MATH 305 STATISTICS AND PROBABILITY I

Sistema Universitario Ana G. Méndez

School for Professional Studies

Florida Campuses

Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo

MATH 305

STATISTICS AND PROBABILITY I

PROBABILIDAD Y ESTADÍSTICA I

© Sistema Universitario Ana G. Méndez, 2008

Derechos Reservados.

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

MATH 305 Statistics and Probability I 2

Prep. 2006. Armando J. Sánchez, MS/IEMS. Rev. 2008. Prof. Armando J. Sánchez, EPM, MS/IEMS

TABLA DE CONTENIDO/TABLE OF CONTENTS

Página/Page

Prontuario ........................................................................................................................ 3

Study Guide .................................................................................................................. 12

Workshop One .............................................................................................................. 20

Taller Dos ...................................................................................................................... 24

Workshop Three ............................................................................................................ 28

Taller Cuatro ................................................................................................................. 31

Workshop Five/Taller Cinco .......................................................................................... 34

Anejo A/Appendix A ...................................................................................................... 39

Anejo B/Appendix B ...................................................................................................... 41

Anejo C/Appendix C ...................................................................................................... 46

Anejo D/Appendix D ...................................................................................................... 47

Anejo E/Appendix E ...................................................................................................... 48

Anejo F/Appendix F ....................................................................................................... 49

Anejo G/Appendix G...................................................................................................... 51

Anejo H/Appendix H ...................................................................................................... 53

Anejo I/ Appendix I ........................................................................................................ 55

Anejo J/Appendix J........................................................................................................ 57

Anejo K/Appendix K ...................................................................................................... 58

Anejo L/Appendix L ....................................................................................................... 59

Anejo M/Appendix M ..................................................................................................... 60

Anejo N/Appendix N ...................................................................................................... 62

Anejo O/Appendix O...................................................................................................... 63

Anejo P/Appendix P ...................................................................................................... 64



Prontuario

Título del Curso Probabilidad y Estadística I

Codificación MATH 305

Duración Cinco Semanas

Prerrequisito MATH 301 o MATH 221

Descripción

MATH 305 es un curso el cual provee los principios básicos de las estadísticas. Esto

incluye recopilación y clasificación de información (datos), y determinar las medidas de

tendencia central y dispersión. El curso también incluye la probabilidad y distribución

(normal, poisson, binomial y otras), la teoría de muestreo en poblaciones finitas y los

principios del diseño experimental.

Objetivos Generales

1. Conocer los fundamentos básicos de las estadísticas.

2. Aplicar los conocimientos básicos y los modelos estadísticos a situaciones

reales.

3. Hacer inferencia sobre los parámetros de una población y definir conclusiones

sobre esta.

4. Reconocer la teoría de los procesos de muestreo y el diseño experimental.

5. Comparar, describir y analizar las características de una población o dos

poblaciones.

6. Aplicar el rigor matemático con el fin de exponer las bases de probabilidad y de

estadísticas.

7. Aplicar las reglas de probabilidad a la solución de problemas.

8. Manejar con propiedad los conceptos de muestreo aleatorio y distribución de

muestreo.

9. Identificar correctamente el modelo o distribución de muestreo.

10. Identificar correctamente el modelo o distribución de probabilidad empleado en

el análisis de una situación dada.

11. Formular procedimientos que puedan ser aplicados para coleccionar, resumir y

presentar datos.



12. Describir y demostrar procedimientos para obtener estimados de características

de una población o parámetros seleccionando muestras representativas en la

población.

Texto y Recursos

Devore, J.L., (2004). Probability and Statistics for Engineering and the Sciences

(6th ed.). Thomson Learning; Brooks/Cole.

Referencias y Material Suplementario

Mendenhall, W., Wackerly, D.D., Scheaffer, R.L., (1996). Mathematical Statistics with

Applications. Belmont CA: Duxbury Press

Anderson, T.W., (1998). The Statistical Analysis of Data. Redwood City, California:

Scientific Press

Weiers, R.M., (2001). Introduction to Business Statistics (4th edition). Belmont CA:

Duxbury Press

Evaluación

1. Trabajos para realizar previo a cada taller 15 %

Antes de cada taller el/la estudiante deberá completar ciertas tareas asignadas que

le ayudarán a prepararse para las actividades que se realizarán durante el taller.

Las mismas constarán de una selección de preguntas, definiciones y ejercicios

asignados en el Módulo o del libro de texto, asignados por el facilitador del curso.

Estos trabajos abarcarán información básica conceptual que le ayudará al

estudiante en la comprensión de los temas bajo estudio. El/La estudiante deberá

incluir el procedimiento que utilizó para llegar a los resultados de los ejercicios

asignados. Si el procedimiento no es incluido, no se le dará crédito completo por el

ejercicio aunque el resultado sea correcto. Estas tareas deberán entregarse a partir

del Taller Uno. Este es un trabajo individual; no se aceptarán copias del Internet o

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

Académica) . Cada trabajo tiene un valor de 100 puntos para un total agregado de

500 puntos. La evaluación de estas tareas estará dividida en 70% por contenido y

30% por objetivos de lenguaje. (Ver Anejo B: Matriz valorativa para tareas

previas a los talleres) . El/la estudiante que entregue la tarea posterior al taller



asignado tendrá un descuento de 20 puntos por cada reunión que pase posterior a

la fecha de entrega.

