|Time in programme||Predominant
|7||3||3 students - stage 2
4 students - stage 3
|1 student - stage 3
6 students - stage 4
|2x30mins weekly +
30 sessions total
We are a decile 4 school with 109 students. Our ethnic background is 60% Maori, 30% NZ European, and 10% Pacific Island and other.
When choosing this targeted group, we made the decision that it would be the students who were “at risk” rather than the “cause for concern” group. While I believe the “cause for concern” group can be picked up by their classroom teachers, the “at risk” group will not catch up unless some intensive teaching is done. The largest group in this area was a group of seven year 3 students.
Teaching is my second life. Prior to that, I was in insurance, and we had lots of conferences and courses that we attended. The conference that was held in Auckland for Accelerated Learning in Mathematics to launch the beginning of the project, was one of the best conferences I’ve ever been to. It gave me an opportunity to really question what I was doing as a teacher, to ask how I was going to carry out this project, it showed me new ways of doing things, and provided me with a chance to meet people who were in the same situation as I was. I saw that it was a challenging project, but I was reassured that the support was there in the form Wellington Accent Learning co-ordinators. I believe that through this project my shift in professional knowledge about mathematics learning has been bigger than I could ever have imagined.
My vision was that the children who were most at risk would not miss out. The students who are in the “cause for concern” category may be covered in their classroom programmes, but there were a significant number who were in the “at risk” category, and I knew that this was an opportunity for those children to catch up.
I believe I already had a good rapport with these children and their families from my year with them in 2009. However, I could not take that for granted, and I organised a fish and chip lunch for the parents and the children of the maths group. I gauged that most of the parents should be able to attend at that time as they were all at home during the day, except one mother. She was the only parent who attended, and she took time off work especially to come to our meeting. We had a thorough discussion about what her child was going to be doing, and answered any questions she had. The children were happy to have fish and chips for lunch, but were disappointed that their parents did not come.
I sent letters home requesting permission for their children to participate in the Accelerated Learning in Mathematics programme, emphasising the importance of their child being at school regularly for the programme to have maximum effect.
I caught two other parents after school for an informal chat to talk to them about the programme that their child would be participating in. In particular, I think it is important to note that one family had requested outside agency support for their children in the past, and unfortunately the parents were embarrassed and worried that their children’s learning difficulties were their fault and that somehow they would be 'found out'. They did not want their children to be labelled at all. They were most concerned that everything to do with their children was kept confidential and I reassured them it would be.
Materials and Equipment: having as much equipment as possible to suit the learning needs of the students, and having it organised and ready was essential. We created our own resources and had our own folders, packs, and books. We used felt pens in our maths books, used whiteboards and whiteboard pens, and decorated our own hundreds board, place value houses, and numeral cards. Students were excited and motivated by having their very own equipment for their use.
Ethic of care
One of my personal beliefs in teaching is that we must, as teachers, show the students that we care about their learning in order to foster a valuing and respect of themselves. At all times, the language that we used in the group was positive. It took a lot of energy in the beginning to stop the habits they had formed of criticising and pointing at someone else’s work if it was different from theirs. We discussed acceptance of others everyday.
Assessment for learning
Once I had completed a full NumPA interview, I needed to analyse carefully where the needs were. I used a colleague’s goals form to mark where they were at, where I wanted them to be, and specifically what skills the students needed to help them achieve the target. I found this a useful exercise to help me plan responsive lessons. I think I knew exactly where I had to go, but the question was, did I know how to do it?
I have always thought I was confident in teaching the Numeracy Project, and a competent teacher. However, as I have discovered doing this project, the more you know about it, the less you actually realise you know. Asking for help has been critical for me knowing where I need to take the students next, and how to do it. Our facilitator was my main support during this time.
The main partnership I needed to have was with the students. I engaged them by:
- giving them ownership of their learning by making their own materials and giving them their own kits
- asking them to have a part in naming their group
- using drama to create enthusiasm and excitement
- displaying their photos on the wall, with their new learning being explained
- using sticker charts with “big, fat, juicy stickers”.
Another major partnership was with my principal:
- It was going to cost us some money as I needed to organise further resources for my group.
- I needed an adequate space within the school to carry out the lessons.
- I was not only going to need a relief teacher, but I also needed my principal to take my class for two half hour sessions of PE per week as well.
The parents needed to be on board:
- I was hoping that, with parent support, I would be able to encourage the students to be at school every day.
