Back-to-Front Maths is a problem-based teaching resource to support schools in using inquiry learning. It contains a series of novel or unfamiliar problems that are used to introduce new topics, uncover student misconceptions, stimulate interest and experimentation and ultimately lead to building new mathematical understanding in students.
Back-to-Front Maths is a series of resources rather than a program to be followed every day. The idea is to be using problem-based teaching for approximately 3 of your 5 lessons per week, and to be using the remaining time for consolidation, drill and practice, and completing larger investigations. Mental mathematics should also be included every day, but resources for this have not been included within Back-to-Front Maths at this stage.
The journal problems from years 3-7 and the first lesson in the Thinking Journals from years 1 and 2 contain novel or unfamiliar problems. These investigations are designed to take a whole lesson, and are to form the basis of the learning for the rest of the week. The teacher introduces the problem to the class (with adjustments as necessary), and prompts students to explore the concept in pairs or threes. As students come up with ideas these are presented to the group for analysis and evaluation. Teachers address misconceptions with groups and with the whole class. Students combine the different ideas to develop new solutions and find patterns. The teacher helps students to access their prior knowledge and understanding that might be useful, and focuses on keeping students thinking. During sharing time the students and the teacher work together to generalise about the principles learned and the strategies that were useful.
Blast activities are included from years 3-7 as a way of combining explicit teaching with a problem-based approach for each specific topic within the curriculum. Each lesson uses targeted questioning to lead students through the thinking required to understand the new concept or develop a new skill. These lessons are to be completed using a combination of class and small-group discussion as led by the teacher. They do not contain practice questions for individual use and are inappropriate for “silent” or busy work.
Years 1 and 2 contain a three lesson sequence for each topic:
- Lesson one is problem-solving, in which the teacher uses a novel or unfamiliar problem to introduce a new concept, and to find student misconceptions. Sharing time concludes the lesson, and explicit teaching of the concepts either follows after or is incorporated with this time.
- Lesson two is for application and practice of the new concept and skills.
- Lesson three is for extending the new concept through unfamiliar and non-standard problems.
- The remaining two lessons in your week should include a combination of regular skill-building from other content areas, consolidation and practice time, and exploring concepts within different contexts. Suggestions for these are included in the Lesson Plan section.
Years 3-7 have a number of Journal problems (novel or unfamiliar problems) and a number of Blast activities (explicit teaching through problem-based leading) for each topic. You can find an alignment table for each grade which shows how to order the Blast activities and Journal problems to get the greatest benefit. Your week should consist of approximately 3 lessons from Back-to-Front Maths (approximately 1 journal problem per week), with the remaining two lessons including a combination of regular skill-building and consolidation tasks, and exploring concepts in different contexts.
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