Instructional models

Launch > Explore > Connect > Summarise

reSolve uses a four-phase instructional model for our problem-solving tasks: Launch, Explore, Connect and Summarise. We use this model as it allows time and space for students to engage in meaningful mathematical activity and to refine their understandings of powerful mathematical ideas. As the teacher, you also play a very important and active role as you implement this model.

Launch

The problem is introduced to the students by the teacher without telling them how to solve it. A ‘hook’ or entry point, such as a realistic or imagined context, is often used as a tool to launch the problem. This hook provides a way for students to think and talk about the mathematics as they engage in the Explore phase.

Explore

Through the Explore phase, students investigate the task and, as they do, they make sense of the important mathematical ideas addressed in the task. The teacher's role is to notice and provoke student thinking. You do this through your observations of what students are doing and saying, in terms of their mathematical activity. You engage in conversations with students about the mathematics, asking carefully crafted questions to assess student understanding and trying to advance them towards the lesson’s learning goal.

You do not provide students with a solution strategy, but help them to navigate the process of their own thinking.

Connect

This is the most important phase where the teacher carefully orchestrates a whole class discussion around the selected students’ strategies, which the whole class are able to see and compare. The focus of this phase is to make connections: connections between the different strategies used by students and connections to the main learning goal of the lesson.

The Connect phase often includes selecting students to share and present their solution strategies to make the mathematics visible. This involves more than a ‘show and tell’ activity of student work. The different solutions are shared and then discussed so that students can compare and highlight differences and similarities between the solution strategies. The similarities between solutions often highlight the important mathematical generalisations that can be made. The Connect phase is also an opportunity for the teacher to explicitly model formal ways of representing mathematics, to teach new mathematical ideas and address misconceptions or gaps in students’ understanding.

The Connect phase is also an important part of the Japanese lesson structure. The Connect phase is known as neriage, which means to ‘polish up’. Here, the teacher orchestrates discussion about the ideas and approaches that students used to solve the problem, to help them polish up their solutions, to learn mathematical content. The whole class discussion is regarded as the heart of the lesson, which can only happen because of the student problem solving done at the beginning.

Summarise

This follows the Connect phase, to conclude the task. In the Japanese classroom, this phase is known as matome, and is seen as an indispensable part of a successful lesson. The teacher pulls the threads of the lesson together to highlight the key ideas of the whole class discussion and summarise what students have learned during the lesson.

Discuss with your colleagues

• How is the Launch Explore Connect Summarise model different to other instructional models that you have used in your mathematics teaching?

 

References

Clarke, D. (2009). Mind your language: Speaking in and about the mathematics classroom. In MAV 2009 Mathematics of Prime Importance: Proceedings of the Mathematical Association of Victoria 46th Annual Conference (pp. 34-49). Melbourne, Australia: The Mathematical Association of Victoria.

Mok, I. A. C. (2015). Research on mathematics classroom practice: An international perspective. In Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 589-605). Springer International Publishing.

Statistical investigation

Statistical investigations give us a process for learning about the world. Children are naturally curious. Statistical investigations, beginning informally, can encourage children to notice and wonder about the world, then guide students to understand that they can follow their observations and curiosity with a way to find out.

A common process for statistical investigations, used both by students and professional statisticians, is the PPDAC cycle. PPDAC stands for: Problem, Plan, Data, Analysis and Conclusion. It emphasises that an investigation is initiated by trying to solve a problem.

• Problem: Define the question to be answered through the investigation.
• Plan: Decide what data is needed to answer the question and how the data will be collected.
• Data: Collect, organise, and clean the data.
• Analysis: Represent the data, look for patterns, and make hypotheses.
• Conclusion: Interpret the results, draw conclusions, and communicate findings.