In the final blog of Ben Harding’s series, he describes how the teacher can bring a whole group of students to become fluent in ‘2-digit add 2-digit’ addition problems at once. He also describes how teachers can ‘smooth’ the edges and ‘plug gaps’ in the process.
This blog follows on immediately from; ‘Using Cognitive Load Theory to Crack Addition!’ Parts 1 & 2.
We pick up from children learning to add two 2-digit numbers together for the very first time in their life, and in the previous blog (Part 2) we looked at using Cognitive Load Theory (CLT) to ensure that the child’s Working Memory (WM) is prepared for this moment. Here is a step by step guide to what this episode of explicit teaching looks like:
1. At the start of the lesson the teacher will quickly revisit the exact pre-requisite skills that we have already secured fluently but are about to use. In this ‘2-digit add 2-digit’ example, this will particularly include a fast-forward version of the journey we have taken to get here, i.e. the six reduced addition facts, and then a quick recap of their application to the context of ‘tens’;
2. (I Do) The teacher then models the whole process with a worked example, using ‘out loud thinking’. This ‘out loud thinking’ includes modelling the ‘answers’ to the questions the teacher is about to ask to check understanding; for example, the teacher might say ‘I know 20 + 40 is 60 because I know 2 + 4 = 6 as a fact, and I’ve swapped ones for tens’.
3. Next the teacher clarifies the exact process for this new skill. I call these the ‘Remember To…’ statements (for a slightly more detailed unpacking of these then see my future blog: ‘Remember To… recall the heart of explicit instruction’) Again, the teacher goes through the whole process of the skill, but this time with the RT statements to navigate them.
4. (We Do) The next step is to involve the students by bolting on each RT part-skill one at a time. So, initially it is just the first RT statement, then 1 and 2, then 1, 2, 3, then 1, 2, 3, and 4, and finally the whole process. Each time an extra RT part-skill is bolted on to the process, the teacher checks in with the children to ensure no one is lost off and that no learning gaps are arising. This ‘checking in’ has 2 dimensions; doing and understanding. The ‘doing’ refers to the actual physical skill of drawing out the process with correct numbers in the correct places, thus revealing correct mental processing skills. This necessitates each student holding up their response on a small whiteboard (large clear digits, holding it still with 2 hands under their chin so the teacher can read it and respond if necessary). This assessment moment is akin to a ‘brain scan’ and many teachers enjoy referring to the little boards as ‘brain-scanners’! The ‘understanding’ dimension is addressed by asking occasionally ‘How do you know?’. For example, ‘How do you know 20 + 40 is 60?’. The child would explain that they have recalled as a fact that 2 + 4 = 6, and merely applied that to ‘tens’. Around 4 or 5 practice questions are given for each build up stage as a further RT statement is bolted on, until the entire process is complete and again 4 or 5 practice questions allow the teacher to check everyone has stayed on the journey.
5. (You Do) From this point onwards the teacher looks not to communicate the process, but to smoothen this process into one smooth skill as the students complete it independently several times. It is very much like learning a physical sporting skill such as a tennis serve or a golf swing etc. The part-skills are staccato at first, and the learner is consciously ‘Remembering To…’. Equally, it is like cooking a new dish, and only after repeated practice will it become one smooth process that allows it to move into a new category of ‘autopilot’ where other skills can be completed simultaneously. Initially then, this ‘smoothening off’ means that practice takes place with no further increase in challenge. Continuing to use the same nine 2-digit numbers for our ‘2-digit add 2-digit’ calculations means the germane load of the WM is entirely devoted to the smoothening process. This too should be made explicit to learners as they are encouraged to quicken their process and lean less on the RT statements, which themselves are reflecting the quicker thought process; ‘Come on children let’s go for it; 2 Qs, tens, ones, and pop them back together again!’ As learners succeed in speeding up, then eventually the RT statements disappear. After all, they were really a message to learners to actually remember rather then continuing to lean on the scaffold.
Here are some further reflections of this 5 step explicit teaching process:
• The two dimensions of ‘doing’ and ‘understanding’ are both vitally important. They support each other. The more the learner can ‘do’ the more they understand it. The more the learner understands it, the faster they can ‘do’.
• We can also see in this description how important it is from a pedagogical point of view to not have the beautiful CLT moment undone by disruptions. Many teachers do indeed face a reality of having learners in the group listening to their teacher input but whose cognitive capacity is immediately overloaded. CLT research tells us that the extraneous load is a major factor to success, and so when the teacher has to constantly break off from the essence of the germane load in order to address an extraneous issue, then the whole CLT journey to fluency quickly becomes a broken journey. Ensuringall children follow the journey of cognitive preparation (described at Part 2) means a large group of students can all hit this moment together.
• This brings me to my next point. The teacher’s job in all of this is to guide the group (each learner) from ‘a’ to ‘b’. At the start of the lesson the child has never added two 2-digit numbers together before. By the end of the lesson they are becoming fluent. As the teacher guides they respond to each individual. The teacher’s job description at this point is ‘potential learning gap spotter’. The response might well be to keep going with the process as planned because all is well, but that is still a guiding response. This brace of skills, ‘guiding and responding’ are at the heart of great teaching (see my blog The 5 Megatruths of Great Teaching?).
• If we take the two points above and combine them we also see that the teacher is playing a role of ‘system-checker’. A whole-school journey to fluency in the fundamentals of maths has been set up by the primary/elementary school. The whole-school system is everything. CLT has to work across year groups or it isn’t really working at all. In recent years, teachers’ jobs have changed from ensuring all children make expected progress, to an understanding now that children ‘off track’ need to be brought ‘on track’, i.e. the teacher takes responsibility for plugging learning gaps that aren’t of their doing. Now though, CLT encourages schools to set up whole-school systems that ‘build thinking’ in a much more profound way. And so, the new generation of teachers need to not just plug gaps but spot system faults and be part of a forensic investigation that seeks to identify, address and remedy the fault. In our example, the teacher would ask, ‘How did this child get all this way through our water-tight CLT system without being able to recall these 6 simple addition facts and then apply them to tens?’. To see a whole school primary maths journey designed with CLT underpinning every step then visit www.bigmaths.com.
• We leave this explicit teaching episode with children beginning to smoothen off the skill of ‘2-digit add 2-digit’ but it is not yet a strong and fluent schema in the LTM for the teacher to progress onwards from. To read about how this happens then visit the future blog ‘Why CLIC makes it stick!’.
• Only once the 2-digit add 2-digit schema is securely in the LTM should we start to inject in new number facts. We therefore move from just using these nine 2-digit numbers to introducing other number facts; same schema, new facts.