- They needed to support and encourage their children with any homework and be able to give them the space at home to complete it.
- They also needed to believe that it was important.
The teacher of the students:
- The teacher of these students was a first-year PRT who I happened to be tutor teacher for. We tried to meet on a weekly basis to discuss what progress was happening with the students and why that might be. We also discussed some of the habits the students had formed that might not be advantageous to their learning (for example worrying about other students' work instead of focusing on their own).
- While I was focusing very much on the knowledge (as I felt they couldn’t progress much further without it), the classroom teacher happened to be focusing on fractions that term. We had to discuss where we would cross over (for example doubles and halves).
Other teachers in the school:
- Everyone was very accommodating. Because we are a small school, there needed to be a lot of timetable shifts, hall times changed, library times etc. to accommodate organization of a reliever for my class.
- We had only one chance to discuss what I was doing with this project with the whole staff. I will be meeting with them and sharing the results of this project. I will also be leading mathematics for the school in 2011.
Summary of programme
As a whole group of seven, we had two half hour lessons, and 2 x 50 minute lesson per week.
As the term progressed, it became very obvious that there were some students who were processing faster, and there seemed to be a gap within this group. Because there were three students who were much slower at processing than the other four, I changed the timetable slightly.
I used the SPRING method where the lessons were structured like this:
It did not always happen as planned as we often ran out of time. I had to go at the pace of the children.
Identification of barriers and how to overcome them
While I have made great efforts to have parents involved in their children’s learning, I don’t think that this was ever a priority for them. The best way I found to resolve this was through the children themselves. They could be motivated and excited to complete their homework independently, and we made it a time where they wanted to come to work with me in maths.
I needed to show them more patterns on the 10's frames. I used lots of examples using real life scenarios, but that seemed to distract them at times and they would get hung up on that idea. Transference of that knowledge is also difficult for them.
The children responded well to ideas like:
- “Lock and Load” (make a noise like shick, shick, lock in the larger number first, then count on)
- “Rainbow numbers”
- “Guess my Number” (said in a game-show host-type way)
- seeing patterns, for example 10's frames
- photos of themselves on the board with comments of knowledge and/or strategies they know.
I hoped that these memory techniques that I developed were novel, dramatic ways of helping the children to remember strategies, and that they were assisted by not only using oral language, but also kinaesthetic and visual activities. Other strategies didn’t seem to be working, so I wondered what might stick.
The diagnostic testing was completed in the week of the 2nd-19th of August. The period of time the students had for the whole programme was 30 sessions, in which we mostly focused on addition/subtraction, although we crossed paths with every area of the numeracy programme along the way.
Initially I could see that A’s gaps were in add/sub, place value, and basic facts. We worked very hard on place value and basic facts because we thought that she needed the knowledge before she could move on the strategy. Add/sub, mult/div and place value have moved two levels to level 4, but basic facts are quite lacking and still at stage 0-1 purely because she wasn’t familiar with the five groupings. She certainly knows groupings to make 10, and doubles to 10, and teens to 20. A is beginning to make the connections you can easily add three or more numbers by first making up pairs that add to 10.
I needed to spend more time with her on patterns and 10's frames, and making connections to patterning, for example, 5 + 6 is only 1 more than 5 + 5.
The ethic of care was hugely important for A. She responded much better in our very small group rather than the larger seven. Once the boys had had their turn, then she had a moment to shine. Unless she is encouraged, A will not offer any solutions.
B needs more time than the other children to process the question being asked of her, and then to think of the strategy in order to answer it. She requires constant repetition to consolidate learning. She found it extremely difficult to find patterns in numbers. For example, when we showed her bundles of sticks, containers of 10 beans, bags of 10 “lollies”, she could not say how many 10s were in 30 or 80. B is really only at the beginning stages of 4 in place value. She required support to answer the 8x10's in 80, and could not order the numbers in the hundreds (although she could say what the numbers were).
C made two stages of progress in add/sub, mult/div, and proportions and ratios. There was no progress made in FNWS, or basic facts. C responded well to competitive games, and worked hard in homework to learn his basic facts within 10. I found he learnt the basic facts by rote rather than finding patterns. With patterning, you could approach this by knowing 5 + 6 is one more than 5 + 5, or just learn 5 + 6 as a basic fact. I would rather he discovered the pattern by himself, but he still requires lots of modelling and visual cues.
