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 quali
Trang 1INTRODUCTION
1 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 ,
Trang 2to 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 do 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
2 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
3 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
4 Hypothesis
Trang 3If 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
5 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
- 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
Trang 4Chapter 1 Overview of Research Issues
Chapter 2 Statistical reasoning and statistical reasoning capability of professional college students
Chapter 3 A number of pedagogical measures to contribute to the development of statistical reasoning capability for professional college students
Chapter 4 Results pedagogical experiments
Chapter 1 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 1
Chapter 2 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
explain Model of
Statistical infomation
Trang 52.3 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:
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
Statistical calculating skill
Statisticalreasoning
S tatistical thinking
Statistical literacy
Trang 6Among 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 do 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
Analysis data Statistical reasoning
Describe data
Data Presentation
Data Organization
Conclusions
Collect data
Trang 7called 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
Trang 8in 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:
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:
1 Induction of the individual case Quy nạp từ những trường
2 To form a hypothesis
3 Proof hypothesis
4 New Knowledge
Trang 92.7.5 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
CONCLUSION
Reasoning from the uncertainty
ANALYSIS DATA
COLLECT DATA
DERCRIBE DATA
PRESENTATION DATA
ORGNIZATION DATA
Reasoning from a representative sample
Reasoning from data
Reasoning from the resentation
Reasoning from the characteristic parameters
Reasoning from
combination
of data
Reasoning from the data
collection
Statistical deductive
Statistical prediction
Statistical
inductive
Trang 10Skill 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
Trang 112.8.2.2 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
Bana
(1963-1966) 377 194 71 99 204 211 164 405 454 869 1378 759 5185 Camle
(1975-1988) 57 17 17 33 97 110 54 92 362 622 417 154 2032
COMCLUSION ANALYSIS
DATA
COLLECT DATA
DERCRIBE DATA
PRESENTATION DATA
ORGNIZATION
DATA
Skill 1 Skill 2 Skill 3 Skill 4
Skill 5 Skill 6 Skill 7 Skill 8
Skill 15 Skill 16
SkillS 9 Skill 10 Skill 11 Skill 12 Skill 13 Skill 14
Trang 12Danang
(1931-1998) 91 33 22 29 72 86 85 109 338 608 382 194 2049 Tiensa
(1975-1988) 81 27 21 29 87 99 64 101 372 760 546 269 2456 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 7 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 9 months, the monthly repayment amount is 2,044 million