitions are complete, clear and well stated. The proper information is provided and examples are provided for each term. The sentences are cohesive and have a proper flow.

20

Part 3 – All the problems are solved, the answers are correct and the procedure used to find the solution is provided (as necessary). The procedure and formulas used are correct. The assignment is clean and the problems are solved in an organized way.

45

Part 5 – The student searched and brought to class an article related to the class objectives. The student is ready to discuss the article in class.

5

Language Demonstrate a command of standard English (vocabulary used, syntax and flow of ideas)

10

Uses grammar appropriately and correctly 10 Manages and uses verbs appropriately and correctly

10

Total Points 100 (70% content and 30% language)

Student’s total Score: _______

Facilitator’s Signature: _________________________

Student’s Signature: __________________________



Tarea Previa al Taller Cuatro


Criterio Puntuación Puntuación Estudiante

Cont enido Parte 2 – Las definiciones están completas, son claras y bien establecidas. Se provee información correcta y se dan ejemplos según necesario. La respuesta se provee en oraciones claras y concisas.

20

Parte 3 – Se contestan todos los problemas, las contestaciones son correctas y se provee el procedimiento por el cual se obtuvo la respuesta (según sea necesario). El procedimiento y las formulas utilizadas son correctas. Los problemas se resuelven y se entrega en forma organizada y limpia.

50


10

Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos

10

Total de Puntos 100 (70% contenido y 30%

lenguaje)

Puntuación total

Estudiante: _______

Firma de Facilitador: _________________________

Firma de Estudiante: __________________________



Tarea Previa al Taller Cinco


Criteria Puntuación Puntuación Estudiante

Contenido Part 2 – All the problems are solved, the answers are correct and the procedure used to find the solution is provided (as necessary). The procedure and formulas used are correct. The assignment is clean and the problems are solved in an organized way.

70


10

Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos 10

Total de Puntos 100 (70% contenido y 30%

lenguaje)

Puntuación total Estudiante:

_______



Anejo C/Appendix C

RUBRIC FOR COLLABORATIVE EXERCISE EVALUATION

Workshop One & Three NAME: _____________________________ Date: ______________

CRITERIA Value Points Workshop 1 Student Score

Workshop 3 Student Score

1. Frequently contribute to group discussions

10

2. Show interest in group discussions

10

3. Answer questions from other students and from the facilitator

5

4. Make questions related to the collaborative exercise

5

5. Present arguments based on the readings and class work

10

6. Show attention and is opened to the arguments from other students

10

7. Answer to the exercise is correct 25 8. Procedures and formulas are

included and correct. 20

9. Work is organized 5 TOTAL Points 100 Student’s

Score WS1:

Student’s Score WS3:

Comments; ________________________________________________________________________



MATRIZ VALORATIVA PARA EVALUAR LA PARTICIPACIÓN EN EL TRABAJO EN GRUPO

Taller Dos & Cuatro NOMBRE: _____________________________ Fecha: ______________

CRITERIA Puntuación Taller 2 Puntos Est.

Taller 4 Puntos Est.

1. Contribuye frecuentemente a las discusiones en el grupo

10

2. Demuestra interés en las discusiones en grupo

10

3. Contesta preguntas del facilitador y sus compañeros

5

4. Formula preguntas pertinentes al ejercicio cooperativo

5

5. Presenta argumentos fundamentados en las lecturas y trabajos de la clase

10

6. Demuestra atención y apertura a los argumentos de sus compañeros

10

7. La respuesta del ejercicio es correcta

25

8. El procedimiento y las formulas están incluidas y son correctas

20

9. El trabajo es organizado 5 TOTAL Puntos 100 Total Puntos

WS2:

Total Puntos WS4:

