Planning

Overview

Unit 3 provides students with a practical introduction to algorithmics. Area of Study 1 provides students with a foundation in the practice of abstracting data. They learn a comprehensive set of data types, with a particular emphasis on graphs, and apply these to model the data in algorithmic problems. Area of Study 2 provides students with a foundation in interpreting and designing algorithms. They learn two specific algorithm design patterns and study several graph algorithms. Area of Study 3 involves the skills learnt in the previous two areas of study and applies them to solve real-world problems. Students are required to begin considering the merits and limitations of different algorithmic approaches to solving a particular problem.

It will often be most appropriate to be teaching elements from all three areas of study in this unit concurrently, rather than teaching them in sequence. It may also be appropriate to introduce students early to some of the time complexity concepts from Unit 4 Area of Study 1 when comparing the graph algorithms in Area of Study 2.

Hands-on activities, such as with pen and paper or physical manipulatives, can often best support students to develop their understanding of particular algorithms.

Area of Study 1: Data modelling with abstract data types

In this area of study, students develop the knowledge and skills required to create abstract data models for algorithmic problems. They learn a catalogue of abstract data types (ADTs), including their characteristic operations and common suitable applications. The graph data type is a significant focus, with students learning about how the weighted and directed properties of graphs can be used to model particular types of relationships.

The focus for learning the different ADTs should be on the structure of the data that the ADT models and the operations they support. Students do not need to learn how these ADTs are implemented at a low level within a computer's memory.

A significant amount of graph terminology is included in the key knowledge. The focus for students should be limited to these graph theory concepts. While there is scope for students to encounter other terms, as they may be used to define the included terms, teachers should not attempt to provide students with a broad introduction to graph theory.

The teaching of Area of Study 1 should include a variety of approaches that may include, but are not limited to: teacher-led tutorials, exercises, use of physical manipulatives, online learning and modelling of data using a high-level programming language. Throughout this area of study, teachers should expose students to a wide range of algorithmic problems drawn from a variety of contexts. A gradual release of responsibility for the selection of design elements is appropriate as students gain more experience.

The assessment task involves students responding to given stimulus material. Students create one or more designs of a data model using abstract data types to capture the salient aspects of a real-world information problem. This could be done over one or more sessions in class time.

As part of the assessment task, teachers are required to provide students with one or more real-world information problems. These must allow for the application of the ADTs studied by the students. In their entirety, the problem(s) must be of sufficient complexity to allow the students to demonstrate their skills with a range of the studied ADTs.

When developing assessment criteria or a marking scheme, teachers are recommended to use the VCAA performance descriptors forUnit 3 Outcome 1.

Area of Study 2: Algorithm design

In this area of study, students develop the knowledge and skills required to select, describe and design algorithms to solve information problems. They learn the building blocks of algorithms and several foundational algorithm design patterns. Graph algorithms are a particular focus and teachers may wish to introduce some of these early on when students are learning the graph data type.

Students are required to learn the induction and contradiction methods of proof for demonstrating the correctness of algorithms but are only expected to be able to apply these to unfamiliar problems when they are simple iterative or recursive algorithms. Students should take away an understanding that it is possible to know for certain that an algorithm will produce a correct result.

Students should be given experience implementing algorithms in a programming language. To prepare students for implementing more complex algorithms, teachers should provide students with opportunities to implement simple functions and simple iterative algorithms. Having students act out an algorithm on paper beforehand can assist students when implementing more complex algorithms. Implementation can be done using either a visual or block-based programming environment, such as Edgy or a general-purpose or text-based programming language, such as Python.

The teaching of Area of Study 2 should include a variety of approaches such as: teacher-led tutorials, exercises, online learning, manually executing algorithms, implementing algorithms and the interpretation of solutions.

Algorithmic thinking or informatics competitions will often have stimulus material that is suitable for developing students’ skills at designing, executing and communicating algorithms.

The assessment task involves students responding to given stimulus material. Students create one or more designs of algorithms that apply algorithm design patterns or select appropriate graph algorithms to solve information problems. Students will also need to implement an algorithm, which could be combined with the design task. This could be done over one or more sessions of class time.

As part of the assessment task, teachers are required to provide students with one or more real-world information problems. These must allow for the application of the algorithm design patterns or graph algorithms studied by the students. In their entirety, the problem(s) must be of sufficient complexity to allow the students to demonstrate their skills with a range of the studied algorithm design techniques.

When developing assessment criteria or a marking scheme, teachers are recommended to use the VCAA performance descriptors forUnit 3 Outcome 2.

Area of Study 3: Applied algorithms

In this area of study, students design complete solutions to real-world problems. The focus for this area of study is on students developing their analysis skills for the selection of appropriate data model designs that will support the application of relevant algorithm designs. It is important that teachers provide suitable time for students to complete Part 1 of the SAT.

