PHÁT TRIỂN KIẾN THỨC VÀ THỰC HÀNH NGHIỆP VỤ CỦA GIÁO VIÊN TOÁN TƯƠNG LAI ĐỂ DẠY HỌC PHẦN THỐNG KÊ.PHÁT TRIỂN KIẾN THỨC VÀ THỰC HÀNH NGHIỆP VỤ CỦA GIÁO VIÊN TOÁN TƯƠNG LAI ĐỂ DẠY HỌC PHẦN THỐNG KÊ.PHÁT TRIỂN KIẾN THỨC VÀ THỰC HÀNH NGHIỆP VỤ CỦA GIÁO VIÊN TOÁN TƯƠNG LAI ĐỂ DẠY HỌC PHẦN THỐNG KÊ.PHÁT TRIỂN KIẾN THỨC VÀ THỰC HÀNH NGHIỆP VỤ CỦA GIÁO VIÊN TOÁN TƯƠNG LAI ĐỂ DẠY HỌC PHẦN THỐNG KÊ.PHÁT TRIỂN KIẾN THỨC VÀ THỰC HÀNH NGHIỆP VỤ CỦA GIÁO VIÊN TOÁN TƯƠNG LAI ĐỂ DẠY HỌC PHẦN THỐNG KÊ.PHÁT TRIỂN KIẾN THỨC VÀ THỰC HÀNH NGHIỆP VỤ CỦA GIÁO VIÊN TOÁN TƯƠNG LAI ĐỂ DẠY HỌC PHẦN THỐNG KÊ.PHÁT TRIỂN KIẾN THỨC VÀ THỰC HÀNH NGHIỆP VỤ CỦA GIÁO VIÊN TOÁN TƯƠNG LAI ĐỂ DẠY HỌC PHẦN THỐNG KÊ.
Trang 1HUE UNIVERSITY UNIVERSITY OF EDUCATION
NGUYEN THI HA PHUONG
DEVELOPING THE KNOWLEDGE AND PROFESSIONAL PRACTICE OF PROSPECTIVE MATHEMATICS TEACHERS FOR TEACHING STATISTICS
Major: Mathematics Teaching Methodology
Code: 9140111
SUMMARY OF PH.D DISSERTATION
Hue, 2022
Trang 2The dissertation was completed at the University of Education,
The dissertation is defended at the Hue University Thesis Evaluation
Committee Meeting at… o’clock day month year
The dissertation can be accessed in the Library:
1 The National Library of Vietnam
2 Library of University of Education, Hue University
Trang 3PREFACE
Developing knowledge for teachers to teach a certain mathematical content effectively is a significant research direction, especially in teacher training The work of Shulman (1986) was pioneering and greatly influenced the field of teacher knowledge research for teaching After that, many researchers have developed the work of Shulman (1986) to study the types of mathematical knowledge required to teach different topics Among those studies, Ball and her colleagues (Ball, et.al, 2008; Hill et al., 2008) made an essential contribution to this area of research by distinguishing six different types of knowledge that teachers need to teach effectively, called mathematical knowledge for teaching (MKT)
Many studies have been based on the MKT model to evaluate and develop the types of knowledge teachers need to teach a particular topic effectively For example, Döhrmann et al (2012) based on the MKT model to develop a model to evaluate the professional competence of mathematics teachers in many countries within the framework of the international assessment program TIMSS Gonzalez (2014) discussed statistical knowledge to teaching by using the MKT model Wilkie and Clark (2015) designed mathematics tasks based on the MKT model to develop teachers' knowledge about teaching functional thinking In Vietnam, Le (2016) studied the knowledge of prospective mathematics teachers (PMTs) to teach functions Minh & Lien (2018) have started researching and applying the MKT model to evaluate and develop the mathematics knowledge of PMTs to teach the application of derivatives
in economics However, knowledge for teaching statistics is still an unclear issue (Eichler & Zapata-Cardona, 2016)
Teaching statistics has common characteristics in teaching and has its particularities (Cobb & Moore, 1997) Many researchers have focused on describing the knowledge needed to teach statistics to help teachers understand statistics deeply (Garfield & Ben-Zvi, 2009; Gfeller, Niess & Lederman, 1999; Leavy & O'Loughlin, 2006; Groth
& Bergner, 2006; Jacobbe, 2008; Santos, 2013; Gonzalez, 2014; Sanchez-Sanchez & Gomez-Blancarte, 2015)
Trang 4Nowadays, in the studies on teaching statistics, there has been little research on teachers' knowledge for teaching statistics to their contextual teaching practice (Cobb and Moore, 1997) In particular, studies on the relationship of knowledge types placed in the context of cooperative teachings, such as lesson study (LS), have been a new approach that has still little exploited Recently, in Viet Nam, although there has been some research related to teaching statistics, almost no analysis has mentioned teachers' knowledge and professional development Besides,
in the current general education curriculum, statistical content is only presented sporadically in some classes However, statistics is one of the three primary knowledge circuits included in the 2018 mathematics curriculum This shows that statistics have been focused on the 2018 mathematics curriculum Therefore, it is urgent and necessary to develop teachers' knowledge for teaching statistics
