2B.tóm Tắt La (T. Anh)_Minh_Ncs.pdf

MINISTRY OF EDUCATION AND TRAINING VINH UNIVERSITY HOANG LE MINH BUILDING A LEARNING ENVIRONMENT OF STATISTICS CONTENT IN HIGH SCHOOL IN THE DIRECTION OF TRAINING STATISTICS REASONING SKILLS FOR STUDE[.]

MINISTRY OF EDUCATION AND TRAINING

VINH UNIVERSITY -

HOANG LE MINH

BUILDING A LEARNING ENVIRONMENT OF STATISTICS CONTENT IN HIGH SCHOOL IN THE DIRECTION OF TRAINING STATISTICS REASONING SKILLS FOR STUDENTS

Major: Mathematics Theory and Teaching Method

Thesis Code: 9140111

PhD THESIS SUMMARY

NGHE AN, 2023

The present study has been completed at Vinh University

Science instructors:

1 Assoc Prof Dr Nguyen Chien Thang

2 Prof Dr Nguyen Van Quang

Reviewer 1:

Reviewer 2:

Reviewer 3:

The thesis will be defended in the institutional review Board

meeting at Vinh University, at ….h… on ………., 2023

The thesis can be found at:

1 The National Library of Vietnam

2 Centre for Information - Library Nguyen Thuc Hao, Vinh University

PREFACE

I THE RATIONALE OF THE RESEARCH

The importance of statistics and statistical reasoning skills for each individual has been confirmed by Vietnamese math educators through the content

of the 2018 Math curriculum with the following requirements that students need

to achieve when completing the high school program is “Improve the ability to collect, classify, represent, analyze and process statistical data; using statistical data analysis tools through central trend measurement and dispersion measures for ungrouped and clustered data samples; using statistical rules in practice; recognize random patterns, basic concepts of probability and the significance of probability in practice” (Ministry of Education and Training, 2018)

In the process of implementing the new general education program, those who are working in the education sector will need many scientists to research and exchange together to be able to contribute to the successful implementation of the task of educational innovation without the need of many scientists social responsibility In this work, we focus on studying the knowledge of statistical reasoning skills on high school students, the manifestations and levels of statistical reasoning skills, statistical reasoning ability, and statistical reasoning skills statistics that students need to be formed and developed to meet their future job needs as well as be ready to deal with situations that appear in real life related

to statistics We also research to design and propose a learning environment for statistical content formed from pedagogical measures to contribute to training students' statistical reasoning skills

For that reason, we have chosen the topic “Building a learning

environment of statistics content in high school in the direction of training statistics reasoning skills for students”

II RESEARCH PURPOSES

To research to build a learning environment of statistics content in order to train students in statistical reasoning skills through the teaching process at high schools

To research on the viewpoints, principles, positions and roles of statistics content and the requirements to be achieved by students in building a high school Mathematics program From there, building a learning environment for statistical content in order to train students in statistical reasoning skills through the teaching process at high schools

3 NEW CONTRIBUTIONS OF THE THESIS

3.1 From theoretical perspective

- Systematizing theoretical issues related to statistical education in high schools, especially in statistical understanding, inference and thinking

- Proposing a concept of statistical reasoning skills of high school students and the manifestations of this skill

- Proposing a concept of a teaching environment that trains statistical reasoning skills and the core components of this environment

- Proposing Rubric on the levels of the students' statistical reasoning skills

- Proposing pedagogical measures to create a statistical learning environment in the direction of training statistical reasoning skills for students

3.2 From practical perspective

- Support teachers in organizing teaching of statistical content in high schools with the expectation of improving teaching effectiveness

- The application of pedagogical measures proposed in the thesis to teaching practice will contribute to innovating teaching methods and achieving the goal of teaching statistics in high schools

Chapter 3 Pedagogical experiments

Chapter 1 THE THEORETICAL AND PRACTICAL BASIS OF TRAINING STATISTICAL REASONING SKILLS FOR HIGH SCHOOL

STUDENTS 1.1 Overview of research works on teaching statistics

1.2 Epistemological features of statistics

1.2.1 A brief history of statistics

1.2.2 The Relationship Between Statistics and Probability

1.2.2.1 Probability

1.2.2.2 Statistics

1.2.2.3 The relationship between statistics and probability

It can be said that probability theory forms the theoretical basis for statistics If we separate Probability Theory from Statistics, Statistics will lose many important results brought by the Deductive Statistics section: then, people only stop at the experimental level, not generalizing to the total body That way, Statistics will no longer hold its great value, especially for practical matters People will not be able to use Statistics as an effective and sharp tool for analysis, prediction, in order to make correct and necessary judgments

