|14||5/6||3 students - stage 3
11 students - stage 4
|12 students - stage 5
2 students - stage 6
|Not specified||Place Value
The school is a decile 4 urban school with an approximate roll of 480.
The students involved (14) were a mixture of year 5 and 6. The students were identified by classroom teachers as those they felt were struggling in mathematics, either in results or motivation/attitude, or a combination of both. Most of the students had previously been involved in other maths support programmes run by the school. Reading results for the majority of these children were also below national expectations. This provided a dilemma when the students came to do the initial PAT test. It was necessary to read some of the questions for some of the students involved.
The teacher involved is an ex-numeracy facilitator who also teaches groups of extension maths students. The teacher has had extensive maths teaching experience with “struggling” students and is leading maths professional development within the school.
The focus of the programme was to improve achievement in place value and basic facts for the students involved. The initial data showed that students were generally achieving around stage four in both of these knowledge domains.
The key ideas I wanted to develop around place value learning were the links between the number (written), the language (how it is said) and the symbolic representation (how it looks and can be made).
I based a lot of the learning around the work done by P. Hughes, Auckland University and the resources he has developed to support learning.
Many of these resources are used within numeracy teaching, but the teacher has to have a clear understanding of how to use these in a systematic and logical way for children and the hierarchy of understanding required for each of the resources. For example, children can see all the popsticks in a bundle of 10 but cannot see the single dollars in a ten dollar note, so the ten dollar note is a more “sophisticated” representation of ten than the bundle of popsticks . We started with numbers that children had already encountered (teen numbers) and we represented them using a variety of place value resources and practiced the language of teen numbers being (….and ten). The exceptions (11 and 12) were explored and we went into some of the linguistic history of how these numbers got their names.
I initially thought the children would have a solid grasp of this understanding but many of them had not previously made the connection. It was a surprise to them that the link was so obvious.
Once the platform had been laid we were able to expand into “ty” numbers (…lots of ten). By using the same resources, same representations and the same language the students gained a sense of predictability (patterning) around the number system. This was to prove very valuable when they started to learn about decimal numbers. Sure, the resources changed (decipipes) but the concept of the 10 base numbering system didn’t. When they got “stuck” we could fall back to our representation/number/language ideas and make sense of it.
Remember that this group of students have been at school for four and a half to five and a half years and were at stage 4. Somewhere the connections had not been made solidly for them.
The other main idea I wanted to explore was the use of memorisation techniques in the context of basic fact learning. These were techniques put forward by research done by D. Gibbs, Massey University. I need to say here that the students did other activities to “learn” their basic facts, such as patterning, but I wanted to increase their speed of recall. The way we looked at it was like organising a filing system, but in your head , so when you were recalling times tables you could access the 5x file quickly.
We used techniques like memorising sets of pictures, letters, numbers, and symbols in ever increasing amounts. Eventually we moved onto equations (1 x 5, 2 x 5 etc). We also played memory games where you turned over two cards and, if they matched you kept the pair, if not you turned them face down again. Eventually we used equations for this as well. The children very much enjoyed these activities as they liked the challenge it posed (especially the boys). Later on we used flashcards as a means of speeding up the recall.
Key pieces of advice
Be explicit (overt) with your teaching. Don’t ever assume that the connection between things is so obvious that children will have made it themselves. This is something that has really bugged me during the project. How many times have I wrongly made the assumption that the connection has been made? I don’t do that any more. This is especially true for teaching place value. The connection between the number, the language and the representation is absolutely crucial for students.
This has to be firmly in place with the teen numbers before you move on. It makes the teaching of place value with larger numbers and with decimals so much easier. It also needs to be said here that the consistency of teaching this across your school is also vital. The appropriate resources and a sound understanding of place value teaching will help your students achieve. I would thoroughly recommend the work done by Hughes, Auckland University, as a basis for this.
Have a specialist run your programmes for underachieving students. The people running these programmes need to be acutely aware of the need to be explicit with children. They also have to have the content knowledge and pedagogical knowledge to be able to support students' progress, especially if you wish to accelerate their learning.
Consider using some of the memorisation techniques I have discussed. Make them a challenge, have the children track their progress. I found that not starting with numbers was a successful strategy. Start with pictures and symbols, words even.
Then make the link to basic facts. Talk about how the patterns of the times tables makes the filing system easy. John van der Walle has done some outstanding research on this and has some valuable resources to use. The recent additions to the NZ Maths website regarding basic facts resources were also found to be useful by the students. It helped them track their progress.
Track achievement against attendance rates at school. I had four children with worrying attendance rates. It is no surprise to see the correlation between achievement and attendance of the children. This did impact on their achievement. Consider how they could access some of the resources/lessons on line if possible. This could be done through a school wikisite or using on line resources from www.nzmaths.co.nz