In this paper we report the results from a major UK government-funded project, started in 2005, t... more In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics within the school mathematics curriculum for students up to age 16. New teaching materials that explicitly use a problem-solving approach through other subjects have been developed. We will report extensive trialing of these, the development of corresponding new assessment regimes and how these work in the classroom. The new ways of assessing are particularly poignant since, in September 2006, the UK government announced that coursework is to be dropped for mathematics exams sat by 16-year-old. As a consequence, areas of the curriculum previously assessed by coursework, are now being ignored. We will provide some new and useful ways of assessing this content. Our findings have implications for teaching, learning and assessing statistics for students of the subject at all ages.
We review our experiences with both CensusAtSchool and ExperimentsAtSchool over the last 10 years... more We review our experiences with both CensusAtSchool and ExperimentsAtSchool over the last 10 years with helping teachers overcome the difficulties of coping with increasingly complex new technologies, larger and more realistic data sets while simultaneously increasing the levels of statistical literacy in students and working more conceptually. We describe our interactive web-based data investigation tool which interacts with our large datasets of real data from learners around the world and describe material and tools that we have used to help improve both teachers' pedagogy and students' learning and understanding of statistics. We believe that the next steps in statistics education should include helping teachers enjoy and understand data exploration which, in turn, will help improve students learning of statistics at school level. In 2000 we started the CensusAtSchool project hoping to " raise statistical standards and practice for teachers and pupils" (see , little knowing that the project would quickly grow into the immense International enterprise it is today, offering access to real data from well over a million school children, a vast bank of curriculum enrichment material and resources for teachers and schools and offering innovative ways for learners to use their own data to compare and contrast themselves to others. It enables teachers and learners to enhance their statistical literacy and data handling skills and to improve pedagogy for teachers. The involvement of a number of different countries increases the potential for exchange of information and widening the cultural experience. It has the added bonus of being based on websites, providing technological opportunities and is motivational for teachers and learners alike. The ExperimentsAtSchool project developed quite naturally as an offshoot of the CensusAtSchool project based on experimental data as opposed to the survey type data of CensusAtSchool. It also helps us to utilise some of the data inputted to the online questionnaires, in particular the interactive questions such as the reaction timer, the angle estimation and the concentration game to name but a few. While teachers have to request their data back from CensusAtSchool and have it sent to them to make decisions about how it is to be used in the classroom the data from ExperimentsAtSchool is accessible directly from the website and therefore the input and retrieval of data for processing and presentation can all be done in one session. This provides opportunities for learners to interact with the data and start exploring the information it is giving them. The increasing need to interact directly with the data led to the development of our new data tool. This tool links directly to most of the main CensusAtSchool databases and provides a way for direct dynamic interaction. It provides a way to allow intuitive graphing of random samples of data direct from the data bases. This use of the real data presents issues and challenges that are often not present in sorted and sanitised data learners are usually given. The data also offer exciting opportunities for discussion and reflection typified by the following questions: Which type of graph shows the data in the 'best' way? What size sample is 'best'? What happens if I resample the database -will I get the same picture? How does this compare to our own data? We will now describe some of the features of the data tool to illustrate how it can help learners to conceptualise and understand how important the processing, presentation and interpretation of real data can be.
In this paper we present examples of improving student communication skills in statistics by usin... more In this paper we present examples of improving student communication skills in statistics by using resources that are created from student and teacher involvement in data production. Collecting real data that the students and teachers can relate to, the creation of data-active worksheets, lessons and projects can help to bring statistics to life. This, in turn, can aid the development of thinking skills that enable students to communicate statistics better, both orally and in writing. We give examples that: • encourage students to learn statistical communication skills through collecting real data and using them to produce useful projects that can yield meaningful conclusions; • enable teachers to be confident and competent about the types of data that should be collected and used, and how they should be organised and presented; • show teachers how to support students in Data Handling and Statistics projects.