Comentarios; ________________________________________________________________



Anejo D/Appendix D

RUBRIC FOR EVALUATION OF THE FINALCOLLABORATIVE EXE RCISE

NAME: _____________________________ Date: ______________

CRITERIA Value Points Student Score 1. Frequently contribute to group discussions 5 2. Show interest in group discussions 5 3. Present arguments based on the readings and

class work 5

4. Make questions related to the collaborative exercise

5

5. Show attention and is opened to the arguments from other students

5

6. Answer to exercise number one is correct, the procedure and formulas used are correct and the work is organized.

15

7. Answer to exercise number two is correct, the procedure and formulas used are correct and the work is organized.

15

8. Answer to exercise number three is correct, the procedure and formulas used are correct and the work is organized.

15

9. Answer to exercise number four is correct, the procedure and formulas used are correct and the work is organized.

15

10. Answer to exercise number five is correct, the procedure and formulas used are correct and the work is organized.

15

TOTAL Points 100 Student’s Score:

Comments;

_______________________________________________________



Anejo E/Appendix E

PARÁMETROS ESPECÍFICOS PARA EVALUAR ASISTENCIA Y P ARTICIPACIÓN

La evaluación de asistencia y participación en los cinco talleres tiene un peso de 15%

del total de la evaluación final del curso MATH 199. Es requisito insustituible la

asistencia a todas las cinco reuniones, dos o más ausencias equivalen a fracaso del

curso. Las actividades realizadas en el taller ausente, sujetas a evaluación, serán

consideradas y ponderadas de acuerdo con los parámetros específicos. Por lo tanto, si

el/la estudiante se ausenta y entrega los trabajos posteriormente, su puntuación

comenzará con descuento porcentual previamente establecido para cada actividad

realizada en la respectiva reunión; como se demuestra a continuación:

Actividad Puntos Descontados

Trabajos a realizar previo a cada taller 20 puntos por cada taller que entregue tarde

Trabajo cooperativo Pierde todos los puntos

Prueba corta 20 puntos / Debe reponer antes del siguiente taller, de no ser así perderá todos los puntos.

Portafolio Pierde todos los puntos

Trabajo Final Cooperativo Pierde todos los puntos

Asistencia & Participación:

En un rango de 1 a 20 puntos, siendo 20 la puntuación mayor por cada taller, se

considerará que el/la estudiante haya efectuado aportaciones o preguntas efectivas en

la discusión de los conceptos, ejercicios y actividades del taller. Debe entenderse por

aportaciones efectivas todas aquellas preguntas, presentaciones o ayudas que dirijan

al grupo hacia un mejor entendimiento de los temas discutidos.



SPECIFIC PARAMETERS FOR THE ATTENDANCE AND PARTICIP ATION

EVALUATION

The evaluation for attendance and participation is worth 15% of the total final evaluation

of the class. Attendance to all five workshops is required and cannot be replaced;

students with two or more absences will fail the class. If the student is absent, the

student must contact the facilitator, in order to be ready for the next workshop. The

students will loose points accordingly based on the specific parameters for all activities

subject to evaluation during the workshop that the student is absent, see table below:

Activity Discounted Points

Assignments prior to each workshop 20 points for each workshop that the work is late.

Collaborative Exercise Loose all the points

Quizzes 20 points / Must be taken prior to the next workshop otherwise will loose all the points.

Portfolio Loose all the points

Final Collaborative Exercise Loose all the points

Attendance & Participation:

In a range from 1 to 20 points, where 20 is the highest score the students can get in

each workshop, this will considered how effective were the students questions and

comments in relation to the discussion of the class topics, problems and workshop

activities. The affectivity of the student participation will be measured based on the how

the questions and comments helped to clarify the concepts and to make it more

understandable.



Anejo F/Appendix F

Diario Reflexivo

Nombre del Estudiante__________________________________________ Taller # :_____________________________ Fecha :__________________ Instrucciones: El propósito del diario reflexivo es provocar en el estudiante una actitud de reflexión o análisis de las experiencias vividas en cada clase o al concluir una actividad educativa. Esta reflexión le permitirá al estudiante a aplicar lo aprendido a su experiencia del diario vivir, así como a analizar las implicaciones de lo aprendido en su desempeño profesional. Este instrumento deberá completarse al concluir cada una de las sesiones lectivas y será entregado al facilitador/a al terminar cada taller. Preguntas guías:

1. ¿Cuál fue el tema discutido en clase que me impactó más como profesional?

2. ¿Qué aplicación puedo dar de lo que aprendí en mi desempeño profesional?

