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“The practice of number talks is one of the most powerful vehicles I know for helping students learn to reason with numbers and make mathematically convincing arguments, for building a solid foundation for algebraic reasoning, and for teaching mathematics as a sensemaking process. If all teachers make this shift in their practice, it would represent a profound advancement in mathematics education.”
Ruth Parker, co-author of Making Number Talks Matter
As mentioned in a previous post, one of the mathematical pedagogies currently generating significant excitement is that of number talks. The buzz in maths education circles is all about developing number sense and number talks is being seen as one of the most powerful ways to enable this.
Here in Ireland, although the Professional Development Service for Teachers (PDST) has advocated the use of number talks in the PDST Mental Maths workshops and supporting manuals, and the more recent PDST Number Sense workshops, number talks is still relatively unknown. Similarly, there is very little in most of the maths text books available here, which explicitly promotes the development of specific mental maths strategies.
Not so Operation Maths. The promotion of the development of number sense is a key principle of the Operation Maths programme, as is the explicit exposure to a wide range of mental calculation strategies, most of which are also specified in the number talks approaches.
In this post, the connections between both number talks and Operations Maths will be shown, while also outlining how Operation Maths is the best programme to support the introduction and use of number talks in Irish classrooms. To read more about number talks generally, and access a whole suite of supporting resources for all classes across the school, please click here. To find out more about how Operation Maths works so well with number talks, please read on.
What does a Number Talk look like?
Number Talks Approach
Operation Maths & Number Talks
|1. The teacher presents a number sentence to the class; the students are given thinking time to mentally solve it.||The horizontal number sentences in Operation Maths can in themselves inspire or be used as the basis for a number talk. For example, similar number sentences to the ones shown below this table were used to encourage the children to use compensation to solve calculations.|
|2. The students start with one fist to their chest; they make a “thumbs-up” on their chest to show that they have found an answer. They then use the remaining time to try to think of another way/strategy which they then indicate by putting up a thumb and a finger, and so on.||While I initially used this “fist and thumbs-up” system when collecting answers, after multiple times hearing “I had the same answer as Jack/Jill”, I returned to my preferred tool of using the Operation Maths mini-whiteboards, (to maximise on participation and honesty regarding answers). It is important to insist that the MWBs are not to be used at all for working out, all of which is to happen in the heads, rather they should only be used to record the answer(s).|
|3. The teacher asks a number of children to volunteer their answers and all given answers are recorded on the board.|
|4. The teacher asks a child to “defend their answer”/”explain their strategy”.||For the children to explain clearly, they need to have the correct mathematical language so that all listeners can follow their thinking. Thus, children who have been using the Operation Maths programme are typically better able to express their thinking using the correct mathematical language and terminology that is being emphasised throughout these books.|
|5. All strategies are recorded on board by teacher, using visuals where possible to make the strategy less abstract for the other listeners.||Many of the visual strategies that are specifically recommended to be used are ones that already used extensively throughout Operation Maths eg frames, empty number lines, bar models (referred to as part/whole models), arrays and area models. Branching is another visual way to demonstrate strategies particularly when partitioning (breaking into place value parts) /or compensation is involved.|
|6. The children agree on the “real” answer.||Depending on the range of possible answers given, the children can also be asked to identify any unreasonable answer from those suggested and explain why they think so. This in turn encourages them to apply the variety of estimation strategies taught in the Operation Maths programme|
Other ways in which Operation Maths and Number Talks work so well together:
- In the junior end of the school, number talks is very much about the children developing their ability to conceptually subitise (i.e. to recognise that there is 8 counters because there is a group of 5 and a group of 3) using a variety of images, including five and ten frames. Operation Maths also recognises the value of using frames throughout the programme in Junior Infants to Second class and provides these frames as part of the pupils’ book packs in these classes, as well as having digital eManipulatives (i.e. the Sorting eManipulative) to support their use.
- In Sherry Parrish’s book Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5, she lists a whole range of specific strategies for the four operations, almost all of which are also explicitly taught or emphasized in the Operation Maths programme, including the strategy of compensation. To see an overview of the number talks strategies and where they overlap with Operation Maths click this link: Strategies in Number Talks & Operation Maths
- For those teachers using Operation Maths, they are already familiar with the structure of having an oral and mental starter at the beginning of each maths lesson. Number talks can be used interchangeable with the starters in the Operation Maths starters bank so as to add further variety to lessons.
- The strong emphasis on talk and discussion ( eg Talk Time in the pupils books, discussion and questions given in the TRBs) in Operation Maths further supports number talks as it prepares the children for situations in which they will be asked to explain their reasoning.
So there you have it, Number Talks & Operation Maths: a perfect partnership for each other!