Canadian Journal for Studies in Discourse and Writing/Rédactologie, 1986
Students learning report writing need to feel that the exercises they do are useful both in impro... more Students learning report writing need to feel that the exercises they do are useful both in improving their writing ability and in providing them with insight into technical writing in the real world. This paper supports earlier work proposing the use of imaginative, credible case studies and underscores the important pedagogical concept that the material taught should clearly reflect defined objectives to meet the overall aim of the course. By describing a planned unit of instruction currently being taught to senior technical students, this paper demonstrates that the instructional strategies and exercises used help students meet practical learning and skill objectives.
In this paper we describe an interactive Flash®-based data interrogation tool which interacts wit... more In this paper we describe an interactive Flash®-based data interrogation tool which interacts with large datasets of real data collected from learners around the world. The dynamic tool can be used online to access in real-time databases stored on the Royal Statistical Society ...
Next Steps in Statistics Education Precedings IASE Satellite Conference
In recent times many authors have advocated change to the way statistics is taught to specialist ... more In recent times many authors have advocated change to the way statistics is taught to specialist and non-specialist undergraduates. One argument has been that adopting an approach that reflects real world experiences would better equip them for joining an evidence-based world after graduating. Even though some progress has been made, steps to change things have not been taken by curriculum designers or the vast majority of teachers of undergraduate statistics courses. More recently, in 2006 in the UK there were urgent calls from the Higher Education Funding Councils and the Economics and Social Science Research Council for proposals to develop undergraduate curricula to address the needs of today’s evidence based world. We describe an approach to teaching statistics to students in the key discipline area of the social sciences using an evidence-based problem-solving approach. Examples of materials that can be used to support this approach are also presented.
In this paper we review the implementation of the international CensusAtSchool (www.censusatschoo... more In this paper we review the implementation of the international CensusAtSchool (www.censusatschool.ntu.ac.uk) and related projects, and suggest lessons that could be learned from them to better promote statistical education at all ages. We emphasise how the project's success has been due, in no small part, to the involvement and support of various levels of each country's government statistical services. These include the UK Office of National Statistics, Statistics South Africa, The Office of Economic and Statistical Research of the Queensland Treasury, the Australian Bureau of Statistics, Statistics New Zealand and Statistics Canada. Lastly, we suggest that the project has important lessons of good practice for learning statistics, not just in schools, but also in universities and the workplace.
"The authors briefly describe an approach fo... more "The authors briefly describe an approach for engaging students in introductory statistics modules with data which the students generate themselves which is returned to them in real-time. We extend an invitation to all to make use of our system and contribute ideas for broadening its use. It has been clear to the authors for some time that more interesting sources of real data for teaching and learning introductory statistics (graphs, descriptive statistics, regression etc) are desirable for motivating students in the subject. Having ‘interesting’ data is key and one approach is to collect data which can be used across disciplines, and which is of interest to all students. Two topics that are often both interesting and useful to them, especially in the first year at university, are accommodation and neighbourhood safety/crime. In any case these are topics students are likely to discuss and can be investigated through the ‘Statistical Problem Solving Approach’ cycle with which many should already be familiar with from studying GCSE mathematics. Our survey tool project extends the LimeSurvey software [www.limesurvey.org] by adding the ability to download participants’ responses to them, in a controlled manner in real time."
sk schoolchildren what a census is and your reward is a sea of blank faces, with maybe a tentativ... more sk schoolchildren what a census is and your reward is a sea of blank faces, with maybe a tentative half hand or two up. Ask them about data handling and statistics and the result may be a little better, but meagre excitement is shown. Many lessons in schools generating and using statistics, be it in geography, mathematics or science, tend to use standard data, and are often delivered using unimaginative methods of teaching and learning.
In this paper we present a "model free' method of outlier detection for Gaussian... more In this paper we present a "model free' method of outlier detection for Gaussian time series by using the autocorrelation structure of the time series. We also present a graphic diagnostic method in order to distinguish an additive outlier (AO) from an innovation outlier (IO). The test statistic for detecting the outlier has a P ² distribution with one degree
Communications in Statistics - Theory and Methods, 1980
In this paper we express the sample autocorrelations for a moving average process of order q as a... more In this paper we express the sample autocorrelations for a moving average process of order q as a function of its own theoretical autocorrelations and the sample autocorrelations for the generating white noise series. Approximate analytic expressions are then obtained forthe moments of the sample autocorrelations of the moving average process.Using these expressions, together with numerical evidence, we show that
... CHATBTELD, C. & PBOTHEBO, DL (1973). Box-Jenkins seasonal forecasting: Problems in a ... more ... CHATBTELD, C. & PBOTHEBO, DL (1973). Box-Jenkins seasonal forecasting: Problems in a case study (with discussion). JB Statist. Soo. A 136, 296-336. HANNAH, EJ (1970). Multiple Time Series. New York: Wiley. MOHAN, PAP (1947). Some theorems on time series. ...