The overarching objective of this study is to evaluate and develop knowledge types of PMTs for teaching statistics Specifically, we evaluated the types of content knowledge and pedagogical knowledge
of PMTs for teaching statistical histograms, the measures of central tendency from statistical graphs, and the dispersion of the data variability on statistical graphs (detail bar charts and histograms) As a next step, a LS cycle was proposed by us from the improved LS cycle
of Lewis (2009) This cycle helped PMTs to develop their mathematics knowledge step by step Finally, based on the obtained research results,
we discussed and made recommendations with a scientific basis to innovate training content and development professional skills for PMTs at teacher training institutions in Vietnam
In addition to the Introduction, the thesis is divided into 6 chapters:
In chapter 1, we have analyzed the studies related to mathematical knowledge for teaching and professional competence
of mathematics teachers, especially studies based on the model of Ball et al (2008); reviewed of studies on teachers' knowledge for teaching statistics In addition, we have analyzed the epistemological characteristics and content of the topic of statistics in high school as well as in the mathematics teachers' training program, as a basis for developing and adjusting the MKT by Ball et al (2008) into the context of teaching statistics
Trang 5In chapter 2, we have detailed the model of mathematical knowledge types of Ball et al (2008) Specifically, we have clearly analyzed each knowledge component of the MKT model and mentioned a number of studies on the statistical knowledge model for teaching Next, we introduced LS and some professional development research for teachers based on LS
In chapter 3, we presented a brief epistemology and history of statistics and some basic knowledge about bar charts and histograms, the measures of central tendency and variability of data in statistical graphs In addition, we have built sets of indicators to assess the knowledge of teachers to teaching statistical graphs, the measures of central tendency and variability of data in statistical graphs At the end of the chapter, the specific objectives of the study were set out and concretized into research questions
The content of chapter 4 details the research method of the thesis Specifically, we have given the context of the experiments; research objectives and methods; experimental procedures and data collection; research tools, a priori analysis of questionnaires and methods of analyzing empirical data
Chapter 5 presents the experimental results Here, we have focused on analyzing four types of knowledge: common content knowledge, specialized content knowledge, knowledge of content and student, knowledge of content, and teaching of PMTs in each practice and describe their knowledge progression while participating in LS Chapter 6, from the research results, we have presented in-depth analysis and explanations for the results obtained in chapter 5 to answer the research questions posed In addition, we have discussed the contributions of the research and the applicability of its findings
in teacher training
Chapter 1 RESEARCH PROBLEM
1.1 Overview of studies on teachers' knowledge for teaching 1.1.1 Shulman’s work
1.1.2 Fennema & Franke’s work
1.1.3 Model of subject knowledge in mathematics
1.1.4 Ball and her colleagues’s work
Trang 61.1.5 The role and importance of subject-specific pedagogical content knowledge
1.2 Research overview of teachers' knowledge for teaching statistics 1.3 Statistics in high school mathematics program in Vietnam 1.4 Teachers’ professional competencies studies in Vietnam 1.5 Current high school Mathematical teacher training program 1.6 Research problem
Chapter 2 THEORETICAL FRAMEWORK
2.1 Model of mathematical knowledge for teaching
Based on Shulman's (1986) classification, Ball et al (2008) developed a theoretical framework for mathematical knowledge for teaching (MKT) to research and evaluation of different types of knowledge that mathematics teachers need to perform effective teaching This model includes two areas of knowledge: subject matter knowledge (SMK) and pedagogical content knowledge (PCK) In each of these areas, the authors divided into three different types of knowledge (Figure 2.1)