2. Pruebas Escritas 20%

El/La estudiante tendrá una prueba escrita en el salón de clases al finalizar el

segundo taller y el cuarto taller. Dichas pruebas se efectuarán para medir

conocimientos en diferentes niveles del dominio del conocimiento de estadística.

Las pruebas escritas tendrán un valor de 100 puntos cada una para un total de 200

puntos. El facilitador determinará que recursos utilizará el estudiante para la prueba

escrita.

3. Trabajos Cooperativos 15%

Durante la primera y la tercera reunión, el/la estudiante tendrá la oportunidad de

trabajar en grupo con diferentes compañeros matriculados en el curso. El facilitador

estará a cargo de incorporar los grupos en cada uno de los talleres. Cada grupo

trabajará una situación asignada que se resolverá y presentará en la clase. La

solución del trabajo se entregará al finalizar el tiempo provisto por el facilitador con

el nombre de todos los participantes por grupo. Habrá dos (2) trabajos cooperativos,

cada uno de ellos con un valor de 100 puntos para un total agregado de 200 puntos.

En el segundo y cuarto taller no se realizará esta actividad ya que habrá una

prueba escrita. Esta actividad no se realizará en el taller cinco ya que habrá un

trabajo final en grupo. (Ver Anejo C: Matriz valorativa para trabajo en gru po) .

4. Portafolio 10%

En el quinto taller, los estudiantes entregarán un portafolio. (Ver Anejo F:

Portafolio). Este trabajo tiene un valor de 100 puntos y se realizará individualmente

(Ver Anejo G: Matriz valorativa para la evaluación del Portafolio). El facilitador

informará 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.

5. Proyecto Final e Informe Oral 25%

El/La estudiante entregará un trabajo final y hará una presentación oral donde se

complementará el dominio teórico conceptual y aplicación práctica del curso para el

Taller Cinco. Desde el segundo taller hasta el quinto taller, el/la estudiante tendrá la



oportunidad de trabajar en grupo. Durante el Taller Dos el Facilitador dividirá la

clase en grupos, el número de grupos dependerá de la cantidad de estudiantes en

la clase. Los grupos deberán de tener un mínimo de tres estudiantes y un máximo

de cinco estudiantes. Cada grupo trabajará una situación donde utilizarán los

conocimientos aprendidos en el curso para analizar y hacer conclusiones de

naturaleza estadística y de probabilidades. Este trabajo será desarrollado durante el

curso y será entregado en el Taller Cinco luego de haber dado una presentación

oral. El Facilitador asignará los problemas para este trabajo investigativo, durante el

Taller Dos. Este es un trabajo en grupo, pero la evaluación tomará en consideración

el trabajo en grupo y el trabajo individual de cada estudiante. Este trabajo

investigativo y la presentación oral serán en Inglés. Este trabajo tendrá un valor total

de 200 puntos. Estos estarán divididos en 100 puntos por la presentación oral

individual y 100 puntos por la presentación y solución de la situación. Las

presentaciones orales no se pueden reponer, si el estudiante esta ausente, perderá

todos los puntos. (Ver Anejo D: Matriz valorativa para presentación o ral, y ver

Anejo E: Matriz valorativa para presentación y solu ción del trabajo

investigativo en grupo) . El itinerario de trabajo para preparar este proyecto es el

siguiente:

a. Taller Dos: Se constituyen los grupos. Los estudiantes dentro de cada grupo

deberán indicar cómo y cuándo pueden ser contactados y se pondrán de

acuerdo en el día o días que se pueden reunir para comenzar a trabajar en el

proyecto.

b. Taller Tres al Taller Cinco: Los grupos se reunirán para desarrollar el tema

y hacer el análisis y el estudio para llegar a las conclusiones. Los grupos

prepararán el informe escrito y la presentación oral.

c. Taller Cinco : Cada grupo tendrá un máximo de 25 minutos para hacer su

presentación oral. La presentación oral (en inglés) debe ser interesante e

impactar al resto de la clase.

6. Asistencia y Participación diaria en cada taller 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 facilitador 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 H: Parámetros Específicos para Evaluar Asist encia y Participación).

7. Escala de evaluación

Se aplicará la curva normal en el proceso de asignar las calificaciones. La misma

escala de notas es la siguiente:

Nota: A B C D F

Puntuación: 100 – 90 89 – 80 79 – 70 69 – 60 59 ó <

NOTA:

Es de suma importancia que el estudiante tenga una calculadora científica o con

funciones estadísticas, 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 “web sites” que podrá

utilizar para la búsqueda de la 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 facilitador puede realizar cambios a las direcci ones 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 Probability and Statistics I

Code MATH 305

Time Length Five Weeks

Prerequisite MATH 301 o MATH 221

Description

MATH 305 is a course that will provide the basic principles of statistics. This includes

data collection and classification of information, measurements of central tendency and

measures of variability. The course also includes probability and distribution (the

normal, Poisson, the binomial and other), sampling theory in infinite populations, and

the principles of experimental design.

General Objectives

1. Recognize the basic fundaments of statistics.

2. Apply the basic knowledge and the statistical models to real situations.

3. Make inferences about population parameters and draw conclusion.

4. Recognize the theory about sampling processes and experimental design.

5. Compare, describe and analyze the characteristics of one or two populations.

6. Apply the mathematical principles to determine the basis of probabilities and

statistics.