, sadly passed away of COVID-19 on the 9th April 2020, aged 80 years. Harvey was a one of the gre... more , sadly passed away of COVID-19 on the 9th April 2020, aged 80 years. Harvey was a one of the great statisticians in the United Kingdom in the 20th and 21st centuries. He had a worldwide reputation for his seminal work on multilevel (hierarchical or nested) modelling. He also was a persistent and insightful critic of several areas of public policy where the use of statistics was suspect. In particular, he was scathing in his criticism of the misapplication of league tables for comparing performance of public bodies such as schools and hospitals. In this important work he was concerned about the statistics of education. His seminal papers with Thomas [1], Spiegelhalter [2] and as sole author [3] about the validity of, and the dangers in, school league tables guiding the assessment of performance and school effectiveness were truly groundbreaking. He spent many years trying to persuade politicians and policy makers that the use, leading to abuse, of such tables was untrustworthy. Finally, in 2016, the Department for Education in the United Kingdom took notice of Harvey's comments and replaced their measure of GCSE secondary school performance with a valueadded one, which attempts to adjust schools' exam results in the light of differences in pupils' prior attainment. Returning more generally to the need for multilevel structures in statistical modelling, the thinking behind this may be unfamiliar to some, but the ideas and results
The Royal Statistical Society (RSS) Centre for Statistical Education runs an on-going internation... more The Royal Statistical Society (RSS) Centre for Statistical Education runs an on-going international CensusAtSchool project that involves, inter-alia, collecting and analysing school pupils' responses to about 18 simple questions. These fall into three areas of interest, namely details about ...
In this paper we report the results from a major UK government-funded project, started in 2005, t... more In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics within the school mathematics curriculum for students up to age 16. New teaching materials that explicitly use a problem-solving approach through other subjects have been developed. We will report extensive trialing of these, the development of corresponding new assessment regimes and how these work in the classroom. The new ways of assessing are particularly poignant since, in September 2006, the UK government announced that coursework is to be dropped for mathematics exams sat by 16-year-old. As a consequence, areas of the curriculum previously assessed by coursework, are now being ignored. We will provide some new and useful ways of assessing this content. Our findings have implications for teaching, learning and assessing statistics for students of the subject at all ages.
We review our experiences with both CensusAtSchool and ExperimentsAtSchool over the last 10 years... more We review our experiences with both CensusAtSchool and ExperimentsAtSchool over the last 10 years with helping teachers overcome the difficulties of coping with increasingly complex new technologies, larger and more realistic data sets while simultaneously increasing the levels of statistical literacy in students and working more conceptually. We describe our interactive web-based data investigation tool which interacts with our large datasets of real data from learners around the world and describe material and tools that we have used to help improve both teachers' pedagogy and students' learning and understanding of statistics. We believe that the next steps in statistics education should include helping teachers enjoy and understand data exploration which, in turn, will help improve students learning of statistics at school level. In 2000 we started the CensusAtSchool project hoping to " raise statistical standards and practice for teachers and pupils" (see , little knowing that the project would quickly grow into the immense International enterprise it is today, offering access to real data from well over a million school children, a vast bank of curriculum enrichment material and resources for teachers and schools and offering innovative ways for learners to use their own data to compare and contrast themselves to others. It enables teachers and learners to enhance their statistical literacy and data handling skills and to improve pedagogy for teachers. The involvement of a number of different countries increases the potential for exchange of information and widening the cultural experience. It has the added bonus of being based on websites, providing technological opportunities and is motivational for teachers and learners alike. The ExperimentsAtSchool project developed quite naturally as an offshoot of the CensusAtSchool project based on experimental data as opposed to the survey type data of CensusAtSchool. It also helps us to utilise some of the data inputted to the online questionnaires, in particular the interactive questions such as the reaction timer, the angle estimation and the concentration game to name but a few. While teachers have to request their data back from CensusAtSchool and have it sent to them to make decisions about how it is to be used in the classroom the data from ExperimentsAtSchool is accessible directly from the website and therefore the input and retrieval of data for processing and presentation can all be done in one session. This provides opportunities for learners to interact with the data and start exploring the information it is giving them. The increasing need to interact directly with the data led to the development of our new data tool. This tool links directly to most of the main CensusAtSchool databases and provides a way for direct dynamic interaction. It provides a way to allow intuitive graphing of random samples of data direct from the data bases. This use of the real data presents issues and challenges that are often not present in sorted and sanitised data learners are usually given. The data also offer exciting opportunities for discussion and reflection typified by the following questions: Which type of graph shows the data in the 'best' way? What size sample is 'best'? What happens if I resample the database -will I get the same picture? How does this compare to our own data? We will now describe some of the features of the data tool to illustrate how it can help learners to conceptualise and understand how important the processing, presentation and interpretation of real data can be.