However, the relationship between probability theory and statistics is not only that probability theory is necessary for statistics There is actually a link in the opposite direction: Statistics, specifically Descriptive Statistics, are also necessary for the study of Probability Theory For example, one of the approaches

to the concept of probability of an event is the concept of frequency - the concept

of descriptive statistics

1.2.3 Sampling method

1.2.4 Characteristic numbers

1.2.4.1 Central trend-measurement characteristic numbers

1.2.4.2 Characteristic numbers measuring the degree of dispersion

1.3 Statistics in Vietnamese Mathematics Education program

1.3.1 Statistical content in the Education program

1.3.2 Expression of mathematical ability of high school students through statistical content

1.4 Statistical reasoning skills

1.4.1 Reasoning

1.4.2 Statistical reasoning

There are divergent views among Mathematics educators about statistical reasoning According to the studies of Chervaney, Collier, Fienberg, Johnson, Neter, Benson and Iyer, they defined statistical reasoning as what students can

do with statistical content, that is: recall, recognize, analyze and differentiate between statistical concepts and experience using statistical concepts to solve real-world problems Lovett has provided a rather detailed overview of Statistical Inference, considering Statistical Reasoning as belonging to one of the following

three approaches: theoretical research, experimental research and classroom

study (from Hoang Nam Hai, 2013) Dani Ben – Zavi, Joan Garfield and Gal all

agreed: Statistical inference is how people reason with statistical ideas and make statistical information meaningful

Statistical reasoning also means understanding and interpreting statistical procedures, being able to fully interpret statistical results (Nicolxki X M, 2002) According to Hoang Nam Hai (2013): Statistical reasoning is a type of inference based on statistical data to identify, interpret, analyze and draw statistically significant conclusions, discover statistical laws of a crowd of the same type

1.4.3 The relationship between statistical reasoning and statistical understanding and statistical thinking

1.4.3.1 Statistical understanding

Statistical understanding is the ability to understand statistical information,

grasp and use the language, tools, and basic concepts of statistics:

- Statistical understanding includes the basic skills which are used to understand statistical information or research results, such as organizing data, constructing and representing tables, and working with other representations of data

- Statistical understanding includes understanding concepts, terms, and symbols, and understanding how to use probability as a measure of uncertainty

1.4.3.2 Statistical reasoning

Statistical reasoning is a way of reasoning with statistical ideas and making

statistical information become meaningful This involves making interpretations based on data sets, representations of data, or statistical summaries of data

1.4.3.3 Statistical thinking

Statistical thinking is the process of reflecting in general the characteristics

of statistical data to draw conclusions and rules on a crowd of statistical phenomena, serving the activities of people's lives through using the knowledge

of statistical probability theory

1.4.3.4 The relationship between statistical understanding, statistical reasoning, and statistical thinking

Figure 1.3 The point of view has the independence and interference between

the three regions

(delMas R C., 2002)

Figure 1.4 Knowledge is the foundation for developing statistical reasoning

and thinking (delMas R C., 2002)

We believe that statistical understanding is the premise and foundation for students to develop their statistical reasoning and statistical thinking abilities Statistical thinking and statistical reasoning are interrelated and they can be used

UNDERSTANDING

THINKING REASONING

UNDERSTANDING

THINKING REASONING

interchangeably to represent cognitive activities of the same kind Reasoning is generally considered a type of thinking

Statistical thinking and statistical inference are interrelated and they can be used interchangeably to represent cognitive activities of the same kind Inference

is generally considered a type of thinking

While statistical literacy can be viewed as understanding and interpreting the statistical information presented, statistical inference can be viewed as the ability to solve specific problems through tools and concepts concepts learned, and statistical thinking is the ability to go beyond what students are taught in the course, which is the ability to ask questions, investigate problems, and related data in a particular context