It is recommended that students commence the Unit 3 Outcome 3 component of the SAT by early to mid-Term 2. By this time, students should have gained experience with selecting appropriate data structures to model algorithmic problems, designing algorithms to solve such problems and communicating these. It is recommended that students should have completed both the Unit 3 Outcome 1 and Outcome 2 School-assessed Coursework tasks and received feedback on them before commencing the School-assessed Task.

The teaching of Area of Study 3 may include a variety of approaches that may include designing solutions to a range of algorithmic problems, including network and planning problems, comparing the merits of different algorithmic approaches to a problem and finding solutions to specific instances of such problems.

Teachers are to assess Unit 3 Outcome 3 using the VCE Algorithmics (HESS) Administrative information for School-based Assessment.

Overview

Unit 4 introduces students to key theoretical principles. Area of Study 1 provides students with a foundation in the analysis of algorithms. They learn the skills required to understand the running time of algorithms and then learn a mathematical framework for classifying problems based on how long they take to solve. Area of Study 2 enables students to further improve their understanding of algorithm design, building on the knowledge and skills that were developed in Unit 3 Area of Study 2. As well as learning new algorithms design patterns, students also learn methods for approximating solutions to problems. Area of Study 3 enables students to explore the limits and potential of computer science. They learn the historical motivation for the development of computer science as its own discipline and key early theoretical findings. They also explore the idea of artificial intelligence and the ethics of modern data-driven algorithms used in machine learning.

Area of Study 1: Formal algorithm analysis

In this area of study, students develop their knowledge and skills at analysing the running time of algorithms and identifying when a problem may be infeasible to solve for large inputs. This area of study requires students to have an understanding of linear and non-linear relations, exponents and logarithms, sequences and developing formulas to describe relationships between variables. Students develop an understanding of recurrence relations in this area of study. Students are expected to learn reasonably rigorous definitions for the P, NP, NP-Hard and NP-Complete complexity classes. Teachers should ensure that students are exposed to real-world examples of problems in NP-Hard that are feasible in practice and problems in P with limits on what can be feasibly solved in practice.

It is important that teachers provide suitable time for students to complete the Unit 4 Outcome 1 component of the School-assessed Task. It is recommended that students complete the components of the School-assessed Task by the third week of Term 3. By this time, students should have learnt the algorithm analysis content from this area of study.

The teaching of this area of study may include a variety of approaches: the time complexity analysis of algorithms using step counting, inspection, the application of the Master Theorem or measuring the execution time of implemented algorithms, discussion of common features of algorithms with particular time complexities, and discussion of the consequences of exponential growth in running times.

Teachers are to assess Unit 4 Outcome 1 referring to the VCE Algorithmics (HESS) Administrative information for School-based Assessment.

Teachers should take steps to ensure that students who have significant errors in the design they produce for the School-assessed Task in Unit 3 Outcome 3 are not prevented from engaging in the remaining parts of the School-assessed Task. If the design of the data model and algorithm combination to solve a real-world / applied problem in Unit 3 Outcome 3 is incomplete or contains significant errors, students have the opportunity to make adjustments to their design. It cannot be reassessed. Teachers can provide feedback on the quality of the design but the adjustments must be initiated by the student and not directed by the teacher. While such adjustment does not change the student’s assessment, it prevents negative consequential effects for the subsequent parts of the School-assessed Task.

Area of Study 2: Advanced algorithm design

In this area of study, students build on the concepts learnt in Unit 3 and develop an understanding of more sophisticated algorithm design strategies. In Area of Study 1, students learn that some algorithms may be infeasible to use to solve for large inputs. This motivates the learning in this area of study. The divide and conquer and dynamic programming algorithm design patterns allow students to develop polynomial time algorithms for problems that are infeasible to be solved using the brute-force search and greedy methods learnt in Unit 3. Students also learn approaches for writing algorithms that produce approximate solutions for problems that cannot be exactly solved in feasible time.

It is important that teachers provide suitable time for students to complete the Unit 4 Outcome 2 component of the School-assessed Task. It is recommended that students complete the School-assessed Task in the middle of Term 3. By this time, students should have developed the skills required to improve the design that they developed in Unit 3.

It may be appropriate to teach some elements of Area of Study 1 and Area of Study 2 concurrently, instead of sequentially. The divide and conquer algorithms studied in this area of study are suitable stimulus material for students when learning time complexity analysis via recurrence relations.

The teaching of this area of study may include a variety of approaches: worked examples, role-plays, paper-based exercises, and programming exercises. Algorithmic thinking or informatics competitions will often have stimulus material that is suitable for developing students’ skills at designing, executing and communicating algorithms.

Teachers are to assess Unit 4 Outcome 2 using the VCE Algorithmics (HESS) Administrative information for School-based Assessment.

