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INTRODUCTION The reason for selecting topics 1.1 The role of statistics Statistics is becoming increasingly important in the social life Statistics provides information on the development of economy and society in future of the country and in relation to the outside world The statistical information is extremely necessary, is the premise to help state lead and direct the economy, making basis to plan policies of developing the economy and society Moreover, it is also a sharp and effective tool to know the society Statistical science not only is a tool to manage, reflect the having things but also the tool to predict, forecast situation, development trend of economic - social phenomena in future This is one of the important characteristics of the information of economy and society, it both ensures high reliability, great persuasion helping managers solve practical problems effectively 1.2 Characteristic of professional college students 1.3 The position, role and meaning of the statistics course in training professional college students Statistics have a position, an important role in training professional college students It not only provides, equip for students initial skills of collecting and processing of statistical data but also the knowledge base to help students learn speciality basic subjects better and really useful for them to finish professional tasks later On the other hand, any parts of college training curriculum have a function to go through the characteristics of each module, coordinate with the other modules, and other activities to educate the all - sided development for students So, the statistic module besides the purposes of equipping statistical knowledge has important task to develop intellectual capability for students 1.4 The requires of real life We are living in the age of "information explosion", we can say that statistical information is "surrounding" us from many directions and becoming "overflowing" in every citizen’s life To be able to receive and process a huge volume of information, every citizen needs to have choosing capabilities, judgment, analysis to draw useful conclusions for the needs of the job of himself as well as the business In 1991, Raja Roy Singh asserted: "To meet the new requirements set out for the explosion of knowledge and the creation of new knowledge, it needs to develop the capability of thinking, problem-solving capability and creativity The capabilities can be brief about the problem-solving capability" [99] Many businesses now require their employees to have quantitative reasoning skills, statistical reasoning skills to solve flexibly problems in life, in the process of labor and in the production and business This demand is gradually becoming a trend, a criteria to appreciate students’ competence when graduating, it has put forward important and heavy tasks for the education in the way of reforming methods of teaching and learning , to contribute the improvement of the quality of training, and tend to train learners’capabilities 1.5 Trends of renovation in teaching statistics In recent years, many math educators in the world have called for innovation in teaching statistics They say that teaching statistics should focus on understanding of statistics, statistical reasoning and statistical thinking, and it is considered as the purpose of entire education, and necessary innovation in teaching statistics 1.6 Identifying the topic of the thesis To develop statistical reasoning capabilities, many maths educators have found the ways to develop statistical reasoning, statistical thinking instead of teaching knowledge alone The purpose of modern mathematics education is to pay attention to the use more data and concepts, reducing theory, and techniques to foster active learning aiming for statistical reasoning The research of the Thesis relies on teaching and learning statistics in the College of Transport No II, Duy Tan University, Dong A University, Duc Tri College in Danang city, which not accelerate to be suitable for the situations as well as the actual requirements People know very little about professional college students how to learn statistics how concepts are misunderstood, what is taught and how evaluation has shown The students who are able to apply statistical reasoning to resolve situations related to future career are not noticed From the above reasons, we choose research topics: Developing statistical reasoning capabilities for professional college students Research objectives The purpose of the thesis is to find methods to develop statistical reasoning capability for professional college students, thereby contributing to improve the quality of teaching statistics and the quality of professional college workforce Research Tasks To achieve the purpose of research, thesis perform the following tasks: - Research on the theoretical basis of statistical reasoning, the characteristics and the basic elements of statistical reasoning - Research some kinds of statistics reasoning that professional college students often use to process data sets - Research on the theoretical basis of statistical reasoning capability of professional colleges students - Research assessment methods of statistical reasoning capability of professional college students in a reliable way - Research the approach in the teaching and some pedagogical methods to develope statistical reasoning capability for professional college students - Pedagogical experiments to evaluate feasibility and results of the pedagogical measures proposed Hypothesis If clarifying the scientific basis of statistical science and statistical reasoning capacity, we can propose pedagogical methods and use them suitably to develop statistical reasoning capacity for students in professional colleges Object and scope of research 5.1 Research objects - The process of teaching mathematics in the professional colleges - The task of developing intellectual capability for professional college students in teaching mathematics 5.2 Scope of research - Thesis focuses on researching the process of teaching statistics in professional colleges in economics and engineering - Thesis focuses on researching the task of developing statistical reasoning capability for college students in economics and engineering - Object of practical survey is in some professional colleges in Danang city Research Methodology 6.1 Research theory 6.2 Investigate, observe 6.3 Pedagogical Experiment The new features of the thesis and arguments given to support 7.1 New Features of the thesis In terms of theory - Clarifying the concept of statistical reasoning, the types of statistical reasoning that college students need to be taught - Proposing the elements of statistical reasoning of professional college students - Proposing the frame of evaluating statistical reasoning capability of professional college students - Building a number of measures to develop pedagogical statistical reasoning capability for professional college students On a practical level The results of research of the thesis will set up the basis to give out pedagogical measures developing statistical reasoning capability for professional college students Students