sistema universitario ana g. méndez school for ... 173 dlp... · clasificar triángulos y...
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Sistema Universitario Ana G. Méndez School for Professional Studies
Florida Campuses Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo
MATH 173
PLANE GEOMETRY AND SPACE I GEOMETRÍA PLANA Y DEL ESPACIO I
© Sistema Universitario Ana G. Méndez, 2008 Derechos Reservados.
© Ana G. Méndez University System, 2008. All rights reserved
MATH 173 Plane Geometry and Space I 2
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
TABLA DE CONTENIDO/TABLE OF CONTENTS
Página/Page
PRONTUARIO ................................................................................................................ 3
STUDY GUIDE .............................................................................................................. 10
WORKSHOP ONE ........................................................................................................ 17
TALLER DOS ................................................................................................................ 22
WORKSHOP THREE .................................................................................................... 26
TALLER CUATRO......................................................................................................... 30
WORKSHOP FIVE/TALLER CINCO ............................................................................. 33
ANEJO A/APPENDIX A ................................................................................................ 40
ANEJO B/APPENDIX B ................................................................................................ 42
ANEJO C/APPENDIX C ................................................................................................ 47
ANEJO D/APPENDIX D ................................................................................................ 49
ANEJO E/APPENDIX E ................................................................................................ 50
ANEJO F/APPENDIX F ................................................................................................. 52
ANEJO G/APPENDIX G ................................................................................................ 54
ANEJO H/APPENDIX H ................................................................................................ 59
ANEJO I/APPENDIX I ................................................................................................... 61
ANEJO J/APPENDIX J .................................................................................................. 62
ANEJO K/APPENDIX K ................................................................................................ 63
ANEJO L/APPENDIX L ................................................................................................. 65
ANEJO M/APPENDIX M ............................................................................................... 66
ANEJO N/APPENDIX N ................................................................................................ 67
ANEJO O/APPENDIX O ................................................................................................ 68
MATH 173 Plane Geometry and Space I 3
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
PRONTUARIO
Título del Curso Geometría Plana y del Espacio I
Codificación MATH 173
Duración Cinco Semanas
Prerrequisitos MATH 151 – 152
Descripción
Este es un curso de geometría para estudiantes de Educación con especialidad en
Matemáticas. El propósito principal del curso es presentar los conceptos fundamentales
de la geometría Euclidiana del plano, y de la geometría del espacio con un enfoque
moderno en términos de las definiciones y notación. Se aspira a que los estudiantes
logren un dominio práctico de la materia a través de la aplicación de los conceptos en
la resolución de ejercicios.
En el curso de Matemáticas 173 se estudiarán temas que incluyen los conceptos
básicos relacionados con planos, líneas rectas, ángulos, polígonos, etc. Se desarrollará
el método deductivo para realizar demostraciones (pruebas), se discutirán los
conceptos de perpendicularidad y paralelismo, las propiedades y los teoremas
relacionados con triángulos, rectángulos y la geometría de coordenadas.
Objetivos Generales
1. Entender los términos básicos de geometría como punto, línea, plano y ángulos.
2. Distinguir entre el razonamiento inductivo y deductivo.
3. Realizar demostraciones (pruebas) geométricas.
4. Utilizar postulados para realizar demostraciones (pruebas) geométricas.
5. Clasificar triángulos y demostrar congruencia entre triángulos.
6. Demostrar y aplicar teoremas sobre rectas y planos.
7. Identificar los diferentes tipos de ángulos.
8. Identificar líneas paralelas y polígonos.
9. Entender los conceptos de perpendicularidad y paralelismo.
10. Entender el sistema de coordenadas cartesianas.
11. Localizar puntos en el plano cartesiano, hallar la distancia entre dos puntos, hallar la
pendiente de una recta y trazar la grafica de ecuaciones.
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Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
12. Resolver problemas verbales utilizando la formula de la distancia y la del punto
medio.
Texto y Recursos
Lial, M. L., Brown, B. A., Steffensen, A. R., & Murphy Johnson, L. (2004). Essentials of
Geometry for College Students. (2nd ed.). Prentice Hall.
Marin Isaacs, I. (2004). Geometry for College Students. (4th ed.). Prentice Hall.
Referencias y Material Suplementario
Baldwin, Harry L. (1993). Essential Geometry. McGraw Hill, New York.
Geiter & Peterson, Prindle. (1991). Geometry for College Students. (1st ed.). Weber &
Schmidt, Boston.
Evaluación
1. Trabajos para realizar previo a cada taller 15%
Antes de cada taller, el/la estudiante deberá completar una variedad de ejercicios y
preguntas guías que le ayudarán en el proceso de comprensión de conceptos que se
desarrollarán en la práctica de las actividades que se efectuarán en el taller. Los
mismos, constarán de una selección de ejercicios asignados por el/la facilitador/a o de
la búsqueda en la Internet de información básica conceptual. Deberán entregarse a
partir de la primera reunión. Cada trabajo tiene un valor de 20 puntos para un total de
100. No entregar éstos en el tiempo establecido conlleva un descuento de 5 puntos por
cada tardanza en la entrega.
2. Cuatro (4) Trabajos Cooperativos 15%
El/la estudiante tendrá la oportunidad de trabajar en grupo con diferentes compañeros
matriculados en el curso MATH 173. El/la facilitador/a estará a cargo de incorporar los
grupos en cada uno de los talleres. Cada grupo trabajará una situación asignada que
resolverá y presentará a la clase. La solución del trabajo se entregará al finalizar la
presentación de los mismos en cada taller con el nombre de todos los participantes por
grupo en la hoja provista por el/la facilitador/a. Habrá cuatro (4) trabajos cooperativos a
partir del primer taller, cada uno de ellos con un valor de 25 puntos para un total
agregado de 100. En la quinta reunión no se realizará esta actividad .
3. Cuatro (4) pruebas para realizar en los talleres 20%
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A partir de la primera reunión y hasta el cuarto taller, una vez discutidas las tareas
realizadas previo a cada taller, el/la estudiante estará capacitado/a para contestar una
prueba corta individual. Esta constará de una selección de ejercicios prácticos que
fortalecerán las destrezas y conceptos estudiados y tendrá un valor de 25 puntos en
cada taller, para un total de 100. En la quinta reunión no se realizará esta actividad .
4. Trabajo Final: Concurso 25%
Durante el quinto taller, se llevará a cabo un trabajo final; concurso. Este, será un
trabajo colaborativo. Sin embargo, la evaluación considerará tanto variables de
desempeño individual como grupal. El/la facilitador/a seleccionará aleatoriamente a
los/las estudiantes que integrarán los grupos. Cada uno de los grupos tendrá la
oportunidad de contestar ejercicios prácticos de los temas que se han facilitado en los
talleres. Esta actividad tiene un valor de 150 puntos. El/la facilitador/a informará la
composición de los grupos en el cuarto taller.
5. Portafolio 10%
En el quinto taller, los estudiantes entregarán un portafolio. (Ver Anejo E: Portafolio).
Este trabajo tiene un valor de 100 puntos y se realizará individualmente (Ver Anejo G:
Rúbrica para la evaluación del Portafolio). El facilitador informara durante el taller uno
cuáles serán los trabajos asignados que se incluirán en el portafolio. Las actividades
efectuadas en cada uno de los talleres, brindarán las destrezas necesarias para que el
estudiante pueda desarrollar el portafolio.
6. Asistencia y Participación 15%
La asistencia a todos los talleres es necesaria e indispensable. En caso de ausencia,
el/la estudiante debe realizar todas las gestiones necesarias para comunicarse con el/la
facilitador/a de manera que pueda prepararse adecuadamente para la próxima reunión.
Todas las actividades realizadas en el taller ausente, sujetas a evaluación, serán
consideradas y ponderadas de acuerdo con los parámetros específicos. Es decir, es
vigente la pérdida de puntuación por cada trabajo del cual no fue partícipe el/la
estudiante por causa de la ausencia. (Ver Anejo A: Parámetros Específicos para
Evaluar Asistencia y Participación)
7. Escala de evaluación
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La evaluación final se calculará a base de promedios ponderados, pero considerando la
escala estándar de por cientos.
Nota A B C D F
Por ciento 90 – 100 80 – 89 79 – 70 69 – 60 59 – 0
NOTA:
Es de suma importancia que el estudiante tenga una calculadora científica , ya que es
una de las herramientas principales para poder realizar eficientemente las tareas y
actividades provistas para cada taller. También deberá tener regla y papel
cuadriculado.
Descripción de las Normas del Curso
1. Este curso sigue el programa “Discipline-Based Dual Language Immersion
Model®” del Sistema Universitario Ana G. Méndez, el mismo esta diseñado para
promover el desarrollo de cada estudiante como un profesional bilingüe. Cada
taller será facilitado en inglés y español, utilizando el modelo 50/50. Esto
significa que cada taller deberá ser conducido enteramente en el lenguaje
especificado. Los lenguajes serán alternados en cada taller para asegurar que
el curso se ofrece 50% en inglés y 50% en español. Para mantener un balance,
el módulo debe especificar que se utilizarán ambos idiomas en el quinto taller,
dividiendo el tiempo y las actividades equitativamente entre ambos idiomas. Si
un estudiante tiene dificultad en hacer una pregunta en el idioma especificado,
bien puede escoger el idioma de preferencia para hacer la pregunta. Sin
embargo, el facilitador deberá contestar la misma en el idioma designado para
ese taller. Esto deberá ser una excepción a las reglas pues es importante que
los estudiantes utilicen el idioma designado. Esto no aplica a los cursos de
lenguaje que deben ser desarrollados en el idioma propio todo en inglés o todo
en español según aplique.
