The Queensland Curriculum and Assessment Authority (QCAA) has introduced Problem Solving and Modelling Tasks (PSMTs) into the maths curriculum for students from years 6 to 12, including students completing the Queensland Certificate of Education (QCE).
The move to open-ended maths assignments provides an opportunity for you to engage your students in critical thinking, creative problem-solving, experimentation, collaboration and decision-making. But many teachers (and students alike) are feeling anxious about this new style of maths assessment.
But never fear! In this article, we’ll discuss the benefits and limitations of using PSMTs, provide you with tips and strategies for successfully implementing PSMTs into your lesson plans, and explore how you can couple PSMTs with technology to enhance the learning experience.
What is a problem-solving and modelling task?
A problem-solving and modelling task (PSMT) is an open-ended assessment designed to test a student’s ability to apply mathematical problem-solving models to real-world situations. This typically involves analysing and interpreting information, and applying mathematical concepts and techniques to a real-world problem.
In completing a PSMT, students must create a multi-page written report that covers:
● How they interpreted the problem
● The procedure they developed for finding a solution to the problem
● Application of mathematical techniques
● Justifications for any decisions they made
● An evaluation of how reasonable their approach was
This shift to open-ended assignments is a move away from traditional mathematics instruction and assessment, in which there is only one “correct” approach and solution to a problem. Instead, PSMTs focus on critical thinking and problem-solving skills. What’s important is how your students approach the problem, use mathematical concepts and techniques, and justify their solutions. This type of assessment is designed to teach students how to apply mathematical concepts to situations in the real world, thus setting your students up for greater success beyond the classroom.
Formulate, solve, evaluate, communicate
The QCAA provides a problem-solving process model that all students should use when completing a PSMT. When designing a PSMT, ensure you base it around this model.
The model includes the following steps:
- Formulate: Students must design a plan to solve the problem, determine the mathematical concepts and techniques that are required, develop a mathematical model to move the problem from the “real world” to the mathematical world, and identify any assumptions and variables.
- Solve: Students must apply mathematical procedures to solve the problem, and generate and test their hypotheses.
- Evaluate: Once they have found a possible solution, students must check the output of their model, evaluate the results, and explore the strengths and limitations of the solution (refining the model if needed).
- Communicate: Students must clearly communicate their findings using mathematical and everyday language, discuss the key results and the strengths and limitations of the solution, and provide any further explanations or recommendations if needed.
What are the strengths and limitations of PSMTs?
Some of the key strengths of PSMTs include:
- They have real-world relevance. PSMTs provide students with opportunities to apply mathematical concepts and skills to real-world situations. This helps students better understand how maths is used in the real world, and sets them up for problem-solving in the future.
- They build critical thinking, problem-solving and decision-making skills. PSMTs encourage students to analyse, interpret, and make connections between different mathematical ideas and techniques. This requires critical thinking, problem-solving, and decision-making skills.
- They allow students to get creative. PSMTs often have multiple possible solutions, allowing students to get creative in their problem-solving. Students are encouraged to think outside the box and explore different strategies. In addition, students can enhance their self-confidence as they learn to tackle these challenges.
- They build communication skills. PSMTs require students to communicate their solutions. Students must present their ideas, justify their solutions, and communicate their findings clearly and concisely.
While PSMTs have many strengths as an instructional tool, there are also a few limitations that must be acknowledged:
- They can be scenario-specific. While in theory, problem-solving skills should be transferable, some assessments can be quite specific to a certain scenario, meaning that they may not be fully transferable to other situations.
- They can be time-consuming. Designing and implementing PSMTs can be time-consuming for teachers. Creating realistic scenarios and assessing students’ work may require more time than traditional maths assessments. Likewise, PSMTs can be time-consuming for students to complete.
- Assessment can be subjective: PSMTs often involve open-ended problems with multiple possible solutions, which means different assessors may interpret students’ work in different ways. This may lead to inconsistent assessment.
- They may have limited scope: PSMTs may not cover the entire maths curriculum or assess all mathematical concepts equally. Due to the focus on problem-solving and modelling, certain topics or skills may get less attention.
- They can make some students anxious: PSMTs can create anxiety or stress for some students who are less comfortable with their open-ended nature.
Best practices for problem-solving and modelling tasks
When developing PSMTs for your class, ensure that it’s structured to encourage your students to use the problem-solving model: formulate, solve, evaluate, communicate. Your PSMT should focus on a real-world scenario (bonus points if the scenario is relevant to your students’ daily lives!), and require your students to analyse data, create mathematical models, make predictions, and provide justifications for their solution.
Here are some other tips to keep in mind when creating PSMTs for your class:
● When creating a PSMT, provide a scenario that is relevant and accessible to your students – a scenario that they could realistically encounter in their everyday lives.
● Encourage class discussion. After introducing the problem, give students the opportunity to discuss the problem and brainstorm as a class or in small groups. Discussion should be focused on the problem-solving process, rather than the exact solutions.
● Encourage your students to discuss the PSMT with family, friends and fellow students. Explaining the problem to others and listening to others’ thoughts can help students develop and refine their solutions.
● When writing their reports and developing their solutions, encourage students to focus on the stages of the QCAA problem-solving flowchart: formulate, solve, evaluate, communicate.
● For younger students (years 6 to 10), guide them to develop an overall solution by splitting the assessment into multiple parts/problems for them to address. However, encourage your students to consider how all the parts relate to each other.
● Build informal problem-solving practice into your everyday instruction. Every time your students are working on a problem, ask them about their assumptions, if their solution is what they expected, and how they’d explain what they’re doing.
PSMT maths example
Here are some problem-solving and modelling task examples to inspire you in developing your own PSMTs. Remember – the more relevant your scenario is to your students’ lives, the more engaging it will be.
- Determine the optimal price of a new electric scooter to maximise profits based on the cost of manufacturing and demand at different price points.
- Design a new zoo enclosure using a fixed amount of land and other materials. Maximise the total area of the enclosure.
- Design a tour schedule for a favourite band to maximise profit without exceeding budget. Consider tour costs (e.g. accommodation, stadium fees, food, travel) against the capacity of different venues and revenue from the sale of tickets in different cities.
For more ideas, the QCAA provides assessment resources to assist and support teachers, including assessment instruments, annotated sample responses and marking guides.
PSMTs and technology
Technology can be used to provide your students with valuable tools to solve complex problems, analyse data, and create mathematical models. Here are some ways technology can be incorporated into your PSMTs:
- Research: Technology provides students with access to a wide range of online resources, which can be used to deepen their understanding of the problem and explore potential solutions.
- Data collection and analysis: Technology can provide students with access to real-world data relevant to the scenario at hand. This can help them create accurate mathematical models.
- Collaboration and communication: Enable students to collaborate and share ideas through technology. Online platforms, discussion forums, and collaborative documents can be used to work on PSMTs in groups.
- Simulation and modelling tools: Students can use simulation and modelling software, such as GeoGebra or MATLAB, to create, test and refine mathematical models.
- Visualisation and graphing: Students can use visualisation tools, such as Microsoft Excel, Looker Studio or Tableau, to visually represent data and solutions.
- Feedback: Technology can make it easier to provide your students with timely feedback. Online tools, like the ActivInspire Annotate app, can be used to track student progress and offer guidance and commentary, enabling your students to refine their solutions accordingly.
Are you exploring the use of PSMTs in your classroom? If you’d like to equip your students with cutting-edge digital tools to help them solve complex problems, we can help. Get in touch to find out more.