Back to Home - Number Sense - Principles for Number Talks - What does a Number Talk Look Like - Questions to Ask - Resources
"Number Talks" is an approach to the teaching and learning of Number Sense. Rather than relying on the rote-memorisation of isolated number facts achieved through drills of "table-facts", Number Talks aim to build confident, number fluency, where learners recognise patterns within and between numbers and understand the properties of numbers and operations. Number Talks are a "mind on" learning task that engages students in an active learning process as they search for patterns, decompose and recompose numbers and develop a flexible understanding. It is achieved through direct instruction methods and facilitative dialogue with the teacher or between groups of peers who have had experience with the number talks methodology. It becomes one of the routines of a classroom focused on mathematical reasoning.
Number talks are a valuable classroom routine for developing efficient computational strategies, making sense of math, and communicating mathematical reasoning. A number talk is structured to help students conceptually understand math without memorizing a set of rules and procedures. (Nancy Hughes)
Number talks are:
a brief daily practice where students mentally solve computation problems and talk about their strategies, as a way to dramatically transform teaching and learning in the mathematics classroom. Something wonderful happens when students learn they can make sense of mathematics in their own ways, make mathematically convincing arguments, and critique and build on the ideas of their peers. (Humphreys & Parker)
Number Talks should be a regular routine within the Mathematics Programme; a tool for building the Mathematical Fluency that underpins an understanding of the "Big Ideas"
Number Sense is fundamental to success in mathematics and involves developing an understanding of number, patterns inside numbers, patterns throughout sets of numbers and the effect that operations have on numbers. It is much more than memorisation of table facts and unlike learning by memorisation develops a deep and flexible understanding that promotes mathematical confidence and is a solid foundation for reasoning and problem solving.
Number sense is important because it encourages students to think flexibly and promotes confidence with numbers. . . . The fact is, students who lack a strong number sense have trouble developing the foundation needed for even simple arithmetic, let alone more complex mathematics. A large body of research has shown that number sense develops gradually, over time, as a result of exploration of numbers, visualizing numbers in a variety of contexts, and relating to numbers in different ways. (Keith Devlin)
Research shows that students who are taught to rely on memorisation of number facts and mathematical processes do not perform as well as students who learn in an environment that emphasises number sense. Memorisation may help with less challenging questions, but is of little use as the questions become more challenging.
Students who avoid making an effort to understand mathematics concepts may succeed in some school environments; but a lack of deep, critical and creative thinking may seriously penalise these students later in life when confronted with real, non-routine problems. PISA results show that, across OECD countries, perseverant students, students with positive attitudes towards problem solving and mathematics, including high instrumental motivation to learn mathematics, interest in mathematics, high self-efficacy and self-concept, and low mathematics anxiety are less likely to use memorisation strategies. - OECD PISA Analysis - Is Memorisation a good strategy for learning mathematics?
Rote practice is fraught with danger. Left unchecked, it can reduce rich mathematical concepts to a slew of rules and procedures that feel arbitrary and confusing to students.
- Junaid Mubeen
Number sense is well supported by Number Talks as these inherently include opportunities for students to engage with the key strategies for number sense identified by Burns:
Number Talks are most effective when they are a routine part of the students mathematical thinking and learning. A Number Talk is an ideal warm-up activity before other mathematical learning. A daily number talk can take between ten and fifteen minutes and this routine engagement with mathematical thinking builds number sense and fluency.
Adapted from "Classroom-Ready Number Talks for Third, Fourth and Fifth Grade Teachers"
Wathc Jo Boaler Teaching A Dot Card NumberTalk from YouCubed.
'My Favourite No' is a strategy shared in this video by Leah Alcala. Here the students are from a Middle School class and are discussing an age appropriate algebra question. The video models many of the fundamental aspects of a Number Talk, although in a typical Number Talk the students do most of the talking and questioning. It demonstrates the learning that can occur from mistakes and has a focus on 'growth' rather than only valuing correct responses and methods. It shows the effective use of a Number Talk like strategy as a learning tool and an Assessment For Learning method as the teacher is gaining valuable information about her student's learning and is able to use this to adjust her instruction.
Questions to focus on sense making at the beginning of the problem:
Questions to redirect students to the problem while solving:
100 Questions that promote Mathematical Discourse - PDF Download
Circle Time is a pedagogical strategy developed to support student well-being, social & emotional learning, building of safe classroom environments and encouraging open discussion with respect for all members of the learning community. Circle Time strategies support Number Talks by ensuring students feel safe when offering their solutions and are therefore more likely to take risks with their thinking and share solutions even if they are not entirely confident with the methods they have chosen.
"Circle Solutions is a philosophy for healthy relationships and a pedagogy for teaching them. It is based in the principles of agency, safety, positivity, inclusion, respect and equality." (Sue Roffey)
Each Circle Time begins with a review of the fundamental principles:
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