2. El curso es conducido en formato acelerado, eso requiere que los estudiantes se
preparen antes de cada taller de acuerdo al módulo. Cada taller requiere un
promedio de diez (10) horas de preparación y en ocasiones requiere más.
3. La asistencia a todos los talleres es obligatoria. El estudiante que se ausente al
taller deberá presentar una excusa razonable al facilitador. El facilitador
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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.
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10. EL uso de celulares esta prohibido durante las sesiones de clase; de haber una
necesidad, deberá permanecer en vibración o en silencio.
11. La visita de niños y familiares no registrados en el curso no está permitida en el
salón de clases.
12. Todo estudiante esta sujeto a las políticas y normas de conducta y
comportamiento que rigen al SUAGM y el curso.
Nota: Si por alguna razón no puede acceder las dire cciones electrónicas
ofrecidas en el módulo, no se limite a ellas. Exis ten otros motores de búsqueda y
sitios Web que podrá utilizar para la búsqueda de l a información deseada. Entre
ellas están:
• www.google.com
• www.altavista.com
• www.ask.com
• www.excite.com
• www.pregunta.com
• www.findarticles.com
• www.telemundo.yahoo.com
• www.bibliotecavirtualut.suagm.edu
• www.eric.ed.gov/
• www.flelibrary.org/
El/la facilitador(a) puede realizar cambios a las d irecciones electrónicas y/o
añadir algunas de ser necesario.
Filosofía y Metodología Educativa
Este curso está basado en la teoría educativa del Constructivismo.
Constructivismo es una filosofía de aprendizaje fundamentada en la premisa, de que,
reflexionando a través de nuestras experiencias, podemos construir nuestro propio
conocimiento sobre el mundo en el que vivimos.
Cada uno de nosotros genera nuestras propias “reglas “y “métodos mentales”
que utilizamos para darle sentido a nuestras experiencias. Aprender, por lo tanto, es
simplemente el proceso de ajustar nuestros modelos mentales para poder acomodar
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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.
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STUDY GUIDE
Course Title Plane Geometry and Space I
Code MATH 173
Time Length Five Weeks
Prerequisites MATH 151 – 152
Description
This is a course in geometry for students specializing in Mathematic Education. The
main purpose of this class is to present the fundamental geometric concepts including
Euclidean geometry of the plane and geometry of the space providing a modern focus
in terms of the definitions and notation. It is expected for the students to obtain a
practical knowledge of the subject by applying the concepts in the solution of exercises.
MATH 173 will cover the basic concepts of geometry including the plane, straight
lines, angles, polygons, etc. This course will develop the deductive method to formalize
geometric proofs; will discuss the concepts of perpendicularity and parallelism, the
properties and theorems related to triangles, rectangles and the geometry of
coordinates.
General Objectives
1. Understand the basic concepts in geometry such as point, line, plane and angles.
2. Distinguish between inductive and deductive reasoning.
3. Formalize geometric proofs.
4. Use postulates to formalize geometric proofs.
5. Classified triangles and demonstrate congruent triangles.
6. Demonstrate and apply theorems on straight lines and planes.
7. Identify the different types of angles.
8. Identify parallel lines and polygons.
9. Understand the concepts of perpendicularity and parallelism.
10. Understand the Cartesian Coordinate System.
11. Find points in the Cartesian plane, find the distance between two points,
calculate the slope of a straight line and construct the graph of an equation.
12. Solve verbal problems using the formula for distance and for the middle point.
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Texts and Resources
Lial, M. L., Brown, B. A., Steffensen, A. R., & Murphy Johnson, L. (2004). Essentials of
Geometry for College Students. (2nd ed.). Prentice Hall.
Marin Isaacs, I. (2004). Geometry for College Students. (4th ed.). Prentice Hall.
References and Supplementary Materials
Baldwin, Harry L. (1993). Essential Geometry. McGraw Hill, New York.
Geiter & Peterson, Prindle. (1991). Geometry for College Students. (1st ed.). Weber &
Schmidt, Boston.
Evaluation
1. Assignment previous to each workshop 15%
Previous to each workshop students must finish certain assignments that will include
exercises and questions that will help them understand the concepts and prepare for
the activities in the workshop. The assignments will be selected by the facilitator from
problems in the textbook and/or Internet sites research related with the current topic.
The assignments must be submitted starting at the first meeting. Each assignment will
be worth twenty (20) points for an accumulated score of one hundred (100) points. Each
late assignment will be penalized with five (5) points.
2. Collaborative Exercises (4) 15%
Collaborative exercises will be given from meeting one until meeting fourth. The student
will have the opportunity to work in groups with different classmates registered in the
course. The facilitator will select randomly the student distribution in each group. Each
group will have assigned a situation or problems that they will develop, solve and
present to the class. The group solution to the exercise will be given to the facilitator at
the end of the class and will include the participants name on each group. It will be four
(4) collaborative exercises starting on workshop I. Each of these exercises will be worth
twenty-five (25) points for an accumulated score of one hundred (100) points. This
activity will not be done during workshop five.
3. Workshop tests (4) 20%
Starting on meeting one until meeting fourth, after the group assignments has been
completed and the assignments to do previous to each workshop have been discussed,
the students will be able to take an in-class test. The test will include several practice
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exercises that will help the students to strengthen their skills obtained in the workshop.
Each test will be worth twenty-five (25) points for an accumulated score of one hundred
(100) points. This activity will not be done during workshop five.
4. Final Work (Contest) 25%
During workshop five, there will be a Final Work; Contest. This will be a collaborative
exercise; however, the evaluation will consider both aspects, individual and group
evaluation. The facilitator will select at random the student for each group. Each group
will have the opportunity to solve several practical exercises related to the topics
discussed during the course in the different workshops. This activity will be worth 150
points. The facilitator may select the groups during workshop four.
5. Portfolio 10%
I workshop five, the students will turn in a portfolio. (See Appendix E: Portfolio). This
activity will be done individually and will be worth one hundred (100) points (See
Appendix H: Rubric for Portfolio evaluation). During workshop one the facilitator will
inform the students the assigned work to be included in the portfolio. The activities
conducted in each workshop will provide the students the skill and knowledge
necessary to do the portfolio.
6. Attendance and participation 15%
Attendance is mandatory in all the workshops. In case of absence, the student will
contact the facilitator, in order to be preparing for the following meeting. All the activities
sustained in his absence will be subject to an evaluation based upon specific
parameters. In other words, the student will be penalized for each assignment that
he/she did not participate due to his/her absence (Annex A).
7. Grade scale
The final grading will be calculated base on average grades within the standard
percentages scale.
Grade A B C D F
Percentage 90 – 100 80 – 89 79 – 70 69 – 60 59 – 0
NOTE:
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It is important that each student bring a scientific calculator . The calculator will be an
important tool to management effectively the task and activities listed in each workshop.
Also, a ruler and graph paper are required.
Description of Course Policies
1. This course follows the Sistema Universitario Ana G. Méndez Discipline-Based Dual
Language Immersion Model® designed to promote each student’s development as a
Dual Language Professional. Workshops will be facilitated in English and Spanish,
strictly using the 50/50 model. This means that each workshop will be conducted
entirely in the language specified. The language used in the workshops will
alternate to insure that 50% of the course will be conducted in English and 50% in
Spanish. To maintain this balance, the course module may specify that both
languages will be used during the fifth workshop, dividing that workshop’s time and
activities between the two languages. If students have difficulty with asking a
question in the target language in which the activity is being conducted, students
may choose to use their preferred language for that particular question. However,
the facilitator must answer in the language assigned for that particular day. This
should only be an exception as it is important for students to use the assigned
language. The 50/50 model does not apply to language courses where the delivery
of instruction must be conducted in the language taught (Spanish or English only).
2. The course is conducted in an accelerated format and requires that students prepare
in advance for each workshop according to the course module. Each workshop
requires an average ten hours of preparation but could require more.
3. Attendance at all class sessions is mandatory. A student that is absent to a
workshop must present the facilitator a reasonable excuse. The facilitator will
evaluate if the absence is justified and decide how the student will make up the
missing work, if applicable. The facilitator will decide on the following: allow the
student to make up the work, or allow the student to make up the work and assign
extra work to compensate for the missing class time.
Assignments required prior to the workshop must be completed and turned in on the
assigned date. The facilitator may decide to adjust the grade given for late
assignments and make-up work.
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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.
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Note: If for any reason you cannot access the URL’s presented in the module, do
not stop your investigation. There are many search engines and other links you
can use to search for information. These are some examples:
• www.google.com
• www.altavista.com
• www.ask.com
• www.excite.com
• www.pregunta.com
• www.findarticles.com
• www.telemundo.yahoo.com
• www.bibliotecavirtualut.suagm.edu
• www.eric.ed.gov/
• www.flelibrary.org/
The facilitator may make changes or add additional web resources if deemed
necessary.
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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.
