Acceleration groups – finding the formula for success in maths

February 2016

 

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SUE TAYLOR discusses how priority learners can achieve better outcomes through focused, high-impact mathematics instruction from their own classroom teacher than from intervention programmes.   

       

Acceleration groups largeWithin every New Zealand classroom exists students who experience difficulty learning, and ultimately, achieving at the same rate as their peers. These struggling students are identified as priority students and require support to achieve National Standard expectations.

The Ministry of Education provides a range of intervention programmes to assist qualifying students to ‘catch up’, to ‘accelerate’ their learning. Schools, and students within, must meet certain criteria to qualify for such programmes. Students involved are expected to increase achievement, and are generally monitored to ascertain whether they maintain these improvements post-intervention.  When they return to learning within their regular class programme, would they suddenly learn at a higher rate and thus achieve on par with their peers? 

According to Suzy Pepper Rollins (2014), year after year the same students are enrolled in intervention programmes, and year after year, the academic gaps don’t narrow. Students need a scaffolding programme that operates regularly, in-class, and with their own classroom teacher – a teacher who ‘knows’ their ability, self-efficacy, participation rates, and learning history. Grouping priority students for the purpose of providing teaching and learning over and above regular classroom programmes can be administered by classroom teachers to accelerate the progress of individual students. This research-based, high-impact instruction will provide support to identified students and ensure equitable learning opportunities that link to equivalent achievement outcomes.

 

The mathematics context

Acceleration groups provide the opportunity for development of students’ mathematical self-efficacy, the development of positive classroom maths norms, and supportive social experiences including collaborative group practices, productive maths discourse (Walshaw & Anthony, 2008), and the promotion of relational equity.

The use of acceleration as a strategy to differentiate instruction will lead to a positive mathematics classroom with higher engagement levels and increased maths thinking, talking, explaining and reasoning by students with positive attitudes to maths (Small, 2012).

Acceleration involves extra teaching sessions, daily, of approximately 15–20 minutes. This teaching occurs over and above regular classroom teaching and can be followed up with daily homework revision of the day’s teaching or knowledge practice. Acceleration groups do not require release time. Acceleration groups do not require students being removed from their classroom environment.  

The operation of acceleration groups can work effectively in any classroom environment. Effective acceleration groups provide learning opportunities for priority students in a safe, supportive and cooperative small-group environment. Utilising good pedagogical practices through teaching specific lessons designed to jumpstart students for new learning ensures students have the prerequisite knowledge to connect new learning to, whilst at the same time, providing remediation of skill gaps that could impede new learning. 

The success of acceleration groups lies in the consistency of the extra lessons, specific, focused teaching of identified learning needs and prior knowledge, provision of follow-up homework practice activities, parental support, and student commitment to learning. The table in Appendix 2 details movement of student achievement in maths when using acceleration groups in a year 6-7-8 classroom.

The culture of acceleration groups can positively impact on students’ self-efficacy through adapted practices that enable priority students to engage in maths. Jo Boaler’s (2015) set of positive math norms develops these behaviours:

  • Everyone can learn maths to the highest levels 
  • Mistakes are valuable
  • Questions are really important
  • Maths is about sense-making
  • Maths is about connections and communicating       
  • Maths class is about learning not performing
  • Depth is more important than speed.

 

It is general practice in New Zealand schools to provide students with daily maths sessions of 45–60 minutes. The sessions are structured with teachers spending allocated time with ability-based, mixed ability, or flexible groups. Classroom teaching can be broken down to approximately three lots of 15–20-minute teaching sessions a day with each group receiving, on average, 45–60 minutes of total maths teaching per week. The little time available to students to learn maths becomes apparent when teaching time is calculated in relation to individualised student-teacher time (Appendix 1).

Evidence drawn from schoolwide data shows schools still have students not participating, not engaging, not learning, not achieving. Therefore teachers must challenge the traditional learning structures and question whether they are sufficient. To provide equitable learning, teachers must use professional noticing to discern students for whom learning is a priority and adapt their classroom programmes to ensure every student receives the opportunity and the tools to participate in, engage with, and access learning.  

 

Identifying priority students

Teacher pedagogy used to identify students requiring acceleration incorporating professional noticing requires teachers to be observant by means of attending, interpreting, and deciding (Thomas et al. 2015).Teacher attending involves noticing actions by students that adversely influence mathematical thinking or lack of prior knowledge that might prevent a student making connections to new concepts. Teacher interpreting involves making connections between student actions noticed and the mathematical development impacted. When teachers plan an effective method by which to reverse or correct the noticed actions or misunderstandings, they are deciding (Thomas et al. 2015). Deciding to include a student in an acceleration group for the purpose of meeting their individual needs reflects professional noticing and attending. 

Children learn maths by actively participating and engaging.  Fredricks et al. (2004, cited in Attard, 2014) describe three engagement factors interdependent within the individual student: behavioural engagement – active participation and involvement; emotional engagement – students’ reactions to school, including teachers and peers; and cognitive engagement – the value of working, wanting to improve own results, and seeing the teacher actions are directed to assist them.