7. Apply the probability rules and laws to solve problems.

8. Apply and manipulate the concepts of random sampling and sampling

distribution.

9. Correctly identify the sampling model or distribution.

10. Correctly identify the probability model or distribution utilize in the analysis of a

specific situation.

11. Develop procedures that could be used for the collection, organization and

presentation of data.

12. Describe and demonstrate the procedures to obtain estimates about the

characteristics of a population or parameters selecting representative samples of

the population.



Texts and Resources

Devore, J.L., (2004). Probability and Statistics for Engineering and the Sciences

(6th Ed.). Thomson Learning; Brooks/Cole

References and supplemental material

Mendenhall, W., Wackerly, D.D. & Scheaffer, R.L. (1996). Mathematical Statistics with

Applications. Belmont CA: Duxbury Press

Anderson, T.W. (1998). The Statistical Analysis of Data. Redwood City, California:

Scientific Press

Weiers, R.M. (2001). Introduction to Business Statistics (4th Edition). Belmont CA:

Duxbury Press

Evaluation

1. Assignment to do previous to each workshop 15 %

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

them to prepare for the activities in the workshop. The assignments will consist of

Internet sites research related of basic conceptual information provided in the

module that will help the learning of the workshop objectives. Additionally, the

students will complete the exercises assigned by the facilitator. The student must

include the procedures utilized to obtain the results of the assigned problems. If the

procedure is not included, there will be no full credit to the assigned problem even if

the result is correct. The assignments must be submitted starting at the first meeting.

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) . Each assignment

will be worth one hundred (100) points for an accumulated score of five hundred

(500) points. The evaluation of these assignments will be 70% for content and 30%

for language objectives. (See Appendix B: Rubrics to evaluate assignments

prior to the workshops) . The students that turn in the assignments after the

corresponding workshop will have a deduction of 20 points per each workshop that

passes before the assignment is turned in.

2. Workshop tests 20%

The students will take a written test in the classroom at the end of Workshops Two

(2) and Four (4). This test will measure the knowledge acquired by the students at



different levels on the concepts of statistics. Each test is worth one hundred (100)

points for a cumulative total of two hundred (200) points. The facilitator will

determine the resources to be used by the student for the written test.

3. Collaborative Exercise 15%

During Workshop One and Workshop Three the student will have the opportunity to

work with other students registered in the course. The facilitator will select randomly

the students to form each group. Each group will work a situation that will be

discussed and presented in the workshop. The solution to this exercise will be

handled out to the facilitator at the end of the activity with all the names of the

members of the team. There will be two (2) collaborative exercises; each one will be

worth one hundred (100) points for an accumulated score of two hundred (200)

points. This activity will not be done in Workshops Two and Four since the

students will take a written test. Also, this activity will not be done in Workshop

Five since the students will participate in the final group presentation. (See

Appendix C: Rubric to evaluate group work).

4. Portfolio 10%

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

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

(See Appendix G: 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.

5. Final Project and Oral Presentation 25%

The students must turn in a final assignment where they will combine the theory and

the practical application of the course in Workshop Five. From Workshop Two to

Workshop Five the students will have the opportunity to work in groups. During

Workshop Two the facilitator will divide the class groups, the number of groups

depend on the amount of students in class. The groups will have a minimum of three

students and no more than five students. Each group will work a situation where

they will use the knowledge and concepts learned in the course to analyze and

make conclusions in terms of statistics and probabilities. This project will be



developed throughout the course and will be turned in after the oral presentation (in

English) in Workshop Five. During Workshop Two, the facilitator will assign the

exercise/situation to each group. This is a group exercise; however, the assessment

will consider group performance and individual work. This group exercise and the

oral presentation will be in English. This group assignment will be worth two hundred

(200) points. They will be divided into one hundred points (100) for the individual oral

presentation and one hundred points (100) points for the presentation and solution

of the problem. The students will not be able to make-up the oral presentation, if a

student is absent, he/she will loose all the points. (See Appendix D: Rubric for

evaluation of Oral Presentation, and see Appendix E : Rubric for evaluation of

presentation and solution of the group assignment) . The schedule for preparing

this project is:

a. Workshop Two: Groups are formed. The students of each group should

indicate how and when they can be contacted and agree what day the group

can start to work in the final project.

b. Workshop Three to Workshop Five: The groups will get together to develop

the topic, conduct the analysis and determine the conclusions. Each group

will prepare a written report and the oral presentation.

c. Workshop Five: Each group will have no more than 25 minutes to give their

oral presentation. The presentation (in English) should be interesting and

should have an impact on the rest of the class. The written report will also be

handed in that week.

6. Attendance and Participation 15%

Attendance to workshops is mandatory; with two or more absences the students will

fail the class. The student should show responsibility for the learning process and

must complete all assigned work. In case of absence, the student must

communicate with the facilitator, in order to be ready for the next workshop. All

classroom activities done in his/her absence will be subject to an evaluation based

upon specific parameters. In other words, absenteeism will produce loss of points.

(See Appendix H: Specific parameters to evaluate at tendance and

participation).



7. Evaluation Scale

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

percentage scale.