3. ¿Que puedo mejorar de la clase?

4. ¿Que recomendaciones puedo hacerle al facilitador/a?



Reflexive Diary

Student Name___________________________________________________ Workshop #:_____________________________ Date :__________________ Instructions: The purpose of the reflexive diary is to create in the students an attitude of reflection or analysis of the experiences learned in class or at the conclusion of an activity. This reflection will allow the students to apply the knowledge acquired in class to the regular day to day living as well as to analyze the implications and applications of the class material to their professional life. This tool must be competed at the conclusion of each section and it must be returned to the facilitator at the end of each workshop. Questions:

1. Which was the topic discussed in class that create the most impact in my

professional life?

2. How I can apply the knowledge learned in class to my professional life?

3. What can I improve in the class?

4. What recommendations I can suggest to the facilitator?



Anejo G/Appendix G

Collaborative Exercises/Ejercicios Colaborativos Workshop One

Answer the following questions in groups:

1. Use inductive reasoning to find the next element in the series:

125, – 25, 5, – 1

2. What type of reasoning should be used to reach the following assertions?

Premise: Michael Jordan eats cereal.

Premise: Larry Bird eats cereal.

Premise: Magic Johnson eats cereal.

Conclusion: All the great basketball players eat cereal.

3. Using add and subtraction laws, complete the following assertion;

If x = y, then x + 2 = __?__

4. Answer (true or false) the following questions using the following figure:

• ABC is adjacent to ABE

• Value of DBE = 90°

• Value of 2 = 65°

• Value of 1 = 65°

• A is in BD

• A is in BD

• If the value of DBE + the value of BED + the value of

EDB = 180°, then the value of EDB = 2 5°

2

1

65°

E

D B C

A

90°



• BED and EDB are supplementary

5. Find the negation assertion of, “The road to success is difficult”.

6. Find the inverse of the assertion, “If it is a Collie, then it is a dog.”

7. Draw an obtuse angle and its bisector.

TRABAJO COOPERATIVO

Taller Dos

1. Explique cual es el error en cada uno de las siguientes figuras:

a. b. c.

110°

100°

7 in

6 in

10 cm

11 cm

12 cm

12 cm



2. Utilizando las siguientes figuras, determine cual aseveración es correcta y cual

no es correcta.

a. BAC ≈ EDF

.......................................................................................................... B. BAC ≈ FED

.......................................................................................................... C. EDF ≈ ABC

................................................ D. LOS DOS TRIÁNGULOS NO SON CONGRUENTES.

3. Determine si las siguientes aseveraciones son ciertas o falsas,

a. La mediana de un triangulo es el segmento que une el vértice con el

punto medio del lado opuesto al vértice.

b. El centroide siempre estará localizado dentro del triangulo.

c. La altura de un triangulo es un segmento desde un vértice perpendicular

al lado opuesto de ese vértice.

d. Las alturas de un triangulo siempre estarán en el interior del triangulo.

4. Dibuje un triangulo obtuso y construya otro triangulo congruente a este.

5 7

E

D

120°

5

7

A

B

120° C

F



Collaborative Exercise

Workshop Three

Answer the following questions in groups:

1. Use the following figure to find the value of x & and find if l & m are parallel.

2. What is the sum of all angles in an hexagon?

3. If the sum of three exterior angles of a quadrilateral is 325°, what is the value of the

fourth exterior angle?

4. Given the following figure where AE ED, DB AC, C = 30°. Find the value of

angles 1, 2 & 3.

E D C

B

1

3

30°

40°

80°

(x + y)°

y° l

m

A



TRABAJO COOPERATIVO

Taller Cuatro

a. Cada grupo dibujara un rectángulo, cuadrado y un rombo con diagonales en

un papel. Las figuras deberán ser identificadas como sigue a continuación;

b. Medirá AC y BD en cada figura, anotará las medidas en la tabla.

c. Con un transportador medirá los ángulos del 1 al 12 en cada figura y anotará

las medidas en la tabla.

