I recently stumbled across the concept of ‘Ambitious Mathematics Instruction’. This term was applied by David Blazar to a set of indicators drawn from the Mathematical Quality of Instruction (MQI) classroom observation tool. It is a neat rhetorical device to give a positive name to a set of practices that you want to promote. Who wouldn’t want to be ambitious in their teaching of maths?
I started thinking about what I stand for. The term ‘explicit teaching’ is technically accurate but it’s a bit like launching a new brand of milk chocolate and calling it ‘cocoa and milk confection’. It’s not going to spread the love. Think about the rocks that are thrown at explicit instruction; its about compliance, drill-and-kill, transmission. It would be hard to be so casually dismissive of something with a fluffier motherhood-and-apple-pie name. And while I’m defining it, I could throw in a few little fancies of my own that don’t strictly derive from explicit instruction. So let’s name it ‘Aspirational Mathematics Education’. This has the three-letter-acronym, ‘AME’, which sounds like ‘aim’ and therefore adds to the positive, aspirational connotations.
I think I’m on to something here.
Principles of AME
I have identified 14 principles of Aspirational Mathematics Education which I have listed below. I have added a link in brackets at the end of each statement where I am aware of research evidence to support it (some of this is a little oblique and some is repeated).
- A calm, positive and orderly classroom environment is required so that students may focus on mathematics (link)
- The classroom climate is such that students feel mistakes are permitted and represent an opportunity to learn (link)
- Students practice recall of maths facts such as number bonds (to 20) and multiplication tables (to at least 100) in the early years of schooling to the point of instant retrieval. It is an expectation that all students can achieve this (link)
- Students are explicitly taught both concepts and standard procedures (link, link)
- Conceptual understanding is expected to influence procedural understanding and vice versa. The concepts underpinning procedures are fully explained to students, as is the procedural application of concepts (link)
- Students practice standard procedures to the point of fluency which is defined as follows: Students can perform the four basic operations on whole numbers (up to five digits), fractions and decimals with accuracy and automaticity (link)
- Teaching sequences start with teacher explanations and modelling followed by a planned, gradual release of teacher guidance (link)
- Teaching sequences start with highly similar examples and practice followed by a planned, gradual move towards more varied examples and practice that eventually cut across concepts (link)
- Key concepts and procedures are revisited many times in a year (link)
- Whole-class instruction is highly interactive. A whole-class segment sees the teacher call on students at random or request whole-class responses to questions. When demonstrating new procedures, teachers call on students to demonstrate steps within that procedure that are already known (link, link)
- Individual practice forms a key part of lessons, is valued and is seen as a means to correct misconceptions before they develop. Self, peer and teacher correction are used (link)
- Students frequently complete short, low-stakes quizzes (link, link)
- Correct, appropriately worked solutions are held to be the best evidence of learning although multiple strategies and student explanations would form part of classroom discussion
- Plans and resources are owned and shared across teaching teams and are refined in the light of assessment evidence. This is the main work of departmental teams
An aspirational model
So there you go. It is worth mentioning that I feel that I have some justification for labelling this as ‘aspirational’. Firstly, look at the built-in expectations of what students will know and understand. But also note the final point; an idea that could easily sneak past given that I can offer no supporting evidence. In Aspirational Mathematics Education, we wish to continually get better at what we do. We want to take last year’s plans and resources and use them as a starting point for this year. We want to build on the past, avoiding the mistakes and furthering the successes.
We want to create a ratchet rather than a wheel.