Grade: A B C D F

Score: 100 – 90 89 – 80 79 – 70 69 – 60 59 – 0

NOTE:

It is very important that each student have a Scientific Calculator or a calculator with

statistical functions . The use of a calculator is a very important tool to be able to finish

the assignments and the work required during the workshops. Also, each student

should have a ruler and graph paper.

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 and 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:

1. Distinguish between Descriptive Statistics and Inferential Statistics.

2. Define the basic statistics terms and concepts.

3. Identify sources for statistical data and organize the data.

4. Prepare frequency distribution tables and calculate the relative frequency.

5. Distinguish between the different types of graphs utilized in the representation of

statistical data.

6. Construct different types of graphs to represent the data such as histograms,

frequency polygons, etc.

7. Analyze statistical data using the Stem-and-Leaf method.

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)

These sites offer examples and information about descriptive statistics, graphical

methods, and Stem-and Leaf method.

http://ftp.medprev.uma.es/libro/node3.htm

http://www.statsoft.com/textbook/esc.html

http://www.monografias.com/trabajos30/conceptos-de-estadistica/conceptos-de-

estadistica.shtml

http://www.richland.edu/james/lecture/m170/ch02-def.html

http://otel.uis.edu/yoder/freq_h.htm

http://www.ucv.cl/web/estadistica/histogr.htm

http://www.ask.com/reference/dictionary/ahdict/14725/histogram

http://www.mathleague.com/help/data/data.htm

http://simon.cs.vt.edu/SoSci/Site/MMM/mmm.html

http://regentsprep.org/Regents/math/data/stemleaf.htm



http://davidmlane.com/hyperstat/A28117.html

http://147.134.144.30/knudsen/DISPERS/sld001.htm

Assignments before Workshop One

1. The students will search information and examples about the objectives for

Workshop One on the recommended textbooks and/or on the Internet, or any other

bibliographic textbooks or Internet addresses.

2. After reading about the objectives in Workshop One, the students will define the

following terms and will provide examples. This must be an individual work; copies

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

Academic Honesty) . 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

prior to the workshops).

a. Define descriptive and inferential statistics.

b. What are the differences between sample and population?

c. Differentiate between discrete and continuous variables.

d. Establish the differences between probabilistic sample and a non-probabilistic

sample.

e. What is the difference between sampling with replacement and without

replacement?

f. Mention different types of graphs used to represent statistical data.

g. Define Frequency and Relative Frequency.

3. Bring an article from a newspaper or a magazine that shows a report of statistical

data. It should include a graphical representation of the data and should mention

some of the measures of central tendency and variability. Bring it to class and be

prepared to explain it to the other students.

Activities

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

the evaluation criteria for the class. 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 needs 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

related with the Program (AHORA), such as new coming courses, holidays, and

dates of the Student Representative meeting.

3. The facilitator will discuss what is 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. The facilitator will explain the final project that will be due in Workshop Five and will

include a written report and the oral presentation (both in English). The facilitator will

notify the students that the groups for the final project will be form during Workshop

Two.

5. The student will submit the assignment to the facilitator. The facilitator will clarify any

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

assignment.

6. The facilitator will start an open discussion to discuss the articles brought by the

students. The facilitator will ask several students to summarize their article and

identify the statistical elements in the article and the importance of the presentation

of statistical data. The facilitator will summarize the most important points from the

articles providing more emphasis on the analysis and presentation of statistical data.

7. 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.

8. 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. The facilitator may select several students and asked them

to solve and present the results of the practice problems. The students will have the

opportunity to discuss their solution and the other students will be able to clarify any

questions they may have on the practice problems.

9. After completion of the previous activities the facilitator will divide the class in groups

of three to five students. Each group will work a collaborative exercise that the

facilitator will provide. 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).

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

The students’ assignment will be evaluated using the rubrics included in Appendix A.

The collaborative exercise, the additional exercises and the discussion in class will

provide the evaluation of the students’ performance in class.

Complete the Reflexive Diary entry (see Appendix G).



Taller Dos

Objetivos Específicos

Al finalizar el Taller, el estudiante:

1. Definir probabilidad y explicar las propiedades.

2. Explicar los diferentes tipos de probabilidades.

3. Calcular la probabilidad de uno o más eventos.

4. Resolver problemas utilizando el “Product Rule” y el diagrama de árbol.

5. Distinguir y explicar las diferencias entre combinaciones y permutaciones.

6. Calcular la probabilidad condicional de un evento.

7. Calcular las medidas de tendencia central.

8. Calcular las medidas de variabilidad o dispersión.

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.

Direcciones Electrónicas

En estos sitios los estudiantes podrán encontrar información sobre probabilidades,

propiedades de las probabilidades, diagrama de árbol, permutaciones, combinaciones,

y probabilidad condicional, medidas de tendencia central y medidas de variabilidad o

dispersión.

http://www.stat.psu.edu/~resources/ClassNotes/hrm_06/sld005.htm

http://www.stat.tamu.edu/stat30x/notes/node51.html

http://www.probabilitytheory.info/

http://platea.pntic.mec.es/anunezca/ayudas/probabilidad/probabilidad.htm

http://www.lawebdefisica.com/apuntsmat/probabilidad/

http://www.cns.uni.edu/~campbell/stat/prob4.html

http://www.math.uni.edu/~campbell/mdm/condprob.html

http://regentsprep.org/Regents/math/tree/Ltree.htm

http://www.easymaths.com/Tree_Diagrams.htm

http://mathforum.org/dr.math/faq/faq.comb.perm.html



http://www.factmonster.com/ce6/sci/A0860531.html

http://www.mathgoodies.com/lessons/vol6/conditional.html


Tareas a realizar 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 buscarán información y ejemplos sobre

los siguientes términos. Este es un trabajo individual; no se aceptarán copias del

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

Académica).

a. Propiedades de las Probabilidades

b. Tipos de Probabilidades

c. Regla de Productos (en inglés “Product Rule”)

d. Permutaciones

e. Combinaciones

a. Medidas de Tendencia Central (Media, Mediana & Moda)

f. Medidas de Variabilidad o Dispersión (Varianza, Desviación Éstandar y

Quartiles)

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.