AC BD 1 2 3 4 5 6 7 8 9 10 11 12 Rectángulo Cuadrado Rombo

d. Utilizando las medidas de los ángulos 9 al 12 para cada figura, ¿son

perpendiculares sus diagonales?

e. Utilizando las medidas de los ángulos 1 al 8 para cada figura, ¿son las

diagonales bisectores de un par de ángulos opuestos?

f. ¿Que figura tiene sus diagonales congruentes?

A

D

10 11 9

12

7 8

6

5

3 4

2 1

C

B



Anejo H/Appendix H

PORTFOLIO

Guidelines to prepare the portfolio

1. Determination of sources of content

2. The following, but not limited to, documentation will be included:

a. Projects, surveys, and reports.

b. Oral presentations

c. Essays: dated writing samples to show progress

d. Research papers: dated unedited and edited first drafts to show progress

e. Written pieces that illustrate critical thinking about readings: response or

reaction papers.

f. Class notes, interesting thoughts to remember, etc.

g. Learning journals, reflexive diaries.

h. Self assessments, peer assessments, facilitator assessments.

i. Notes from student-facilitator conferences.

3. Organization of documentation

Documentation will be organized by workshop, and by type of assignment within

workshops. Workshops will be separated from one another using construction paper

or paper of different colors, with tabs indicating the workshop number.

4. Presentation of the portfolio

• Documentation will be posted in a binder or in a digital version (e-portfolio).

• The cover page will follow exactly APA guidelines applied to a cover page of

research papers submitted at Metro Orlando Campus. This cover page will be

placed at the beginning of the portfolio.

• The entire portfolio will follow APA style: Courier or Times New Roman font,

size 12, double space, and 1-inch margins. See a “Publication Manual of the

APA, Fifth Edition”

• A log of entries that can be expanded with each new entry properly

numbered. The table, which should be located at the beginning, should

include a brief description, date produced, date submitted, and date evaluated

(Appendix I ).



• Introduction and conclusion of the income and outcome of the portfolio.

• A list of references and appendixes of all assignments included will be added

to the end of the portfolio.

• The Portfolio Informational Sheet will be placed in the transparent front pocket

of the binder for identification purposes (Appendix O ).

5. Student-Facilitator Feedback Template: Progression follow-up

The final step in implementing portfolios, before returning them to the student or

school life, is sharing feedback with each student to review the contents, student

reflections, and your evaluations of individual items and all of the work together as

related to learning targets (Banks, 2005).

Facilitators will e-mail a feedback template to all students. This template will contain

information pertaining to weaknesses and strengths found in students’ portfolios

(Appendix L ). Facilitators will focus their attention on showing students what is

possible and their progress rather than what is wrong; however, this does not mean

that facilitators will not cover weaknesses and areas for improvement during the

conference. Facilitators will send this feedback template upon completion of

workshop one.

Students will also have the opportunity to respond to the facilitator’s feedback and

write their own comments and/or ideas of how to improve the quality of their

portfolios, and how to become better metacognitive learners on the feedback

template. Students will e-mail the template with their comments back to the facilitator

after every workshop.

6. Portfolio storage:

• Portfolio samples will be safely stored for a six-month term on campus.

• Students will sign an official document empowering Ana G. Mendez

University System with rights to use their portfolios with educational or

accreditation purposes during this term (Appendix M ).

• After this term, and if their authors authorize Ana G. Mendez University

System to discard their portfolios by signing an official document, portfolio

samples will be destroyed; otherwise, they will be returned to their original

authors (Appendix N ).



Anejo I/Appendix I

Log of Entries

Entry Description

Date of Entry

Date

Submitted

Date

Evaluated

Page #

1

2

3

4

5

6

7

8

9

10



Anejo J/Appendix J

Checklist for Portfolio Assessment

Has the student set academic goals?

Does the portfolio include enough entries in each area to make

valid judgments?

Does the portfolio include evidence of complex learning in realistic

setting?

Does the portfolio provide evidence of various types of student

learning?

Does the portfolio include students’ self-evaluations and

reflections on what was learned?

Does the portfolio enable one to determine learning progress and

current level of learning?

Does the portfolio provide clear evidence of learning to users of

the portfolio?

Does the portfolio provide for student participation and

responsibility?

Does the portfolio present entries in a well-organized and useful

manner?