MATH 173 Plane Geometry and Space I 17
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Workshop One
Specific Objectives:
At the end of this workshop, the student will be able to:
1. Distinguish between deductive and inductive reasoning examples.
2. Identify the points, lines, planes and real numbers postulates.
3. Define a line segment, ray and angles.
4. Identify the adjacent, supplementary, complementary, and special angles.
5. Measure, build and classify angles according to its measure.
6. Write assertions of the form "If…then".
7. Determine if an assertion "If…then" is true.
8. Give examples to illustrate that an assertion is true or false.
9. Rewrite direct and indirect tests.
Language Objectives
1. Demonstrate a command of standard English (vocabulary used, syntax and flow
of ideas)
2. Uses grammar appropriately and correctly.
3. Manages and uses verbs appropriately and correctly.
Electronic Links (URLs):
Inductive and Deductive Reasoning
http://ai.eecs.umich.edu/cogarch0/common/capa/reason.html
http://www.math.toronto.edu/mathnet/questionCorner/deductive.html
http://mathforum.org/library/drmath/view/55695.html
http://www.sparknotes.com/math/geometry3/inductiveanddeductivereasoning/sectio
n1.html
Angles
http://www.regentsprep.org/Regents/math/angles/LAngles.htm
http://www.homeschoolmath.net/teaching/g/angles.php
Points, Lines, Segments and Rays
http://www.learningwave.com/lwonline/geometry_section1/lessons/lines1.html
http://www.math.com/school/subject3/lessons/S3U1L2GL.html
Conditional Assertions
MATH 173 Plane Geometry and Space I 18
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
http://www.regentsprep.org/regents/math/tables/ifthen.htm
http://hubpages.com/hub/Geometry-Tutor
Assignments before Workshop One:
1. Take a look at the module. Pay close attention to the rubrics since they will be
used to assess your knowledge, language skills and class participation.
2. The student will search the internet links provided for the first workshop to find
the concepts that will be covered during the first meeting. Also, the student will
use the suggested textbook and/or the references indicated in the bibliography,
to study those chapters that cover the topics of deductive and inductive
reasoning, points, lines, planes, real numbers, angles, assertions, and geometric
tests. The student will turn it the homework properly identifying its name, course,
section and day.
3. Find information and examples on the following terms. If some of these concepts
are defined and denoted with symbols, the student should include them in the
homework:
• Inductive Reasoning
• Deductive Reasoning
• Points, lines, planes and real numbers
• Angles
• Classification of angles (i.e. Complementary, supplementary, adjacent)
• Geometric Assertions
• Geometric Tests
If the student has access to computer programs such as MS Office or Lotus
SmartSuite, he/she will be able to use them for the homework. This must be an
individual work; copies from the internet or from the URLs used will not be
accepted. (See Appendix A: Academic Honesty Policy).
Note: The facilitator can assign a selection of exercises that cover the topics of the
workshop. The student will solve the exercises and turn them in to the facilitator.
4. After searching the terms in part two above, the students will answer the
following questions as part of the assignment. Again, this must be an individual
MATH 173 Plane Geometry and Space I 19
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
work; copies from the internet or from the URLs used will not be accepted. (See
Appendix A: Academic Honesty Policy).
A. Answer the following questions in brief form:
• What is the difference between a postulate and a definition?
• What is the difference between a postulate and a theorem?
• How many lines can be built between two points?
• Can two supplementary angles be both obtuse?
B. Answer true or false using the following figure:
• Point B is in AC
• Point C is in AB
• If AC = 15 cm and CB = 10 cm, then AB = 150 cm
• ACD is another name for 2
• 1 and 2 are adjacent angles
• 1 is supplementary to DCB
C. Answer the following questions using the following figure:
2 1
D
B C A
45° 7 6
5 4
3
2
1 30°
MATH 173 Plane Geometry and Space I 20
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
• How much does 1 measures?
• How much does 4 measures?
• How much does 7 measures?
• How much does 5 measures?
5. This assignment shall be turn in to the facilitator and shall be properly identified
with the student name, date and workshop. This assignment is worth 100 points;
the evaluation of this assignment will be 70% for content and 30% for language
objectives. (See Appendix B: Rubrics to evaluate assignments p rior to the
workshops).
Activities :
1. The facilitator will present and explain the objectives, the teaching methodology,
and the evaluation criteria for MATH 173. During this process, the facilitator will
verify that every student in the class has been registered in order to take this
course. Furthermore, the facilitator will review that every student has the module
and the textbook. Also, the facilitator will provide his/her contact information in
case of students need to contact him/her. The facilitator will establish the
schedule and days of contact.
2. The facilitator may conduct an ice breaking exercise to have the students
introduce them self. After all the students have been presented, a Student
Representative will be selected. Also, the facilitator will inform about other issues
or announcements such as new coming courses, holidays, and dates of the
Student Representative meeting.
3. The facilitator will discuss what should be included in a portfolio and what should
be included in it. The facilitator will provide specific information about the work to
be included in the portfolio and the rubrics for the portfolio evaluation. The
facilitator will answer any questions the students may have related to the
portfolio.
4. Assignment to be completed before workshop one: The student will submit the
assignments to the facilitator. The facilitator will clarify any doubts and will
answer any questions the student’s may have regarding the assignment.
MATH 173 Plane Geometry and Space I 21
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
5. The facilitator will discuss the material related to the objectives in workshop one
and may provide and discuss some practice problems during the workshop. The
facilitator will discuss the terms and provide examples that will help the learning
process and the application of these terms.
6. The facilitator will provide additional problems for the students to practice the
procedures associated with the solution of application problems. These problems
will allow the students to clarify any questions and to improve their skills and
knowledge in the workshop material.
7. Collaborative Exercise (see Appendix G ): After completion of the previous
activities the facilitator will divide the class in groups of three to five students.
Each group will work the following collaborative exercise. A speaker will be
selected in each group. The facilitator will let the students know how much time
they have to solve the problem. The solution will be turn in to the facilitator on a
piece of paper with the name of all the members of the group. (See appendix C:
Rubric to evaluate group work).
8. The facilitator will select one group and will ask them to solve and present results
of the collaborative exercise. Each group will have the opportunity to discuss
their solution if different from the solution presented by the first group.
9. Short Test : At the end of the workshop the students will take a short test that will
include the material covered during workshop one.
10. The facilitator will discuss the assignment to be completed before workshop two.
Also, the facilitator will provide a list of problems to be included as part of the
assignment before workshop two.
Assessment:
Short Test: The students will answer a short test at the end of the workshop about the
material discussed during workshop.
The students must also complete the Reflexive Diary found in Appendix F. These
activities must be included in the student portfolio to be submitted in Workshop Five.
MATH 173 Plane Geometry and Space I 22
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Taller Dos
Objetivos Específicos:
Al finalizar el Taller, el estudiante:
1. Clasificará triángulos, identificará las partes del triángulo, y definirá ángulos
internos y externos de un triángulo.
2. Definirá segmentos congruentes, ángulos y triángulos.
3. Utilizará los postulados de congruencia para determinar si dos triángulos son
congruentes.
4. Demostrará y aplicará los teoremas de perpendicularidad.
5. Probará algunas propiedades de triángulos isósceles.
6. Definirá y demostrará líneas concurrentes, mediana, altura y ángulos bisectores
de un triangulo.
7. Definirá y probará la congruencia del triangulo recto.
8. Construirá diferentes tipos de triángulos.
Objetivos de Lenguaje:
1. Demostrar dominio del idioma Español (vocabulario, sintaxis, presentación de
ideas).
2. Utilización apropiada y correcta de gramática.
3. Aplicación y utilización correcta y apropiada de los verbos.
Enlaces Electrónicos:
Triángulos
http://www.aaamath.com/geo318-triangle-angles.html
http://www.aaamath.com/geo318-triangle-sides.html
http://www.math.clemson.edu/~rsimms/triangle/
http://home.blarg.net/~math/triangles.html
http://patricia91ej.wiki.zoho.com/Resoluci%C3%B3n-de-tri%C3%A1ngulos.html
Líneas y Planos
http://www.bymath.com/studyguide/geo/sec/geo14a.htm
http://tutormatematicas.com/GEO/Introduccion_puntos_lineas_segmentos_planos.html
MATH 173 Plane Geometry and Space I 23
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Asignaciones antes del Taller Dos:
1. El/la estudiante leerá y buscará información relacionadas a los objetivos del taller
dos en los libros de texto recomendados o en direcciones electrónicas o cualquier
otra referencia bibliográfica.
2. Una vez realice la lectura, los estudiantes contestarán las siguientes preguntas.
Este es un trabajo individual; no se aceptarán copias del Internet o de las
direcciones electrónicas utilizadas. (Ver Anejo A: Política de Honestidad
Académica).
• Triángulos
• Diferente tipos de triángulo
• Segmentos congruentes, ángulos y triángulos.
• Postulados de congruencia
• Teoremas de perpendicularidad
3. El facilitador asignará problemas adicionales del libro de texto como parte de esta
tarea para entregar. Estos problemas ayudarán a los estudiantes a entender los
objetivos del taller. Este es un trabajo individual; no se aceptarán copias del Internet
o de las direcciones electrónicas utilizadas. (Ver Anejo A: Política de Honestidad
Académica).