In order to achieve the goal of the teaching process, it is necessary to have many influencing factors and flexible pedagogical measures to suit each content, context and target audience But first, teachers need to understand the levels of the students' cognitive processes, the specific expressions that can be achieved

by the learners, so that they can apply flexible pedagogical methods , suitable to influence that cognitive process to achieve teaching goals If we want to evaluate students on cognitive ability and mathematical thinking, but only ask students to identify, describe, or rephrase, then that is only the level of cognitive ability

1.4.4 Comparing statistical reasoning and mathematical reasoning

First, we consider the similarity of these two types of inference Statistical reasoning and mathematical reasoning are both separate instances of human reasoning Therefore, they are procedural and follow the rules of inference Any inference generally has a logical structure A=>B, where A is the premise, B is the conclusion (Nguyen Duc Dong, Nguyen Van Vinh, 2001) Rossman, Chance, and Medina (2006) describe statistics as a science using mathematics Therefore, when students make statistical reasoning and mathematical reasoning, both use mathematical knowledge

Second, we look at the difference between statistical inference and mathematical reasoning According to Polya (1995), there are two types of inferences: demonstrative reasoning and rational inference Proving inference is

a particularity of mathematical reasoning based on general logic rules, which determine that if the premises are true, then the conclusion is also true Meanwhile, statistical inference based on the collected data sample, makes a conjectural conclusion about all the individuals in a population; Generalizing from the characteristics of a relatively small sample to infer the characteristics of

a sometimes very large population makes it impossible to avoid the risk of making mistakes (Duong Thieu Tong, 2003) Therefore, the conclusions drawn from statistical inference only guarantee a certain degree of confidence, which means that statistical inference is a form of logical inference

There is another difference between these two types of inference, which is contextuality in statistical inference Although data may seem like numbers, Moore (1992) argues that data are “contextual numbers” And unlike mathematics, where context obscures the underlying structure, in statistics context provides meaning to numbers and data cannot be meaningfully analyzed without careful consideration their context: how they are collected and what they represent (Cobb & Moore, 1997)

1.4.5 Skills

Although there are many concepts related to skills, the concepts of skills are basically unifying that skill is the ability to apply human knowledge and understanding to perform a job that is to produce the desired result

1.4.6 Statistical reasoning skills

From analyzing and learning about the above statistical inference concept,

we can understand: Statistical reasoning skill is the ability to draw conclusions,

make predictions about all survey elements based on information and statistical data collected from samples and presented in the form of articles, tables or graphs That process is reflected in the human mind, filtered, linked, analyzed, transformed to perceive the real world and draw meaningful statistical conclusions

1.5 The reality of teaching and learning statistics in high schools

In fact, the teaching of statistical content in Vietnamese high schools needs

a lot of changes In our daily lives, we often encounter uncertain election results, collapsed bridges, stock market downturns, unreliable weather forecasts, false predictions about population growth, inefficient economic models and other manifestations of uncertainty in our real world (OECD, 2003, 2009) Faced with such uncertain sources of information, the question is “How do we make the right judgments?”, or “What competencies does each citizen need to handle? sources

of this information?” In today's modern life, a citizen needs skills different from those of previous decades, in which statistical skills are considered as important

as writing and reading skills for each person

An objective reason that statistical content has not received the proper attention of teachers and students in the past is due to the Covid-19 epidemic situation, teaching and learning have been affected by the Ministry of Education and Training (2020) issued the Official Dispatch on load reduction (CV3280/BGDĐT – GDTrH dated August 27, 2020) in which 50% of the time for teaching statistical content is reduced

By observing the current learning situation and exam form, we can see that the statistical knowledge achieved by high school students after graduation is not high, the interest of students is not much, some Studies closely related to statistics such as data science have only had a few open universities recently (Even universities in the Central region opened a major after data science after 02 years,

but too few candidates registered, so in 2023 in the enrollment notice, they had

to stop recruiting)

Conclusions of Chapter 1

In fact, in the world with today's amount of information, people need knowledge and skills about statistics, students need to be equipped with this knowledge fully and early, this is even more important confirmed through the content of Mathematics in the general education curriculum in 2018 with the increase of the duration of the statistical content