are able to apply the types of statistical reasoning to serve the basic and specialized subjects, then resolving situations related to their careers after graduation as well as the ability to deal with the problems they encounter in their real life Thereby, fostering critical thinking, judgment ability, critical as they face the data 7.2 The arguments given to support - It is necessary to develop statistical reasoning capability for professional college students - The nature of the concept of statistical reasoning; characteristics of statistical reasoning; the types of statistical reasoning that professional students need to be equipped and developing; the elements of statistical reasoning capability and the frame of evaluating statistical reasoning capability for professional college students - A number of pedagogical measures to to develop statistical reasoning capability for professional college students Structure of thesis Besides the introduction, conclusion and references, the lay-out of thesis is chapters as following: Chapter Overview of Research Issues Chapter Statistical reasoning and statistical reasoning capability of professional college students Chapter A number of pedagogical measures to contribute to the development of statistical reasoning capability for professional college students Chapter Results pedagogical experiments Chapter OVERVIEW OF RESEARCH ISSUES 1.1 About statistical science 1.1.1Development history of statistics 1.1.2 Statistical activities 1.2 A brief history of research problems 1.2.1 History of research on statistics literacy 1.2.2 History of research on statistical reasoning 1.2.3 History of research on statistical thinking 1.3 Conclusion chapter Chapter STATISTICAL REASONING AND STATISTICS REASONING CAPABILITY OF PROFESSIONAL COLLEGE STUDENTS 2.1 The general concept of reasoning 2.2 The concept of statistical reasoning Combining with the research and analysis in Section 1.1.2, we think that: Statistical reasoning is reasoning based on statistical data to identify, explain, analyze and make conclusions with significance statistical as well as to find out statistical rule for the majority of the same type In our point of view, statistical reasoning is a multi-stage process, the connecting stages having mutual relationships can be illustrated by the diagram 2.1 Statistical situation thống Reading and understanding tables, charts Campare, analysis explain Build hypothesis Take out conclusion Solve problem Model of Statistical infomation Check 2.3 Characteristics of statistical reasoning Statistical reasoning always occurs in the context of the real world, depending on the context and is affected opposite by the context to statistical reasoning Statistical reasoning has general in nature, broad language and occurs daily in all areas of life activities It is really necessary in state administration, the working life of all citizens and businesses Based on rules of the majority, the results of statistical reasoning are exact However, these results are still meaningful in practical activities, if applied in certain conditions, they can be still acceptable to give out correct actions 2.4 The relationship between literacy, reasoning and statistical thinking The diagram 2.2 following shows the relation between statistical literacy, statistical reasoning and statistical thinking: Statistical thinking Statisticalreasoning Statistical literacy Statistical calculating skill Diagram 2.2 The relationship between literacy, reasoning and statistical thinking 2.5 Some mathematical reasoning involved in the process of statistical reasoning 2.5.1 Deductive reasoning 2.5.2 Inductive reasoning 2.5.3 Reasoning rational, reasonable reasoning 2.6 Comparison of statistical reasoning and mathematical reasoning In summary, there are many similar aspects of statistical reasoning and mathematical reasoning However, the requirements of each subject can create different sources of errors in reasoning Teaching both subjects can be led and facilitated by context In the practice of statistics, it depends on a lot of contexts of real-world but practice of maths tends to be away from the real world context The dependence on the context of statistical reasoning can lead to mistakes in reasoning Those mistakes are difficult to overcome even for the good and experienced experts 2.7 The model of developing statistical reasoning 2.7.1 The basis of modeling statistical reasoning development Building the model of developing statistical reasoning, we base on the following basis: The process of statistics activity - From cognitive development model of Biggs and Collis [55], [63] - From the basis of psychology and education 2.7.2 Model of developing statistical reasoning Collect data Describe data Conclusions Analysis data Statistical reasoning Data Organization Data Presentation Among them: 2.7.2.1 Collect and describe data There are two types of reasoning formation and developing through collection and description of statistical data We believe that reasoning from the data collection is statistical reasoning relating to the preparation of tools, manpower and time appropriate for each type of separate data collection activities As about reasoning from a representative sample is statistical reasoning that gives the way how to get the sample in accordance with the probability and what can affect a sample; how to select a representative sample or nonrepresentative for research objects, how to skepticize with the conclusions drawn from small samples or bias 2.7.2.2 Data Organization Data collected through the survey is often raw If we want to use the data, we must rearrange the data If students want to sort, categorize or summarize data, they must distinguish whether the data is qualitative or quantitative, discrete or continuous, so that it is possible to select the form of arrangement and suitable classification Moreover, students must understand the meaning of the statistics in the assessment of product quality, in controlling experiments This reasoning process appears in students’ data activities , it relates directly to the raw data collected We call this kind of reasoning reasoning from data Thus, the reasoning from the data is the statistical reasoning concerning identification of the type of data of qualitative, discrete or continuous, and the significance of the statistics gathered in estimating product quality or control 2.7.2.3 Data Presentation The process of presenting data includes the data display in the form of tables or graphs Showing data relating to the choice of representation for statistical data, this is tool to structure the data Statistical data presented in graphical form provide a visual image, facinating the viewers and showing clear trends of phenomena To this, students must know what type of data should be used with the most suitable type of chart When looking at the statistics graphs, students can understand and explain the statistical significance, can determine the characteristic parameters This process reasoning is called reasoning from statistical data representation So in our opinion, reasoning from the statistical representation of data is the statistical reasoning concerning the meaning of statistical graphs; choosing an