Plan de estudio para el refuerzo de trigonometra y matemticas en los grados superiores del GI School

Study plan for the reinforcement of Trigonometry in High SchoolPresented by:David Snchez LondooNicols Arango ToroJuan Sebastin Gmez RomeroMay 22nd, 2012GI School

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IntroductionIntended to create a plan that allowed students to have a deeper knowledge of trigonometry.To reach this goal, first we had to fix the theoretical gaps in the students of GI school; this was done using the Easy Trigo program.

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For juniors, there was a space in their regular classes for these lessons.We also opened a space for extra-class tutorships that anyone in High School was able to attend.The areas involved were mathematics and pedagogy.

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With the final results, the students showed great improvements: both the Juniors and the 8 students in the tutorships increased their grades drastically.JS4

JustificationLack of knowledge in the area of math and trigonometry.Dangers learning for collegeImproves the possibility of better ICFES scores.NAT5

Intention: fix theoretical gaps in trigonometry.The students would not see this as a requirement for graduating, but as something useful for their learning lives.

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Mission: To form well-rounded successful leaders who communicate effectively and confidently on a universal level.

Second component:Guided by the requirements of the Ministry of Education of Colombia and those of a U.S-type school, our academic program prepares students to continue their studies at any university in Colombia or in any English-speaking country.

NATThe school mission has 4 specific components, and one of them is the one here7

EasyTrigoMade with Flash

Used to teach trigo

It was never used in class

DSCreators: Daniel Estrada, Maria Camila Ariza, Ana Mara Donneys.8

Research questions?What would be the impact of implementing a review plan based on EasyTrigo so that the students will learn topics related to trigonometry?How can the formation of more conceptual gaps be avoided in the future?JSWhat would be the impact that will generate the implementation of a review program based on the learning platform EasyTrigo so that the students will review or learn for the first time topics related with trigonometry and mathematics that they are not aware of? How can be avoided the formation of more conceptual gaps in the future?9

General objective

Design and apply a pedagogical plan using EasyTrigo that will allow the 2013 promotion of the GI School to have enough trigonometric knowledge to take on the ICFES and the university.NAT10

Specific objectivesIdentify the problems that the students have.Design a study plan to teach trigonometry.Measure the improvements in the students.Design an exam template.NATEl exam template es para poder medir si un estudiante necesita o no EasyTrigo.11

HypothesisCreating and applying a teaching plan using EasyTrigo will improve the students understanding of trigonometry.JS

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Conceptual frameworkTrigonometryGeometrySides and anglesMeasurement of points, lines, curves, surfacesNATLageometraes larama de las matemticasque se dedica alestudio de las propiedades y de las medidas de las figuras en el espacio o en el plano. En su desarrollo, la geometra utiliza nociones como puntos, rectas, planos y curvas, entre otros. (Definicin de Geometra. Definicin De. Recuperado el 11 de septiembre de 2011, de http://definicion.de/geometria/)13

Theoretical frameworkWhy?How?What?La Revolucin EducativaPedagoga a partir de la neurologaLa solucin de problemas y ejercicios matemticosDSThree different theories were used in the process of designing ET classes, showing us, why, how and wat to teach in Trigonometry.14

Why: The Educational RevolutionMinisterio de Educacin NacionalDescribe and model real-world phenomena using trigonometric relationships and functions.Improve the quality of education.Learning whats truly important to form competent citizens.JSMejorar la calidad de la educacin, que hoy est debajo del nivel latinoamericano.15

How: The Neurologic MethodThe brain is designed to learn.Repetition creates new connections between neurons.E. JensenNAT16

Develop more synaptic connections between brain cells and not losing existing connections.The key:Cerebro y Aprendizaje, Jensen, E. 1998NAT17

AnswerChallengesDynamismNoveltyDifficultyRewardsNAT18

What: Problem SolvingTheoriesStepsProcessesFormulasExercisesDSAfter deciding why and how to teach trigo, we asked what to teach (many things you can teach about trigo!)19

M. del Puy PrezDSBook La Solucin de Problemas (chapter Math), ciclo entre mates y lgica. Si aprenden lgica y trigo, mejor que solo trigo.20

TheoriesStepsProcessesFormulasExercisesProblems

Exercises = single-step problems

Problems = multi-step exercisesDSThese elements, specially exercises, are mechanical, memory/Para + lgica, hacen falta PROBLEMAS21

ExerciseIf 3 pizzas cost 9 dollars, how much does each pizza cost?Pizza = $33X = 9DSExercise: one or two steps involved, easy to solve, only memory is necessary22

ProblemLast Friday, Juan bought 2 pizzas and one soda for $5 on store A. On Saturday, Nicols bought the same items for $11. When he asked why it cost more, it turned out that pizzas cost 60% less on Fridays. When David went to store B, he got one pizza and 3 sodas for $10, and Ana Mara got two pizzas and one soda for the same prize.

