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Teaching Guide for Senior High School

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- 1. TEACHING GUIDE FOR SENIOR HIGH SCHOOL Statistics and Probability CORE SUBJECT This Teaching Guide was collaboratively developed and reviewed by educators from public and private schools, colleges, and universities. We encourage teachers and other education stakeholders to email their feedback, comments, and recommendations to the Commission on Higher Education, K to 12 Transition Program Management Unit - Senior High School Support Team at k12@ched.gov.ph. We value your feedback and recommendations. Commission on Higher Education in collaboration with the Philippine Normal University INITIAL RELEASE: 13 JUNE 2016
- 2. This Teaching Guide by the Commission on Higher Education is licensed under a Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License. This means you are free to: Share — copy and redistribute the material in any medium or format Adapt — remix, transform, and build upon the material. The licensor, CHED, cannot revoke these freedoms as long as you follow the license terms. However, under the following terms: Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. NonCommercial — You may not use the material for commercial purposes. ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. Printed in the Philippines by EC-TEC Commercial, No. 32 St. Louis Compound 7, Baesa, Quezon City, ectec_com@yahoo.com Published by the Commission on Higher Education, 2016 Chairperson: Patricia B. Licuanan, Ph.D. Commission on Higher Education K to 12 Transition Program Management Unit Office Address: 4th Floor, Commission on Higher Education, C.P. Garcia Ave., Diliman, Quezon City Telefax: (02) 441-1143 / E-mail Address: k12@ched.gov.ph DEVELOPMENT TEAM Team Leader: Jose Ramon G. Albert, Ph.D. Writers: Zita VJ Albacea, Ph.D., Mark John V. Ayaay Isidoro P. David, Ph.D., Imelda E. de Mesa Technical Editors: Nancy A. Tandang, Ph.D., Roselle V. Collado Copy Reader: Rea Uy-Epistola Illustrator: Michael Rey O. Santos Cover Artists: Paolo Kurtis N. Tan, Renan U. Ortiz CONSULTANTS THIS PROJECT WAS DEVELOPED WITH THE PHILIPPINE NORMAL UNIVERSITY. University President: Ester B. Ogena, Ph.D. VP for Academics: Ma. Antoinette C. Montealegre, Ph.D. VP for University Relations & Advancement: Rosemarievic V. Diaz, Ph.D. Ma. Cynthia Rose B. Bautista, Ph.D., CHED Bienvenido F. Nebres, S.J., Ph.D., Ateneo de Manila University Carmela C. Oracion, Ph.D., Ateneo de Manila University Minella C. Alarcon, Ph.D., CHED Gareth Price, Sheffield Hallam University Stuart Bevins, Ph.D., Sheffield Hallam University SENIOR HIGH SCHOOL SUPPORT TEAM CHED K TO 12 TRANSITION PROGRAM MANAGEMENT UNIT Program Director: Karol Mark R. Yee Lead for Senior High School Support: Gerson M. Abesamis Lead for Policy Advocacy and Communications: Averill M. Pizarro Course Development Officers: John Carlo P. Fernando, Danie Son D. Gonzalvo Teacher Training Officers: Ma. Theresa C. Carlos, Mylene E. Dones Monitoring and Evaluation Officer: Robert Adrian N. Daulat Administrative Officers: Ma. Leana Paula B. Bato, Kevin Ross D. Nera, Allison A. Danao, Ayhen Loisse B. Dalena
- 3. Introduction As the Commission supports DepEd’s implementation of Senior High School (SHS), it upholds the vision and mission of the K to 12 program, stated in Section 2 of Republic Act 10533, or the Enhanced Basic Education Act of 2013, that “every graduate of basic education be an empowered individual, through a program rooted on...the competence to engage in work and be productive, the ability to coexist in fruitful harmony with local and global communities, the capability to engage in creative and critical thinking, and the capacity and willingness to transform others and oneself.” To accomplish this, the Commission partnered with the Philippine Normal University (PNU), the National Center for Teacher Education, to develop Teaching Guides for Courses of SHS. Together with PNU, this Teaching Guide was studied and reviewed by education and pedagogy experts, and was enhanced with appropriate methodologies and strategies. Furthermore, the Commission believes that teachers are the most important partners in attaining this goal. Incorporated in this Teaching Guide is a framework that will guide them in creating lessons and assessment tools, support