appropriate type of graph to represent a kind of data, understanding the way how to read and interpret a statistical graph; inferring the random elements in a distribution to identify parameters with characteristic patterns The process of organizing and presenting data also form and develop aother kind of reasoning That is reasoning from characteristic parameters Reasoning from the characteristic parameters is a kind of statistical reasoning relating to understanding the specific parameters and their implications for data collection; understanding the use of the characteristic of large samples to predict more accurately than small samples; knowing the specific parameters of the data set – it will be useful to compare with other data sets 2.7.2.4 Analysis, interpretation of data and conclusions The process of analysis and interpretation of data is the most important and essential to form statistical reasoning for subjects This process includes the recognition of patterns, trends of data and reasoning to give out predictions and conclusions from statistical data In the process of analyzing and interpreting data, it forms the kind of reasoning when students test, evaluate and explain the relationship between two variables, know how to define and explain the relationships, explain a two-way table when considering bilateral relationship, grasp cause and effect relationship, reciprocal between two variables The reasoning process we call reasoning from combination of data We believe that reasoning from combination of data is the statistical reasoning concerning the examination, evaluation and explaining the relationship between two variables; defining and explaining the relationship, interpreting a two-way data table when considering the causal relationship between the two variables All the process statistics from collecting, describing the data to analysing, interpreting to conclusion, confirming the significance, students will realize that the conclusions are probabilistic and uncertainty From the sample, the representativeness of the sample, the sample size, sampling method to analyze the overall conclusions All this uncertainty will directly affect the analysis to propose hypotheses, leading to statistical conclusions This process directly impacts on students' reasoning We call this kind of reasoning forming in an environment of uncertainty reasoning from the uncertainty Reasoning from the uncertainty is the statistical reasoning concerning understanding and use of the ideas of chance, random, chance and uncertainty, giving out the assessment of the uncertain facts; knowing all possibilities aren’t equal, using suitable methods to consider the similarity of the various events 2.7.3 The significance of the cognitive development models statistical reasoning in teaching statistics 2.7.4 Some types of statistical reasoning that students need to be equipped through teaching Statistics 2.7.4.1 Prediction statistics a.The general concept of prediction in our opinion, predicting is a form of thinking to reflect the thing, the phenomenon in the future on the basis of the knowledge and experience b Prediction method We believe that there are many ways to predict, although whatever method is used, the prediction will follow a common method described by the following diagram 2.4: To form a hypothesis Induction of the individual case Quy nạp từ trường Proof hypothesis New Knowledge c Statistical prediction: In our research basing on professional students, they are learning maths statistics, as well as in a number of majors learning statistical principles, sociological statistics, so we consider statistical prediction is a form of thinking to reflect the thing, the phenomenon in the future based on the statistics data and past experience Example 2.9 A company plans to introduce a new product to consumers in a residential area with the population of 2.5 million people Researching the market shows that in 1500 per 3500 people are willing to buy that product a With 95% confidence, please predict the potential of the business b Predict how many potential customers that the business will hope to get in new markets are ? 2.7.4.2 Statistical deductive, statistical inductive We know that the "law of the probability distribution of the sample statistics reflects tight relationship between the parameters of the model with the corresponding parameters of the overall studied" [46] so those statistical reasonings include the participation of deductive reasoning and inductive reasoning We call these two types of statistical reasoning statistical deductive and statistical inductive Thus, statistical deductive is deducing about a part of the overall set of data based on the statistics of that overall In contrast, statistical inductive is deducing the whole based on the overall data set, statistical indicate of a part of that overall 2.7.4.3 Some types of statistical reasoning need to equip for professional college students Ten types of statistical reasoning described by the following diagram 2.6: Reasoning from the data collection Statistical deductive Reasoning from COLLECT DATA Reasoning from a representative sample combination Statistical inductive CONCLUSION of data DERCRIBE DATA ANALYSIS DATA Statistical prediction Reasoning from the uncertainty Reasoning from data ORGNIZATION DATA PRESENTATION DATA Reasoning from the characteristic parameters Reasoning from the resentation 2.7.5 Impact of statistical reasoning to professional college students 2.8 Statistical reasoning capability of professional students 2.8.1 The groups of statistical reasoning skills of professional students Psychologists believe that, skills are understood in different ways On the action side, the skills are to understand the way of acting a certain action and achieve results On the second aspect, the skills are to understood to apply the knowledge, skill and experience to proceed with certain actions Since then, we believe that the statistical reasoning skills are the ability to infer or perform an action resulting by selecting, applying statistical knowledge and past experience to identify, explain, apply and draw statistical conclusions from statistical data Based on the basis of psychology, education, and models developed statistical reasoning, we split the statistical reasoning skills into skill groups corresponding to each type of statistical reasoning needing to use in each stage of the development model of statistical reasoning as following: 2.8.1.1 Group of statistical reasoning skills from data collection and describing statistical data Skill 1: Understanding what data can be collected andsuitable data collection forms Skill 2: Identifying and making the decision which tools to use , manpower and time for data collection Skill 3: Knowing how to take a representative sample and the influence on the overall sample Skill 4: Reading raw data obtained through data collection 2.8.1.2 Group of statistical reasoning skills from organizational activities and presentation of statistical data Skill 5: Identifying data is qualitative or quantitative, discrete or continuous to choose forms sorted, categorized appropriately Skill 6: Recognizing and understanding the significance of the statistics figures