This document, written by Steve Thornton, Executive Director of the reSolve project, frames mathematical inquiry in the context of the Australian Curriculum. Using links to evidence-back research, Thornton argues that inquiry in mathematics enables students to become involved in the process of Mathematics rather than just the product, and that this has great social and cognitive benefits. Thornton describes inquiry learning as a process where students can "ask questions, test ideas, seek meaning and explain ideas throughout their mathematics learning". This document provides the theoretical background to allow teachers to break free of the already existing templates of inquiry and to come to their own method or understanding of inquiry if they wish, so that they can implement the teaching approach more readily in their classroom. It also provides the research-based background for the reSolve project.
This Government-funded project springs from a joint venture by the Australian Association of Mathematics Teachers and the Australian Academy of Science, in response to the flat-lining of student results in Mathematics and the lack of highly effective teaching resources or methods in Mathematics in Australia. reSolve: Mathematics by Inquiry is a national program that provides Australian schools in Foundation to Year 10 with resources to help promote a spirit of inquiry in Mathematics. The website, while still a work in progress, contains inquiry units for Years 5 and up that are aligned to the Australian curriculum and have been trialled in Australian classrooms. Teachers are able to access the members section where trial resources for Year 4 and under are available. The resources are quite challenging, start with a question, require students to hypothesize and experiment and to share their findings through discussion. The focus of these units is on learning the Australian Curriculum content through exploring the answers to a challenging question.
Inquiry Maths is an excellent website created by Andrew Blair, a secondary Mathematics teacher. Blair’s site contains a myriad of resources that are helpful in planning, teaching and assessing inquiry learning in Mathematics. Of particular relevance to my primary inquiry question are the pages “An inquiry Maths lesson”, “Assessment for Inquiry” and “inquiry and curriculum”. These contain a detailed outline of the components of a mathematical inquiry and a number of different inquiry models and templates to assist in planning, which helped me to formulate my ideas about how to initiate an inquiry unit and ensure that the experience was a rich one throughout the whole process. To assist with beginning investigations, the author has included example prompts which have been tried and tested by classroom teachers, as well as advice on how to create your own prompts. The curriculum pages gives examples of how curriculum content can be mapped to support an inquiry, which is useful for building my understanding of how to make the transition from textbook to purposeful unit planning with the curriculum. The assessment page contains detailed information of how to assess throughout the inquiry unit, and the articles page contains links to posts by the author, but also to published articles and class-room based research. Andrew Blair’s website also collates tested resources from other teachers as well.
This well-written and resourced article, written by Katie Makar, supports the process of planning a cycle of inquiry through the 4Ds; Discover, Devise, Develop, Defend. This study gives a detailed explanation of the 4Ds and provide concrete examples through two extensive case studies. It also highlights the importance of repeated opportunities to engage in inquiry using the same concepts, as this gives students the opportunity to draw on their learning and apply it independently. Katie Makar is a reputable author and Associate Professor in mathematics education at the University of Queensland, and is known for her extensive work in Mathematical Inquiry.
Authentic Inquiry Maths is a longstanding blog written by Australian educator Bruce Ferrington. The blog is a valuable collection of real-life classroom activities that Bruce undertakes with students at his school. His blog entries contain detailed notes on student behaviours, questions and include many photos. The posts are all tagged, making it easy to search, and as such Authentic Inquiry Maths is a great source of inspiration for teachers planning inquiry units with Australian Curriculum content.
This article, written by Kym Fry, addresses the question of how to assess student understanding in inquiry learning Mathematics. Fry highlights the importance of regular formative assessment to inform students about their own learning, through the phrases "Where are you going?", "Where are you now?" and "How are you going to get there?". She details some methods of eliciting evidence of learning through the 4D cycle of inquiry. Fry's article is easy to read and references other well-known inquiry authors, such as Makar, Allmond et al and Dewey.
This video provides a general overview of problem-based learning in Mathematics. It is a useful starting point for anyone new to inquiry maths and helps to illustrate this type of learning as a process that begins with a question.
Primas is an international project between members of the European Union, formed with the purpose of supporting the implementation of Inquiry learning in Mathematics and Science in Primary and Secondary schools. There are some excellent teaching materials on this site that serve as examples of inquiry learning; this can be grouped by age group and subject area. The Professional Learning section of the site contains links to free, online professional development that supports teachers in implementing inquiry learning in their mathematics or science classroom. The final publication booklet available for download on the home page documents examples of inquiry learning in practice, as well as advice on how to transition from direct instruction to inquiry learning.
This article is an informative study of PBL Maths in a second-grade classroom, in the United States. Chapter 3 focusses on effective methods for differentiation. The study argues that effective differentiation must be proactive rather than reactive, which means “planning a lesson, from the outset, which addresses the needs of all learners instead of planning a "one size fits all" lesson” (p125). The document goes on to list methods such as use of small teaching groups, where students are placed into in purposefully-planned groups so the teacher can meet their common needs and are expected to collaborate and work together. Each group (and sometimes individual) is also provided varied materials based on their abilities, and pacing. While differentiation was planned, opportunities arise where differentiation can occur in a teachable moment. Trinter points out that in order to take advantage of these moments, teachers must have a strong content knowledge, teaching knowledge and student knowledge. This study helps to build understanding of differentiation as purposeful, planned and embedded in the inquiry learning experience.
Another overview of a Problem Based Learning unit from start to finish. This example shows how one teacher uses the cycle of inquiry in his Mathematics classroom, in units of work spread out over several days. It demonstrates how he assesses student understanding and how direct teaching can be integrated in an inquiry-based model when needed.