Interpreting algorithmics in the Victorian Curriculum

04 AUGUST 2016
David Greenwood, lead author of the highly respected Essential Mathematics resources for Years 7-10, A discusses the introduction of algorithmic thinking in the Victorian maths curriculum

What is the relationship between algorithmic thinking and coding?
DG: Algorithmic thinking is less about coding or any specific technology than it is about a systematic method for solving problems. Coding is part of the story, but so is the use of flow diagrams, spreadsheets, calculators, dynamic geometry software and even pencil and paper.

What is algorithmic thinking as it applies to maths?
DG: An algorithm is a step-by-step process that is used to solve a problem, so you could say algorithmic thinking is about coming up with step-by-step processes to solve mathematical problems. Essentially it means solving problems by thinking in the way a computer operates.

Could you give us an example of a problem involving algorithmic thinking?
DG: Let’s say that a pile of 100 unlabelled and identical aluminium tins in a factory has one tin full of fruit and the rest contain peas. Each of the 99 tins of peas weigh exactly 300g and the tin of fruit weighs exactly 400g. What is the smallest number of groups of tins that must be weighed in order to guarantee the isolation of the tin of fruit?

Solution: Seven groups must be weighed. Split into two groups of 50 tins and weigh the total of one of the two groups. If the weight of that group indicates that the fruit tin is present then split again into two groups of 25 tins. Otherwise split the other group of 50. Keep going until the 400g tin is located. The number of times we need to do this is seven.

How do Essential Mathematics for the Victorian Curriculum and Essential Mathematics Gold incorporate algorithmic thinking?
DG: In two ways. First, there is a new chapter dedicated to algorithmic thinking in each book in both series. Each chapter features guided, project-based activities– one for each content strand in the Victorian mathematics curriculum. The activities utilise a range of readily-available technologies (e.g. spreadsheets), introduce a bit of coding, and do not rely on prior knowledge. Second, we have indicated questions in other chapters throughout the books that are algorithmic in nature.

Do you specify to teachers which coding language they should use, e.g. Scratch or Python?
DG: No. All material is presented without the need to focus on a particular programming language. Different language forms are used for different types of pencil and paper problems as well as problems that can be solved using computers and calculators. Examples include flowcharts, Excel functions, dynamic geometry instructions and pseudo programming code.

Will there be support material for teachers for the new algorithmic thinking content in the books?
DG: Yes. Each activity will be supported by a teacher file including tips, answers and electronic starting points for activities where appropriate.

How can algorithmic thinking be incorporated into the mathematics classroom? Is there an ideal time to teach it?
DG: The activities span all three content descriptors, so they could be completed as part of a normal unit of work as an investigation. Alternatively, if time permits teachers could use the activities to run an Algorithmic Thinking topic separately.

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