Skill 7: Modeling of statistical data to look for relationships and trends of the phenomena studied Skill 8: Understanding and explaining appropriately the tables and statistical charts 2.8.1.3 Group of statistical reasoning skills from the analysis, interpretation and conclusion Skill 9: Using inductive reasoning, deductive reasoning to draw conclusions Skill 10: Using of electronic devices to analyze data to draw conclusions with high reliability Skill 11: Using basic statistical techniques to interpret or draw conclusions for the whole Skill 12: Evaluating and drawing the correct, logical conclusions, from models of statistical data Skill 13: Testing hypotheses based on controlling or statistical procedures Skill 14: Predicting statistics from the statistical data presented in the form of tables or statistics graphs 2.8.1.4 Group of skills to apply statistical reasoning in real life Skill 15: Checking the validity of the issues related to statistics on the media or in the practical activities Skill 16: Applying statistical reasoning and statistical knowledge to solve practical problems of life related to statistics data 2.8.2 Statistical reasoning capability Capability in general and capability of the students in particular are often expressed through the following features: - The existing and developing capability through activities - Capability revealed through skills in action - The different individuals will have different capabilities - Capability completely can foster to develop through education and training So we think: Statistical reasoning capability is the integration of statistical reasoning skills, impact naturally on the statistical content in the practical context related statistical data to solve the problems that that context set the scene 2.8.2.1 Model developing statistical reasoning capability 2.8.2.1.1 The basis to model 2.8.2.1.2 Model developing statistical reasoning capability 10 Skill 15 Skill 16 COLLECT DATA Skill Skill Skill Skill DERCRIBE DATA COMCLUSION ANALYSIS DATA ORGNIZATION DATA SkillS Skill 10 Skill 11 Skill 12 Skill 13 Skill 14 PRESENTATION DATA Skill Skill Skill Skill 2.8.2.2 Group of statistical reasoning capability from collection and data description a Capability 1: Capability reasoning from preparation for data collection B Capability 2: Capability reasoning from representative sample 2.8.2.3 Group of statistical reasoning capability from organization and presentation of data a Capability 3: Modelling the statistical information through formulas, tables and statistics in charts Example 2:18 Returning the example 2.11 with the question: Create a chart to confirm that this is a stable and effective investment channel ? What is mathematical basis of the technique ? b Capability 4: Reading statistical information from the mathematical models showing statistical information such as formulas, tables and statistical charts - The concept of reading statistical information - The capability of reading information from tables, charts 2.8.2.4 Group of statistical reasoning capability from the analysis, interpretation and conclusion a.Capability 5: Observing statistical information to draw statistical conclusions Example 2:20 Survey hydrology to report for the feasibility study of an investment project to build statistical tables we have average rainfall (mm) per month and year in the Danang area as following: Table 2.9 Distribution of rainfall in Danang Month Location Year 10 11 12 Bana 377 194 71 99 204 211 164 405 454 869 1378 759 5185 (1963-1966) Camle 57 17 17 33 97 110 54 92 362 622 417 154 2032 (1975-1988) 11 Danang 91 33 22 29 72 86 85 109 338 608 382 194 2049 (1931-1998) Tiensa 81 27 21 29 87 99 64 101 372 760 546 269 2456 (1975-1988) Question 1: Comment annual rainfall in the Da Nang area, with the increasing trend of rainfall? Question 2: If knowing the limit of total monthly rainfall is 100 mm, What month does the rainy season in the Danang area start? What month is the highest? Question 3: What is the distribution of rainfall over time in the Danang areas like? b Capability 6: Evaluate the limitations of the study, such as the reliability and efficiency of measurement, the relevance of experimental forms, sample size and sample characteristics Example 2.21 In one country, we conduct an opinion poll to find the level of support for the presidential candidates in the next election Four newspapers carry out independent exploration nationwide Four exploration results are announced as following: The first newspaper : 36.5% support (exploration is conducted on of March, with a random sample of 500 residents with the right to vote) The 2nd paper: 41% support (exploration is conducted on 23 of March, with a random sample of 500 residents having the right to vote) The 3rd paper: 39% support (exploration is conducted on 23 of March, with a random sample of 1,000 residents having the right to vote) The 4th newspaper : 44.5% support (exploration is conducted on 23 of March, 1000 readers called to vote) What newspaper has the best result of exploration to predict the level of support if the presidential election was held on 28 March? Please explain for your answer c Capacity 7: Intuition statistics d Capacity 8: Find predict, detect problems e Capability 9: Analysis of prediction g Capacity 10: Experimental statistics to predict Example 2:22 Before the car tire produced by DRC company took 42% market share At present, with the fierce competition of product market, the board of directors fear that the company's market share is hard to be kept on With the 0.01 significance level, you make conclusions about the fear of the board 2.8.2.5 Group of capacity use statistical reasoning in real life a Capacity 11: Estimating and checking answers for real life problems related statistically to determine reasonability and identify a lot of capabilities, from that choosing the most reasonable optimal option Example 2.23 Anh’s mother wants to buy a motorcycle 20 million VND, but hesitates between two options: - Gradual payment plan: prepaying 30% the remaining paid through a finance company within months, the monthly repayment amount is 2,044 million 12 - The second option: Borrowing from the banks with consumer interest of 4% per month to buy a motorcycle right You advice to help her choose the best option b Capacity 12: Analyzing, explaining and completing the professional task as well as society concerned about the statistics Example 2.24 In the “secret doorway game” on television, Dung team won in round and have the opportunity to open “the secret door” to receive the award There are three doorways, knowing that behind one of prizes doorway has a high quality fridge, and the two boxes left have small gifts Question 1: How many percents does Dung team have the opportunity to get the fridge? Question 2: Dung team chose the doorway No The program conductor open the third doorway and that's not the refrigerator How many percents does Dung team have the chance to get the fridge 2.9 Assessment of statistical reasoning capability of professional college students Table 2:10 Frame of statistical reasoning capability of students Process Level Describing the level of statistical reasoning capability The inability of the analysis to clarify