International Journal of Mathematical Education in Science and Technology, 2021
One of the key problems to be solved in mathematics education in England is that the demand for m... more One of the key problems to be solved in mathematics education in England is that the demand for mathematics teachers is far in excess of the supply. Acknowledging that there are simply too few mathematics teachers, the UK government has invested significantly in retraining programmes. These programmes 'retrain' out-of-field teachers, that is, teachers of other subjects or from other phases, to teach secondary mathematics. The increased mathematical demand of the reformed GCSE courses coupled with the expectation that most post-16 students will engage with some mathematics (studying for A and AS levels, a Core Maths qualification or re-sitting GCSE) means many more teachers of mathematics will be needed. We consider the viability of a retraining course as an effective way of alleviating the problem of the lack of well qualified teachers for mathematics. In this four-year longitudinal study, we followed teachers during their year of 'retraining' and in the succeeding years. Once a participant completes their part-time one-year course, the teacher is considered 'retrained'. However, we conclude that without ongoing professional development involving collaborative support retraining courses alone can have little impact on the problem of the lack of competent and confident teachers of mathematics in the secondary sector.
Systems dynamics and differential equations Transfer functions and block diagrams State-space for... more Systems dynamics and differential equations Transfer functions and block diagrams State-space formulation Transient and steady state response analysis Stability Controllability and observability Multivariable feedback and pole location Introduction to optimal control Variational calculus Optimal control with unbounded continuous controls Bang-bang control Applications of optimal control Dynamic programming Appendices: Partial fractions Notes on determinants and matrices Solutions to problems.
THE UNIVERSITIES of Exeter (Centre for Innovation in Mathematics Teaching) and Kassel (Mathematic... more THE UNIVERSITIES of Exeter (Centre for Innovation in Mathematics Teaching) and Kassel (Mathematics Department) have been working closely together over the past few years as they have a common interest in encouraging the teaching of mathematics through its ...
... Germany WERNER BLUM, DAVID BURGHES, NIGEL GREEN and GABRIELE KAISER-MESSMER ... pp. 66-72. 7.... more ... Germany WERNER BLUM, DAVID BURGHES, NIGEL GREEN and GABRIELE KAISER-MESSMER ... pp. 66-72. 7. Hearnden, A., Oxford Review of Education, 1986, 12, 187-194. 8. Glowka, D., Comparative Education, 1989, 25, 319-332. ...
1. Background RECENT (1994) examination results including mathe-matics at A-level and GCSE (Natio... more 1. Background RECENT (1994) examination results including mathe-matics at A-level and GCSE (National Curriculum Key Stage 4) have, as usual, caused concern. Trends of increasing success have continued almost un-abated, and we have the sceptics who question whether ...
THE UNIVERSITIES of Exeter (Centre for Innovation in Mathematics Teaching) and Kassel (Mathematic... more THE UNIVERSITIES of Exeter (Centre for Innovation in Mathematics Teaching) and Kassel (Mathematics Department) have been working closely together over the past few years as they have a common interest in encouraging the teaching of mathematics through its ...
International Journal of Mathematical Education in Science and Technology, 1984
A one‐factor economic growth model is introduced in this paper. Pollution as a byproduct of produ... more A one‐factor economic growth model is introduced in this paper. Pollution as a byproduct of production accompanies economic growth which in turn is required for meeting consumer demand for goods. A proportion of the output should be devoted to pollution control and consequently the capital accumulation is being affected. The relationships between production, consumption and pollution are studied with the aid of optimal control theory. The closed economic model is solved numerically by using the sequential gradient‐restoration algorithm.
International Journal of Mathematical Education in Science and Technology, 1979
ABSTRACT This article deals with the problem of modelling the population densities of cities. A h... more ABSTRACT This article deals with the problem of modelling the population densities of cities. A historical introduction is given. There are two types of models, namely the ‘quadratic gamma’ family which can be summarized by the formulaD(r) = A exp(br + cr )r where Dis the population density, rthe radial distance, A, b, cand dconstants; and the ‘equilibrium’ models which have been derived by using civic state and equilibrium equations. Details of the development and verification of the various types of models are given, and finally the models are tested and compared using the data for the city of Coventry.