Figure 2.1 Model of mathematical knowledge for teaching
(Ball, Thames, & Phelps, 2008)
2.1.1 Common content knowledge
2.1.2 Specialized content knowledge
2.1.3 Horizon content knowledge
2.1.4 Knowledge of content and student
2.1.5 Knowledge of content and teaching
2.1.6 Knowledge of Content and Curriculum
2.2 Statistical knowledge for teaching
2.3 Lesson study
Trang 72.4 Lesson study cycle
2.4.1 Baba's lesson study cycle (2007)
2.4.2 Lewis lesson study cycle (2009)
2.4.3 Murata lesson study cycle (2011)
2.4.4 Proposing the lesson study cycle
Through the analysis of some LS cycles, we have proposed a suitable LS cycle for the experimental implementation of this study The purpose of our LS cycle was development mathematics PMTs' knowledge for teaching Each step of the curriculum has contributed to the development of specific types of knowledge For example, in the planning step, teachers have developed CCK, SCK when discussing content lessons, KCS when predicting student responses, or KCT when teachers formulate questions or design teaching activities
Figure 2.6 Proposed lesson study cycle
The steps of this LS cycle are described in detail as follows: + Identify topics and set common goals: the topics selected may not
be entirely within the general curriculum, but maybe extra-curricular topics, application topics, or integrated topics in STEM education Teachers must determine the overall goal when choosing a teaching topic + Planning: The members of the LS team discuss the research lesson, prepare the same lesson plan, design teaching activities, build
a system of closed and open questions, predict students' answers + Teaching practice and observation: A teacher in the LS group teaches the lesson The remaining members observe, take notes to comment The collected data focus on the logic, the appropriateness
of the lesson plan, the teaching steps and the teacher's pedagogical ability, the teacher's analytical and feedback on the students' answers + Reflection and adjustment: After the lesson, the LS group discusses, gives suggestions, edits the lesson plan, and adjusts the teacher's
Trang 8methods if necessary The reflection step can be reflection after each teaching session or reflection at the end of the research process In the step
of reflection and teaching practice, we can repeat it many times This improves and enhances knowledge and professional practice for PMTs During the LS cycle, teachers work together with their peers to learn about the topic, pedagogy, and student thinking They then apply what they have learned to develop a lesson plan The implementation of the lesson plan in the real classroom context makes the case study an effective way to improve the teacher's pedagogical content knowledge However, many researchers have shown that although the process of performing LS seems simple, conducting research effectively is not an easy task (Chokshi & Fernandez, 2004; Yoshida, 2008) For LS effective, teachers need to develop additional skills such as how to research instructional materials, plan lessons, observe and collect data on student learning, reflect on lessons, and participate to discuss the lesson with colleagues The researchers believe that in order for the research to
be effective and successful, teachers need to have enough time to study the content, teaching materials and anticipate students' reactions during the research and must perform these exercises more purposeful and explicit (Yoshida & Jackson, 2011)
2.5 Research on mathematical knowledge for teaching through lesson study
Chapter 3 MATHEMATICAL KNOWLEDGE FOR
TEACHING STATISTICAL 3.1 Brief history and epistemology of the concept of statistics 3.2 Bar charts and histograms
3.2.1 Bar charts
3.2.2 Histograms
3.2.3 Common confusions between bar charts and histograms
3.3 Comparison of the measures of central tendency from statistical graphs
3.4 Teachers' mathematical knowledge for teaching histograms 3.5 Teachers' mathematical knowledge for teaching the measures of central tendency from statistical graphs
Trang 93.6 Teachers' mathematical knowledge for teaching variability
of data in bar charts and histograms
3.7 Objectives of the study