the information relating Level data or incorrect comparison between the data or the irrelevant data Level Restrictions on the ability to analyze to clarify statistical information, correct comparison between the data Knowing analysis to clarify the statistical information, Level including the correlation and causal relationships inside and between data sets together Analysis Perfect analysis in clarifying the statistical information, Level including the correlation and causal relationships within and outside the scope of the data set Analyzing like experts to clarify the statistical information, including the correlation and causal relations and integration Level into meaningful structures Using excellent reasoning, prediction from context much useful information outside the scope of the data set Interpretation Level Inability to explain, to clarify issues related to statistical data or incorrect interpretation Level Restrictions on the ability to explain, to clarify issues related to statistical data or incomplete explanations Knowing to explain, to clarify issues within the statistic data Level set including statistical significance and statistic descriptive (average, median, mode) Explaining perfectly the issues related to statistical data, Level including statistical significance and statistic description 13 (average, median, mode) Appropriate interpretation of a number of issues outside the scope of the data set Explaining skillfully issues related to statistical information, including statistical significance and statistic description Level (average, median, mode) Explaining excellently the issues from contexts related inside and outside the scope of the data set Level Inability to apply and make decisions with an understanding of the different scenarios or improper use Restrictions on the ability to manipulate and difficulty in Level making decisions with an understanding of the different scenarios or use incomplete Knowing application and deciding with an understanding Level different scenarios related directly to the statistic data Application collection Proficient in use and make rational decisions outside the Level scope of the data set Use in quality, completely and validity the statistical reasoning Skill in the application and make a logical decision from the Level contexts outside the scope of the data set Applying perfectly statistical reasoning to solve the problems from the context 2.10 Assessment of the status of the teaching of development statistical reasoning capability in professional colleges and business needs 2.10.1 The purpose of the survey 2.10.2 Object survey 2.10.3 Content survey 2.10.4 Survey methods 2.10.5 Analysis of survey results 2.10.5.1 About textbooks 2.10.5.2 Lecturers’ perceptions of developing statistical reasoning capability 2.10.5.3 About the students 2.10.5.4 Assessment social needs of statistical reasoning capability 2.11 Applying some theories of teaching in teaching statistics 2.11.1 Tectonic theory 2.11.1.1 Concept of tectonic 2.11.1.2 View of tectonic theory in teaching 2.11.1.3 Model of teaching and learning in view of tectonic theory 2.11.1.4 Applying tectonic theory in teaching statistics 2.11.2 Theory of operation 2.11.3 Theory of situations 2.12 A number of approaches in teaching statistics in professional colleges 14 Approach 1: The data taught in colleges should be based on the actual data in accordance with practical production activities, the ages of students and the majors Approach 2: Establishing methods for collecting and processing data for students through teaching statistics Approach 3: Teaching statistics should focus on improving the capability of reading tables, charts Approach 4: Focusing on understanding statistics and developing statistical reasoning capability for students through teaching statistics Approach 5: Enhancing the exploitation of practical applications in teaching statistics in professional colleges 2.13 Conclusion for chapter Chapter of the thesis has achieved some results as follows: - Contributing to clarify the connotation of definition of statistical reasoning - Proposing 10 types of statistical reasoning integrated in models developing statistical reasoning that students often use in analysis and processing of statistical data - We propose definition of statistical reasoning skills is that human’s reasoning ability or perform an activity having results by selecting, applying statistical knowledge and past experience to identify, explain, apply and draw meaningful conclusions from statistical data; Based on the model of developing statistical reasoning, we propose four groups of statistical reasoning skill integrated in models of developing statistical reasoning - On the basis of considering statistical reasoning capability, that is an individual ability to master the statistical reasoning skill, we propose a definition: Statistical reasoning capability From the above concepts, the model of developing statistical reasoning, from the distributing group of statistical reasoning skills, we divide the elements of statistical reasoning capability of students into groups of statistical reasoning capability - We propose a framework of assessing the statistical reasoning capability of professional college students - To assess the status of teaching statistical development statistical reasoning capability in professional colleges, we have conducted a survey From the results we obtained, we have processed the data and analyzed, assessed the initial qualitative, quantitative - From practical teaching, from demands innovation of teaching in recent years, from teaching statistical trends in the world, we suggest five approaches in teaching statistics at the high and professional schools should focus on statistical literacy, statistical reasoning and statistical thinking Chapter SOME PEDAGOGY MEASURES TO DEVELOP STATISTICAL REASONING CAPABILITY FOR PROFESSIONAL COLLEGE STUDENTS 3.1 A number of orientation of building and performing pedagogical measures to develop statistical reasoning capability 15 3.1.1 Orientation 1: System pedagogical measures are built on the basis of ensuring the program of teaching statistics for professional college students and follow the principles of teaching 3.1.2 Orientation 2: System pedagogical measures must have a positive impact to the mission of developing statistical reasoning capability for professional college students 3.1.3 Orientation 3: System pedagogical measures must be feasible, can be applied to the process of teaching in general and teaching process in particular statistic 3.1.4 Orientation 4: The system pedagogical measures designed on approaches of statistical learning and teaching to contribute innovation of teaching statistical methods in professional colleges 3.1.5 Orientation 5: The pedagogical measures must be directed to the students in studying in the statistical activities to gradually create and dominate statistical knowledge, contribute to the formation of new human in creative work and achieve high effect in real life 3.2 A number of pedagogical measures contribute to the development of statistical reasoning capability for professional college students 3.2.1 Measure 1: Organizing for students to practise statistical