One team of Year 6 teachers was interested in developing a Guided Inquiry for exploring positive and negative integers with their students. They wanted the inquiry to involve investigating everyday situations that use integers and to generate an authentic need for locating and representing these numbers on a number line (ACMNA125). What better way to engage students with learning about integers in Year 6, than with their inquiry, What is the best game that you can create to model positive and negative integers? If you would like to try this inquiry in your own classroom then please see the four phases of the 4D framework (Allmond, Wells & Makar, 2010) outlined below:
In all phases of the inquiry, Checkpoints can be used to share interim ideas and challenges. You can download the Authentic Problems Teachers’ Guide from the re(Solve): Maths by Inquiry website to find more information on this Guided Inquiry process.
The Year 6 teachers who designed this unit were also interested in using the information about their students’ learning, generated through the inquiry, as summative assessment information. This assessment information would contribute to their current assessment schedule. The team here at Inquiry Maths Pedagogy in Action (IMPACT) worked with the Year 6 teachers to develop possible formative and summative assessment opportunities that could complement the Guided Inquiry, What is the best game that you can create to model positive and negative integers? (Now available from the Members section of this website). Part of this required the students to apply ideas gained from playing games with integers to an unfamiliar context to demonstrate transfer to cartesian planes. If you wish to use Our Marking Guide and suggested summative assessment questions in your own classroom, then you will need to ensure you do not explore games involving locating and representing positive and negative integers on a cartesian plane, such as in Battleships, prior to the assessment.
Our Marking Guide - available from the Members section of this website
If you decide to give this inquiry a try then we hope your class enjoys finding out What is the best game that you can create to model positive and negative numbers? You can use Our Marking Guide as well as the suggestions for assessment to generate assessable information about your students. We hope you find this useful and welcome your feedback (Contact).
What mathematical problem solving could students participate in when engaged in the Guided Inquiry, Record Breaking: Are athletes getting better over time? The open-ended nature of this question lends itself to students devising multiple solution pathways as students consider the authenticity of the context. The ambiguity of the word ‘athletes’ means an answer depends upon whether students focus on women, men or children. Does getting ‘better’ mean faster, jumping higher/further, lifting more? Described in detail in the Record Breaking inquiry unit (Thinking Through Mathematics, Book 3, unit 8), adaptations for conducting the inquiry in different year levels – and alignment with the Australian Curriculum in each of these year levels – can be found below on this Research Page of the IMPACT website.
An article exploring this inquiry has recently been published in the Australian Primary Mathematics Classroom journal (Muir & Wells, 2019) and includes further illustrations of the mathematics in action in an Australian Year 5/6 classroom. These illustrations include different data displays typical of the work produced by students and exchanges made by students that include conclusions made in the Defend phase.
From the article:
Student's refined question: Are athletes getting better at jumping?
The Guided Inquiry approach provided students in Year 5/6 the opportunity to engage in authentic mathematical problem solving that required understanding of data representations, and fluency with interpretation, beyond simplistic representations. The reasoning by students (see the above example) required explanation of their analysis and evaluation of authentic data (about athletes) to justify conclusions reached in the Defend phase.
From Muir, T. & Wells, J. (2019). Are athletes getting better over time? Australian Primary Mathematics Classroom, 24(3), 15-20.