In this paper we present examples of improving student communication skills in statistics by usin... more In this paper we present examples of improving student communication skills in statistics by using resources that are created from student and teacher involvement in data production. Collecting real data that the students and teachers can relate to, the creation of data-active worksheets, lessons and projects can help to bring statistics to life. This, in turn, can aid the development of thinking skills that enable students to communicate statistics better, both orally and in writing. We give examples that: • encourage students to learn statistical communication skills through collecting real data and using them to produce useful projects that can yield meaningful conclusions; • enable teachers to be confident and competent about the types of data that should be collected and used, and how they should be organised and presented; • show teachers how to support students in Data Handling and Statistics projects.
Canadian Journal for Studies in Discourse and Writing/Rédactologie, 1986
Students learning report writing need to feel that the exercises they do are useful both in impro... more Students learning report writing need to feel that the exercises they do are useful both in improving their writing ability and in providing them with insight into technical writing in the real world. This paper supports earlier work proposing the use of imaginative, credible case studies and underscores the important pedagogical concept that the material taught should clearly reflect defined objectives to meet the overall aim of the course. By describing a planned unit of instruction currently being taught to senior technical students, this paper demonstrates that the instructional strategies and exercises used help students meet practical learning and skill objectives.
In this paper we describe an interactive Flash®-based data interrogation tool which interacts wit... more In this paper we describe an interactive Flash®-based data interrogation tool which interacts with large datasets of real data collected from learners around the world. The dynamic tool can be used online to access in real-time databases stored on the Royal Statistical Society ...
Next Steps in Statistics Education Precedings IASE Satellite Conference
In recent times many authors have advocated change to the way statistics is taught to specialist ... more In recent times many authors have advocated change to the way statistics is taught to specialist and non-specialist undergraduates. One argument has been that adopting an approach that reflects real world experiences would better equip them for joining an evidence-based world after graduating. Even though some progress has been made, steps to change things have not been taken by curriculum designers or the vast majority of teachers of undergraduate statistics courses. More recently, in 2006 in the UK there were urgent calls from the Higher Education Funding Councils and the Economics and Social Science Research Council for proposals to develop undergraduate curricula to address the needs of today’s evidence based world. We describe an approach to teaching statistics to students in the key discipline area of the social sciences using an evidence-based problem-solving approach. Examples of materials that can be used to support this approach are also presented.
In this paper we review the implementation of the international CensusAtSchool (www.censusatschoo... more In this paper we review the implementation of the international CensusAtSchool (www.censusatschool.ntu.ac.uk) and related projects, and suggest lessons that could be learned from them to better promote statistical education at all ages. We emphasise how the project's success has been due, in no small part, to the involvement and support of various levels of each country's government statistical services. These include the UK Office of National Statistics, Statistics South Africa, The Office of Economic and Statistical Research of the Queensland Treasury, the Australian Bureau of Statistics, Statistics New Zealand and Statistics Canada. Lastly, we suggest that the project has important lessons of good practice for learning statistics, not just in schools, but also in universities and the workplace.