4. Esta tarea deberá entregarla al facilitador debidamente identificada con su nombre,
fecha y taller. La misma tiene un valor de 100 puntos. La evaluación de esta tarea
estará dividida en 70% por contenido y 30% por objetivos de lenguaje. (Ver anejo
B: Matriz valorativa para evaluar tareas previas a los talleres).
Actividades:
1. El facilitador devolverá los trabajos completados por los estudiantes durante el taller
uno (Tarea y Trabajo Cooperativo). Estos trabajos estarán evaluados de acuerdo
con las matrices valorativas incluidas en el módulo. El facilitador discutirá la
puntuación obtenida con los estudiantes según sea necesario. El facilitador
contestará cualquier pregunta que los estudiantes tengan en relación a los trabajos
del taller uno. Estos trabajos serán incluidos en el Portafolio el cual será entregado
en el taller cinco.
MATH 173 Plane Geometry and Space I 24
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
2. Trabajo para realizar previo al Taller Dos : El/la estudiante entregará la tarea
asignada. El facilitador contestará preguntas relacionadas a la tarea y aclarará
todas las dudas que los estudiantes tengan.
3. El facilitador discutirá en la clase el material relacionado a los objetivos del taller y
podrá asignar o hacer algunos problemas de práctica durante el taller. Estos
problemas ayudarán a los estudiantes a aclarar dudas y contestar cualquier
pregunta que tengan lo cual los ayudará a mejorar su conocimiento y destrezas
referentes al material de la clase.
4. El facilitador dará problemas adicionales para que los estudiantes los resuelvan en
clase para practicar los procedimientos asociados con la solución de los mismos.
Estos problemas ayudarán a los estudiantes a clarificar cualquier duda o pregunta
que tengan, también los ayudará a mejorar el conocimiento sobre el material
discutido en el taller.
5. Trabajo cooperativo (ver Anejo G) : Luego de terminadas las actividades
anteriores, el facilitador dividirá la clase en grupos de tres a cinco estudiantes
dependiendo del tamaño de la clase. Cada grupo trabajará el siguiente ejercicio. El
facilitador les dirá a los estudiantes cuanto tiempo tienen para resolver el problema.
La solución será entregada en una hoja de papel con los nombres de los miembros
del grupo. (Ver anejo C: Matriz valorativa para evaluar trabaj o en grupo).
(Nota : El facilitador puede asignar otro trabajo cooperativo diferente al que esta en el
mádulo. Si el trabajo cooperativo es cambiado, el facilitador debe notificar al los
estudiantes del cambio en el taller anterior)
6. Prueba corta: Al final del taller los estudiantes tomarán una prueba corta sobre el
material discutido en el taller.
7. El facilitador discutirá la tarea que los estudiantes deben completar antes del
próximo taller. En adición, el facilitador proveerá una lista de los problemas a
resolver como parte de la tarea a entregar en el taller tres.
Avalúo
Prueba corta : Los estudiantes tomarán una prueba corta al final del taller sobre el
material del taller.
MATH 173 Plane Geometry and Space I 25
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
También redactará el Diario Reflexivo hallado en Anejo F. Estas actividades serán
incluidas en el Portafolio del estudiante que será entregado en el Taller Cinco.
MATH 173 Plane Geometry and Space I 26
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Workshop Three Specific Objectives:
At the end of this workshop, the student will be able to:
1. Define parallel lines.
2. Determine if two lines are parallel using parallelism theorems and postulates.
3. Demonstrate and apply the transverse line theorem.
4. Define the angles formed by parallel lines.
5. Define and identify different types of polygons.
6. Determine if a figure is a polygon and if it is convex.
7. Find the sum of internal angles of a polygon.
8. Construct parallel lines and polygon
Language Objectives:
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):
http://www.terragon.com/tkobrien/algebra/topics/parallellines/parallellines.html
http://www.math.psu.edu/geom/koltsova/section3.html
http://www.mathleague.com/help/geometry/polygons.htm
http://www.math.com/school/subject3/lessons/S3U2L1GL.html
http://www.aaamath.com/geo318-polygons-numbers.html
http://www.math.com/tables/geometry/polygons.htm
http://www.mathsisfun.com/geometry/parallel-lines.html
http://mathforum.org/~sarah/hamilton/ham.lines.html
http://regentsprep.org/regents/math/angles/Lparallel.htm
http://library.thinkquest.org/2647/geometry/angle/parallel.htm
Assignments before Workshop Three:
1. The student will search the internet links provided for the third workshop to find
the concepts that will be covered during the first meeting. Also, the student will
MATH 173 Plane Geometry and Space I 27
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
use the suggested textbook and/or the references indicated in the bibliography,
to study those chapters that cover the topics of deductive and inductive
reasoning, points, lines, planes, real numbers, angles, assertions, and geometric
tests. The student will turn it the homework properly identifying its name, course,
section and day.
2. Find information and examples on the following terms. If some of these concepts
are defined and denoted with symbols, the student should include them in the
homework:
• Parallel Lines
• Parallelism Postulates and Theorems
• Transverse lines Theorem
• Polygons (Types of polygons)
If the student has access to computer programs such as MS Office or Lotus
SmartSuite, he/she will be able to use them for the homework. This must be an
individual work; copies from the internet or from the URLs used will not be
accepted. (See Appendix A: Academic Honesty Policy).
Watch the following video regarding parallel lines:
http://www.youtube.com/watch?v=1_3anRenfwA&feature=user
3. The facilitator will assign additional problems from the textbook as part of this
assignment. These problems will help students understand the terms and
objectives of this workshop. This must be an individual work; copies from the
internet or from the URLs used will not be accepted. (See Appendix A:
Academic Honesty Policy).
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 pr ior to the
workshops).
5. You should be working with your portfolio.
Activities:
MATH 173 Plane Geometry and Space I 28
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
1. The facilitator will return the work completed by the students during workshop
two (Assignment, Short Test and Collaborative Exercise). The work completed
would be assessed based on the rubrics included in the module. The facilitator
will discuss the points obtained with the students as necessary. The facilitator will
answer any questions the students may have related to the workshop one. The
assessed work from workshop one will be included in the Portfolio that will be
turn in during workshop five.
2. The students will submit the assignments to the facilitator. The facilitator will
clarify any doubts and will answer any questions the student’s may have
regarding the assignment.
3. The facilitator will discuss the material related to the objectives in workshop three
and may provide and discuss some practice problems during the workshop.
These problems will allow the students to clarify any questions and to improve
their skills and knowledge in the workshop material.
4. Collaborative Exercise (see Appendix G): After completion of the previous
activities the facilitator will divide the class in groups of three to five students.
Each group will work the following collaborative exercise. A speaker will be
selected in each group. The facilitator will let the students know how much time
they have to solve the problem. The solution will be turn in to the facilitator on a
piece of paper with the name of all the members of the group. (See appendix C:
Rubric to evaluate group work). (Note : The facilitator can assign another
collaborative exercise different from the one in the module. If the collaborative
exercise is changed, the facilitator should notify the students about the change in
the previous workshop).
5. The facilitator will select one group and will ask them to solve and present results
of the collaborative exercise. Each group will have the opportunity to discuss
their solution if different from the solution presented by the first group.
6. Short Test : At the end of the workshop the students will take a short test that will
include the material covered during the workshop.
MATH 173 Plane Geometry and Space I 29
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
7. The facilitator will discuss the assignments to be completed before workshop
four. Also, the facilitator will provide a list of problems to be included as part of
the assignment before workshop four.
Assessment:
Short Test: The students will answer a short test at the end of the workshop about the
material discussed during the workshop.
The students must also complete the Reflexive Diary found in Appendix F. These
activities must be included in the student portfolio to be submitted in Workshop Five.
MATH 173 Plane Geometry and Space I 30
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Taller Cuatro
Objetivos Específicos:
Al finalizar el Taller, el estudiante:
1. Definirá paralelogramos.
2. Demostrará las propiedades de un paralelogramo.
3. Definirá un rombo.
4. Demostrará las propiedades de un rombo.
5. Definirá un rectángulo y un cuadrado.
6. Demostrará las propiedades de un rectángulo y un cuadrado.
7. Definirá un trapezoide y un trapezoide isósceles.
8. Demostrará las propiedades de un trapezoide.
9. Construirá diferente tipos de figuras.
Objetivos de Lenguaje:
1. Demostrar dominio del idioma Español (vocabulario, sintaxis, presentación de
ideas).
2. Utilización apropiada y correcta de gramática.
3. Aplicación y utilización correcta y apropiada de los verbos.
Enlaces Electrónicos:
http://www.ies.co.jp/math/products/geo1/applets/para/para.html
http://deaver.barry.edu/bankef/P-GRAM.HTM
http://www.mathleague.com/help/geometry/polygons.htm
http://www.math.com/school/subject3/lessons/S3U2L3GL.html
http://id.mind.net/~zona/mmts/geometrySection/commonShapes/trapezoid/trapezoid.
html
http://argyll.epsb.ca/jreed/math9/strand3/trapezoid_area_per.htm
http://www.escolar.com/geometr/06cuadrila.htm
http://roble.pntic.mec.es/jarran2/cabriweb/Poligonos.htm
http://www.educacionplastica.net/poligonos.htm
http://www.enchantedlearning.com/math/geometry/shapes/
MATH 173 Plane Geometry and Space I 31
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Asignaciones antes del Taller:
1. El/la estudiante leerá y buscará información relacionadas a los objetivos del taller
cuatro en los libros de texto recomendados o en direcciones electrónicas o cualquier
otra referencia bibliográfica.
