Curriculum
Explainer: Problem Solving
Over the course of the next fortnight, you will see a Mathematics problem-solving work sample uploaded to your child's Seesaw portfolio. Whilst this is shared on Seesaw as a 'Common Assessment Task', students are actually working on similar problems every week of the school year as teachers aim to build the four key mathematical proficiencies of fluency, reasoning, problem-solving and understanding. Problems are designed to stretch the students' thinking, build the courage to take risks and develop their ability to articulate their thinking and justify their solutions. In this process, teachers are challenged to initially stand back and allow students to experience a necessary period of productive struggle - something that we refer to as the 'zone of confusion'. From there, students are provided with the necessary scaffolds to support their learning which could include an 'enabling' prompt for those having difficulty or an 'extension' prompt for those who require further challenge.
It can be tough to allow students to operate outside their comfort zone, but 'productive struggle' is essential as it stimulates brain growth and helps students develop a growth mindset. Peter Sullivan, a Mathematics consultant we have worked with at the school, says: "while it is possible for everyone to learn mathematics, it takes concentration and effort over an extended period of time to build connections between topics and understand the coherence of mathematical ideas. When solving tasks students are encouraged to persist, believe they can succeed and appreciate that learning mathematics takes effort. In order to foster this behaviour, students need to engage in challenging tasks and lessons that allow for sustained thinking, decision making, and some risk-taking by the students."
The Common Assessment Task has an associated assessment rubric, which is unpacked with students to ensure they understand that solving problems requires considerably more than just arriving at the correct answer. Whilst finding a correct answer is important, there are a number of other skills and understandings that students are required to draw on to effectively solve a problem. These are organised into the four proficiencies and include:
Understanding
- represent concepts in different ways
- describe their thinking mathematically
- interpret mathematical information
Problem-solving
- apply existing strategies to seek solutions
- verify that their answers are reasonable
Fluency
- make reasonable estimates
- calculate answers efficiently
- recall definitions and use known facts
Reasoning
- explain their thinking
- deduce and justify strategies used and conclusions reached
- prove that something is true or false
When assessing a student's work, teachers will look for evidence of achievement in these areas and provide feedback that aims to highlight areas of strength and next steps for learning. The work samples are collected and then analysed by all teachers within the year-level team to identify patterns, trends, areas of strength and areas for further development. This information is used by teachers to guide planning and future differentiated instruction.
When you see this Common Assessment Task posted with feedback from the teacher, try to follow it up with a positive and encouraging comment. These can be brief but it shows that you're interested in their learning and proud of their achievements. Seesaw is an excellent way to engage with your child's learning and allows for a greater connection between home and school to be built. Contemporary research consistently finds a strong and positive correlation between parents actively supporting their child’s learning and student achievement (Education Endowment Foundation, 2018; Barker & Harris, 2020).
Keep connecting and engaging!
Timothy Bernau | Assistant Principal