Q: On what store is pizza cheaper on a normal day?Matrices2p + s = $5N / J / D / AStore A = $5Store B = $4DSProblem: many paths to take, many steps involved, many ways to find the answer23

Field work

DS3 classes per session, two 11s and the tutorship after classes24

1st SessionIn this session the survey was implemented.14 questions that measured the students willingness to participate.

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Implementation of the first diagnosis test.13 questions: theory, practice, and a problem.

2nd Session

JSAs the results arrived it was decided to teach the whole program instead of group difficulties thanks to the poor level in the areas that were going to be teached.26

3rd SessionWe taught the basics of triangles and solving roots.Our adviser taught roots for the first class.Student booklets.

DSIn this class, we studied the basics of triangles (180, classification) and how to solve roots without calcs as suggested by our adviser. Tri OK, roots NO27

We reviewed root solving first.This class we taught radian angles.

4th Session

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5th SessionSupplementary and complementary angles.The students were great with the theory, but not so much with actual exercises and problems

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6th SessionFirst trigonometric lessons.Big changes in the investigation schedule.

DSAntes solo geometry, ahora trigo. Pithagorean Theorem and Trigonometic functions (explicar cuales son), GOOD UNDERSTANDING30

7th SessionGeneral review of all the previous topics.Only with 11th honors and standard, no tutorship.

NATNo se vio en tutoras por la falta de tiempo31

8th SessionReview about trigonometrical identities.Unit circle: used to be taught at the beginning.We used the circle to teach Sin, Cos, and Tan.

JSEn EasyTrigo el Unit circle iba al principio y era solo teora, nosotros lo enseamos al final y le pusimos ejercicios (aprenderse sin cos tan)32

9th SessionWe studied the Sine and Cosine Theorems.The Cosine formula was wrong in EasyTrigo.

DSThe next step after the unit circle 33

10th SessionReview of everything thus far for the exam.The students didnt take their notes to study.

NATLos estudiantes de las pedan que apresuraran la clase.34

11th SessionSecond diagnostic test and final survey.

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Diagnostic test13 questions in total19 answers6 theory questions6 exercises1 problem1 hourDS

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TheoryExercisesTrigonometric functions

Suplementary and Complementary

Radian angles

Characteristics of trianglesUsing the trigonometric functions

Pithagorean Theorem

Sine and Cosine Theorems

Applying trigonometric rules in real life situationsDS

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NATThere were 13 questions, but #1 and #7 required many different answers, so in total the exam had 19 questions. You can see here that the students from both 11 grade and the tutorships improved greatly.38

NATIn the second diagnostic test, the students marked less questions as unknown. For the tests, the students had the option to mark any question as unknown, meaning that even though they tried to answer the question, they werent very sure of the answer. This graph shows that they were more confident, since the students marked less questions as Unknown.39

Problem- Great in theory and exercises.- Not so much in the problem.NATOne of the prolbems that the results showed was that, even though the performance of the students was in better general, the area where we wanted to work the most, problems, didnt see as much improvement as the other areas, but the theory questions and the exercises were generally answered correctly.40

Survey9 questions in totalGenerally good responseTrigonometry improvementOpinions about EasyTrigoJSThe survey asked questions of how the students felt about trigonometry and about the EasyTrigo program.According to the survey, the students generally liked the classes. NOW, WELL SEE SOME OF THE QUESTIONS.41

JSThe exam showed that the students knew about trigonometry, and the survey also showed that they were very confident of their abilities.42

JSWith a few exceptions on grade 11, all of the students believed that the given classes were of quality, showing that EasyTrigo is a good platform to teach trigonometry.43