them in facilitating activities and questions, and assist them towards deeper content areas and competencies. Thus, the introduction of the SHS for SHS Framework. The SHS for SHS Framework The SHS for SHS Framework, which stands for “Saysay-Husay-Sarili for Senior High School,” is at the core of this book. The lessons, which combine high-quality content with flexible elements to accommodate diversity of teachers and environments, promote these three fundamental concepts: SAYSAY: MEANING Why is this important? Through this Teaching Guide, teachers will be able to facilitate an understanding of the value of the lessons, for each learner to fully engage in the content on both the cognitive and affective levels. HUSAY: MASTERY How will I deeply understand this? Given that developing mastery goes beyond memorization, teachers should also aim for deep understanding of the subject matter where they lead learners to analyze and synthesize knowledge. SARILI: OWNERSHIP What can I do with this? When teachers empower learners to take ownership of their learning, they develop independence and self- direction, learning about both the subject matter and themselves.
- 4. The Parts of the Teaching Guide This Teaching Guide is mapped and aligned to the DepEd SHS Curriculum, designed to be highly usable for teachers. It contains classroom activities and pedagogical notes, and integrated with innovative pedagogies. All of these elements are presented in the following parts: 1. INTRODUCTION • Highlight key concepts and identify the essential questions • Show the big picture • Connect and/or review prerequisite knowledge • Clearly communicate learning competencies and objectives • Motivate through applications and connections to real-life 2. INSTRUCTION/DELIVERY • Give a demonstration/lecture/simulation/ hands-on activity • Show step-by-step solutions to sample problems • Use multimedia and other creative tools • Give applications of the theory • Connect to a real-life problem if applicable 3. PRACTICE • Discuss worked-out examples • Provide easy-medium-hard questions • Give time for hands-on unguided classroom work and discovery • Use formative assessment to give feedback 4. ENRICHMENT • Provide additional examples and applications • Introduce extensions or generalisations of concepts • Engage in reflection questions • Encourage analysis through higher order thinking prompts 5. EVALUATION • Supply a diverse question bank for written work and exercises • Provide alternative formats for student work: written homework, journal, portfolio, group/individual projects, student-directed research project Pedagogical Notes The teacher should strive to keep a good balance between conceptual understanding and facility in skills and techniques. Teachers are advised to be conscious of the content and performance standards and of the suggested time frame for each lesson, but flexibility in the management of the lessons is possible. Interruptions in the class schedule, or students’ poor reception or difficulty with a particular lesson, may require a teacher to extend a particular presentation or discussion. Computations in some topics may be facilitated by the use of calculators. This is encour- aged; however, it is important that the student understands the concepts and processes involved in the calculation. Exams for the Basic Calculus course may be designed so that calculators are not necessary. Because senior high school is a transition period for students, the latter must also be prepared for college-level academic rigor. Some topics in calculus require much more rigor and precision than topics encountered in previous mathematics courses, and treatment of the material may be different from teaching more elementary courses. The teacher is urged to be patient and careful in presenting and developing the topics. To avoid too much technical discussion, some ideas can be introduced intuitively and informally, without sacrificing rigor and correctness. The teacher is encouraged to study the guide very well, work through the examples, and solve exercises, well in advance of the lesson. The development of calculus is one of humankind’s greatest achievements. With patience, motivation and discipline, teaching and learning calculus effectively can be realized by anyone. The teaching guide aims to be a valuable resource in this objective.