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 tareas previas a los tall eres).

5. Luego de haber completado esta tarea, los estudiantes estudiarán el material de los

talleres anteriores en preparación para tomar la prueba escrita en el salón de clase.

Esta prueba incluirá material de los Talleres Uno y Dos.



6. Observe los siguientes videos y tome notas para discutirlas en la sala de clases

http://www.youtube.com/watch?v=P1emX7jukq0&feature=related;

http://www.youtube.com/watch?v=Hn6C21GC0vA&feature=related

7. No olvide que debe ir trabajando con su portafolio.

Actividades

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

2. 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 incluidas en el módulo. El facilitador discutirá la

puntuación obtenida con los estudiantes. 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. 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 dividirá la clase en los grupos para el trabajo final. El número de

grupos dependerá de la cantidad de estudiantes en la clase. Los grupos deberán de

tener un mínimo de tres estudiantes y un máximo de cinco estudiantes. El

Facilitador asignará los problemas para este trabajo investigativo o les indicará a los

estudiantes como buscar un problema para este trabajo. Cada grupo trabajará el

problema, este será analizado y presentado durante el Taller Cinco. Los estudiantes

dentro de cada grupo indicarán cómo y cuándo pueden ser contactados y se

pondrán de acuerdo en el día o días que se pueden reunir para comenzar a trabajar

en el proyecto. El Facilitador dará los detalles de este trabajo y contestará las

preguntas de los estudiantes. Este trabajo final y la presentación oral serán en

inglés.

5. Los estudiantes discutirán las notas de los videos que observaron antes del taller.

6. 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.



7. El facilitador podrá dar 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. Los estudiantes tendrán la oportunidad de discutir los

resultados y aclarar cualquier duda que tengan.

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.

9. Luego de haber completado la tarea previa al taller, resolver los problemas de

práctica en el salón, participar en el trabajo cooperativo del taller anterior y haber

participado en clase, los estudiantes estarán preparados para tomar una prueba

escrita en el salón de clase. Esta prueba incluirá el material estudiado en el Taller

Uno y el Taller Dos.

Evaluación

La tarea de los estudiantes será evaluada utilizando las matrices incluidas en el

Anejo A. Los problemas de práctica en el salón, la discusión en clase y la prueba

escrita proveerán la evaluación del trabajo hecho por los estudiantes en clase.

Complete el Diario Reflexivo (ver Anejo G).



Workshop Three

Specific Objectives


1. Define discrete random variable and probability distribution.

2. Solve problems with probability distributions of discrete random variable.

3. Solve problems using the function for a cumulative distribution.

4. Calculate the expected value for a distribution of discrete random variables.

5. Describe the Binomial Probability Distribution.

6. Describe the Poisson Probability Distribution.

7. Solve problems using the Binomial and Poisson Distributions model.

Language Objectives


of ideas)




These sites offer examples and information about discrete random variables, probability

distributions, cumulative distribution, Binomial Distributions and Poisson Distributions.

http://cablemodem.fibertel.com.ar/coya/formulas/est/E04.html

http://www.herkimershideaway.org/apstatistics/ymmsum99/ymm771.htm

http://www.staff.city.ac.uk/g.e.g.ismail/statsprobmaths/1ps03_5.htm

http://www.stat.psu.edu/~lsimon/stat250/sp99/Slides/binomial/sld004.htm

http://freespace.virgin.net/liam.mullan/maths/DPDs.html

http://www.treestar.com/flowjo/v3/html/graphcdf.html

http://www.stat.wvu.edu/SRS/Modules/Binomial/binomial.html

http://www.berrie.dds.nl/poisson.html


Assignments before Workshop Three


Workshop Three on the recommended textbooks and/or on the Internet, or any other

bibliographic textbooks or Internet addresses.



2. After reading about the objectives in Workshop Three, the students will define and

provide examples about the following terms. Defining these terms will help the

students understand the objectives of the workshop. 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. Discrete Random Variables

b. Probability Distributions

c. Binomial Probability Distributions

d. Poisson Probability Distributions

3. Work with the assigned problems. These problems will help the 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.

4. 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 prior to the

workshops).

5. The students should get together in their individual groups to continue working on

the final project and oral presentation.

Activities

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

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

(Assignment, and Written Test). The work completed would be assessed based on

the rubrics included in the module. The facilitator will discuss the points obtained

with the students. The facilitator will answer any questions the students may have

related to the Workshop Two completed work. The assessed work from Workshop

Two will be included in the Portfolio that will be turn in during Workshop Five.

3. The students will submit the assignment to the facilitator. The facilitator will clarify

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

assignments.