If the formal time complexity analysis of the designed algorithm for the applied problem in Unit 4 Outcome 1 is incomplete or contains significant errors, students have the opportunity to make adjustments to their analysis. It cannot be reassessed. Teachers can provide feedback on the quality of the analysis but the adjustments must be initiated by the student and not directed by the teacher. While such adjustment does not change the student’s assessment, it prevents negative consequential effects for the final part of the SAT. Teachers should design tasks in such a way that there are no consequential issues for students in Outcome 2 from their Outcome 1 School-assessed Task.

Area of Study 3: Computer science: past and present

In this area of study, students develop their knowledge of key early findings in the field of computer science; they are introduced to the technical ideas that support modern data-driven computation and investigate conceptions of artificial intelligence. In earlier areas of study, students encounter the concept that problems may be relatively fast or slow to solve. In this area of study, students are introduced to the new idea that problems may be impossible to solve algorithmically for large inputs. It is important that students do not conflate undecidability and infeasibility. Teachers should ensure that students become fluent with standard replies to the Chinese Room Argument, such as the Systems reply, Robot reply, Brain Simulator reply and the Other Minds reply, and their counter-replies.

Hands-on activities, such as with pen and paper, or out-of-the-box libraries can be used to develop students' understanding of data-driven computation and the use of training data to create a predictive algorithm. Students are not expected to be able to implement support vector machines (SVM) or neural network training algorithms.

The teaching of Area of Study 3 should include a variety of approaches such as: teacher-led tutorials, exercises, online learning, research projects and debates.

The assessment task is to be at least one task selected from the following: a response to a case study or stimulus material, a written report, an annotated visual report, an oral report or structured questions. Teachers may wish to give students choice about the format of their response in the assessment task. It is important that the assessment task contains sufficient scope for students to demonstrate the knowledge and skills developed across this area of study.

When developing assessment criteria or a marking scheme, teachers are recommended to use the VCAA performance descriptors forUnit 4 Outcome 3. 

Aboriginal and Torres Strait Islander Perspectives in the VCE
On-demand video recordings, presented with the Victorian Aboriginal Education Association Inc. (VAEAI) and the Department of Education (DE) Koorie Outcomes Division, for VCE teachers and leaders as part of the Aboriginal and Torres Strait Islander Perspectives in the VCE webinar program held in 2023.

The VCE Algorithmics (HESS) study provides students with the opportunity to engage in a range of learning activities. In addition to demonstrating their understanding and mastery of the content and skills specific to the study, students may also develop employability skills through their learning activities.

The nationally agreed employability skills* are: Communication; Planning and organising; Teamwork; Problem solving; Self-management; Initiative and enterprise; Technology; and Learning.

*The employability skills are derived from the Employability Skills Framework (Employability Skills for the Future, 2002), developed by the Australian Chamber of Commerce and Industry and the Business Council of Australia, and published by the (former) Commonwealth Department of Education, Science and Training.

The unit planner below represents a mostly simultaneous approach to delivering Unit 3: Algorithmics problem-solving. It is a sample guide only and teachers are advised to consider their own contexts when implementing this unit and when developing learning activities. Consideration should be given to the student cohort and available resources. Teachers should modify this sample weekly planner according to relevant school events.

Those wishing to adopt a purely sequential approach can modify the detailed planner accordingly.

It is recommended that students complete both the SACs for Unit 3, Area of Study 1 Data modelling and abstract data types and Unit 3, Area of Study 2 Algorithm design in Term 1 and receive feedback on these SACs before commencing the Unit 3 SAT Applied algorithms in Term 2.

*SAT Submission date(s) should take into account the following:

• Internal school programs and key dates
• Sufficient time to assess and moderate student submissions
• Sufficient time to enter SAT criteria scores into VASS
• VASS submission dates.

The unit planner below represents a mostly simultaneous approach to delivering Unit 4: Principles of algorithmics. It is a sample guide only and teachers are advised to consider their own contexts when implementing this unit and when developing learning activities. Consideration should be given to the student cohort and available resources. Teachers should modify this sample weekly planner according to relevant school events.

Those wishing to adopt a purely sequential approach can modify the detailed planner accordingly.

Students with significant errors in their already assessed SAC for Unit 3, Area of Study 3 Applied algorithms will need to adjust their algorithmic solutions with teacher advice prior to commencing the Unit 4, Area of Study 1 Formal algorithm analysis SAC in order to be able to access all criteria to the highest level.

It is recommended that the SAT for Unit 4, Area of Study 1 Formal algorithm analysis be completed and feedback provided to students in order that they are able to access all criteria to the highest level before commencing the SAT for Unit 4, Area of Study 2 Advanced algorithm design.

*SAT Submission date(s) should take into account the following:

• Internal school programs and key dates
• Sufficient time to assess and moderate student submissions
• Sufficient time to enter SAT criteria scores into VASS
• VASS submission dates.