JSThis final graph shows that most students thought that it would be very good to use EasyTrigo in the future, and to not let this proyect end this year.44

Final products44.7%75.2%

DSOne primary product (high school studients without theorical gaps) and two secondary products (EasyT manual + EasyT test outline)45

Design and apply a pedagogical plan using EasyTrigo that will allow the 2013 promotion of the GI School to have enough trigonometric knowledge to take on the ICFES and the university.Design a study plan to teach trigonometry.Design an exam template.ConclusionsIdentify the problems that the students have.Measure the improvements in the students.JSIdentify: se pudo pero eran muy lame y tuvimos que ensear todo.46

Future applications

NATIf this proyect was taken again by someone in the future, they should have in mind what made things easier for us and what made them harder.47

StrengthsWe had good mathematical abilities.We had a statistics program (PASW 18) that allowed us to analyze the data given by the surveys easily.NAT48

OpportunitiesInitially, we were going to design the lessons from scratch, but EasyTrigo was used instead.Teachers were really permissive when allowing us to use their class time to teach.Teachers from the math department were willing to cooperate to promote our classes.NAT49

WeaknessesWe had to blindly trust the lessons in EasyTrigo.Things were rushed because we didnt schedule our lessons in advance.The group didnt have enough Senior Project passes to leave class.

NATWe had to blindly trust the lessons in EasyTrigo to give the classes because we didnt know about trigonometry either50

ThreatsSeniors have many activities other than the Senior Project.It was uncertain if wed get a class from a teacher each week.The tutorships were optional, so very few students participated.

NATEach week we had to ask the teachers if theyd give us one of their classes, we were lucky that we got a class most weeks.51

Bibliography Bubbl.us: brainstorm and mind map online (2006). Recuperado de https://bubbl.us/ del Puy Prez, M. (1994). La Solucin de Problemas en Matemticas. En Pozo Municio, J. I. (1994). La Solucin de Problemas. Madrid: Grupo Santillana de Ediciones, S. A. del Puy Prez, M. y Pozo Municio, J. I. (1994). Aprender a Resolver Problemas y Resolver Problemas para Aprender. En Pozo Municio, J. I. (1994). La Solucin de Problemas. Madrid: Grupo Santillana de Ediciones, S. A. Estrada, D., Ariza, M. C. y Donneys, A. M. (2011). Diseo e implementacin de software para facilitar el aprendizaje de contenidos de trigonometra en los estudiantes del grado dcimo del GI School. Salento, Colombia: Fundacin GI School. Godino, J. D. (2004). Didctica de las Matemticas para Maestros. Andaluca: Universidad de Granada. Recuperado el 8 de septiembre, 2011 de http://www.juntadeandalucia.es/averroes/~cepco3/competencias/mates/primaria/didactica_maestros.pdf Jensen, E. (1998). Cerebro y Aprendizaje, Competencias e implicaciones educativas. Madrid: Narcea, S.A. de Ediciones..DS52

BibliographyMinisterio Nacional de Educacin (2002). Seminario Nacional de Formacin de Docentes: Uso de Nuevas Tecnologas en el Aula de Matemticas. Bogot: Enlace de Editores Ltda. Ministerio Nacional de Educacin (2003). La Revolucin Educativa: Estndares Bsicos de Matemticas y Lenguaje, Educacin Bsica y Media. Red de Centros Educativos. Recuperado el 11 de mayo, 2011 de http://redced-co.relpe.org/node/150 Mosquera, J. (2005). Didctica del lgebra y de la Trigonometra. Caracas. Recuperado el 8 de septiembre, 2011 de http://biblo.una.edu.ve/docu.7/bases/marc/texto/m5925gi.pdf PASW Statistics (2009) (Versin 18.0.0). Chicago: Predictive Analytics SoftWare. Programa computacional. Prieto Alberca M. y Sondesa Freire M. D. (2006). Geometra Aplicada I: Mtodo Newton-Cramer. Madrid. Recuperado el 7 de septiembre, 2011 de http://books.google.com.co/books/about/M%C3%A9todo_de_Newton_Cramer.html?id=FP4yAAAACAAJ Sothink SWF Quicker (2012) (Versin 5.4 build 40795). Hubei, China: SourceTec Software Co., LTD. Programa computacional.DS53

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