Improvement in Mathematics Education:

07 Lifting Expectations

At the end of Year 1 of Hangaia Te Urupounamu Pāngarau Mō Tātou, Head Teacher Mathematics at Shirley Primary School, Kelly Sheppard, reports parents have given feedback that their children are loving mathematics at school. She explains a new way in which teachers are engaging parents and whānau with the children’s mathematics learning when they get to discuss these after their children have worked on the problems. Parents are “blown away” by the challenging level of the mathematics.

I te mutunga o te tau tuatahi o Hangaia te urupounamu pāngarau mō tātou, ko te kaiwhakaako matua o te Pāngarau i te kura tuatahi o Shirley, ko Kelly Sheppard, e kii ana i ngā kōrero urupare a ngā mātua e aroha ana a rātou mokopuna i te mate pāngarau i te kura. Ka whakamārama ia i tētahi huarahi hou e whai wāhi ai ngā kaiako ki ngā mātua me te whānau ki te ako i te pāngarau o te tamaiti, ina tae atu ki te whakawhiti kōrero mo ēnei i muri i te mahi a a rātou tama ki ngā raruraru. Ko ngā mātua ka 'peia atu' e te taumata whakahirahira o te pāngarau.

Video 07: Lifting Expectations / Te whakatipu I ngā tumanakohanga

Key Content

Teacher, Kate Walters, explains how "Maths was something streamed; something that separated them from the rest of the they are desperate to know when maths is".

E whakamarama ana te Kaiako, a Kate Walters, "Ko ngā pāngarau he mea rereke; he mea i wehehia mai i te nuinga atu o te akomanga ... inaianei e hiahia ana ki te mohio I te wa e pa ana te mahi pāngarau".

Principal Kylie Piper reflects that the inclusive pedagogy has provided a new way for the school to more quickly and effectively integrate the large numbers of children who come new to the school through the year.

Ko te Tumuaki, a, Kylie Piper e whakaatu ana kua whakaratohia e te kohinga whakauru he huarahi hou mo te kura ki te tere ake, ki te whai hua hoki ki te whakauru i te maha o ngā tamariki e haere mai ana ki te kura puta noa i te tau.

The video highlights the big shift in the teachers' expectations for next steps: "Our knowledge as mathematicians has grown immensely but we can still grow".

E whakaatu ana te ataata i te huringa nui o ngā tumanako a ngā kaiako mo ngā waahanga e whai ake nei: "Kua tipu haere to tātou mohiotanga ki te hunga pāngarau, engari kei te piki ake tonu mātou".

Staff reflect on the assessment results showing accelerated mathematics achievement for the younger children. Year 2 students have been "acing it" with problems at the Year 4 and 5 level.

Ka whakaarohia e ngā kaimahi i ngā hua aromatawai e whakaatu ana i te angitu o te paetae pāngarau ki ngā tamariki taiohi. Ko ngā Tauira I te tau tuarua, e "tau ana" ki ngā raru i te tau e wha me te rima.

Principal Kylie Piper explains: "Lids of expectation have been lifted... that will mean for a much more challenging starting level for next year's mathematics problems".

Ko te tumuaki a Kylie Piper e whakaatu ana: "Kua piki ake ngā waahanga mo te tumanako ... ko te tikanga mō te timatanga o te taumata whakaeke mo ngā raruraru pāngarau o muri mai".

Associate Professor Bobbie Hunter concludes: "We are talking about much more challenging tasks... Don't make it simple ...don't save the children, push them really hard then they will have much more opportunity to learn".

Te mutunga o te Ahorangi Tuarua a Bobbie Hunter: "Kei te korero nui atu mātou i ngā mahi wero ... Kaua e whakaiti . . . kaua e tiaki i ngā tamariki, kia kaha rawa te akiaki ia rātou ka nui ake te whai waahi ki te ako".

Find out more

Read the UNESCO Paper:
PDF Icon 'Walking the talk' matters in the use of evidence for transformative education
Alton-Lee, A. (2017, September) This paper was prepared in response to an invitation for a think piece for the UNESCO Project: Rethinking and repositioning curriculum in the 21st century: A global paradigm shift.


View the Videos: Best Evidence in Action

15 Videos: Best Evidence in Action
These videos feature the use of evidence to make a much bigger difference in mathematics education.