- 5. On DepEd Functional Skills and CHED’s College Readiness Standards As Higher Education Institutions (HEIs) welcome the graduates of the Senior High School program, it is of paramount importance to align Functional Skills set by DepEd with the College Readiness Standards stated by CHED. The DepEd articulated a set of 21st century skills that should be embedded in the SHS curriculum across various subjects and tracks. These skills are desired outcomes that K to 12 graduates should possess in order to proceed to either higher education, employment, entrepreneurship, or middle-level skills development. On the other hand, the Commission declared the College Readiness Standards that consist of the combination of knowledge, skills, and reflective thinking necessary to participate and succeed - without remediation - in entry-level undergraduate courses in college. The alignment of both standards, shown below, is also presented in this Teaching Guide - prepares Senior High School graduates to the revised college curriculum which will initially be implemented by AY 2018-2019. College Readiness Standards Foundational Skills DepEd Functional Skills Produce all forms of texts (written, oral, visual, digital) based on: 1. Solid grounding on Philippine experience and culture; 2. An understanding of the self, community, and nation; 3. Application of critical and creative thinking and doing processes; 4. Competency in formulating ideas/arguments logically, scientifically, and creatively; and 5. Clear appreciation of one’s responsibility as a citizen of a multicultural Philippines and a diverse world; Visual and information literacies Media literacy Critical thinking and problem solving skills Creativity Initiative and self-direction Systematically apply knowledge, understanding, theory, and skills for the development of the self, local, and global communities using prior learning, inquiry, and experimentation Global awareness Scientific and economic literacy Curiosity Critical thinking and problem solving skills Risk taking Flexibility and adaptability Initiative and self-direction Work comfortably with relevant technologies and develop adaptations and innovations for significant use in local and global communities; Global awareness Media literacy Technological literacy Creativity Flexibility and adaptability Productivity and accountability Communicate with local and global communities with proficiency, orally, in writing, and through new technologies of communication; Global awareness Multicultural literacy Collaboration and interpersonal skills Social and cross-cultural skills Leadership and responsibility Interact meaningfully in a social setting and contribute to the fulfilment of individual and shared goals, respecting the fundamental humanity of all persons and the diversity of groups and communities Media literacy Multicultural literacy Global awareness Collaboration and interpersonal skills Social and cross-cultural skills Leadership and responsibility Ethical, moral, and spiritual values
- 6. Preface Prior to the implementation of K-12, Statistics was taught in public high schools in the Philippines typically in the last quarter of third year. In private schools, Statistics was taught as either an elective, or a required but separate subject outside of regular Math classes. In college, Statistics was taught practically to everyone either as a three unit or six unit course. All college students had to take at least three to six units of a Math course, and would typically “endure” a Statistics course to graduate. Teachers who taught these Statistics classes, whether in high school or in college, would typically be Math teachers, who may not necessarily have had formal training in Statistics. They were selected out of the understanding (or misunderstanding) that Statistics is Math. Statistics does depend on and uses a lot of Math, but so do many disciplines, e.g. engineering, physics, accounting, chemistry, computer science. But Statistics is not Math, not even a branch of Math. Hardly would one think that accounting is a branch of mathematics simply because it does a lot of calculations. An accountant would also not describe himself as a mathematician. Math largely involves a deterministic way of thinking and the way Math is taught in schools leads learners into a deterministic way of examining the world around them. Statistics, on the other hand, is by and large dealing with uncertainty. Statistics uses inductive thinking (from specifics to generalities), while Math uses deduction (from the general to the specific). “Statistics has its own tools and ways of thinking, and statisticians are quite insistent that those of us who teach mathematics realize that statistics is not mathematics, nor is it even a branch of mathematics. In fact, statistics is a separate discipline with its own unique ways of thinking and its own tools for approaching problems.” - J. Michael Shaughnessy, “Research on Students’ Understanding of Some Big Concepts in Statistics” (2006) Statistics deals with data; its importance has been recognized by governments, by the private sector, and across disciplines because of the need for evidence-based decision making. It has become even more important in the past few years, now that more and more data is being collected, stored, analyzed and re-analyzed. From the time when humanity first walked the face of the earth until 2003, we created as much as 5 exabytes of data (1 exabyte being a billion “gigabytes”). Information communications technology (ICT) tools have provided us the means to transmit and exchange data much faster, whether these data are in the form of sound, text, visual images, signals or any other form or any combination of those forms using desktops, laptops, tablets, mobile phones, and other gadgets with the use of the internet, social media (facebook, twitter). With the data deluge arising from using ICT tools, as of 2012, as much as 5 exabytes were being created every two days (the amount of data created from the beginning of history up to 2003); a year later, this same amount of data was now being created every ten minutes.