4. The facilitator will discuss the material related to the objectives in Workshop Three



process and the application of these terms.

5. 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. The facilitator will select several students and ask them to

solve and present the results of the practice problems. The students will have the

opportunity to discuss their solution and the other students will be able to clarify any

questions they may have on the practice problems.

6. After completion of the previous activities the facilitator will divide the class in groups

of three to five students. Each group will work a collaborative exercise that the

facilitator will provide. 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 turned 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).

7. The facilitator will ask one of the groups to present and discuss the solution to the

collaborative exercise in front of the class. The other groups will have the opportunity

to agree or disagree with the solution presented. In case of disagreement, the other

group will present their solution in front of the class. The students will have an

opportunity to clarify any doubts they may have.

8. The facilitator will discuss the assignment 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

The students’ assignment will be evaluated using the rubrics included in the

Appendix section. The collaborative exercise, the additional exercises and the

discussion in class will provide the evaluation of the students’ performance in class.

Complete the Reflexive Diary entry (see Appendix G).



Taller Cuatro

Objetivos Específicos

Al finalizar el Taller, el estudiante:

1. Definir variable aleatoria continua.

2. Resolver problemas de distribución de probabilidades para variables aleatorias

continuas.

3. Calcular el valor esperado en una distribución con variables aleatorias continuas.

4. Describir una distribución normal.

5. Resolver problemas utilizando los valores de Z.

6. Describir una distribución Gamma.

7. Resolver problemas utilizando el método de la distribución Gamma.

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.

Direcciones Electrónicas

En estos sitios los estudiantes podrán encontrar información sobre distribuciones y

variables aleatorias continuas, distribuciones Normales, y distribuciones Gamma.


http://www.stat.psu.edu/~lsimon/stat250/fa99/slides/normal/sld002.htm

http://www.ucl.ac.uk/Mathematics/geomath/level2/prob/pb7.html

http://www.berrie.dds.nl/normal.html

http://www.stat.wvu.edu/SRS/Modules/Normal/normal.html

http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm

Tareas a realizar antes del Taller Cuatro

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 definirán y buscarán ejemplos de los

siguientes términos. Este es un trabajo individual; no se aceptarán copias del



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

Honestidad Académica).

a. Variables Aleatorias Continuas

b. Valor esperado

c. Valores Z

d. Distribución Normal

e. Distribuciones Gamma

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.

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 para evaluar tareas previas a los tallere s).

5. Luego de haber completado esta tarea, los estudiantes estudiarán el material de los

talleres anteriores en preparación para tomar la prueba escrita en el salón de clase.

Esta prueba incluirá material de los Talleres Tres y Cuatro.

6. Los estudiantes deberán reunirse en los grupos para continuar trabajando el trabajo

final y preparar la presentación oral.

Actividades

1. El facilitador comenzará la clase con una actividad para repasar el material cubierto

en el taller anterior.

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 matrices incluidas en el modulo. El facilitador discutirá la

puntuación obtenida con los estudiantes. El facilitador contestará cualquier pregunta

que los estudiantes tengan en relación a los trabajos del Taller Tres. Estos trabajos

serán incluidos en el Portafolio el cual será entregado en el Taller Cinco.

3. 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. El facilitador repasará las matrices del Portafolio que los estudiantes tienen que

entregar en el Taller Cinco y contestará cualquier duda o pregunta que los

estudiantes tengan en relación al Portafolio.

7. El facilitador nuevamente discutirá en detalles lo que los estudiantes tienen que

hacer sobre el trabajo final y la presentación oral en grupo. Este es el trabajo final

de la clase el cual será presentado en el Taller Cinco. En adición, el facilitador

discutirá la tarea que los estudiantes deben completar antes del próximo taller y

proveerá una lista de los problemas a resolver como parte de la tarea a entregar en

el Taller Cinco.

8. Luego de haber completado la tarea previa al taller, resolver los problemas de

práctica en el salón, participar en el trabajo cooperativo del taller anterior y haber

participado en clase, los estudiantes estarán preparados para tomar una prueba

escrita en el salón de clase. Esta prueba incluirá el material estudiado en el Taller

Tres y el Taller Cuatro.

Evaluación

La tarea de los estudiantes será evaluada utilizando las rúbricas incluidas en el

sección de Anejos. Los problemas de práctica en el salón, la discusión en clase y la

prueba escrita proveerán la evaluación del trabajo hecho por los estudiantes en

clase.

Complete el Diario Reflexivo (ver Anejo G).



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


1. Describe an Exponential Distribution.

2. Describe a Chi Square Distribution.

3. Solve problems utilizing the Exponential and Chi Square Distribution methods.

4. Apply the knowledge obtained in the course MATH 305.

5. Active participation in the final exercise and the oral presentation.

Language Objectives


of ideas)




For this workshop, the students should use all the URLs included in the previous

workshops to review the objectives learned in class. Also, the following URLs contain

information about Exponential Distributions and Chi Square Distributions.