Researching the works on the levels of statistical competence, we have synthesized and clarified the concepts and relationships between the levels: statistical understanding, reasoning and thinking We have also pointed out the specific manifestations of these levels, and at the same time focused on further analyzing the students' statistical reasoning skills This is the level that we think

is suitable for the purpose of teaching the General Education Curriculum 2018

We also investigated and surveyed the reality of teaching statistics in high schools, there were many results that were not as expected Because of objective and subjective reasons, both teachers and students now pay little attention to statistical content, leading to the formation of this skill for students is still limited

From the school year 2022-2023, the new General Education Curriculum will be implemented, which is very necessary and a favorable condition for both teachers and students to change their views and traditional teaching methods There will be many difficulties and challenges for those who implement teaching statistical content, but we have already predicted that and have taken the necessary preparation steps In chapter 2, we will propose pedagogical measures

to build a positive learning environment to train statistical reasoning skills for students

Chapter 2 BUILDING A LEARNING ENVIRONMENT OF STATISTICS CONTENT IN HIGH SCHOOL IN THE DIRECTION OF TRAINING STATISTICS REASONING SKILLS FOR HIGH SCHOOL

First: It must be suitable with the cognitive process of students (from

concrete to abstract, from easy to difficult); attach importance to the logic of mathematical science and at the same time pay attention to the approach based

on the experience capital and experience of students;

Second: Mastering the spirit of "taking learners as the center", promoting

the positivity, self-discipline, paying attention to the needs, cognitive abilities, and different learning styles of each individual student; organize the teaching process in a constructivist direction, in which students can participate in exploring, discovering, reasoning and solving problems;

Third: Flexibility in applying active teaching methods and techniques;

combine skillfully and creatively with the application of traditional teaching methods and techniques; combine teaching activities in the classroom with hands-on experiences, applying mathematical knowledge into practice The lesson structure ensures a balanced and harmonious ratio between core knowledge, applied knowledge and other components

Fourth: Using sufficient and effective means and equipment for teaching

at least as prescribed for Mathematics; can use self-made teaching aids suitable

to the learning content and the students' subjects; increase the use of information technology and modern teaching facilities and equipment in an appropriate and effective manner;

The characteristics of the 2018 Math Program in general, and the Statistics content in particular, as indicated above, require basic orientations in teaching this content in high schools In our opinion, the major orientations in teaching and learning statistical content in the 2018 math program are:

Orientation 1: Choosing examples in teaching statistics to create

opportunities for students to form and develop their capacity

Orientation 2: Applying active teaching methods and techniques to

teaching statistical content

Orientation 3: Applying methods and forms of testing and assessment

towards developing students' learning capacity in teaching statistics content

Orientation 4: Using information technology in teaching statistics

The reality of teaching statistical content as described in Chapter 1 needs a big change if it wants to meet the requirements of the General Education Program

in Mathematics 2018, positive and result-oriented new perspectives Teaching that meets the requirements of educational goals is essential The above orientations both show the need to build a learning environment to overcome the reality of teaching statistical content and also contribute to identifying the main components of that environment We believe that educational methods need to

be seriously studied and experimented before being applied, the learning environment to practice literacy skills for students is one of the pedagogical methods suitable to the trend education direction of the world and will play a

role in the implementation of the General Education Program in Mathematics

2.2.2 Learning environment to develop statistical reasoning skills

From the above analysis, we come up with a conception of the learning environment with the aim of training students' statistical reasoning skills as follows: The learning environment to develop statistical reasoning skills is an active learning environment in which students work independently or cooperatively to draw conclusions and make predictions about all survey elements based on on the information, statistical data is collected and presented

in the form of articles, tables or graphs

The statistical content learning environment that we proposed above is based on constructivist theory, which is a general teaching theory that itself contains some basic ideas of problem-solving teaching and situation theory (or other active teaching methods currently being advocated) Constructivist theory holds that learners' activities must repeat at least part of the constitutive features

of scientific activity, as a guarantee for the efficient construction of knowledge This is not an invention but to create conditions and an environment for students

to grasp the problem in the "proximal development zone" of students, in order to appear in students, the need to create new knowledge The constructivist teaching model is built on four assumptions: learning in action, learning in overcoming obstacles, learning in social interaction - in connected activities, and learning through problem solving problem