- 7. In order to make sense of data, which is typically having variation and uncertainty, we need the Science of Statistics, to enable us to summarize data for describing or explaining phenomenon; or to make predictions (assuming trends in the data continue). Statistics is the science that studies data, and what we can do with data. Teachers of Statistics and Probability can easily spend much time on the formal methods and computations, losing sight of the real applications, and taking the excitement out of things. The eminent statistician Bradley Efron mentioned how diverse statistical applications are: “During the 20th Century statistical thinking and methodology has become the scientific framework for literally dozens of fields including education, agriculture, economics, biology, and medicine, and with increasing influence recently on the hard sciences such as astronomy, geology, and physics. In other words, we have grown from a small obscure field into a big obscure field.” In consequence, the work of a statistician has become even fashionable. Google’s chief economist Hal Varian wrote in 2009 that “the sexy job in the next ten years will be statisticians.” He went on and mentioned that “The ability to take data - to be able to understand it, to process it, to extract value from it, to visualize it, to communicate it's going to be a hugely important skill in the next decades, not only at the professional level but even at the educational level for elementary school kids, for high school kids, for college kids. “ This teaching guide, prepared by a team of professional statisticians and educators, aims to assist Senior High School teachers of the Grade 11 second semester course in Statistics and Probability so that they can help Senior High School students discover the fun in describing data, and in exploring the stories behind the data. The K-12 curriculum provides for concepts in Statistics and Probability to be taught from Grade 1 up to Grade 8, and in Grade 10, but the depth at which learners absorb these concepts may need reinforcement. Thus, the first chapter of this guide discusses basic tools (such as summary measures and graphs) for describing data. While Probability may have been discussed prior to Grade 11, it is also discussed in Chapter 2, as a prelude to defining Random Variables and their Distributions. The next chapter discusses Sampling and Sampling Distributions, which bridges Descriptive Statistics and Inferential Statistics. The latter is started in Chapter 4, in Estimation, and further discussed in Chapter 5 (which deals with Tests of Hypothesis). The final chapter discusses Regression and Correlation. Although Statistics and Probability may be tangential to the primary training of many if not all Senior High School teachers of Statistics and Probability, it will be of benefit for them to see why this course is important to teach. After all, if the teachers themselves do not find meaning in the course, neither will the students. Work developing this set of teaching materials has been supported by the Commission on Higher Education under a Materials Development Sub-project of the K-12 Transition Project. These materials will also be shared with Department of Education. Writers of this teaching guide recognize that few Senior High School teachers would have formal training or applied experience with statistical concepts. Thus, the guide gives concrete suggestions on classroom activities that can illustrate the wide range of processes behind data collection and data analysis.