http://ftp.medprev.uma.es/libro/node3.htm

http://www.statsoft.com/textbook/esc.html

http://www.monografias.com/trabajos30/conceptos-de-estadistica/conceptos-de-

estadistica.shtml

http://www.stat.psu.edu/~resources/ClassNotes/hrm_06/sld005.htm


http://www.probabilitytheory.info/

http://personal5.iddeo.es/ztt/Tem/t18_variable_aleatoria_discreta.htm



http://cablemodem.fibertel.com.ar/coya/formulas/est/E04.html


http://www.staff.city.ac.uk/g.e.g.ismail/statsprobmaths/1ps03_5.htm

http://www.stat.psu.edu/~lsimon/stat250/fa99/slides/normal/sld002.htm

http://www.stat.wvu.edu/SRS/Modules/Binomial/binomial.html

http://www.berrie.dds.nl/poisson.html


http://www.berrie.dds.nl/normal.html

http://www.stat.wvu.edu/SRS/Modules/Normal/normal.html

http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm

http://www.weibull.com/LifeDataWeb/the_exponential_distribution.htm



Assignments before Workshop Five


Workshop Five on the recommended textbooks and/or on the Internet, or any other

bibliographic textbooks. Also, as a final review the students will search information

and examples about the objectives learned in class during all the previous

workshops.

2. After reading about the objectives in Workshop Five, the students will define and

provide examples about the following terms (this will be in English ). Defining these

terms will help the students understand the objectives of the workshop. 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. Descriptive Statistics

b. Probabilities

c. Exponential Distributions

d. Chi Square Distributions

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; copies from the Internet or from the

URLs used will not be accepted (in Spanish) .

4. 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: Rubric to evaluate assignments pr ior to the

workshops).

5. The students should get together in their individual groups to finalize the analysis for

the final exercise and complete the preparation of the Group Presentation for the

oral and written reports.

6. Finalize the organization and preparation of the Portfolio in accordance with the

guidelines provided and the rubrics for evaluation of the Portfolio (English and

Spanish).

Activities

1. The class will start with a short review (in Spanish).

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

(Assignment and written test). The work completed would be assessed based on the

rubrics included in the module. The facilitator will discuss the points obtained with

the students (this will be done in Spanish ). The facilitator will answer any

questions the students may have related to the Workshop Four completed work. The

assessed work from Workshop Four will be included in the Portfolio that will be turn

in during at the end of Workshop Five.

3. Assignment to be completed before Workshop Five: 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 (this will be done

in English ).

4. The facilitator will discuss the material related to the objectives in Workshop Five



process and the application of these terms (this will be done in English ).



5. Final Group Report and Oral Presentation: The students will do an oral

presentation (in English ) of the situation previously assigned to each group. Each

group will have a maximum of 25 minutes for their presentation. This will be a

teamwork, however, the assessment will consider both, individual and group

performance appraisal. Each member of the group must have an active participation

and must do part of the oral presentation. (See Appendix D: Rubric for evaluation

of Oral Presentation, and see Appendix E: Rubric fo r evaluation of

presentation and solution of the group assignment) .

6. After the oral presentations the facilitator will provide time at the end of class for the

students to finish the organization of the Portfolio. The facilitator will answer any final

questions the students may have.

7. The students will complete the course evaluation. The student representative will

return the course evaluation to the front office.

8. The students must turn in the Portfolio at the end of the class.

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

Assessment

The students’ assignment will be evaluated using the rubrics included in Appendix A.

The students’ Oral Presentation and Group Report will be evaluated as a group and

individually per the rubrics included in the appendixes. The students will turn in the

Portfolio to the facilitator at the end of the class, which will provide an assessment of

the student progress during the course.

Complete the Reflexive Diary entry in Spanish (see Appendix G).



Anejos/Appendix



Anejo A/Appendix A

Academic Honesty and 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



Honestidad Académica y 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 answers are complete, clear and well stated. The proper information and examples are provided for each question. The sentences are cohesive and have a proper flow.

50

Part 3 – The student brought an article with statistical data represented in graphical form and/or table. The student came prepared to discussed the article and provide an explanation.

20

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:

_______

Facilitador’s Signature: _________________________

Student’s Signature: __________________________



Tarea Previa al Taller Dos

Nombre Estudiante: ______________________ Fecha: _______________

Criteria 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.

25

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.

45

Languaje Demostrar dominio del idioma Español (vocabulario, sintaxis, 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% languaje)

Puntuación total Estudiante: _______

Firma de Facilitador: _________________________

Firma de Estudiante: __________________________



Assignment before Workshop Three


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.

50

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

Nombre Estudiante: ______________________ Fecha: _______________

Criteria 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

Languaje Demostrar dominio del idioma Español (vocabulario, sintaxis, 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%

languaje)

Puntuación total

Estudiante: _______

Firma de Facilitador: _________________________

Firma de Estudiante: __________________________



Assignment before Workshop Five


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.

50

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

10


Manages and uses verbs appropriately and correctly 10

Total Points 100 (70% content and 30%

language)

Student’s total Score: _______



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:

Facilitator Signature

Student Signature

Comments: _________________________________________ __________________



Anejo D/Appendix D

Rubric for evaluation of Oral Presentation

Student Name: _____________________________Date:___________________

Criteria Value Points Student Total Score

Content

The speaker provides a variety of types of content appropriate for the task, such as generalizations, details, examples and various forms of evidence.

10

The speaker takes into account the specific knowledge and experience of the listener.

10

The speaker maintains visual contact with the audience at all time without reading the notes.

10

The speaker voice is loud and clear, everyone can understand and hear the presentation.

