This paper focuses on a major part of a two-year intervention, ScratchMaths (SM), which seeks to exploit programming for the learning of mathematics. The SM hypothesis is that given the right design of curriculum, pedagogy and digital tools, pupils can engage with and express important mathematical ideas through computer programming. We describe the overall design of SM and as an illustration of the approach, we elaborate a more detailed description of the specific SM activities that seek to harness the programming concept of 'objects communicating with one another' for the exploration of the mathematical concept of place value through a syntonic approach to learning. We report a case study of how these activities were implemented in two primary classes. Our findings constitute a kind of existence theorem: that with carefully designed and sequenced learning activities and appropriate teacher support, this approach can allow pupils to engage with difficult mathematical ideas in new, meaningful and generalisable ways. We also point to the challenges which emerged through this process in ensuring pupils encounter these mathematical ideas.

The long‐standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from 5 years old. Algorithm is introduced early in the English computing curriculum, yet there is limited knowledge of how young pupils view this concept. This paper explores pupils' (aged 10–11) understandings of algorithm following their engagement with 1 year of ScratchMaths, a curriculum designed to develop computational and mathematical thinking skills through learning to program. A total of 181 pupils from 6 schools undertook a set of written tasks to assess their interpretations and evaluations of different algorithms that solve the same problem, with a subset of these pupils subsequently interviewed to probe their understandings in greater depth. We discuss the different approaches identified, the evaluation criteria they used, and the aspects of the concept that pupils found intuitive or challenging, such as simplification and abstraction. The paper ends with some reflections on the implications of the research, concluding with a set of recommendations for pedagogy in developing primary pupils' algorithmic thinking.

This report documents one phase of an effort to provide users, of the facility operated by the National Bureau of Standards* Computer Services Division, with reliable , well-tested , clearly-described solution algorithms for selected frequently-arising classes of special mathematical problems. The report presents algorithms for the simplex and revised simplex methods of linear programming, as well as their adaptations to quadratic programming. Set up as subroutines, the present versions of these codes use internal storage only, with resultant limitations on the size of the problems which can be treated.