2. Una vez realice la lectura, los estudiantes contestarán las siguientes preguntas.
Este es un trabajo individual; no se aceptarán copias del Internet o de las
direcciones electrónicas utilizadas. (Ver Anejo A: Política de Honestidad
Académica).
• Cuadriláteros
• Paralelogramos
• Rombo
• Rectángulos
• Cuadrados
• Trapezoides
3. El facilitador asignará problemas adicionales del libro de texto como parte de esta
tarea para entregar. Estos problemas ayudarán a los estudiantes a entender los
objetivos del taller. Este es un trabajo individual; no se aceptarán copias del Internet
o de las direcciones electrónicas utilizadas. (Ver Anejo A: Política de Honestidad
Académica).
4. Esta tarea deberá entregarla al facilitador debidamente identificada con su nombre,
fecha y taller. La misma tiene un valor de 100 puntos. La evaluación de esta tarea
estará dividida en 70% por contenido y 30% por objetivos de lenguaje. (Ver anejo
B: Matriz valorativa para evaluar tareas previas a los talleres).
Actividades:
1. El facilitador comenzará la clase con un breve repaso.
2. El facilitador devolverá los trabajos completados por los estudiantes durante el taller
tres (Tarea y Trabajo Cooperativo). Estos trabajos estarán evaluados de acuerdo
con las rubricas incluidas en el modulo. El facilitador discutirá la puntuación
obtenida con los estudiantes según sea necesario. El facilitador contestará cualquier
pregunta que los estudiantes tengan en relación a los trabajos del taller uno. Estos
trabajos serán incluidos en el Portafolio el cual será entregado en el taller cinco.
MATH 173 Plane Geometry and Space I 32
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
3. Trabajo para realizar previo al Taller Cuatro : El/la estudiante entregará la tarea
asignada. El facilitador contestará preguntas relacionadas a la tarea y aclarará
todas las dudas que los estudiantes tengan.
4. El facilitador discutirá en la clase el material relacionado a los objetivos del taller y
podrá asignar o hacer algunos problemas de práctica durante el taller. Estos
problemas ayudarán a los estudiantes a aclarar dudas y contestar cualquier
pregunta que tengan lo cual los ayudará a mejorar su conocimiento y destrezas
referentes al material de la clase.
5. El facilitador dará problemas adicionales para que los estudiantes los resuelvan en
clase para practicar los procedimientos asociados con la solución de los mismos.
Estos problemas ayudarán a los estudiantes a clarificar cualquier duda o pregunta
que tengan, también los ayudará a mejorar el conocimiento sobre el material
discutido en el taller.
6. Trabajo cooperativo (ver Anejo G) : Luego de terminadas las actividades
anteriores, el facilitador dividirá la clase en grupos de tres a cinco estudiantes
dependiendo del tamaño de la clase. Cada grupo trabajará el siguiente ejercicio. El
facilitador les dirá a los estudiantes cuanto tiempo tienen para resolver el problema.
La solución será entregada en una hoja de papel con los nombres de los miembros
del grupo. (Ver anejo C: Matriz valorativa para evaluar trabaj o en grupo).
7. Prueba corta: Al comienzo del taller los estudiantes tomaran una prueba corta
sobre el material discutido en el taller.
8. El facilitador discutirá la tarea que los estudiantes deben completar antes del
próximo taller. En adición, el facilitador proveerá una lista de los problemas a
resolver como parte de la tarea a entregar en el taller tres.
Avalúo
Prueba corta : Los estudiantes tomarán una prueba corta al final del taller sobre el
material del taller. También redactará el Diario Reflexivo hallado en Anejo F. Estas
actividades serán incluidas en el Portafolio del estudiante que será entregado en el
Taller Cinco.
MATH 173 Plane Geometry and Space I 33
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Workshop Five/Taller Cinco
NOTA: Este taller es bilingüe. Tanto,
el Facilitador como los estudiantes,
deberán utilizar el idioma asignado
para cada tarea y actividad.
NOTE: This is a bilingual workshop.
Both the facilitator and student
should use the language assigned
for each homework and activity.
Specific Objectives:
At the end of this workshop, the student:
1. Recognize the Cartesian Coordinate System.
2. Find different points in a Cartesian Coordinate System.
3. Construct lines using tables and using x & y intercepts.
4. Solve problems requiring the use of the distance formula and the midpoint
formula.
5. Find the slope of a line using two points or its equation.
Language Objectives:
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):
Cartesian Coordinate System
http://www.blc.edu/fac/rbuelow/CAL/nt1-3.htm
http://www.onlineconverters.com/cartesianexp.html
http://www.math.utah.edu/online/1010/coord/
Slope
http://www.purplemath.com/modules/slope.htm
http://id.mind.net/%7Ezona/mmts/functionInstitute/linearFunctions/lsif.html
http://math.about.com/library/weekly/aa120502a.htm
http://cs.selu.edu/~rbyrd/math/slope/
http://www.math.com/school/subject2/lessons/S2U4L2DP.html
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Distance Formula
http://www.purplemath.com/modules/distform.htm
Midpoint Formula
http://www.purplemath.com/modules/midpoint.htm
http://www.regentsprep.org/Regents/Math/midpoint/Lmidpoint.htm
Assignments before Workshop Five:
1. The student will search the internet links provided for the third workshop to find
the concepts that will be covered during the first meeting. Also, the student will
use the suggested textbook and/or the references indicated in the bibliography,
to study those chapters that cover the topics of deductive and inductive
reasoning, points, lines, planes, real numbers, angles, assertions, and geometric
tests. The student will turn it the homework properly identifying its name, course,
section and day.
2. Find information and examples on the following terms in English. If some of
these concepts are defined and denoted with symbols, the student should
include them in the homework:
• Cartesian Coordinate System
• Distance formula
• Midpoint formula
• Slope of a line
If the student has access to computer programs such as MS Office or Lotus
SmartSuite, he/she will be able to use them for the homework. This must be an
individual work; copies from the internet or from the URLs used will not be
accepted. (See Appendix A: Academic Honesty Policy).
3. The facilitator will assign additional problems as part of this assignment. These
problems will help the students understand the terms and objectives of this
workshop. This must be an individual work written in English and Spanish; copies
from the internet or from the URLs used will not be accepted. (See Appendix A:
Academic Honesty Policy).
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;
MATH 173 Plane Geometry and Space I 35
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the evaluation of this assignment will be 70% for content and 30% for language
objectives. (See Appendix B: Rubrics to evaluate assignments pr ior to the
workshops).
5. The students will review and study ALL the material presented in the previous
workshops. It is very important to review the collaborative exercises solved
already in the other workshops. In addition the students should review the
practice problems and the exercises included in the assignments. This will help
them get prepared to participate and solve the problems to be included in the
final collaborative exercise (debate-contest).
6. Give the final touches to the portfolio and bring it to the classroom.
Activities:
1. The facilitator will start the class with a short review (English).
2. The facilitator will return the work completed by the students during workshop
four (Assignment, Short Test and Collaborative Exercise). The work completed
would be assessed based on the rubrics included in the module. The facilitator
will discuss in English the points obtained with the students as necessary. The
facilitator will answer any questions the students may have related to the
workshop one completed work. The assessed work from workshop one will be
included in the Portfolio that will be turn in during workshop five
3. The students will include the assignment in the Portfolio. The facilitator will clarify
any doubts and will answer any questions the student’s may have regarding the
assignment (in English).
4. Short Test: At the beginning of the workshop the students will answer the short test
in Spanish about the material discussed during the workshop.
5. Portfolio: The students will finalize the Portfolio in accordance with the guidance
previously provided by the facilitator. They will ensure that all the work is included
and everything is in order. The students then will turn in the Portfolio to the facilitator
(English and Spanish).
6. Final Collaborative Exercise (Debate-Contest): During this workshop the students
will participate in a final collaborative exercise (Debate-Contest). This will be a team
work, however, the assessment will consider both, individual and group performance
MATH 173 Plane Geometry and Space I 36
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appraisal. Based upon the number of students registered in this course, the
facilitator will select at random a maximum of six (6) groups with no more of five (5)
students in each group. Each group will have the opportunity to answer applications
and practical exercises related to the concepts that were presented in ALL the
previous workshops. (See Appendix D: Rubric for evaluation of the final
collaborative work). The rules for this final collaborative exercise are as follows:
a. The collaborative exercise will consist of five (5) application problems that will
cover the objectives learned in the course workshops. Half of these exercises will
be in English and the other half will be in Spanish.
b. The application problems will cover the objectives, concepts and procedures
learned in class. Each problem will have a time limit of no more than 30 minutes
to be solved by each group.
c. After the facilitator divide the class in groups, the member of each group will seat
together in order to discuss and solve the problems.
d. The facilitator will provide the final instructions and rules to complete the
collaborative exercise. Any questions regarding the exercise or the rules will be
answer by the facilitator.
e. The applications problems will be solve one at a time; each group will work the
same exercise at the same time in the time allowed by the facilitator. The
facilitator has the option to let the students use the book and class notes as
reference.
f. The facilitator will give a copy of the first problem to each group; at that time the
facilitator will tell the students the amount of time the have to solve the problem
and then they will start. The solution of the problems will be in the language the
problem was written.
g. The groups will work quietly and without interruptions. If a student do not follow
the rules and disrupt the other groups, his/her group will have a penalty
(deduction) of five (5) points from that problem.
h. The first group to finish the problem before the time allowed, will obtained a
bonus of five (5) points and will present their solution in front of the class.