10

The speaker delivers the message in a lively, enthusiastic fashion.

10

The volume varies to add emphasis and interest. 10

Pronunciation and enunciation are very clear. The speaker exhibits very few disfluencies, such as "ahs," "uhms," or "you knows."

10

Language

Student pronounces words in a clear and correct manner so as to make language understood to others

10

Correct use of grammar and verb conjugation 10

Use of correct use of vocabulary words to express message

10

Total Points 100 (70% of content and

30% of language)

Student’s Total Score:

Facilitator’s Signature: ____________________________

Student’s Signature: _____________________________



Anejo E/Appendix E

Rubric for evaluation of Final Report and Solution

Student Name: _____________________________Date:___________________

Criteria Value Points Student Total Score

Content

The information is presented in a logical, organized and clear format, which is totally understood.

10

The students understood the problem and identified the variables and the facts provided in the problem.

10

The students identified the correct procedures to solve the problem and used the correct formulas.

10

The students applied the formulas correctly and showed all the calculations.

10

All the graphs and tables are clear and represented the statistical analysis done.

10

The solution of the problem is well organized and understandable all the calculations are included and the procedures are clearly identified.

10

The students find the correct answer and provide a conclusion using their analysis and calculations to answer the question provided.

10

Language

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

10


Manages and uses verbs appropriately and correctly 10

Total Points 100 (70% of content and

30% of language)

Student’s Total Score:

Facilitator’s Signature: ____________________________

Student’s Signature: ________________________



Anejo F/Appendix F

MATRIZ VALORATIVA PARA PARTICIPACIÓN EN GRUPO

Nombre del Estudiante: _____________________ Fecha: _______________

Grupo: ________ Nombre del estudiante evaluador: _____________________

Criteri o Puntos Puntuación del estudiante

Asistió a las reuniones o actividades del grupo.

10

Colaboró en la planificación y organización de las reuniones o actividades de grupo.

10

Demostró disposición para cooperar con el grupo.

10

Contribuyó frecuentemente a las discusiones del grupo

10

Participó activamente en las reuniones y actividades.

10

Demostró interés en las discusiones y actividades del grupo.

10

Vino preparado(a) a las reuniones, actividades y discusiones del grupo.

10

Demostró atención y apertura a los puntos y argumentos de sus compañeros.

10

Contribuyó al grupo con material e información adicional.

10

Contribuyó significativamente al trabajo que presentó el grupo.

10

Totals 100



RUBRIC TO EVALUATE PARTICIPATION IN GROUP ACTIVITIE S

Students name: _________________________ Date: _______________

Group: ________ Name of evaluating student: ______________________

Criteri a Points Students Points

Attended all the meetings and activities of the group.

10

Collaborated with the planning and organization of activities of the group.

10

Demonstrated cooperation and team work with the group.

10

Contributed frequently with the discussions of the group.

10

Participated actively in the meetings and activities.

10

Demonstrated interest in the discussions and activities of the group.

10

Came prepared to meetings, activities and discussions of the group.

10

Demonstrated attention to the arguments within the group.

10

Contributed to the group with additional information.

10

Contributed significantly with the work that presented the group.

10

Totals 100



Anejo G/Appendix G

DIARIO REFLEXIVO Nombre ____________________________

Fecha ____________________________

El propósito de este diario es el de reflexionar y escribir sobre los conceptos, los

sentimientos y las actitudes que se desatan a partir de la discusión y los trabajos de

cada taller. Este proceso le ayudará en su autoanálisis, así como propiciará la auto

evaluación.

Utilizando las siguientes preguntas guías, reflexione sobre lo presentado en el taller y

conteste las mismas en forma de ensayo con excelente gramática, ortografía y

puntuación:

1. Hoy aprendí….

2. Este tema presentado en clase me ayuda a……

3. Puedo aplicar lo discutido en la clase a mi vida y experiencias personales…



Reflexive Diary

Name ____________________________

Date ____________________________

The purpose of this diary is to reflect and write about the concepts, feelings, and

attitudes experienced after class discussion and assignments. This process will help

your self-assessment.

Using the following questions, reflect about what was presented in this workshop and

answer the questions following an essay style using excellent grammar, syntax and

punctuation:

1. Today I learned…

2. The topic presented today helps me…

3. I can apply today’s discussion to my life and personal experiences…



Anejo H/Appendix H

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 305. 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

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

Trabajos Cooperativos Pierde todos los puntos

Portafolio Pierde todos los puntos

Trabajo Final (Presentacion Oral y

trabajo escrito)

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.

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

Collaborative Exercises Loose all the points

Portfolio Loose all the points

Final Exercise (Oral Presentation and

written report)

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 I/ Appendix I

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 K ).



• 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 J ).

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 N ). 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 O ).

• 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 P ).



Anejo J/Appendix J

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



Anejo K/Appendix K

Log of Entries

Entry Description

Date of Entry

Date

Submitted

Date

Evaluated

Page #

1

2

3

4

5

6

7

8

9

10



Anejo L/Appendix L

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 M/Appendix M

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 = Needs 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 N/Appendix N

Portfolio Assessment Feedback Template Strengths Weaknesses Improvement Ideas Facilitator’s comments

Student’s response and comments

Anejo O/Appendix O

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 P/Appendix P

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

Documents

MATH 305 STATISTICS AND PROBABILITY I