Learning in activities: The first thing in building knowledge is the

intellectual activity of the learner This has its roots in the psychological basis of constructivism (Pieget) Learning is an adaptive activity of learners Therefore, teaching must be teaching activities, organizing learning situations that require student adaptation, through which students construct knowledge and develop their intelligence and personality

Learning is overcoming obstacles: Students' new knowledge is only

established on the basis of existing knowledge, and at the same time, it changes old and inappropriate views Thus, learning is not just an acquisition but a cognitive transformation

Learning in social interaction - in connected activities: Human perception

evolves in social interaction and social conflict perceives learning to be more

favorable and more effective through discussion and debate among classmates

Learning through problem solving: The starting point of learning is to

discover a problem to be solved Teachers need to make students see the need to

solve that problem, attach that problem to the interest of students, when creating

a need to find a way to solve the problem, not merely the repetition of knowledge mode and mode of operation, that is, requires students to have adaptation to certain situations Problem solving is done through question-answering activities

If there is no question, no problem, there is no scientific knowledge

An effective and active statistics classroom can be viewed as a learning environment to develop in students a deep and meaningful understanding of statistics and to help students develop their ability to statistical thinking and reasoning This is a learning environment to develop statistical reasoning skills

By viewing it as a learning environment, we emphasize that it represents more than a textbook, activities, or exercises that we provide to students That environment is a combination of real data, activities and cultures in the classroom, discussion, technology, teaching methods and a variety of forms of assessment The principles of instructional design described by Cobb & McClain,

2004 (according to Joan B., Garfield J., Ben-Zvi D 2008) recommendations for application to the teaching of statistics are the use of real data, classroom activities, technology, and assessment From that, we believe that the learning environment for students to practice literacy skills has the following model:

Figure 2.3 Learning environment for statistical content to practice statistical reasoning skills

A change in the method of teaching statistical content in high schools is necessary, because it is a task that teachers need to implement if they want to achieve the goals of the 2018 Math education program With the above proposed model, students will receive the overall impact in the process of receiving statistical knowledge, the teacher plays the role of creator, observer, support, and control the student's learning process in order to guide the students' learning process to develop statistical reasoning skills for students

The learning environment for training statistical reasoning skills made up

of the above factors can be considered as a positive learning environment to

Diversifying assessment methods in teaching to develop statistical reasoning skills

Increase the use of information technology

to support teaching and learning to train statistical reasoning skills.

Using real-life data in teaching

statistics.

Applying suitable teaching

methods for training statistical

reasoning skills.

develop students' deep and meaningful statistical understanding, to help them develop their thinking and statistical reasoning skills

For example, the collection of data from practical problems is a very important premise that determines the process of analyzing and drawing statistical conclusions and predictions Due to the limited amount of study time

in the program, the textbook only provides a brief introduction to the problem of collecting and describing statistical data The data in the textbooks given are usually available, hypothetical, so the students' statistical reasoning skills are less interested in training, mainly remembering and applying formulas to calculate certain characteristics To create a positive learning environment to practice statistical reasoning skills, in teaching, teachers can divide the class into small groups and assign the task of collecting data before coming to class

In order to create and practice statistical reasoning skills for students, teachers need to create a positive learning environment as analyzed and built with the above components An effective and active statistics classroom will be a learning environment that can deepen students' understanding of statistics, and at the same time develop their ability to think and make statistical inferences That type of classroom is a kind of learning environment that trains statistical reasoning skills

2.3 Pedagogical measures to build a learning environment to train students' statistical reasoning skills

2.3.1 Measure 1: Organizing for students to search and exploit practical data in daily life to teach statistical content in high schools

2.3.1.1 Proposal basis

2.3.1.2 Purposing and meaning of the measure

a Using real data in teaching statistics contributes to the completion of some necessary mathematical knowledge and skills for students to be able to apply their knowledge to practice

b Finding and using real data in statistics teaching situations helps students build knowledge in a better way

c Using real data in teaching statistics contributes to the development of intellectual abilities for students

d Exploiting and using real data in teaching statistics helps students develop statistical reasoning skills

2.3.1.3 Method to perform

There are many ways to collect data sets to serve the teaching of statistics, the convenience of accessing data today also greatly supports teachers in using real data

Teachers also need to be aware that questions used with datasets will interest learners and not all datasets will interest all students, so data should be used from a range of different contexts