MATH 173 Plane Geometry and Space I 37
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i. If none of the groups finish the problem before the time allowed, the facilitator will
provide an additional five (5) minutes to finish the problem and there won’t be a
bonus of five (5) points.
j. When the time allowed is finished, the facilitator will collect the solution from all
the groups. Then the facilitator will select a person from one of the groups to
present their solution in front of the class.
k. After one of the groups present their solution in front of the class, the other
groups will have the opportunity to agree or disagree with the solution presented.
In case of a disagreement a group can challenge the first group, the second
group will present their solution in front of the class. If the second group is
correct, they will receive a bonus of five (5) points. In case that none of the
groups obtained the correct answer, the facilitator will provide and discuss the
correct solution.
l. If the solution from a group is incorrect but the procedure used is correct, the
group will get partial credit for the problem.
m. After completing the discussion on the first problem, the facilitator will provide a
copy of the next problem to each group. The process will be repeated until all the
problems in the collaborative exercise are completed and their solution has been
presented.
n. All the students should have an active participation in the discussion and solution
of the problems to earn individual points. The individual points will be between 5
and 10 points per problem depending on the type of exercise.
o. The facilitator can grant additional points to a group depending on the number of
correct solutions and the participation of the group members.
7. After completion of the final collaborative exercise, the students will write two or
three paragraphs in Spanish were they will provide feedback to the facilitator about
the course and his/her teaching techniques. The students should include if their
expectations about the course were met. These activities must be included in the
student portfolio to be submitted in Workshop Five.
8. The students will complete the class evaluation. The student representative will
return the course evaluation to the front office.
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9. Closing activity – to be determined by the facilitator. Assessment:
Short Test: The students will answer a short test at the end of the workshop about the
material discussed during the workshop.
MATH 173 Plane Geometry and Space I 39
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Anejos/Appendixes
MATH 173 Plane Geometry and Space I 40
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo A/Appendix A
Plagiarism
Dear Student:
The internet, although a very resourceful tool in today’s world has become a tool where
students and other professionals can find what others have done in seconds; thus
promoting or developing the temptation to use what others have done without giving
them the appropriate credit for their work. In an article published by Indiana University, it
was stated that using the ideas of others without giving proper credit to the source of
that information is considered plagiarism .
Whenever we use information from other sources it is extremely important that you:
1. Give credit to the person’s ideas, theories or opinions.
2. Give credit to a person if we use a chart, graph, drawing or any other type of
knowledge needed to support a paper.
3. Give credit to a person or source if we use a quotation or paraphrase ideas that
belong to them.
For more information go to http://www.indiana.edu/~wts/pamphlets/plagiarism.shtml
or simply search for the topic of plagiarism under: www.plagiarism.org.
Important Note: Plagiarism is a serious issue and i t is considered an offense that has
serious consequences; which in turn may affect your academic success and
professional career. There are workshops offered to help you when writing papers to
avoid falling into this serious matter. You can che ck for time and dates of these
workshops in the Learning Resources Center. Our fa cilitators can also provide you with
help when writing papers and/or assignments.
Sincerely, Ricardo Ortolaza, Ed.D. Chief Learning Officer
MATH 173 Plane Geometry and Space I 41
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
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
MATH 173 Plane Geometry and Space I 42
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo B/Appendix B
Matriz Valorativa para Tareas Previas al Taller
Assignment Before Workshop One
Student Name: ______________________ Date: _______________
Criteria Value Points Student Score
Content Part 2 – The definitions are complete, clear and well stated. The proper information and examples are provided for each term. The sentences are cohesive and have a proper flow.
20
Part 3 (a) – The answer is correct for each of the equations. 5
Part 3 (b) – The answer is clear and well stated. The addition and multiplication properties are clearly explained. The sentences are cohesive and have a proper flow.
10
Part 3 (c) – The answer is clear and well stated. The explanation is complete and provides enough information. The sentences are cohesive and have a proper flow.
10
Part 3 (d) – The answer is clear and well stated. It provides the necessary details to explain what a slope is. The sentences are cohesive and have a proper flow.
5
Part 3 (e) – The answer is clear and well stated. It provides the necessary details to explain how to determine if a graph is a function. The sentences are cohesive and have a proper flow.
5
Part 3 (f) – The answer is clear and well stated. The explanation provides enough information to establish the relationship between functions and equations. The sentences are cohesive and have a proper flow.
5
Part 3 (g) – The answer is clear and well stated. The general steps are provided and clearly explained. The sentences are cohesive and have a proper flow.
10
Language Demonstrate a command of standard English (vocabulary used, syntax and flow of ideas)
10
Uses grammar appropriately and correctly 10 Manages and uses verbs appropriately and correctly 10
Total Points 100 (70% content and
30% language )
Student’s total Score:
_______
Facilitator’s Signature: _________________________
Student’s Signature: __________________________
MATH 173 Plane Geometry and Space I 43
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Tarea Previa al Taller Dos
Nombre Estudiante: ______________________ Fecha: _______________
Criterio Puntuación Puntuación Estudiante Cont enido
Parte 2 – Las definiciones están completas, son claras y bien establecidas. Se provee información correcta y se dan ejemplos según necesario. La respuesta se provee en oraciones claras y concisas.
20
Parte 3 – Se contestan todos los problemas, las contestaciones son correctas y se provee el procedimiento por el cual se obtuvo la respuesta (según sea necesario). El procedimiento y las formulas utilizadas son correctas. Los problemas se resuelven y se entrega en forma organizada y limpia.
50
Lenguaje Demostrar dominio del idioma Español (vocabulario, syntax, presentación de ideas)
10
Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos
10
Total de Puntos 100 (70% contenido y
30% lenguaje)
Puntuación total Estudiante: _______
Firma de Facilitador: _________________________
Firma de Estudiante: __________________________
MATH 173 Plane Geometry and Space I 44
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Assignment Before Workshop Three
Student Name: ______________________ Date: _______________
Criteria Value Points Student Score Content
Part 2 – The definitions are complete, clear and well stated. The proper information is provided and examples are provided for each term. The sentences are cohesive and have a proper flow.
20
Part 3 – All the problems are solved, the answers are correct and the procedure used to find the solution is provided (as necessary). The procedure and formulas used are correct. The assignment is clean and the problems are solved in an organized way.
45
Part 5 – The student searched and brought to class an article related to the class objectives. The student is ready to discuss the article in class.
5
Language Demonstrate a command of standard English (vocabulary used, syntax and flow of ideas)
10
Uses grammar appropriately and correctly 10 Manages and uses verbs appropriately and correctly
10
Total Points 100 (70% content and 30% language)
Student’s total Score: _______
Facilitator’s Signature: _________________________
Student’s Signature: __________________________
MATH 173 Plane Geometry and Space I 45
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Tarea Previa al Taller Cuatro
Nombre Estudiante: ______________________ Fecha: _______________
Criterio Puntuación Puntuación Estudiante
Cont enido Parte 2 – Las definiciones están completas, son claras y bien establecidas. Se provee información correcta y se dan ejemplos según necesario. La respuesta se provee en oraciones claras y concisas.
20
Parte 3 – Se contestan todos los problemas, las contestaciones son correctas y se provee el procedimiento por el cual se obtuvo la respuesta (según sea necesario). El procedimiento y las formulas utilizadas son correctas. Los problemas se resuelven y se entrega en forma organizada y limpia.
50
Lenguaje Demostrar dominio del idioma Español (vocabulario, syntax, presentación de ideas)
10
Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos
10
Total de Puntos 100 (70% contenido y 30%
lenguaje)
Puntuación total
Estudiante: _______
Firma de Facilitador: _________________________
Firma de Estudiante: __________________________
MATH 173 Plane Geometry and Space I 46
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Tarea Previa al Taller Cinco
Nombre Estudiante: ______________________ Fecha: _______________
Criteria Puntuación Puntuación Estudiante
Contenido Part 2 – All the problems are solved, the answers are correct and the procedure used to find the solution is provided (as necessary). The procedure and formulas used are correct. The assignment is clean and the problems are solved in an organized way.
70
Lenguaje Demostrar dominio del idioma Español (vocabulario, syntax, presentación de ideas)
10
Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos 10
Total de Puntos 100 (70% contenido y 30%
lenguaje)
Puntuación total Estudiante:
_______
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Anejo C/Appendix C
RUBRIC FOR COLLABORATIVE EXERCISE EVALUATION
Workshop One & Three NAME: _____________________________ Date: ______________
CRITERIA Value Points Workshop 1 Student Score
Workshop 3 Student Score
1. Frequently contribute to group discussions
10
2. Show interest in group discussions
10
3. Answer questions from other students and from the facilitator
5
4. Make questions related to the collaborative exercise
5
5. Present arguments based on the readings and class work
10
6. Show attention and is opened to the arguments from other students
10
7. Answer to the exercise is correct 25 8. Procedures and formulas are
included and correct. 20
9. Work is organized 5 TOTAL Points 100 Student’s
Score WS1:
Student’s Score WS3:
Comments; ________________________________________________________________________
MATH 173 Plane Geometry and Space I 48
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MATRIZ VALORATIVA PARA EVALUAR LA PARTICIPACIÓN EN EL TRABAJO EN GRUPO
Taller Dos & Cuatro NOMBRE: _____________________________ Fecha: ______________
CRITERIA Puntuación Taller 2 Puntos Est.