reasoning capability from activities of collecting and describing data 3.2.1.1 The purpose of the measure This measure affects to groups of skill and statistical reasoning capability from activities of collection and data description 3.2.1.2 Basis and role of measures 3.2.1.3 Content and guiding to perform First, students need to understand that to collect data for research purposes, they must master the following procedures: - Defining which data need to be collected, the order of their priority If this is not specified, the collected data is less significant in the analysis and drawing statistical conclusions - Methods of collecting primary data: + Collect directly as observed; live interview + Collect indirectly as exchanging via telephones, emails, via vouchers and books available - Develop a plan for statistical surveys: Describe the purpose of the investigation; objects and investigation units; the content, time, the period of investigation, the investigation tables To practise statistical reasoning capability from collecting activities and describing data, teachers must practise students with the following reasonings: - Depending on the purpose and the content of the study to reason the form of data collection, selection of equipment, manpower and proper time to investigate - Practising students to identify representative sample, the sample size, the way to solve, the way of presentation and calculation of the characteristic patterns to draw conclusions 16 overall are completely reliable But they also have to understand that there is sampling error, how to limit bias, the sample size selection will affect the reasoning results Example 3.1 Topic: "Investigation of the level of satisfaction of students in the canteen of the dormitory" 3.2.2 Measure 2: Modeling of data in the form of tables, charts statistics to draw conclusions and finding development trend of the phenomenon of study 3.2.2.1 The purpose of the measure This measure impact positively on group of skills and statistical reasoning capability from organizing activities and presenting statistical data 3.2.2.2 Basis and role of measures 3.2.2.3 Content and guiding a Some charts used to show statistics data b Modeling the statistics data in the form of tables and statistical charts Modeling statistical data focus on establing and pesenting data, model and find relationships The form of data representation through graphics, attract students to participate enthusiastically in statistical reasoning in decision making, reasoning and prediction The process of modeling the statistical data to highlight trends, statistical laws of phenomena studied To model data, they must know what data is to use what type of graph is most reasonable In addition, students must know how to use technology to draw graphs of statistics c The way of performing - Training students to make reasoned and logical conclusions from tables and statistical charts - Training for students to find relationships and discover trends of the phenomenon through tables of statistical data - Training for students to find relationships and discover trends of the phenomenon through statistical graphs - Training for students to make decisions of performing from modeling statistical data Example 3.2 Phone subscribers in 2009 as following: Table 3.2 phone subscribers in 2009 Month 10 11 12 Milion of 82,52 86,6 89,19 89,5 92,92 101,7 107,84 110,3 113,5 106,4 107,5 130,4 subscribers Source:http://mic.gov.vn/vn/newsdetail/solieuthongke_vienthong/4901/index.mic Question 1: Select the appropriate form of diagrams to represent data in the abpve table? Explain your choice Question 2: Telcos wants to emphasize that the amount of subscribers in 2009 increased rapidly each month You help them provide a solution Draw the chart aiming at achieving that purpose? What is this mathematical basis of the technique? 3.2.3 Measure 3: Developing reading capability of tables and statistical charts as a precondition for statistical reasoning 3.2.3.1 The purpose of the measure 17 This measure impact positively on groups of skills and statistical reasoning capability from organizing activities and presentation of statistical data 3.2.3.2 Basis and role of measures 3.2.3.3 Content and guiding a Reading information from statistical tables b Reading information from statistical charts Example 3.4 We return to example 2.7 on page 61, with the following two new questions: Question 1: How much is the total number of students in Vietnam in year the 2008-2009? How many percents does the number of High School students take? Question 2: How many high school students are there in the 2008-2009? Present the calculation 3.2.4 Measure 4: Increasing to practise and enhance statistical capability for students to have a solid foundation for statistical reasoning 3.2.4.1 The purpose of the measure Pedagogical measure will develop groups of skills and statistical reasoning capability from the analysis, interpretation and conclusion 3.2.4.2 Basis and role of measures 3.2.4.3 Content and guiding To obtain that, it is to practise the students with the following activities: - Mastering the art of every kind of statistical problem Train students to master the techniques of statistical calculations, statistical formulas, procedures and some statistical algorithms of statistical problems For example, the process of solving a problem of statistical hypothesis testing when know before  level of significance including the following steps: - Step Develop statistical hypothesis pair H0, the set H1 - Step Make a random sample of size n: (X1, X2, , Xn) - Step Choose standards of checking - Step Find the rejection region W - Step Find the value of observation, comparing with W to make conclusions - Step Evaluation of mistakes Example 3.5: Packaging weight of sacks of rice in stock are normally distributed random variable with an average weight of 50 kg Suspect rice is balanced incorrectly, storekeeper balances random 25 sacks and have results: Table 3.4 Packaged weight of sacks of rice Weight of rice Nember 48,0 – 48,5 48,5 – 49,0 49,0 – 49,5 10 49,5 – 50,0 50,0 – 50,5 18 Sum 25 With  = 0.01 significance level, make conclusions about the suspect - To establish formulas to calculate the statistics through problem situations - Develop systems themed exercises to practice the ability to memorize formulas, statistical calculation process for students 3.2.5 Measure 5: Fostering for students the capability of detecting statistical rules 3.2.5.1 The purpose of the measure Pedagogical measures that we propose not only help develop capability of detecting statistical rules hidden in data, but also contribute to the development groups of skills, statistical reasoning capability from analysis, expression and making conclusion and group of ability of applying statistical reasoning in real life 3.2.5.2 Basis and role of measures 3.2.5.3 Content and way of performing Thus, to build the capacity of detecting statistical rules for professional students, teachers have to design, create problematic situations related to statistics data in which students can be positive, active in detecting statistical rules The problematic situations related statistics data can create in the following ways: - A problem