Does the portfolio include assessments based on clearly stated

criteria of successful performance?

Does the portfolio provide for greater interaction between

instruction and assessment?

Adapted from: Gronlund, N. E. (2003). Assessment of student achievement. 7th ed. Boston: Pearson

Education, Inc.



Anejo K/Appendix K

Portfolio Rubric

4 3 2 1

PORTFOLIO APPEARANCE

� Readable: Are entries typed in an appropriate font and size? Are

entries free of errors? Do ideas expressed in entries follow a logical sequence with appropriate transitions among paragraphs and topics?

� Professionalism: Is the appearance of the portfolio

professional? Are graphics, colors and portfolio language consistent with professional workplace expectations? Is the portfolio presented in a neat and orderly manner?

� Organization: Is the portfolio organized in a manner that makes

it easy to follow and easy to quickly locate information?

PORTFOLIO CONTENT AND FUNCTION

� Content: Are all required entries included in the portfolio? Are

entries relevant to the content of the portfolio? Do all entries contain the student’s reaction or reflection on the selected topics? Do entries provide thorough understanding of content? Resume, Activities List, Varied Samples of Written Work, Evidence of Problem Solving, and Evidence of Decision Making.

� Authenticity: Are the samples and illustrations a true reflection

of the student’s efforts and abilities?

� Growth/Development: Do samples provide thorough

understanding of growth and development related to their field of concentration? Do items show what the student has learned?

� Collaboration: Do items show examples of both individual and

group work? Does the student provide clear understanding of collaboration, and use collaboration to support his/her learning?



� Reflection and Personal growth: Do items show exceptional

understanding of how to be a reflective thinker and how to seek opportunities for professional growth? Does the student include self-reflective comments? Does the student reflect enthusiasm for learning?

� Professional Conduct: Do items show clear understanding of

ethical behavior and professional conduct? Do items display the pride the student has in his or her work?

Overall Portfolio Impact

� Is this portfolio an asset in demonstrating the student’s value

(skills, abilities, knowledge) to a potential employer or college representative?

Rating Scale 4 = Outstanding 3 = Very good 2 = Good 1 = Need s improvement Source: Retrieved from www.lcusd.net/lchs/portfolio/rubric.htm on February 10th, 2007. Adapted 02/10/2007 by Fidel R. Távara, M.Ed. Coordinator of Assessment and Placement – Metro Orlando Campus



Anejo L/Appendix L

Portfolio Assessment Feedback Template Strengths Weaknesses Improvement Ideas Facilitator’s comments

Student’s response and comments



Anejo M/Appendix M

Use and Return of Portfolio

Sistema Universitario Ana G. Méndez Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo

I, ____________________________________, grant permission to the office of

Assessment and Placement of the Ana G. Méndez University System, to keep in

their records a copy of my portfolio. I understand that the portfolio is going to be

used for accreditation or educational purposes only, and that is not going to be

disclosed without my consent.

By signing this document I authorize the office of Assessment and Placement to

keep a copy of my portfolio for six months and return it to me at the end of this

period of time.

_______________________________ ___________

Student’s Name (print) Date

_______________________________ ___________

Student’s Signature Date



Anejo N/Appendix N

Use and Discard of Portfolio

Sistema Universitario Ana G. Méndez Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo

I, ____________________________________, grant permission to the office of

Assessment and Placement of the Ana G. Méndez University System to keep in

their records a copy of my portfolio. I understand that the portfolio is going to be

used for accreditation or educational purposes only, and that is not going to be

disclosed without my consent.

By signing this document I authorize the Office of Placement and Assessment to

keep a copy of my portfolio for six months and discard it at the end of this period

of time.

_______________________________ ___________

Student’s Name (print) Date

_______________________________ ___________

Student’s Signature Date



Anejo O/Appendix O

PORTFOLIO INFORMATIONAL SHEET

Sistema Universitario Ana G. Méndez Metro Orlando Campus

Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo Check one: � Universidad del Este � Universidad Metropolitana � Universidad del Turabo Check one: � Undergraduate

� Graduate

Concentration

Student’s Name

Facilitator’s Name

Course:

Portfolio rated as

Reason of this rate

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