|Year|| Initial stage
| Final stage
| Time in
||Stage 5||Not specified||Sequence and order
Initial data collection
- Attitude Survey
- Just doing the survey was a revelation.
- Due to low literacy levels we knew we would have to read the survey for the students. BUT we also found we had to interpret the questions into plain language and ensure the categories (that is, agree, disagree, ethnicity, etc) were very explicitly understood. This took a lot of time.
- The language was more suited to students with high decile school experiences.
- One student almost refused.
- Many students thought a home computer was a play-station or x-box.
- Most needed a lot of support and encouragement to persevere.
- The findings were interesting. Many liked maths but thought they were ‘dumb’ at it and they didn’t feel particularly well supported in their classes.
- Diagnostic Interview
- This showed unexpected gaps in forward and backwards number sequencing. Initially this was going to be a hot-spot focus at the beginning of lessons but it quickly became apparent that the gaps were too big. Hence we made FNWS and BNWS part of the focus.
- It confirmed gaps in place value and basic facts.
- This was a new assessment for our students.
- It needed to be read to them.
- They found it very difficult because comprehension was involved and also maths strands, which we know is a next learning focus for our school.
- We sent this to the NZCER.
Key pieces of advice for other teachers and principals who want to accelerate learning for students
How do I know what to teach or what students need and when?
- Use NumPA data to inform planning and teaching. Look for an area of need according to student response. If they demonstrate success within an identified area of need, then move onto another area of need (no need to teach when understanding is already there).
- Record learning in a modelling book. Ensure the student and teacher voice is evident.
- Work closely with the class teacher to introduce a new strategy as knowledge is consolidated in a particular area.
- Change grouping quickly according to learning needs.
- Use a hundred board and simple equipment to ascertain student knowledge of counting forward and backwards up to hundred. I discovered quickly that students were able to write numbers but unable to demonstrate their knowledge using equipment and maths language.
- Whanganui, Inner-city school
- Contributing school years 1-6
- Decile rating 2
- Number of teachers, 13
- School roll, 250+
- Gender composition, Male: 44% Female: 56%
- Ethnic composition, Maori: 55% Non-Maori: 45%
- High transiency
- High SENCO register, a disproportionate number of high needs children
- ESOL Programmes, Other ethnicities: Korean, Indian, Fijian Indian, Other Pacific Island Group, Thai, Chinese, Samoan, Vietnamese, Cook Is. Maori, Tongan and NZ Maori.
We chose year 5 students because we wanted to invest in students who would still be at the school next year.
We started off working with 6 students, but it quickly became apparent (after about six lessons) that there were three separate groups emerging within these six.
We have found that to fast track students it is important to work with groups with similar understanding. This may mean changing grouping to meet needs.
Our goal was to move the students as fast and as far as we could in the time we had:
- to improve forwards and backwards number sequencing
- to improve achievement in place value
- and to improve basic facts recall.
We changed the main focus after analysing the data from the: Diagnostic Interview; Attitude Survey and the PATs.
Summary of the programme
Learning to count forwards and backwards by ones, tens and hundreds and understanding place value.
- Students were asked to count to 10 using the 100 board.
- They were then asked to show 10, using equipment – ice block sticks.
- Students were given a different number each and they had to show it using equipment.
- We realised that the students would not get past 20. They did not have the mathematical language to describe teen numbers and the place values represented in them. We did a lot of work around teen numbers.
- The next teaching point became the function of zero as a place holder.
- It was obvious that this was all NEW learning for the students.
- Explicit teaching on teen numbers as ten and…, and using te reo language of tekau ma…
- Then we looked at interesting patterns up to 50.
- Next we did the same but backwards, and the students used equipment to show how they went from 5 bundles of 10, backwards to 49.
- See modelling book for more detail.
Reflection on bundles activity
Most students took one stick out of one bundle of 10 and said they had 49 but they had left the group of 9 as a bundle. It was evident that they were not aware of re-naming the ten as 10 ones and then taking one away.