D made shifts in every stage except proportions and ratios. In proportions and ratios, we never worked beyond numbers up to 100, so that is probably the reason why she didn’t move there, although we did write and say numbers beyond 1000. She met her goals in 3 out of the 8 focus areas of the Numeracy Project. Her biggest shift was in basic facts where she went from stage 0-1 to stage 4. She has worked hard at remembering groups within 5 and 10, doubles, and teens.
D was always able to find patterns within numbers and relationships. D was beginning to see relationships with adding large quantities of numbers, for example, when adding 5 + 6 + 7 + 3 + 4 she learned to first make pairs that add to 10 . With support from her teacher, I believe she’ll make it to beginning stage 5 by the end of the year.
E can be very articulate and could explain exactly what was happening with his thinking when using his counting on strategy. We used the term “locked and loaded”. So if you had 8 + 6, you lock and load 8 (make the sound and action), then count on 6 more. While he didn’t reach his goal of stage 5 in addition/subtraction, he did move one stage, from stage 3-4. E met his stage 5 goal in proportions and ratios (he could see the pattern of eight 10's and 23 10s as he talks his thinking aloud), and FNWS. It is important for E’s learning that he has his say, then he can move on to the next subject.
F did not make any progress on place value, add/sub., or basic facts. She struggled to identify numbers beyond 20. Interestingly, when she was asked to add numbers, she counted from one and could image the numbers in her head, but could not remember to use the lock and load strategy for counting on. F is currently being referred to SLST for learning assistance. With support, she could count all objects in the mult/div question on the interview sheet.
G has made shifts in every area except place value. It is possible that G made no shifts in place value as we really didn’t use 3 digit numbers other than when we were writing them from dictation. He reached his goal of stage 5 in FNWS, and I think this was more due to the fact that we practised and wrote numbers in the hundreds and thousands most days. G was beginning to see the connections in adding larger quantities of numbers, and with support and further focus, I think he could easily be at beginning stage 5 for add/sub by the end of the year. G was at all times enthusiastic about his mathematics. His mum told me that in the evenings he would take out his homework unprompted by her, as he wanted to learn his basic facts. She made the comment that he was as enthusiastic as when he was on Reading Recovery. G responded well to the close attention of the teacher.
Overall comment on results
I am concerned that these seven students needed more practice than most children and that it will be essential that they have lots of opportunity to experience a variety of visual patterning. It is also important to make sure that they are not moved on until they have the proper concepts, yet not held back. There must be open discussion with teachers about progress being made or concerns they have about students. These are the students who don’t make connections on their own – they need lots of support to find them.
Despite there being no or very little focus on mult/div during this programme, there was always a natural link to what we were doing in add/sub, and what they were working on in their classroom during fractions work.
What I am still wondering
Why did only 3 out of the 7 make shifts in place value? I am very aware that learning needs to be meaningful for the students, and even when I changed the question of how many $10 notes do you need to pay for $80 worth of their favourite toys, it still didn’t help them to shift. It is extremely difficult for them to transfer knowledge they have into a new situation. For example, if we had a hundreds board in front of us, and we’d been counting in 10's, and then I asked them how many 10's in 80, they may have been able to tell me “8”.
Why didn’t the shifts in basic facts happen for four of the students? What is interesting to note in the interview sheets, is that A can say her doubles to 10, and most teen facts, but when it comes to groups within 5, she really struggles. With groups within 10 she is getting there, but she struggles to remember groups to 5. I know that I didn’t spend a lot of time with them on the groups within 5, but I assumed that if they knew the groups within 10, they would know the 5's. 4 students just cannot see patterns on their own. For example, they needed to be shown the +1 and -1 patterns over and over. Even 4 + 1 was not clear.
Did I involve the students enough in their goal setting? I know that the boys are particularly competitive, but that was an issue that interfered with their learning, as well as motivating them to learn. They would call out any answer just to be the first, and loudest, even if the answer was not necessarily correct. I think now that I could have given them a more visual guide as to where they were heading.
- Partner with the teacher to see how we can get these children on track to achieve stage 5 by the end of the year.
- We have applied for SLST support for F, and she is currently second on the waiting list.
- D, E, A, and G are working hard towards meeting their stage 5 goal by the end of the year.
- We are working hard to consolidate C and B’s new learning at their current stages.
- Discuss how we, as a school, are going to target the students who are not achieving for 2011. I will use the new knowledge I have gained and seek the support of the staff.