The overall objective of this study is to evaluate and develop the knowledge and professional practice of teachers for teaching statistics The specific objectives of this study are:
• Objective 1: Giving the characteristics of PMTs’ MKT for teaching histograms; examines the progression of PMTs' professional knowledge and practice on teaching histograms through conducting LS
• Objective 2: Giving the characteristics of PMTs’ MKT for teaching the measures of central tendency (mean, median, mode) from bar charts and histograms; examines the progression of PMTs' professional knowledge and practice on teaching the measures of central tendency through conducting LS
• Objective 3: Giving the characteristics of PMTs’ MKT for teaching variability of data in bar charts and histograms; examines the progression of PMTs' professional knowledge and practice on teaching variability of data through conducting LS
• Objective 4: Provide scientific and meaningful proposals to innovate training content and develop professional skills for PMTs in Mathematical teacher training institutions in Vietnam today
3.8 Research questions
For each research objective, the following research questions were asked:
• Question 1: How are the characteristics of the PMTs' mathematical knowledge for teaching histograms? How has PMTs' knowledge and professional practice in teaching histograms progressed through the implementation of the lesson study?
• Question 2: How are the characteristics of the PMTs' mathematical knowledge for teaching the measures of central tendency (mean, median, mode) from bar charts and histograms? How has PMTs' knowledge and professional practice in teaching the measures
of central tendency (mean, median, mode) from bar charts and histograms progressed through the implementation of the lesson study?
• Question 3: How are the characteristics of the PMTs' mathematical knowledge for teaching variability of data in bar charts and histograms? How has PMTs' knowledge and professional
Trang 10practice in teaching variability of data in bar charts and histograms progressed through the implementation of the lesson study?
• Question 4: From the research results of the topic, how can we make suggestions to reform the training content and develop the professional skills for PMTs in current teacher training institutions?
Chapter 4 RESEARCH METHODS
In this chapter, we present the context of the experiments, research tools, participants, data collection and analysis methods of the study
of statistics teaching as follows:
Table 4.1 Summary table of the number of people participating in
the experiments
The first experiment
The second experiment
The third experiment
The fourth experiment
Experimental content
Characteristics
of the PMTs' mathematical knowledge for teaching histograms
Characteristics
of the PMTs' mathematical knowledge for teaching the measures of central tendency (mean, median, mode) in statistics graphs
Characteristic
s of the PMTs' mathematical knowledge for teaching variability of data in statistics graphs
Applying LS to develop knowledge to teach histograms, the measures of central tendency in statistical graphs, variability in statistical charts
Trang 114.2 Experimental procedure and data collection
4.2.1 Experiment 1, 2, 3
For experiments 1, 2, 3, we carried out an experimental procedure consisting of similar steps In the lesson before taking the survey, we informed the PMTs about the survey content and how to do the test
We conducted a survey within one class session (which can last up to 5 lessons) in class in a module on teaching methods The PMTs were informed that taking the survey is considered a routine test The PMTs were allowed to use reference materials during the test After collecting, processing and analyzing data, we conducted semi-structured interviews to better understand the ideas and mistakes of PMTs to know why they made such mistakes We selected a number
of PMTs for private interviews and recorded the interview process Prioritization of interview selection was based on PMTs with typical true/false answers and demonstrated effort in their survey responses The interviews were conducted in a voluntary and cooperative spirit by the PMTs The interview question system was designed based on the tasks in the survey, including pre-prepared questions and arising questions based on the answers of the interviewees