International Journal of Mathematical Education in Science and Technology, 2021
One of the key problems to be solved in mathematics education in England is that the demand for m... more One of the key problems to be solved in mathematics education in England is that the demand for mathematics teachers is far in excess of the supply. Acknowledging that there are simply too few mathematics teachers, the UK government has invested significantly in retraining programmes. These programmes 'retrain' out-of-field teachers, that is, teachers of other subjects or from other phases, to teach secondary mathematics. The increased mathematical demand of the reformed GCSE courses coupled with the expectation that most post-16 students will engage with some mathematics (studying for A and AS levels, a Core Maths qualification or re-sitting GCSE) means many more teachers of mathematics will be needed. We consider the viability of a retraining course as an effective way of alleviating the problem of the lack of well qualified teachers for mathematics. In this four-year longitudinal study, we followed teachers during their year of 'retraining' and in the succeeding years. Once a participant completes their part-time one-year course, the teacher is considered 'retrained'. However, we conclude that without ongoing professional development involving collaborative support retraining courses alone can have little impact on the problem of the lack of competent and confident teachers of mathematics in the secondary sector.
Systems dynamics and differential equations Transfer functions and block diagrams State-space for... more Systems dynamics and differential equations Transfer functions and block diagrams State-space formulation Transient and steady state response analysis Stability Controllability and observability Multivariable feedback and pole location Introduction to optimal control Variational calculus Optimal control with unbounded continuous controls Bang-bang control Applications of optimal control Dynamic programming Appendices: Partial fractions Notes on determinants and matrices Solutions to problems.
THE UNIVERSITIES of Exeter (Centre for Innovation in Mathematics Teaching) and Kassel (Mathematic... more THE UNIVERSITIES of Exeter (Centre for Innovation in Mathematics Teaching) and Kassel (Mathematics Department) have been working closely together over the past few years as they have a common interest in encouraging the teaching of mathematics through its ...
... Germany WERNER BLUM, DAVID BURGHES, NIGEL GREEN and GABRIELE KAISER-MESSMER ... pp. 66-72. 7.... more ... Germany WERNER BLUM, DAVID BURGHES, NIGEL GREEN and GABRIELE KAISER-MESSMER ... pp. 66-72. 7. Hearnden, A., Oxford Review of Education, 1986, 12, 187-194. 8. Glowka, D., Comparative Education, 1989, 25, 319-332. ...
1. Background RECENT (1994) examination results including mathe-matics at A-level and GCSE (Natio... more 1. Background RECENT (1994) examination results including mathe-matics at A-level and GCSE (National Curriculum Key Stage 4) have, as usual, caused concern. Trends of increasing success have continued almost un-abated, and we have the sceptics who question whether ...
THE UNIVERSITIES of Exeter (Centre for Innovation in Mathematics Teaching) and Kassel (Mathematic... more THE UNIVERSITIES of Exeter (Centre for Innovation in Mathematics Teaching) and Kassel (Mathematics Department) have been working closely together over the past few years as they have a common interest in encouraging the teaching of mathematics through its ...
International Journal of Mathematical Education in Science and Technology, 1984
A one‐factor economic growth model is introduced in this paper. Pollution as a byproduct of produ... more A one‐factor economic growth model is introduced in this paper. Pollution as a byproduct of production accompanies economic growth which in turn is required for meeting consumer demand for goods. A proportion of the output should be devoted to pollution control and consequently the capital accumulation is being affected. The relationships between production, consumption and pollution are studied with the aid of optimal control theory. The closed economic model is solved numerically by using the sequential gradient‐restoration algorithm.
International Journal of Mathematical Education in Science and Technology, 1979
ABSTRACT This article deals with the problem of modelling the population densities of cities. A h... more ABSTRACT This article deals with the problem of modelling the population densities of cities. A historical introduction is given. There are two types of models, namely the ‘quadratic gamma’ family which can be summarized by the formulaD(r) = A exp(br + cr )r where Dis the population density, rthe radial distance, A, b, cand dconstants; and the ‘equilibrium’ models which have been derived by using civic state and equilibrium equations. Details of the development and verification of the various types of models are given, and finally the models are tested and compared using the data for the city of Coventry.
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Papers by David Burghes