Mathematics learning: Three tiers of support
The importance of leadership
The 2008 Education Review Office report Schools’Provision for Students at Risk of Not Achieving emphasises the importance of focused senior leadership in improving outcomes for students:
Principals and senior school leaders have a central role in guiding the school’s practice for students at risk of not achieving. Most importantly they determine the rationale for the school’s provision [for the type and range of support]. Asking the questions about how best to meet the needs of this group requires informed decision-making about the organisation and resourcing that will offer the greatest leverage in improving achievement outcomes for students in the context of their school.
ERO report – Schools’ Provision for Students at Risk of Not Achieving, 2008, p. 1
All students begin school with the expectation that they will be successful learners. They bring with them many different strengths, needs and cultural backgrounds. To support students’ progress, teachers need to recognise and build on their prior learning experiences, continually affirming their identity, language, and culture.
Supported by strong senior leadership and effective teaching, students will develop the mathematical understandings, skills, language, and confidence they need for learning across the curriculum and in their everyday lives.
Ethic of care
Effective mathematics teaching is underpinned by the belief that:
- every student’s identity, language, and culture must be respected and valued
- every student has the right to effective mathematics education
- every student can become a powerful learner of mathematics.
Glenda Anthony and Margaret Walshaw (2009) describe 10 pedagogical practices that have been shown to impact positively on students’ achievement in mathematics. One of these is an ethic of care. Where such an ethic characterises all classroom interaction, students experience what Anthony and Walshaw describe as “caring classroom communities that are focused on mathematical goals that help develop [their] mathematical identities and proficiencies” (page 7).
Many teachers have noted that students who struggle with learning mathematics can quickly start to doubt their ability and come to see mathematics as “too hard” and something “I’m not any good at”. Caring classroom communities encourage students to develop self-belief based on evidence of their own learning.
… as soon as the children viewed themselves as being good at maths, and as being “mathematicians”, they seemed to want to … learn and were more willing to have a go at an answer, even if they weren’t sure if it was right. Building the environment and “climate” in which the children felt safe to take these risks was also very important from the beginning.
The classroom teacher has primary responsibility for creating this caring community of mathematical practice. When targeted intensive support is required in addition to effective classroom teaching, a close working relationship between the mathematics support teacher and the classroom teacher is essential to ensure that the student receives support from both teachers. The roles and the work of the two teachers must complement and inform each other.
We can view support for mathematics learning in terms of three tiers. The first and most fundamental tier is effective classroom teaching. For students who require additional support to reach the expected levels of achievement, there is the intensive and targeted support described as tier 2. The shape of the specialised support envisioned as tier 3 is currently being explored by the Ministry.
Tier 1: Effective classroom teaching
In effective classroom teaching:
- all students actively engage in well planned classroom programmes designed by observant, knowledgeable teachers
- teachers deliver appropriate, explicit mathematics instruction and provide plenty of opportunities for students to acquire and practice mathematical skills
- teachers devise meaningful tasks that enable students to connect new learning in mathematics with their prior knowledge and experience
- teachers foster students’ understanding and use of mathematical language and mathematical argumentation
- teachers carefully monitor progress and ensure that their instruction is culturally responsive to the learning strengths and needs of all their students.
Classroom teaching is effective when students make the expected or accelerated progress in relation to the New Zealand Curriculum and the mathematics standards. For a variety of reasons, some students will need additional support.
Tier 2: Intensive and targeted support
This tier of provision aims to accelerate learning in mathematics by effective, intensive, and targeted support that is led by the classroom teacher or by a mathematics support teacher (MST). Within this tier there are two levels of support to meet the needs of groups of students who are achieving below or well below expectations.
Tier 2, level A
An Accelerating Learning in Mathematics (ALiM) programme led by a teacher.
This involves short-term, targeted instruction for small groups of students who are just below the relevant mathematics standards, with the aim of accelerating their progress in a short period of time.
Tier 2, level B
An ALiM programme led by a mathematics support teacher (MST).
This involves targeted instruction by the MST for individual students or small groups who are achieving well below the standard and/or making limited progress. Targeted instruction is planned and co-ordinated by the MST in close communication with the classroom teacher, other specialist teachers, and family or whānau.
Both levels of programme are effective when students make accelerated progress as measured against the mathematics standards.
Tier 3: Specialist support
Effective specialist support involves:
- deliberate, intensive, longer term support (two or more terms) designed by a specialist teacher for students who have specific learning needs and who are achieving well below the standard
- learning time with the specialist teacher, who works in collaboration with the classroom teacher.
In 2012, there will be an exploratory study that will involve six specialist teachers. The study will explore the type of support for mathematics learning required by students who are making limited or no progress during their school year. These teachers will be working across schools to support teaching and learning and provide specialist support for the identified students.
Tier 1: Effective classroom teaching
What evidence do you have that mathematics teaching in your school is effective for the students?
Numeracy Professional Development Project Book 3, Getting Started (pages 3–4), outlines the dimensions of quality mathematics teaching, based on current research. The table below puts each of these dimensions alongside one or more reflective questions for teachers. A review team could use these questions to compile an evidential base for practice across the school.
In order to address each of these dimensions effectively, teachers need to have a strong foundation of pedagogical content knowledge:
It is essential that you know the mathematical content that you are teaching and understand the conceptual difficulties that your students may have in learning this mathematics. This is central to your ability to create coherent, targeted planning to assist this learning.
