Submission to the Commons Select Committee on Education

Computing is a rigorous, intellectually rich discipline alongside Maths, Science, or History. Like those subjects, Computing explores foundational principles and ideas, rather than training students in skills that date quickly. In an increasingly digital, knowledge-based age, Computing is fundamental both to full citizenship, and to our economic health as a nation. Yet, incredibly, Computing is virtually absent from UK schools. Instead, secondary schools in England currently teach ICT. The original concept behind ICT was to teach students how to use software to solve real-world problems. That would have been a tremendous achievement had it succeeded. However, what has actually happened in far too many schools is that ICT focuses solely upon IT literacy, and supporting teaching and learning in other curriculum contexts. ICT is not the discipline of understanding and knowledge of computers and the way they work.The creation of the EBac provides the perfect opportunity to send a clear signal to schools and pupils of the importance of Computing. Our key recommendation is that Computing (unlike ICT) should “count” towards the English Baccalaureate.On behalf of Computing at School:Dr. John WoollardProf. Simon Peyton-JonesDr. Bill Mitchel

Mathematical thinking of undergraduate students when using three types of software

The research investigates how conceptual understanding of mathematics is promoted when using three types of software: black-box (no mathematical intermediate steps shown), glass-box (intermediate steps shown) and open-box (interaction at each intermediate step). Thirty-eight students were asked to think-aloud and give detailed explanations whilst answering three types of tasks: mechanical (mostly procedural), interpretive (mostly conceptual) and constructive (mixture of conceptual and procedural). The software types had no impact on how students answered the mechanical tasks; however students using the black-box did better on the constructive tasks because of their increased explorations. Students with low maths confidence resorted to using real-life explanations when answering tasks that were application related

Birth of a Learning Law

Defense Advanced Research Projects Agency; Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657, N00014-92-J-1309

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Computer algebra techniques in object-oriented mathematical modelling.

This thesis proposes a rigorous object-oriented methodology, supported by computer algebra software, to generate and relate features in a mathematical model. Evidence shows that there is little heuristic or theoretical research into this problem from any of the three principal modelling methodologies: 'case study’, ‘scenario’ and ‘generic’. This thesis comprises two other major strands: applications of computer algebra software and the efficacy of symbolic computation in teaching and learning. Developing the principal algorithms in computer algebra has sometimes been done at the expense of ease of use. Developers have also not concentrated on integrating an algebra engine into other software. A thorough review of quantitative studies in teaching and learning mathematics highlights a serious difficulty in measuring the effect of using computer algebra. This arises because of the disparate nature of learning with and without a computer. This research tackles relationship formulation by casting the problem domain into object-oriented terms and building an appropriate class hierarchy. This capitalises on the fact that specific problems are instances of generic problems involving prototype physical objects. The computer algebra facilitates calculus operations and algebraic manipulation. In conjunction, I develop an object-oriented design methodology applicable to small-scale mathematical modelling. An object model modifies the generic modelling cycle. This allows relationships between features in the mathematical model to be generated automatically. The software is validated by quantifying the benefits of using the object-oriented techniques, and the results are statistically significant. The principal problem domain considered is Newtonian particle mechanics. Although the Newtonian axioms form a firm basis for a mathematical description of interactions between physical objects, applying them within a particular modelling context can cause problems. The goal is to produce an equation of motion. Applications to other contexts are also demonstrated. This research is significant because it formalises feature and equation-generation in a novel way. A new modelling methodology ensures that this crucial stage in the modelling cycle is given priority and automated

GRAPH ISOMORPHISMS AND MATRIX SIMILARITY: SWITCHING BETWEEN REPRESENTATIONS

A proof whether two graphs (possibly oriented graphs or multigraphs, etc.) are isomorphic or not can be derived by various methods. Some of them are reasonable for small numbers of vertices and/or edges, but not for larger numbers. Switching from iconic representation to a matrix representation transforms the problem of Graph Theory into a problem in Linear Algebra. The support provided by a Computer Algebra System is analyzed, in particular with regard to the building of new mathematical knowledge through a transition from graphical to algebraic representation. Moreover two important issues are discussed: a. the need for more than one representation; b. the direction of the switch between representations, which is non standard, from graphical to algebraic

Innovative pedagogical practices in the craft of Computing

Computer programming, the art of actually instructing a computer to do what one wants, is fundamentally a practical skill. How does one teach this practical skill in a university setting, to students who may not be initially motivated to acquire it, and who may have a variety of past experience, or none at all? Furthermore, how does one do it in a resource-efficient way to large classes? Students are largely motivated by assessment: what is the best way to assess this skill? How does this skill relate to more abstract concepts like “computational thinking”? In this piece NTFs from very different universities explain their solutions