- Formative Assessment related to above– numbers were dictated and the students wrote them on post-its. Students were also asked to say, talk about and show the number using equipment.
Reflection after teaching teens FWNS and BWNS
Students needed explicit teaching, using equipment, that adding one to 9 makes it roll over to the next place value and vice versa.
I realised that some students in this group were making quicker logical connections than others.
I also realised I had gone too fast into bigger numbers and the students could not make connections or explain them. I decided to work on numbers, 100 at a time, gradually increasing their size.
- The next step was to get students to use place values blocks and number fans to show number identification.
- They were given a thousands books and asked to qualify what happened to these bigger numbers with one more or one less.
- 10 more / 10 less was then introduced.
- Te Reo was integrated again.
Reflection on tens
I began to realise that some students were getting the concept by using equipment. Other students still needed consolidation around tens. One student even needed work still on counting in ones. I got more able students to use the thousands book.
- I used the ‘snakes’ activity to reinforce going up and down by ones and tens, using the 100 board to support them when they got stuck and making connections to a variety of equipment.
Reflection on snake activity
I gave the ‘snake’ activity as homework and when it came back I realised that quite a few students needed to fold back to the hundreds board.
Reflection on splitting the group
We made the decision to fast track the two students whom we thought would move quickly and because we felt that working with them would best fit the hypothesis outlined by the ALiM project. This decision was negotiated with our maths advisor.
After meeting with my advisor I decided to focus on and consolidate forward/backward numbers to hundred and, once students could talk about these numbers with ease, move on to 1000. I will also continue to work with place value.
Excellent teaching activities
See, say, do
This powerful teaching model is based on recognising that there are six things that students need to understand before they can be said to understand the meaning of 2 digit numbers.
Process to See, Say, Do (Example)
- Students were starting to talk about their learning using mathematical language.
- In this session I realised that the students were able to say how many tens in numbers up to 100. I needed to reinforce this with equipment for bigger numbers. The students needed to visualise the tens and be able to see and talk about, ‘ How many tens in the number?’ and make connections back to 100 or to the thousands book.
- Ten ones = one ten
- Ten tens = one hundred
- Ten hundreds = one thousand
- Working gradually with numbers up to 1000, students could see a pattern emerging and without equipment (imaging) were able to state how many tens in their number.
- However with bigger numbers they sometimes needed to rename the hundred to tens using equipment, to ascertain how many tens in their number.
- In order to maintain the knowledge acquired so far I realised the students needed to continue to do this sort of activity as a daily hot spot, with larger numbers.
- As the students got better at being able to identify bigger numbers they became confident in talking about their numbers and what the digits meant. The students were now more focused, as they felt successful, and were starting to take risks with more challenging numbers.
Reflection to date
- Both students are getting confident with large digit numbers.
- They are starting to make connections to their learning using a variety of equipment.
- This learning can further be linked to other mathematical strand areas like measurement.
- I have discovered it is important to always use materials when initially introducing a new concept and for as long as the students need it to talk about their learning.
- When students were able to give me the correct answer I discovered they could not always show me evidence of their findings. As the students used a variety of materials, their knowledge was consolidated.
- Also I found using place value houses the students quickly learned to read numbers to 1 000 000. The next step would be to consolidate using materials.
My next step would be to introduce them to basic facts, connecting back to the place value knowledge they have now acquired. For example, 2+3=5
- 2 + 3 = 5 20 + 30 = ?
- 3 + 2 = 5 30 + 20 = ?
- 5 - 3 = 2
- 5 - 2 = 3
- 3 + ? = 5 etc.
On reflection this would be an important place to liaise closely with the class teacher. The students are starting to be aware of partitioning numbers and would benefit from working with new strategies using rounding and compensating as well as place value partitioning. This would have helped them to move faster in their strategy stage.