- 8. It would be ideal to use technology (i.e. computers) as a means to help teachers and students with computations; hence, the guide also provides suggestions in case the class may have access to a computer room (particularly the use of spreadsheet applications like Microsoft Excel). It would be unproductive for teachers and students to spend too much time working on formulas, and checking computation errors at the expense of gaining knowledge and insights about the concepts behind the formulas. The guide gives a mixture of lectures and activities, (the latter include actual collection and analysis of data). It tries to follow suggestions of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Project of the American Statistical Association to go beyond lecture methods, and instead exercise conceptual learning, use active learning strategies and focus on real data. The guide suggests what material is optional as there is really a lot of material that could be taught, but too little time. Teachers will have to find a way of recognizing that diverse needs of students with variable abilities and interests. This teaching guide for Statistics and Probability, to be made available both digitally and in print to senior high school teachers, shall provide Senior High School teachers of Statistics and Probability with much-needed support as the country’s basic education system transitions into the K-12 curriculum. It is earnestly hoped that Senior High School teachers of Grade 11 Statistics and Probability can direct students into examining the context of data, identifying the consequences and implications of stories behind Statistics and Probability, thus becoming critical consumers of information. It is further hoped that the competencies gained by students in this course will help them become more statistical literate, and more prepared for whatever employment choices (and higher education specializations) given that employers are recognizing the importance of having their employee know skills on data management and analysis in this very data-centric world.
- 9. C h a p t e r ( 1 : ( E x p l o r i n g ( D a t a ( – ( L e s s o n ( 1 ( Page(1( ( Chapter 1: Exploring Data Lesson 1: Introducing Statistics TIME FRAME:1 hour session OVERVIEW OF LESSON In decision making, we use statistics although some of us may not be aware of it. In this lesson, we make the students realize that to decide logically, they need to use statistics. An inquiry could be answered or a problem could be solved through the use of statistics. In fact, without knowing it we use statistics in our daily activities. LEARNING COMPETENCIES: At the end of the lesson, the learner should be able to identify questions that could be answered using a statistical process and describe the activities involved in a statistical process. LESSON OUTLINE: 1. Motivation 2. Statistics as a Tool in Decision-Making 3. Statistical Process in Solving a Problem DEVELOPMENT OF THE LESSON A. Motivation You may ask the students, a question that is in their mind at that moment. You may write their answers on the board. (Note: You may try to group the questions as you write them on the board into two, one group will be questions that are answerable by a fact and the other group are those that require more than one information and needs further thinking). The following are examples of what you could have written on the board: Group 1: • How old is our teacher? • Is the vehicle of the Mayor of our city/town/municipality bigger than the vehicle used by the President of the Philippines? • How many days are there in December? • Does the Principal of the school has a post graduate degree? • How much does the Barangay Captain receive as allowance? • What is the weight of my smallest classmate? Group 2: • How old are the people residing in our town?
- 10. C h a p t e r ( 1 : ( E x p l o r i n g ( D a t a ( – ( L e s s o n ( 1 ( Page(2( ( • Do dogs eat more than cats? • Does it rain more in our country than in Thailand? • Do math teachers earn more than science teachers? • How many books do my classmates usually bring to school? • What is the proportion of Filipino children aged 0 to 5 years who are underweight or overweight for their age? The first group of questions could be answered by a piece of information which is considered always true. There is a correct answer which is based on a fact and you don’t need the process of inquiry to answer such kind of question. For example, there is one and only one correct answer to the first question in Group 1 and that is your age as of your last birthday or the number of years since your birth year. On the other hand, in the second group of questions one needs observations or data to be able to respond to the question. In some questions you need to get the observations or responses of all those concerned to be able to answer the question. On the first question in the second group, you need to ask all the people in the locality about their age and among the values you obtained you get a representative value. To answer the second question in the second group, you need to get the amount of food that all dogs and cats eat to respond to the question. However, we know that is not feasible to do so. Thus what you can do is get a representative group of dogs and another representative group for the cats. Then we measure the amount of food each group of animal eats. From these two sets of values, we could then infer whether dogs do eat more than cats. So as you can see in the second group of questions you need more information or data to be able to answer the question. Either you need to get observations from all those concerned or you get representative groups from which you gather your data. But in both cases, you need data to be able to respond to the question. Using data to find a