4.3.3 Experiment 3: Assessing PMTs' mathematical knowledge for variability of data in bar charts and histograms
To assess PMTs' mathematical knowledge for variability of data in bar charts and histograms, we designed a survey consisting of 4 exercises Each question is a task to assess knowledge in the MKT model
Trang 124.3.4 Experiment 4: Applying lesson study to development PMTs' mathematical knowledge for statistical charts
The research tool is PMTs' teaching practices involved in the research The purpose of this experiment was to develop PMTs' mathematical knowledge to teaching statistics related to the contents surveyed in experiments 1, 2, 3 Specifically, we chose three topics: Lesson 1: Bar charts and histograms
Lesson 2: The measures of central tendency from bar charts and histograms
Lesson 3: Variability of data in bar charts and histograms
The knowledge content of the study is mentioned in the current general education curriculum in the statistics section of grade 7 and grade 10, but only at a simple level In the 2018 general education curriculum, these topics are fully and deeply covered in the statistics section in grades 9-12
4.4 Data analysis
4.4.1 Experiments 1, 2 and 3
a) Survey data
After collecting data, to evaluate PMTs' mathematical knowledge,
we used a qualitative analysis method based on specific keywords of knowledge types and aimed to collect information (description) about PMTs' knowledge types Along with the qualitative analysis process,
we combined quantitative analysis by building rating scales of 5 levels numbered from 0 to 4 to code for each task corresponding to the knowledge type of the user MKT model to serve as a basis for analysis and statistics on the work of PMTs
b) Interview data
We listened to recordings of the interviews and took notes The data
of the interviews were aimed at clarifying the answers of the PMTs in the survey and the causes of the mistakes that the PMTs made
4.4.2 Experiment 4
During the experiment, data were used from sources such as observational data made by the researchers themselves by taking notes, recording, filming the experimental process, data from
Trang 13documents such as lesson plans, versions of lesson plans prepared by
LS groups, and final evaluation sheets of PMTs participating in the lesson The collected data focused on examining the impact of PMTs' participation on PMTs' mathematical knowledge for teaching
In this study, we used the MKT model of Ball et al., (2008) as the basis for analyzing PMTs' mathematical knowledge for teaching Based on the sets of indicators, the characteristics of knowledge types, and teaching content, we proposed indexes to evaluate PMTs' knowledge of teaching Data analysis was carried out continuously during the experiment We summarized the evaluations of the manifestations PMTs' knowledge types participating in the study in each step of the lesson study In addition, the data were analyzed based on the PMTs' own reflections Questions asked teachers to describe what they had learned, and their own progression of knowledge in discussions or throughout the entire LS cycle The data sources collected have shown a high degree of uniformity
Chapter 5 RESEARCH RESULTS
In this chapter, we analyze and evaluate the results in experiments 1, 2, and 3 to see the current status of PMTs' knowledge for teaching histograms, the measures of central tendency from statistical graphs, and the variability of data in statistical graphs Then, we analyze the LS steps of the PMTs in experiment 4 to see the progress of their knowledge A number of comments and suggestions are given to us to improve the training of PMTs
5.1 Orientation to analyze research results
The results of this study were obtained in all 6 types of knowledge according to the MKT model of Ball et al., (2008) However, we only focus on analyzing 4 types of knowledge including Common Content Knowledge (CCK), Specialized Content Knowledge (SCK) in the field of Subject Matter Knowledge (SMK); and Knowledge of Content and Student (KCS), Knowledge of Content and Teaching (KCT) in the field of Pedagogical Content Knowledge (PCK) The scope of knowledge in our research focuses
on the teaching of statistical graphs, the measures of central tendency, and variability of data in statistics graphs