What made the biggest difference to the student’s achievement?
Assessment for learning
- Assessment that informs what the student can do and where the gaps are, as well as daily formative practices.
- Modelling the student’s thinking to show how many different ways we can solve the same problem.
- Reflective questioning by the teacher to ascertain students thinking and understanding and next step in learning.
- Realistic high expectations and feedback through discussion.
A caring atmosphere
- Having a positive relationship with the students who feel safe to take risks and make mistakes.
- Creating a positive learning atmosphere where students feel successful and are able to talk and share their learning with others.
Building on students' thinking
- Teacher’s own mathematical knowledge is critical as is their enquiry to fast track students.
- It is important to make learning fun and interactive with materials.
- Clear boundaries and expectations for learning must be shared.
- It is important to keep the learning simple to start with and use a variety of materials and ways to consolidate learning and gradually move on to more complex ideas.
- Students must be aware that it is ok to take risks and make mistakes as learning comes from being able to prove your answer is right when asked “How do you know?"
- Visual and concrete materials should be used to consolidate learning. Materials should be available at all stages for the student, for introduction of new learning, to show their thinking, and to demonstrate their learning when appropriate.
- 1-on-1 works for some students who have low self esteem and think they are dumb in a group situation.
- Where the students lacked mathematical language, explicit think alouds are necessary. For example I would say: “My number has three digits, 563. It has 5 hundreds, 6 tens and 3 ones. There are 56 tens (50 tens + 6 tens).” This was an essential ingredient for students to start using and practising mathematical language.
- I know when I was accepted on the project I felt excited and enthusiastic to be part of this programme to fast track students making slow progress in their maths.
- I have a strong belief that I, as a teacher, need to enquire into ways of connecting to the student.
- It is also very important to involve students and talk to them about the wider world and connecting their learning to it.
- The consolidation of forward and backward number sequencing, and the knowledge gained, needs to be maintained throughout the year as students go up in stages, working with more complex problems and new strategies. This includes making connections to place value teaching and basic facts.
- Students need to be able to talk about their answer using mathematical language and knowledge.
- Use of interactive websites enhance student learning.
- It is useful to use a digital camera to record evidence of learning by the students.
- The Numeracy Advisor's support to a school was important.
- The school needs a policy and high expectations for student outcomes.
- It is important to show and feel enthusiastic about exploring and discovering different mathematical concepts and ideas.
- Using Te Reo to explain some concepts was also beneficial.
Recommendation for our school as a result of this project
- Our school needs to consider making policy: Our school is now looking at ways to fund a programme to fast track our underachieving students next year. We would however liaise more closely with the class teacher and parents, where appropriate, to achieve even greater results.
- Building FNWS and BNWS knowledge is instrumental to fast tracking students and appeared to be the FIRST important gap to fill. This knowledge then needed aligning to place value and basic facts. The student is then able to pick up a new strategy to solve more complex problems when this knowledge is consolidated.
- Teaching a new strategy before the student is ready can turn the student off mathematics.
- Our school needs to consider making policy: Students who show slow progress in mathematics or who come into the school as transients should be given a Diagnostic Interview to ascertain the gaps. In our sample, this test informed our planning to meet the students needs more than the IKANs and GLoSS.
- Our school needs to consider making policy: mandatory time allocation to maths in a classroom timetable, minimum of four hours per week.
- Our school needs to consider making policy: that materials are always used to introduce new learning, no matter what the number stage, and that teachers make materials available as needed during follow-up activities.
- We found the diagnostic tests showed unexpected gaps in forward and backwards number sequencing. Initially this was going to be a hot-spot focus at the beginning of lessons but it quickly became apparent that the gaps were too big. Hence we made FNWS and BNWS part of the focus. It also confirmed gaps in place value and basic facts domains.
We also felt that ongoing maintenance, across number knowledge and strands (and given according to ability) was essential to maintain new knowledge and to apply it throughout the year.