Taller 4 Puntos Est.
1. Contribuye frecuentemente a las discusiones en el grupo
10
2. Demuestra interés en las discusiones en grupo
10
3. Contesta preguntas del facilitador y sus compañeros
5
4. Formula preguntas pertinentes al ejercicio cooperativo
5
5. Presenta argumentos fundamentados en las lecturas y trabajos de la clase
10
6. Demuestra atención y apertura a los argumentos de sus compañeros
10
7. La respuesta del ejercicio es correcta
25
8. El procedimiento y las formulas están incluidas y son correctas
20
9. El trabajo es organizado 5 TOTAL Puntos 100 Total Puntos
WS2:
Total Puntos WS4:
Comentarios; ________________________________________________________________
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Anejo D/Appendix D
RUBRIC FOR EVALUATION OF THE FINALCOLLABORATIVE EXE RCISE
NAME: _____________________________ Date: ______________
CRITERIA Value Points Student Score 1. Frequently contribute to group discussions 5 2. Show interest in group discussions 5 3. Present arguments based on the readings and
class work 5
4. Make questions related to the collaborative exercise
5
5. Show attention and is opened to the arguments from other students
5
6. Answer to exercise number one is correct, the procedure and formulas used are correct and the work is organized.
15
7. Answer to exercise number two is correct, the procedure and formulas used are correct and the work is organized.
15
8. Answer to exercise number three is correct, the procedure and formulas used are correct and the work is organized.
15
9. Answer to exercise number four is correct, the procedure and formulas used are correct and the work is organized.
15
10. Answer to exercise number five is correct, the procedure and formulas used are correct and the work is organized.
15
TOTAL Points 100 Student’s Score:
Comments;
_______________________________________________________
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Anejo E/Appendix E
PARÁMETROS ESPECÍFICOS PARA EVALUAR ASISTENCIA Y P ARTICIPACIÓN
La evaluación de asistencia y participación en los cinco talleres tiene un peso de 15%
del total de la evaluación final del curso MATH 199. Es requisito insustituible la
asistencia a todas las cinco reuniones, dos o más ausencias equivalen a fracaso del
curso. Las actividades realizadas en el taller ausente, sujetas a evaluación, serán
consideradas y ponderadas de acuerdo con los parámetros específicos. Por lo tanto, si
el/la estudiante se ausenta y entrega los trabajos posteriormente, su puntuación
comenzará con descuento porcentual previamente establecido para cada actividad
realizada en la respectiva reunión; como se demuestra a continuación:
Actividad Puntos Descontados
Trabajos a realizar previo a cada taller 20 puntos por cada taller que entregue tarde
Trabajo cooperativo Pierde todos los puntos
Prueba corta 20 puntos / Debe reponer antes del siguiente taller, de no ser así perderá todos los puntos.
Portafolio Pierde todos los puntos
Trabajo Final Cooperativo Pierde todos los puntos
Asistencia & Participación:
En un rango de 1 a 20 puntos, siendo 20 la puntuación mayor por cada taller, se
considerará que el/la estudiante haya efectuado aportaciones o preguntas efectivas en
la discusión de los conceptos, ejercicios y actividades del taller. Debe entenderse por
aportaciones efectivas todas aquellas preguntas, presentaciones o ayudas que dirijan
al grupo hacia un mejor entendimiento de los temas discutidos.
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SPECIFIC PARAMETERS FOR THE ATTENDANCE AND PARTICIP ATION
EVALUATION
The evaluation for attendance and participation is worth 15% of the total final evaluation
of the class. Attendance to all five workshops is required and cannot be replaced;
students with two or more absences will fail the class. If the student is absent, the
student must contact the facilitator, in order to be ready for the next workshop. The
students will loose points accordingly based on the specific parameters for all activities
subject to evaluation during the workshop that the student is absent, see table below:
Activity Discounted Points
Assignments prior to each workshop 20 points for each workshop that the work is late.
Collaborative Exercise Loose all the points
Quizzes 20 points / Must be taken prior to the next workshop otherwise will loose all the points.
Portfolio Loose all the points
Final Collaborative Exercise Loose all the points
Attendance & Participation:
In a range from 1 to 20 points, where 20 is the highest score the students can get in
each workshop, this will considered how effective were the students questions and
comments in relation to the discussion of the class topics, problems and workshop
activities. The affectivity of the student participation will be measured based on the how
the questions and comments helped to clarify the concepts and to make it more
understandable.
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Anejo F/Appendix F
Diario Reflexivo
Nombre del Estudiante__________________________________________ Taller # :_____________________________ Fecha :__________________ Instrucciones: El propósito del diario reflexivo es provocar en el estudiante una actitud de reflexión o análisis de las experiencias vividas en cada clase o al concluir una actividad educativa. Esta reflexión le permitirá al estudiante a aplicar lo aprendido a su experiencia del diario vivir, así como a analizar las implicaciones de lo aprendido en su desempeño profesional. Este instrumento deberá completarse al concluir cada una de las sesiones lectivas y será entregado al facilitador/a al terminar cada taller. Preguntas guías:
1. ¿Cuál fue el tema discutido en clase que me impactó más como profesional?
2. ¿Qué aplicación puedo dar de lo que aprendí en mi desempeño profesional?
3. ¿Que puedo mejorar de la clase?
4. ¿Que recomendaciones puedo hacerle al facilitador/a?
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Reflexive Diary
Student Name___________________________________________________ Workshop #:_____________________________ Date :__________________ Instructions: The purpose of the reflexive diary is to create in the students an attitude of reflection or analysis of the experiences learned in class or at the conclusion of an activity. This reflection will allow the students to apply the knowledge acquired in class to the regular day to day living as well as to analyze the implications and applications of the class material to their professional life. This tool must be competed at the conclusion of each section and it must be returned to the facilitator at the end of each workshop. Questions:
1. Which was the topic discussed in class that create the most impact in my
professional life?
2. How I can apply the knowledge learned in class to my professional life?
3. What can I improve in the class?
4. What recommendations I can suggest to the facilitator?
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Anejo G/Appendix G
Collaborative Exercises/Ejercicios Colaborativos Workshop One
Answer the following questions in groups:
1. Use inductive reasoning to find the next element in the series:
125, – 25, 5, – 1
2. What type of reasoning should be used to reach the following assertions?
Premise: Michael Jordan eats cereal.
Premise: Larry Bird eats cereal.
Premise: Magic Johnson eats cereal.
Conclusion: All the great basketball players eat cereal.
3. Using add and subtraction laws, complete the following assertion;
If x = y, then x + 2 = __?__
4. Answer (true or false) the following questions using the following figure:
• ABC is adjacent to ABE
• Value of DBE = 90°
• Value of 2 = 65°
• Value of 1 = 65°
• A is in BD
• A is in BD
• If the value of DBE + the value of BED + the value of
EDB = 180°, then the value of EDB = 2 5°
2
1
65°
E
D B C
A
90°
MATH 173 Plane Geometry and Space I 55
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• BED and EDB are supplementary
5. Find the negation assertion of, “The road to success is difficult”.
6. Find the inverse of the assertion, “If it is a Collie, then it is a dog.”
7. Draw an obtuse angle and its bisector.
TRABAJO COOPERATIVO
Taller Dos
1. Explique cual es el error en cada uno de las siguientes figuras:
a. b. c.
110°
100°
7 in
6 in
10 cm
11 cm
12 cm
12 cm
MATH 173 Plane Geometry and Space I 56
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
2. Utilizando las siguientes figuras, determine cual aseveración es correcta y cual
no es correcta.
a. BAC ≈ EDF
.......................................................................................................... B. BAC ≈ FED
.......................................................................................................... C. EDF ≈ ABC
................................................ D. LOS DOS TRIÁNGULOS NO SON CONGRUENTES.
3. Determine si las siguientes aseveraciones son ciertas o falsas,
a. La mediana de un triangulo es el segmento que une el vértice con el
punto medio del lado opuesto al vértice.
b. El centroide siempre estará localizado dentro del triangulo.
c. La altura de un triangulo es un segmento desde un vértice perpendicular
al lado opuesto de ese vértice.
d. Las alturas de un triangulo siempre estarán en el interior del triangulo.
4. Dibuje un triangulo obtuso y construya otro triangulo congruente a este.
5 7
E
D
120°
5
7
A
B
120° C
F
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Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Collaborative Exercise
Workshop Three
Answer the following questions in groups:
1. Use the following figure to find the value of x & and find if l & m are parallel.
2. What is the sum of all angles in an hexagon?
3. If the sum of three exterior angles of a quadrilateral is 325°, what is the value of the
fourth exterior angle?
4. Given the following figure where AE ED, DB AC, C = 30°. Find the value of
angles 1, 2 & 3.
