How to get your Grade 1 and 2 students to think like mathematicians

How to get your Grade 1 and 2 students to think like mathematicians

A team from Monash Education have been working with teachers to trial the effectiveness of teaching with challenging maths tasks in the early years of primary school.

Monash’s Dr Sharyn Livy outlines what this approach looks like in the classroom.

In 2018, we worked with more than 100 teachers and 22 Victorian primary schools to trial mathematical lessons based on ten sequences of challenging tasks.

The tasks are connected, cumulative and challenging and are presented as a sequence of learning. Each task builds on the learning of the previous one.

In this approach – which builds on the research of Emeritus Professor Sullivan – teachers stand back and let their students work out the answers for themselves, providing support at key strategic times.

See this approach in practice.

Lesson structure

There are three phases in the lesson approach: launch, explore and summarise. These phases are cyclical and may occur more than once during the lesson.

  • Launch the task to your students without giving them instructions on how to solve the problem.
  • Allow students time to explore and engage with task by themselves.
  • During the summarise phase the teacher selects students to share their thinking and solutions.

Lesson structure diagram: Launch, Explore, Summarise

The teacher can also choose an enabling or extending prompt to support students of all levels:

  • Enabling prompts are designed to help students who are having difficulty with the main task. They are designed so that once the prompt is completed students can solve the initial task.
  • Extending prompts are for those who finish the main task and designed to extend student thinking by encouraging abstraction or generalisation.

Ideal characteristics of tasks

  • Tasks build on what students already know
  • Take time
  • Are engaging for students – students should be interested and see value in persisting
  • Focus on important aspects of mathematics (as identified in curriculum documents)
  • Are simply posed using a relatable narrative
  • Foster connections within mathematics and across domains
  • Can be undertaken when there is more than one correct answer and/or more than one solution pathway

Example: 12 cubes task

Here's how it might work in practice.

Teacher Mark Pietrick used the 12 cubes task at his school, a lesson about measurement and geometry. His students used cubes to look at different ways to make prisms.

The lesson was designed to assist students to develop understanding, that the same number of cubes can be used to make different prisms. The big idea was the same volume can look different.

“What I really like about this sequence is the tasks were challenging and it enabled the students to go beyond their Grade 1-2 level. It enabled them to make connections themselves, and to see themselves as mathematicians.”

The launch phase

Mark launched the task with the question: A rectangular prism is made from 12 cubes. What might the prism look like? Give some different answers.

He then allowed his students to explore different solutions and strategies on their own before they shared their thinking with other students and the teacher.

This approach of using challenging tasks engages students’ higher order thinking and is when learning is most effective.

The exploration phase

All students used their 12 blocks to make prisms, and took a photo of the various prisms they created on an iPad. They drew and labelled their answers on paper. As there was more than one solution, students repeated the process, constructing different prisms with the same volume and number of cubes.

Mark had completed the task prior to his lesson so he could anticipate how the students might respond to the task and identified prompts that would assist their learning:

  • Enabling prompt: Build a rectangular prism from 6 cubes.
  • Extending prompt: Convince me you have found all the solutions.

The summarise phase

In this phase of the lesson, Mark selected students to share, explain and justify their mathematical thinking.

These students’ ideas were chosen to support other students to develop and deepen their approaches to the task.

“I like maths because it’s easy, the answers always make sense and it’s never really hard to understand when you find out the answer.”

child's hands building with purple cubes
12 cube task: A rectangular prism is made from 12 cubes. What might the prism look like? Give some different answers.

Outcomes you can expect

Proficiency strandCurriculum outcome
Understanding Describing the relationship between different prims.
Fluency Using informal units iteratively to compare measurements.
Problem-solving Using materials to model authentic problems.
Reasoning Includes students explaining and justifying their thinking.
Generalising when students find and compare the number of solutions.

It can feel like a disaster, but give it a go

Mark has been trialling these kinds of tasks in his classroom for two years.

“If you are not used to this technique, it can feel like a bit of a disaster, especially if you haven’t done it before,” Mark said. “It can feel like you’ve lost a bit of control as you step back.”

“But, it does really work. The kids love it. They enjoy the challenge of the tasks and making those connections.

“It is a shift in pedagogy. It can feel challenging at the start. Once you go through the sequences and see what the kids do, the thinking and the language that really develops, you really do see the benefits of this type of learning and where it can take the kids with their maths.”

In March 2019 our research project received a three-year Australian Research Council linkage grant. We are delighted to partner with Catholic Education Diocese of Parramatta in NSW.

Resources

Examples of 2 lessons on Volume (pdf)

References

Sullivan, P., Bobis, J., Downton, A., Livy, S., Hughes, S., McCormick, M., & Russo, J. (under review). Ways that relentless consistency and task variation contribute to teacher and student mathematics learning.

Sullivan, P. A., Askew, M., Cheeseman, J., Clarke, D. M. Mornane, A., Roche, A., & Walker, N., (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks, Journal of Mathematics Teacher Education, 18(2), 123-140.

Sullivan, P., Borcek, C., Walker, N., & Rennie, M. (2016). Exploring a structure for mathematics lessons that initiate learning by activating cognition on challenging tasksJournal of Mathematical Behavior, 41, 159-170.