Read the BES Exemplar:
BES Exemplar 1 | Ngā Kete Rakura He Tauira 1: Developing communities of mathematical inquiry [PDF 3.8MB]
Accelerate achievement and counter bullying through effective mathematics teaching.
The Importance of the 'how' of equity, excellence and inclusion in education File Type & Size

Alton-Lee, A. (2016, April).
PDF IconEvidence in Action: Bringing the 'how' of equity, excellence and inclusion in education to the forefront of policy dialogue [PDF 154KB]
Statement prepared for the invited seminar 'Thinking about Teachers, Teaching and the 2030 Agenda for Sustainable Development' University of Cambridge, Education International, Open Society Foundations, and the Centre for Research and Innovation, Organisation for Economic Co-operation and Development.


Learning from Māori and Pasifika Expertise File Type & Size

Alton-Lee, A. (2015, September).
PDF IconDisciplined innovation for equity and excellence in education: Learning from Māori and Pasifika change expertise [LINK]
Invited paper for the World Educational Research Association Focal Session: Education of Diverse Students: A Multi Country Perspective. Budapest, Hungary. [By Skype]


Why mixed ability groups matter for equity and excellence File Type & Size

Anthony, G., & Hunter. (2016).
Grouping practices in New Zealand Mathematics classrooms: Where are we at and where should we be? [LINK]
New Zealand Journal of Educational Studies

Caygill, R., Singh, S., & Hanlar, V.  (2016).
PDF IconTIMSS 2014/15: Mathematics | Year 5   [Trends over 20 Years in TIMSS] [PDF 2.4MB]
Wellington: Ministry of Education.

Hanushek E., & Woessmann, L. (2006).
Does educational tracking affect performance and inequality? Differences-in-differences evidence across countries [LINK]
Economic Journal, Royal Economic Society, 116(510), pp. 63-76.

OECD (2016).
Equations and inequalities; Making mathematics accessible to all. [LINK]
PISA, OECD Publishing, Paris.

Webb, N.M. (1991).
Task-related verbal interaction and mathematics learning in small group [LINK]
Journal for Research in Mathematics Education, 22, 366-89.


In a synthesis of research, Webb (1991) found that helping other students (giving an explanation of an idea, method or solution) was positively related to achievement for the giver of help, although the student receiving the help only benefited when the help included an elaborated explanation rather than an answer. Webb found the effectiveness of group work to be related to teacher training of students to give and receive help appropriately. When students received no feedback or irrelevant feedback, that is feedback unrelated to the task, such feedback was negatively related to achievement. Webb's finding is particularly important because it shows the potential benefit to high achievers as well as low achievers, when students are effectively trained to participate in co-operative interaction.

I roto i te pāhekohekotanga o te rangahau, i mōhio a Webb (1991) ko te āwhina i ētahi atu ākonga (ko te whakamāramatanga o tētahi tīkanga, whakaaro ranei) i tino whai paanga ki te painga mo te kaituku i te āwhina, ahakoa te painga o te ākonga i te āwhina i te wā i uru mai ai te āwhina i te whakamāramatanga kua whakamāramatia nui atu i te whakautu. I kitea e Webb te whai huatanga o te mahi a te rōpū ki te whakangungu kaiako mō ngā ākonga ki te tuku, ki te āwhina i ngā āwhina. A, no te kore ngā ākonga i whai urupare, he urupare kore rānei, ko ngā urupare kaore i te hono ki te mahi, ko te urupare kaore e pa ana ki te whakatūtukitanga. He mea tino nui te rapu i a Webb hei whakaatu i te painga ki te hunga angitu me te iti o te whakatūtukitanga, ina tino whakangūngūhīa ngā akonga ki te uru atu ki te tāunekeneke ngātahi.

Effective pedagogy in mathematics

English Version:

Authors:  G. Anthony, G. & Walshaw, M. (2009)
International Academy of Education and International Bureau of Education, Paris, UNESCO.

Te Reo Version:

Authors:   Anthony, G., & Walshaw, M. (2009)
Te Wānanga Mātauranga o te Ao, Te Whare Mātauranga o te Ao, Paris, UNESCO.

It is also available in different languages, on the International Bureau of Education website.