related to the statistical data in practice need to be solved For example, sewing uniforms for students, why don’t people take the measurements of each student? In equiping military necessities for the army, why they don’t take measurements of each soldier? - Observe a sufficiently large number of observational results to detect statistical rules - Generalizing from the observed phenomena related to statistics data The process of detecting statistical rules requires skills and statistical reasoning capability of students If we want to foster the capability of detecting statistical rules, we have to: - Train students thinking ways such as specializing, generalizing, integratedly analyzing to draw the signs of nature, the overall trend of the research from results obtained by analyzing a sufficiently large sample - Visualizing activities to discover the laws of statistics - Control students to choose intellectual activities, math activities by the way of statistics induction , modeling statistical data to draw general features, the laws of the phenomena studied - Through practical survey to detect statistical rules - Train students to model statistical data to highlight trends, laws of statistics - Consider the causal relationships to detect statistical rules Example 3.7 A footwear company intends to produce 10.000 pairs of shoes for male students in the new school year 2012 As head of planning department, Help our company determine how many shoes for each size we have to produce so that the power consumption is highest Knowing the need to buy shoes of everyone is the same 3.2.6 Measure 6: Design methods of statistical prediction through teaching statistics 19 3.2.6.1 The purpose of the measure The measure will develop group of skills and statistical reasoning capability from the analysis, interpretation and making conclusions and group of ability of applying statistical reasoning in real life 3.2.6.2 Basis and role of measures 3.2.6.3 Content and guiding In the process of teaching statistics to train students statistical prediction, the teacher must keep in mind: - Selection of predicting activities compatible with statistical content that should be conveyed in the program - Predicting must be feasible and consistent with the level and awareness of students - Predicting activity must enhance the activeness, creative exploration and help students step by step create and dominate knowledge To foster predicting statistics capability for professional students through teaching statistics, the teacher should organize to train students statistical predicting methods as following: a Statistical predicting method through observing statistics information b Statistical predicting method through proposing statistical hypothesis, prediction Example 3.9: The teacher gives the class a situation to study: "The rate of Nokia product customers was 60% before After improving product quality, marketing research department has made a advertising campaign for that product and surveyed 400 random customers and finding that there were 250 people using that new product With 95% confidence, according to you, Is advertising campaign really effective? " c.Statistical predicting method through generalizing activities, spealizing, similaritifying visualizing activities Example 3.10 To train students in road and bridge major to have the ability to collect, process statistical data and predict the future, we can design a situation having pedagogical intention as folloing: To determine the level of the land roads to build in the future, it must be based on several factors, including factors of vehicle traffic flow in the future How to predict traffic flow of vehicles in the future? d Statistical predicting method through the path through experiment, reconstruction 3.2.7 Measures 7: Enhancing the exploitation of statistical problems with practical contents related to statistical reasoning suitable with the major to train students 3.2.7.1 The purpose of the measure Measure would impact positively on group of capability appying statistical reasoning to real life 3.2.7.2 Basis and role of measures 3.2.7.3 Content and guiding To exploit the statistical problems with practical contents related to statistical reasoning suitable with the training major of students, teachers should pay attention to: 20 - Exploiting the statistical situations in practice to help students create concepts, new statistical formulas - Exploiting the statistics data in practice, consistent with each major of students to bring joy, excitement and encourage students to participate excitingly in learning statistics - Trying to exploit the practical problems relating to statistics to make examples, train students to develop statistical reasoning capability 3.2.8 Measure 8: Constructing learning environment to bring up and develop statistical reasoning capability 3.2.8.1 The purpose of the measure This pedagogical measure impacts positively to the entire groups of skills and groups of statistical reasoning capability 3.2.8.2 Basis and role of measures 3.2.8.3 Content and way of performing We think that, to build learning environments to develop statistical reasoning capability for students, we have to carry out a number of following tasks: a Focusing on developing a number of important statistical concepts b Enhancing to exploit data from real life appropriate for each age and each major of students c Enhancing to exploit technology supporting teaching to develop statistical reasoning capability d Enhancing to organize learning activities to develop statistical reasoning capability for students e Building systems of exercises being suitable with the development of statistical reasoning capability g Use alternative methods of assessment Example 3.14 Project "Evaluation of traffic accidents in the first three months of 2013" 3.3 Conclusion chapter 3: On the basis of statistical approach of teaching and orientations, we buil pedagogical measures to impact on each group of capability to contribute development of statistical reasoning capability for professional students Especially, we propose statistical predicting methods needing development for professional students Chapter EXPERIMENTAL RESULTS 4.1 Purpose, requirement of pedagogical experiment: Evaluation of the effectiveness and feasibility of pedagogical measures to develop statistical reasoning capability for economics and engineering students, in teaching statistics at professional colleges 4.2 Experimental pedagogical content 4.2.1 A number of basis to choose experimental pedagogical content 4.2.2 Pedagogical pedagogical experimental content 4.3 Organization of pedagogical experiment Pedagogical experiment has been conducted in two phases The first phase was conducted in the period from march 2012 to the mid of May 2012, on the 11th college 21 class (students entered the school in september 2011), at the College of Transport II in Danang CD11K3 was the class of experiment taught by lecturer Hoang Nam Hai CD11K2 was the class of control, taught by lecturer Tran Thi Huong The second phase of experiments was conducted in the period of mid May 2012 to the end of 06 June 2012, on the banking courses from Duy Tan University in Danang Experimental class is K17QCD5.6 