Some additional thoughts for starting out teaching the times tables with year 2s onwards, prompted by a #MathsCPDChat
These are the things I think are important for mastery of the tables (most of which, I suspect our primary colleagues are doing):
1. Begin with manipulatives – physical objects to aid in seeing multiplication as repeated addition, e.g. 2 beads + 2 beads + 2 beads is equivalent to 3 lots of 2 beads. [15 mins in the first ever lesson, then 15 minutes of the same at the end of the same day. On subsequent days you can repeat the same in less time (but still come back at the end of the day. It’s an important part of the memorisation process.)]
2. Number line – progress to a number line so that they can see the repeated addition as a form of skip counting. [As before, 15 minutes at the beginning and end of the first ever day. Then repeated exposure – 5 mins at the beginning and end of the day.]
3. Skip-counting – using a big number line on the board, the teacher should lead lots of skip counting, up and back the number line. Can be done with the whole class or individually on paper. [A short and sharp 3 minutes, twice a day.]
Rolling numbers is a great way to support the skip-counting. Have I shown you this?
As you can see, with 1 to 3 above, I would adopt an over-arching approach of little-and-often. This extends to how many facts to be learning at any one time. So when starting out with the year 2s, I would just go up to 2 x 6 and use steps 1 to 3 for a week, maybe even two. Teachers may say that is too slow – that their highest-attaining already know them or pick them very quickly. I’m sure that’s true but as we’ve learned from Shanghai, it’s important for maths culture to keep the class together.
The following is for week 2 or 3.
4. Direct instruction – explicitly teach what the times tables are (up to this point, there needn’t have been any mention of “times tables”) and introduce the multiplication symbol. Pupils copy the facts down. Teach the first half of the 2 times table. [5 mins, twice a day.]
5. Matching – pupils match the question to the answer (still just up to 2 x 6) [5 mins, twice a day.]
6. Flash cards – with a partner, pupils use flash cards (up to 2 x 6) to quiz each other. [5 mins, twice a day.]
So far, they’ve barely had to write anything – just a bit with 3, 4 and 5. This is a deliberate attempt to minimise cognitive load and pressure so that the ones who are weak writers aren’t compromised in the early days. Cognitive overload is a recurring theme of mine as it is very damaging to learners’ motivation and success.
The other thing that’s important to me is a pupil’s self-efficacy – the feeling they have that it (maths) is in their power to master. Up to this point (and beyond), I wouldn’t put the class under pressure. Pressure in terms of against-the-clock activities and pressure in terms of asking a pupil a times tables question publicly. Both of these are a quick way to limit a pupil’s self-efficacy. Before long, low self-efficacy becomes self-fulfilling and these pupils perform poorly and continue to do so. In my opinion, it’s the single biggest limiting factor that we see in secondary schools.
7. Written times tables questions – finally, after 3 or 4 weeks, it’s time for the classic activity of writing the answers to tables questions. Again, it’s just up 2 x 6 and it’s just a short amount twice a day for a week. We should also be keeping up some skip counting/rolling numbers and flash cards.
At that point it’s time to start over again and introduce the second half of the 2 times table. Some things will take less time, particularly giving all the instructions because the pupils should know the routine now.
8. Intraconnections – time for the teacher to make explicit the connections with the 2 times table. For example, 8 lots of 2 is double 4 lots of 2 which is double 2 lots of 2. Or 6 lots of 2 is one more lot than 5 lots of 2. Or 9 lots of 2 is one fewer lot than 10 lots.
And now repeat with 5s and 10s!
If you’ve read this far, thank you. The headline is to take into account how memory works by:
- Using multiple representations
- Little and often
- Primacy and recency effect (hence the beginning and end of day thing)
- Low stakes to keep the emotional stress of feeling slow and hopeless to a minimum
Caveats: They’re sketchy and my best guess – I haven’t worked closely enough with primary children. Please tear it apart in the comments.