"The authors briefly describe an approach fo... more "The authors briefly describe an approach for engaging students in introductory statistics modules with data which the students generate themselves which is returned to them in real-time. We extend an invitation to all to make use of our system and contribute ideas for broadening its use. It has been clear to the authors for some time that more interesting sources of real data for teaching and learning introductory statistics (graphs, descriptive statistics, regression etc) are desirable for motivating students in the subject. Having ‘interesting’ data is key and one approach is to collect data which can be used across disciplines, and which is of interest to all students. Two topics that are often both interesting and useful to them, especially in the first year at university, are accommodation and neighbourhood safety/crime. In any case these are topics students are likely to discuss and can be investigated through the ‘Statistical Problem Solving Approach’ cycle with which many should already be familiar with from studying GCSE mathematics. Our survey tool project extends the LimeSurvey software [www.limesurvey.org] by adding the ability to download participants’ responses to them, in a controlled manner in real time."
sk schoolchildren what a census is and your reward is a sea of blank faces, with maybe a tentativ... more sk schoolchildren what a census is and your reward is a sea of blank faces, with maybe a tentative half hand or two up. Ask them about data handling and statistics and the result may be a little better, but meagre excitement is shown. Many lessons in schools generating and using statistics, be it in geography, mathematics or science, tend to use standard data, and are often delivered using unimaginative methods of teaching and learning.
In this paper we present a "model free' method of outlier detection for Gaussian... more In this paper we present a "model free' method of outlier detection for Gaussian time series by using the autocorrelation structure of the time series. We also present a graphic diagnostic method in order to distinguish an additive outlier (AO) from an innovation outlier (IO). The test statistic for detecting the outlier has a P ² distribution with one degree
Communications in Statistics - Theory and Methods, 1980
In this paper we express the sample autocorrelations for a moving average process of order q as a... more In this paper we express the sample autocorrelations for a moving average process of order q as a function of its own theoretical autocorrelations and the sample autocorrelations for the generating white noise series. Approximate analytic expressions are then obtained forthe moments of the sample autocorrelations of the moving average process.Using these expressions, together with numerical evidence, we show that
... CHATBTELD, C. & PBOTHEBO, DL (1973). Box-Jenkins seasonal forecasting: Problems in a ... more ... CHATBTELD, C. & PBOTHEBO, DL (1973). Box-Jenkins seasonal forecasting: Problems in a case study (with discussion). JB Statist. Soo. A 136, 296-336. HANNAH, EJ (1970). Multiple Time Series. New York: Wiley. MOHAN, PAP (1947). Some theorems on time series. ...
, sadly passed away of COVID-19 on the 9th April 2020, aged 80 years. Harvey was a one of the gre... more , sadly passed away of COVID-19 on the 9th April 2020, aged 80 years. Harvey was a one of the great statisticians in the United Kingdom in the 20th and 21st centuries. He had a worldwide reputation for his seminal work on multilevel (hierarchical or nested) modelling. He also was a persistent and insightful critic of several areas of public policy where the use of statistics was suspect. In particular, he was scathing in his criticism of the misapplication of league tables for comparing performance of public bodies such as schools and hospitals. In this important work he was concerned about the statistics of education. His seminal papers with Thomas [1], Spiegelhalter [2] and as sole author [3] about the validity of, and the dangers in, school league tables guiding the assessment of performance and school effectiveness were truly groundbreaking. He spent many years trying to persuade politicians and policy makers that the use, leading to abuse, of such tables was untrustworthy. Finally, in 2016, the Department for Education in the United Kingdom took notice of Harvey's comments and replaced their measure of GCSE secondary school performance with a valueadded one, which attempts to adjust schools' exam results in the light of differences in pupils' prior attainment. Returning more generally to the need for multilevel structures in statistical modelling, the thinking behind this may be unfamiliar to some, but the ideas and results
The Royal Statistical Society (RSS) Centre for Statistical Education runs an on-going internation... more The Royal Statistical Society (RSS) Centre for Statistical Education runs an on-going international CensusAtSchool project that involves, inter-alia, collecting and analysing school pupils' responses to about 18 simple questions. These fall into three areas of interest, namely details about ...
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