taught by lecturer Hoang Nam Hai Control class is K17 QCD1,2 4.4 Process of pedagogical experimental data From the data collected through the survey process and organization of pedagogical experiments, we use statistical methods to process statistical data 4.5 Empirical Evaluation 4.5.1 Contents of the tests 4.5.2 Preliminary analysis of the tests 4.5.3 Analysis of experimental results 4.5.3.1 Qualitative Analysis a Qualitative analysis through questionnaires From summary we see, clearly over 80% students are satisfied with the data that we put into teaching taken from real data, in accordance with physiology training majors of students Over 90% students are satisfied with learning environment of statistics developing reasoning capability, predict that we designed with the pedagogical measure In the environment in which the students study in mutual interaction, with the support of technology There are 70% students agreeing with traditional teaching methods not very exciting, but 80% of the students are exciting to new pedagogical measure our Thus, it can be said, Applying and coordinating and pedagogical measures in statistics teaching have brought the joy and excitement of learning statistics for students, made the passive learning process into active learning one, they themselves construct their own statistics knowledge b Qualitative analysis through tests Observation of control classes in both waves we see clearly the surprise of students when they received the test from teachers Although the problem was not difficult to their levels, but it seems a bit strange, it required them to apply the knowledge of statistics, statistical reasoning capability to solve problems, draw judgments, conclusions from different contexts of life For the experimental class, because of training and regular exercise of statistical reasoning capability in the learning process, so they did not surprise with the test They were a bit confident when facing with problems taken from real life Through these pedagogy measures integrated in teaching statistics, teacher gradually train, develop statistical reasoning capability for students Problem-solving capabilities, ability to draw conclusions from statistical data helped them more confident when facing the problems appearing in the context of life That is a powerful demonstration of the scientific hypothesis, the pedagogy measures proposed 4.5.3.2 Quantitative analysis From treated results, we think that: the average score; satisfactory rate; percentage of pretty and good points of the experimental class higher than the control class The results of the second round test of experimental class 5.6 and class K17QCD5,6 and control K17 QCD1,2 From processing the results, we find that: 22 the average score; satisfactory rate, average rate, percentage of pretty and good points of the experimental class higher than the control class Two experimental results make a question for us: Does pedagogical measure that we have designed to teach the experimental class better statistical teaching methods in class control ? Or just so random? Conducting to check the given hypothesis, we build statistical hypothesis pairs as following: Suppose H0: "The results of the test from experimental class are not higher than the examination results for control class,” For setting H1: "The examniation results from experimental class is higher than the examination results for the control class." Get 5% significance level We have: Table 4.8 General Results Experiment Parameters Phase Phase Experiment Control Experiment Control Total number of students 54 53 75 76 Average scores 6,2 4,77 5,96 5,01 The standard deviation 1,82 2,08 1,96 3,7 uob 3,78 1,98 The meaning 0,05 0,05 Critical value 1,96 1,96 Compare 3,78 > 1,96 1,98 > 1,96 Conclusion Reject H0 , H1 admits Reject H0 , H1 admits The results of verification demonstrate proposed pedagogical measures applied on the experimental class give results higher than the control class 4.6 Conclusion for Chapter Purpose of experiments has been achieved, the proposed pedagogical measures really give high effects and can be applied in the teaching process to develop the capability of statistical reasoning for students in professional colleges CONCLUSION OF THE THESIS In terms of theory Consensus with researchers in the world of education, teaching statistics should innovate towards reducing calculating, focus on developing capability of statistics literacy, statistical reasoning and statistical thinking From the objective developing statistical reasoning capability for professional college students, the thesis has contributed to clarify: Explicit definition for statistical reasoning; propose 10 types of statistical reasoning that professional college students often use in the process they engage in the process of a statistical activity We have proposed definition of statistical reasoning capability We consider statistical reasoning capability proficiency level of statistical reasoning skills From that, we propose four groups of statistical reasoning skills, groups of statistical reasoning capability and methods to predict statistics which professional students often use 23 We research the way how to design lessons, the way of organizing learning activities to develop statistical reasoning capability for professional students We haved proposed pedagogical measures to practice, foster development of statistical reasoning capability for professional college students Through pedagogical experiment, proposed pedagogical measures are highly effective in fostering and developing the capability of statistical reasoning for professional college students On a practical level We have clearly contributed to the colorful picture in the teaching and learning of statistics in colleges and universities today We contribute to the movement reforming the contents of the currriculum, editing the lessons and the methods of statistical teaching in professional colleges Some proposed pedagogical measures in the thesis has been tested the effectiveness, and feasibility through pedagogical experiments, can apply to renew the teaching and learning of statistics in the current context Teaching methods focusing on developing statistical reasoning capability which we study contribute much to students’ learning activities Development of statistical reasoning capability for professional college students through teaching statistics to help students not ony practise students basic statistics skills and develop problem-solving ability in life and in professional careers but also contribute to improve the quality of college education workforce for the country 24 ... determine reasonability and identify a lot of capabilities, from that choosing the most reasonable optimal option Example 2.23 Anh? ??s mother wants to buy a motorcycle 20 million VND, but hesitates... Vietnam in year the 2008-2009? How many percents does the number of High School students take? Question 2: How many high school students are there in the 2008-2009? Present the calculation 3.2.4... activity - From cognitive development model of Biggs and Collis [55], [63] - From the basis of psychology and education 2.7.2 Model of developing statistical reasoning Collect data Describe data