Teachers will recognise that priority students participate and engage to a much lesser degree than their peers. Are your priority students often sitting passively in a group? Do your priority students join in mathematical discussions and collaborations voluntarily? Boaler (2010) states that talking to explain, justify and reason is critical to maths learning. When students participate, teachers are able to ascertain what students understand and do not understand (Small, 2012).

Students who are struggling to achieve at the National Standard, or are not progressing at the same rate as their peers, need the most powerful and effective instructional practices that research and pedagogy have to offer (Pepper Rollins, 2014): more teacher-time focused on developing prior knowledge so students can access and connect learning; opportunities for increased participation  rates; teaching to address misconceptions or errors in understanding; more thinking time; and practice to grow mathematical discussions. Supportive teaching through acceleration grouping is an effective pedagogical practice that gets students moving in the right direction and empowers teachers to ensure every student has access to an equitable and inclusive mathematics education. 

 

References

  • Attard, C. (2014). 'If I could pick any subject, it wouldn’t be maths’: Foundations for engagement with mathematics during middle years. Mathematics Education Research Journal, 25, 569-587.
  • Boaler, J. (2010). The Elephant in the Classroom: Helping Children Learn and Love Maths. (Rev. ed.). London: Souvenir Press Ltd.
  • Boaler, J. (2015). What’s Math Got To Do With It? (Rev. ed.). New York, NY: Penguin Group.
  • Pepper Rollins, S. (2014). Learning in the Fast Lane: 8 Ways to Put ALL Students on the Road to Academic Success. Alexandria, VA: ASCD.
  • Small, M. (2012). Good Questions. Great Ways to DIFFERENTIATE MATHEMATICS Instruction. New York, NY: Teachers College Press.
  • Thomas, J. N., Eisenhardt, S., Fisher, M. H., Schack, E. O., Tassell, J., & Yoder, M. (2015). Professional noticing: Developing responsive mathematics teaching. Teaching Children Mathematics, 21(5), 295-303.
  • Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematical classrooms. Review of Educational Research, 78(3), 516-551.

 


 

APPENDIX 1

STANDARD MATHS LESSON TIMETABLE

 

MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

11-11.20

Green Group

Orange Group

Blue Group

Pink Group

Red Group

11.20-11.40

Blue Group

Pink Group

Red Group

Green Group

Orange Group

11.40-12.00

Red Group

Green Group

Orange Group

Blue Group

Pink Group

 

Sarah is in the Green Group (5 students). She receives three 20-minute group sessions per week or 60 minutes of group maths per week (12 minutes of personalised maths teaching per week).

 

 

CLASS USING ACCELERATION GROUPS MATHS LESSON TIMETABLE

 

MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

11-11.20

Green Group

Orange Group

Blue Group

Pink Group

Red Group

11.20-11.40

Blue Group

Pink Group

Red Group

Green Group

Orange Group

11.40-12.00

Red Group

Green Group

Orange Group

Blue Group

Pink Group

 

9.10-9.30

Acceleration

Acceleration

Acceleration

Acceleration

Acceleration

 

If Sarah is a priority student, she is in an acceleration group (6 students) and receives an extra five 20-minute sessions per week or 20min/wk of personalised instruction. For her regular maths, Sarah is also in the Green Group (5 students); she receives three 20-minute sessions per week of regular group maths or 12 minutes per child of personalised maths teaching per week. Total maths instruction: 160 minutes per week of group instruction or 32 minutes  per week of individualised maths instruction.

 

APPENDIX 2

Student achievement data over a period of 2 terms using acceleration grouping and one term of regular classroom instruction to show maintaining of accelerated achievement rates.

TEACHING NEED AND FOCUS:  KNOWLEDGE AND UNDERSTANDING OF DECIMALS AND FRACTIONS

STUDENT

YR

EXPECTED STAGE

OTJ STAGE PRIOR TO INTERVENTION

March 2014

PERIOD OF INTERVENTION

OTJ STAGE AFTER INTERVENTION

September 2014

OTJ at end of year

 

December 2014

A

6

6

Stage 5

2 terms

Stage E7

Stage 7

B

6

6

Stage E6

2 terms

Stage E7

Stage E7

C

6

6

Stage 5

2 terms

Stage 6

Stage 6

D

6

6

Stage 5

2 terms

Stage E6

Stage E6

E

7

E7

Stage 5

3 terms

Stage 6

Stage E7

F

8

7

Stage 5

3 terms

Stage E8

Stage E8

 

Sue Taylor is Learning Centre MiLearning facilitator at Lake Rerewhakaaitu School.

Traits of an effective maths acceleration group

  •  Extra specific teaching for students below or well-below the National Standard
  • Providing extra teaching time to address students’ misconceptions or errors
  • Development of productive mathematical discourse to improve students’ mathematical vocabularies
  • Opportunities to use ‘talk moves’ in a small-group environment
  • Introduction of new learning to ‘preload’ students prior to regular maths group sessions
  • Higher behavioural, emotional and cognitive engagement levels
  • Increased active participation rate
  • More thinking time to construct understanding
  • Supportive social experiences including collaborative group practices
  • Promotion of relational equity
  • Increased chances for maths thinking, explaining,  justifying and reasoning.

 


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