If the evidence is that mathematics teaching in your school is not as effective as it should be, a programme of professional learning may be the first step. A second step may be to ensure that teachers can identify students who need further support.
| Quality teaching dimension | Reflective question(s) |
|---|---|
| Inclusive classroom climate | Do we have students (or groups of students) who are not actively engaging in mathematics learning? If so, how are we addressing this issue? |
| Focused planning | How are we using assessment evidence to plan teaching – for example, to identify gaps in understanding and to sequence learning experiences? |
| Problem-centred activities | How are we ensuring that all our students are challenged by worthwhile mathematical tasks that build problem-solving confidence? |
| Responsive lessons | How do we ensure that planning is flexible – that it allows for (and expects) teachers to respond to daily feedback about what is and what is not working? |
| Connections | How do we link learning in mathematics to the interests and the wider lives of our students? How do we form alliances for learning with families and whānau? |
| High expectations | How do we convince all our students that we see in them the potential to become powerful learners of mathematics? |
| Equity | How are we ensuring that all our students are resourced to achieve and that factors such as language or cultural background do not become excuses for underachievement? |
Tier 2: Intensive and targeted support
The intensive, targeted support in tier 2 is not separate from effective classroom teaching – it is designed to complement it and to accelerate the progress of students who are not achieving as expected.
The two scenarios given below illustrate the two levels of support that are possible at tier 2.
Level A scenario: A classroom teacher-led ALiM programme
Three students within a year 4 class are having difficulty in applying their place-value knowledge to combine and partition whole numbers in problem-solving contexts.
Their teacher devises an eight-week programme of targeted support in which they receive an extra 15-minute group lesson four days a week while the rest of the class practise basic facts in pairs.
The target students work on a daily problem, modelling the calculations with place-value equipment and learning a new place-value game that they take home for practice.
Level B scenario: A mathematics support teacher-led ALiM programme
The MST, who is also the teacher in charge of mathematics, is released to run a programme of targeted support for year 7–8 students who are achieving well below the standard in applying additive strategies to decimals.
The MST works with the classroom teachers to devise a targeted programme of strategy development that is related to the syndicate’s units on measurement and science for the term.
Six students meet with the MST for 45 minutes four times per week to work together on their understanding of place value and decimals through problem-solving tasks. The MST observes the students in class, gives the teachers feedback, and suggests further ways to support the students’ understanding of decimals when they are working in small groups.
The success of tier 2 programmes is strongly influenced by the support and involvement of the school’s senior leadership and the degree of engagement with family and whānau: The support of parents and the principal … was immensely appreciated.
Both parties … often checked in with the students about their progress. I also had an open-door policy and the parents were in touch with the teacher to discuss progress over the course of the intervention. The students were encouraged to share their learning with their parents and had follow-up work that they could do at home. The principal also checked in with the students, who were very proud to talk about their learning. This level of care and genuine interest in student learning ensured that all students knew how important their learning was to us all.
Carterton School, Wairarapa
It is the expectation of our school that all children are able to use and understand mathematics. We believe that some children may benefit from specific interventions to accelerate their learning when they experience difficulty.
Alison Woollard, Principal
In 2010, Alison Woollard and her senior management team at Carterton School devised a plan to raise student achievement in mathematics by improving teaching practices across the school. The board of trustees appointed a respected teacher and facilitator as part-time co-teacher of mathematics to implement a school-wide professional learning programme, using the school’s teaching-as-inquiry coaching model. The co-teacher worked alongside classroom teachers and school leaders to develop effective differentiated practices in mathematics across the school.
A mid-year analysis of school data showed that some students were not making the expected progress. As a result, two teachers undertook further professional learning in initiatives designed to be implemented alongside everyday effective teaching practice.
Targeted and intensive support
In term 3 of 2010, Carterton School trialled two ALiM programmes.
1. Mathematics support teacher-led ALiM trial
The co-teacher worked as an MST to provide targeted in-class support for twelve year 3–8 students with weak place-value understanding who had been referred to the school’s special needs committee.
This programme is described in Carterton School’s ALiM story.
2. Classroom teacher-led ALiM trial
A classroom teacher ran a programme targeted specifically at five year 5 students in her class, and reviewed its effectiveness and feasibility.
The assessments from these two programmes showed accelerated student achievement. The feedback from students, parents, and classroom teachers was very positive.
[I learned about] Tens and ones and hundred. I didn’t know how that worked before. I thought the big numbers were just lots of zeros.
Year 4 Carterton student
Now when we buy something I can sort it out, I know it in my head
Year 4 Carterton student
The data was used to inform the school’s next steps.
Deciding on next steps
In 2011, Alison asked her teachers what would make the biggest difference to the students who were underachieving in mathematics at the school. The teachers responded with a range of suggestions, including short-term programmes by an MST for targeted groups and the employment of a teacher aide to support the classroom teacher.
The school’s mathematics committee presented these two recommendations to the board as part of their regular achievement report. The board approved funding for a part-time teacher to deliver a specific mathematics programme of three 30-minute sessions a week for each of four groups of students during one term. Mid-year data showed that this ALiM programme was very successful for 14 of the 17 students involved.
A teacher aide was employed for one term to support students working independently while their classroom teachers worked with targeted mathematics groups. So far, feedback on this from teachers has been enthusiastic:
I am really excited about what I’m seeing this [targeted] group do this term. Having my undivided attention even for 30 minutes twice a week has been so important for their learning. I am very explicit about what we are working on during these times. They get that this is valuable time.
I’m encouraged that the teacher aide support for my other students during the targeted group times has meant that they are learning to be more self-managing.
My “untargeted” groups are starting to lobby for “targeted” time. I think they sense the kind of attention these kids are getting is exciting.
Throughout these initiatives the focus for mathematics teaching in the school has been on effective classroom teaching first and foremost, with underachieving students receiving support in targeted groups as part of their regular classroom programme.
Comments by the Principal and teachers are quoted from interview transcripts.
Comments by students are quoted from the school's ALiM story.