E D C
B
1
3
30°
40°
80°
(x + y)°
y° l
m
A
MATH 173 Plane Geometry and Space I 58
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
TRABAJO COOPERATIVO
Taller Cuatro
a. Cada grupo dibujara un rectángulo, cuadrado y un rombo con diagonales en
un papel. Las figuras deberán ser identificadas como sigue a continuación;
b. Medirá AC y BD en cada figura, anotará las medidas en la tabla.
c. Con un transportador medirá los ángulos del 1 al 12 en cada figura y anotará
las medidas en la tabla.
AC BD 1 2 3 4 5 6 7 8 9 10 11 12 Rectángulo Cuadrado Rombo
d. Utilizando las medidas de los ángulos 9 al 12 para cada figura, ¿son
perpendiculares sus diagonales?
e. Utilizando las medidas de los ángulos 1 al 8 para cada figura, ¿son las
diagonales bisectores de un par de ángulos opuestos?
f. ¿Que figura tiene sus diagonales congruentes?
A
D
10 11 9
12
7 8
6
5
3 4
2 1
C
B
MATH 173 Plane Geometry and Space I 59
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo H/Appendix H
PORTFOLIO
Guidelines to prepare the portfolio
1. Determination of sources of content
2. The following, but not limited to, documentation will be included:
a. Projects, surveys, and reports.
b. Oral presentations
c. Essays: dated writing samples to show progress
d. Research papers: dated unedited and edited first drafts to show progress
e. Written pieces that illustrate critical thinking about readings: response or
reaction papers.
f. Class notes, interesting thoughts to remember, etc.
g. Learning journals, reflexive diaries.
h. Self assessments, peer assessments, facilitator assessments.
i. Notes from student-facilitator conferences.
3. Organization of documentation
Documentation will be organized by workshop, and by type of assignment within
workshops. Workshops will be separated from one another using construction paper
or paper of different colors, with tabs indicating the workshop number.
4. Presentation of the portfolio
• Documentation will be posted in a binder or in a digital version (e-portfolio).
• The cover page will follow exactly APA guidelines applied to a cover page of
research papers submitted at Metro Orlando Campus. This cover page will be
placed at the beginning of the portfolio.
• The entire portfolio will follow APA style: Courier or Times New Roman font,
size 12, double space, and 1-inch margins. See a “Publication Manual of the
APA, Fifth Edition”
• A log of entries that can be expanded with each new entry properly
numbered. The table, which should be located at the beginning, should
include a brief description, date produced, date submitted, and date evaluated
(Appendix I ).
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• Introduction and conclusion of the income and outcome of the portfolio.
• A list of references and appendixes of all assignments included will be added
to the end of the portfolio.
• The Portfolio Informational Sheet will be placed in the transparent front pocket
of the binder for identification purposes (Appendix O ).
5. Student-Facilitator Feedback Template: Progression follow-up
The final step in implementing portfolios, before returning them to the student or
school life, is sharing feedback with each student to review the contents, student
reflections, and your evaluations of individual items and all of the work together as
related to learning targets (Banks, 2005).
Facilitators will e-mail a feedback template to all students. This template will contain
information pertaining to weaknesses and strengths found in students’ portfolios
(Appendix L ). Facilitators will focus their attention on showing students what is
possible and their progress rather than what is wrong; however, this does not mean
that facilitators will not cover weaknesses and areas for improvement during the
conference. Facilitators will send this feedback template upon completion of
workshop one.
Students will also have the opportunity to respond to the facilitator’s feedback and
write their own comments and/or ideas of how to improve the quality of their
portfolios, and how to become better metacognitive learners on the feedback
template. Students will e-mail the template with their comments back to the facilitator
after every workshop.
6. Portfolio storage:
• Portfolio samples will be safely stored for a six-month term on campus.
• Students will sign an official document empowering Ana G. Mendez
University System with rights to use their portfolios with educational or
accreditation purposes during this term (Appendix M ).
• After this term, and if their authors authorize Ana G. Mendez University
System to discard their portfolios by signing an official document, portfolio
samples will be destroyed; otherwise, they will be returned to their original
authors (Appendix N ).
MATH 173 Plane Geometry and Space I 61
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo I/Appendix I
Log of Entries
Entry Description
Date of Entry
Date
Submitted
Date
Evaluated
Page #
1
2
3
4
5
6
7
8
9
10
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Anejo J/Appendix J
Checklist for Portfolio Assessment
Has the student set academic goals?
Does the portfolio include enough entries in each area to make
valid judgments?
Does the portfolio include evidence of complex learning in realistic
setting?
Does the portfolio provide evidence of various types of student
learning?
Does the portfolio include students’ self-evaluations and
reflections on what was learned?
Does the portfolio enable one to determine learning progress and
current level of learning?
Does the portfolio provide clear evidence of learning to users of
the portfolio?
Does the portfolio provide for student participation and
responsibility?
Does the portfolio present entries in a well-organized and useful
manner?
Does the portfolio include assessments based on clearly stated
criteria of successful performance?
Does the portfolio provide for greater interaction between
instruction and assessment?
Adapted from: Gronlund, N. E. (2003). Assessment of student achievement. 7th ed. Boston: Pearson
Education, Inc.
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Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo K/Appendix K
Portfolio Rubric
4 3 2 1
PORTFOLIO APPEARANCE
� Readable: Are entries typed in an appropriate font and size? Are
entries free of errors? Do ideas expressed in entries follow a logical sequence with appropriate transitions among paragraphs and topics?
� Professionalism: Is the appearance of the portfolio
professional? Are graphics, colors and portfolio language consistent with professional workplace expectations? Is the portfolio presented in a neat and orderly manner?
� Organization: Is the portfolio organized in a manner that makes
it easy to follow and easy to quickly locate information?
PORTFOLIO CONTENT AND FUNCTION
� Content: Are all required entries included in the portfolio? Are
entries relevant to the content of the portfolio? Do all entries contain the student’s reaction or reflection on the selected topics? Do entries provide thorough understanding of content? Resume, Activities List, Varied Samples of Written Work, Evidence of Problem Solving, and Evidence of Decision Making.
� Authenticity: Are the samples and illustrations a true reflection
of the student’s efforts and abilities?
� Growth/Development: Do samples provide thorough
understanding of growth and development related to their field of concentration? Do items show what the student has learned?
� Collaboration: Do items show examples of both individual and
group work? Does the student provide clear understanding of collaboration, and use collaboration to support his/her learning?
MATH 173 Plane Geometry and Space I 64
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
� Reflection and Personal growth: Do items show exceptional
understanding of how to be a reflective thinker and how to seek opportunities for professional growth? Does the student include self-reflective comments? Does the student reflect enthusiasm for learning?
� Professional Conduct: Do items show clear understanding of
ethical behavior and professional conduct? Do items display the pride the student has in his or her work?
Overall Portfolio Impact
� Is this portfolio an asset in demonstrating the student’s value
(skills, abilities, knowledge) to a potential employer or college representative?
Rating Scale 4 = Outstanding 3 = Very good 2 = Good 1 = Need s improvement Source: Retrieved from www.lcusd.net/lchs/portfolio/rubric.htm on February 10th, 2007. Adapted 02/10/2007 by Fidel R. Távara, M.Ed. Coordinator of Assessment and Placement – Metro Orlando Campus
MATH 173 Plane Geometry and Space I 65
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo L/Appendix L
Portfolio Assessment Feedback Template Strengths Weaknesses Improvement Ideas Facilitator’s comments
Student’s response and comments
MATH 173 Plane Geometry and Space I 66
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo M/Appendix M
Use and Return of Portfolio
Sistema Universitario Ana G. Méndez Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo
I, ____________________________________, grant permission to the office of
Assessment and Placement of the Ana G. Méndez University System, to keep in
their records a copy of my portfolio. I understand that the portfolio is going to be
used for accreditation or educational purposes only, and that is not going to be
disclosed without my consent.
By signing this document I authorize the office of Assessment and Placement to
keep a copy of my portfolio for six months and return it to me at the end of this
period of time.
_______________________________ ___________
Student’s Name (print) Date
_______________________________ ___________
Student’s Signature Date
MATH 173 Plane Geometry and Space I 67
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo N/Appendix N
Use and Discard of Portfolio
Sistema Universitario Ana G. Méndez Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo
I, ____________________________________, grant permission to the office of
Assessment and Placement of the Ana G. Méndez University System to keep in
their records a copy of my portfolio. I understand that the portfolio is going to be
used for accreditation or educational purposes only, and that is not going to be
disclosed without my consent.
By signing this document I authorize the Office of Placement and Assessment to
keep a copy of my portfolio for six months and discard it at the end of this period
of time.
_______________________________ ___________
Student’s Name (print) Date
_______________________________ ___________
Student’s Signature Date
MATH 173 Plane Geometry and Space I 68
Prep. 2006. Armando J. Sánchez, MS/IMS. Rev. 2008. Pedro R. Nieves
Anejo O/Appendix O
PORTFOLIO INFORMATIONAL SHEET
Sistema Universitario Ana G. Méndez Metro Orlando Campus
Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo Check one: � Universidad del Este � Universidad Metropolitana � Universidad del Turabo Check one: � Undergraduate
� Graduate
Concentration
Student’s Name
Facilitator’s Name
Course:
Portfolio rated as
Reason of this rate