Poutama Pāngarau

Te Ara Tohu

Kua whanake ake te Poutama Pāngarau hei hanganga ara whakaako mō ngā takiwā reo Māori. He anga māihiihi tō te hōtaka nei hei whakaako i te pāngarau, ā, ka whai i ngā huatau o te Mata Ako e tohutohu atu rā i ngā peka matua o ngā akoranga tūāpapa nō ngā whenu katoa o te pāngarau. Kei reira tohutohu ai hoki i ngā hononga i waenga o aua whenu, me te mārohirohi i ngā ara hei whakarite i te hōtaka i roto i te akomanga.

Mau ana i te Poutama Pāngarau ngā huihuinga rauemi tatanga mō ngā akomanga hei tautoko i te whakaakoranga o te pāngarau, hei whai hononga hoki ki ngā rauemi pāngarau kē atu. Kua whakaritea kia toru ngā taumata matua o te hōtaka, hei tauira, huaina ai hei tūārere:

Tūārere 1 (Tau Ako 0-3): Ko ngā huatau tūāpapa o te pāngarau.
Tūārere 2 (Tau Ako 4-6): Ko te mātauranga tūāpapa, e puta ake rā i ngā mōhiotanga tōmua, hei tāpiripiri atu i ngā tikanga tuatini ake o te pāngarau.
Tūārere 3 (Tau Ako 7-8): Ko ngā huatau tuatini, he whakariterite i ngā mokopuna mō ngā tūārere ako e whai ake ana.

Hei reira e hāngai ai ngā rauemi ki te pakeke o te mokopuna, arā, ka uaua ake, kia hāngai hoki ki ngā tūārere whānakenake.

Poutama Pāngarau

Kua ahu ake te ingoa ‘Poutama Pāngarau’ i ngā ingoa me ngā tikanga nō te whakaakoranga pāngarau i te 30 tau kua pahure. I te whanaketanga tuatahi o te marautanga i te tau 1995, i hōmai a Kahu Waititi i te whakataukī:
Kei hopu tōu ringa ki te aka tāepa, engari kia mau ki te aka matua.

Nā, kei roto i te horopaki o te marautanga pāngarau, whakamāoritia ai taua whakataukī nei hei huatau mō te akoranga arotahi me te whai atu i te māramatanga hōhonu.

Anei ngā āhuatanga o te māramatanga atu:

Tohu ai te aka tāepa i te mātauranga akahu, pāpaku, i te pīroiroi, i ngā whāinga e pai ana te āhua, engari kāore i te hāngai ki ngā mātāpono matua rānei, ki te māramatanga hōhonu rānei.
Tohu ai te aka matua i ngā mātāpono tūāpapa, i te mātauranga hira pū, i ngā tikanga matua e pakari ai te ako.

Kua whakamahia nuitia hoki te huahuatau o te poutama i roto i te whakaakoranga pāngarau, ā, hei tauira ko te kaupapa rā, ko Te Poutama Tau.

Tautohu ai te kupu poutama i te hoahoa kaupae e kitea nuitia ana i ngā toi Māori hei tohu i te ahunga o te mātauranga me te tupuranga, hei tohu hoki i te pikinga ā-tūārere e āhuatia ai tētahi i runga i te mea o mua.

Arotahi ai te Poutama Pāngarau ki te kāinga (ko ngā mea me whakaako), ki te raupapa (ko te hātepe me whakaako i te kāinga), ki te pāpātanga (ko ngā pahurenga wā me whakaako te kāinga). Ko te mea nui, kua whakawhanakehia te Poutama Pāngarau kia hāngai pū ai ki te Wāhanga Ako Pāngarau nō roto i Te Marautanga o Aotearoa.

Ko ngā wāhanga ako tūāpapa e ono, huaina ai ngā Mata Ako, kua whakaritea ki te tautohutohu i ngā pūkenga tūāpapa matua me te mātauranga nō te pāngarau kura tuatahi e āhua ake ai ngā huatau o te huinga peka o te pāngarau, ā, hei mātauranga tūāpapa hoki mō te akoranga e whai atu ana i te kura tuarua.

I te Poutama Pāngarau e arotahi ana ki aua pūkenga, ki aua huatau tūāpapa, he hira pū tonu te aro atu ki te kāinga katoa e tautuhi ana te Wāhanga Ako Pāngarau o te marautanga ā-motu. Hei reira whāia ai ngā wāhanga katoa o te mātauranga pāngarau e whānui ai, e taurite ai te hōtaka whakaakoranga.

Ngā Mata Ako: He Whakamārama

E ono ngā Mata Ako:

Te Uara Tū
Te Whakarea me te Whakawehe
Ngā Tau Whakahau
Ngā Waeine me ngā Āwhata
Te Mokowā me ngā Āhua
Te Tātari Raraunga.

Tohutohu ai ngā Mata Ako i te hōtaka nei i ētahi o ngā pūkenga hihira pū me te mātauranga taketake o te pāngarau. Ehara i te mea he wāhanga noa iho o te whatu o te pāngarau aua huatau nei, engari ka whakarato hoki i te tīrewa taketake e tauhonohono ai i ngā tini wāhanga o te pāngarau. Heoi, he mea hira pū te āhukahuka ki te mea he maha ngā huatau matua e hira pū ana hoki ki te māramatanga o ngā mokopuna. Me āta whakaaro aua huatau nei e ka māherehere atu i te marautanga matarau o te pāngarau.

Te Uara Tū

Ahu atu ai te uara tū i te tūāpapa o te pūnaha tau katoa.

Mā te māramatanga atu ki te uara tū e mōhio ai ngā mokopuna ki te ritenga o ngā mati o tētahi tau e ai ki te taunga – he tikanga hira pū hei tātaitai i ngā paheko taketake, he pērā me te tāpiritanga, te tangohanga, te whakareatanga, te whakawehenga.

Tautokona atu ai hoki ngā mokopuna kia mārama atu ki ngā huatau, he pērā me ngā tau ā-ira, me ngā hautau, e āhei ai rātou ki te whakaotioti i ngā rapanga pāngarau tuatini ake.

Ki te kore ngā tikanga uara tū e mau, ka pōnē ngā mokopuna i ngā tikanga tau me te tauhonohono atu, ā, hei reira ka uaua te whai rānei i ngā pūkenga pāngarau o ngā taumata o runga, te whakahāngai rānei i te pāngarau ki ngā horopaki kikokiko.

Te Whakarea me te Whakawehe

He paheko taketake o te pāngarau te whakarea me te whakawehe, arā, he mea hihira pū hei ako mā ngā mokopuna i te mea koirā ngā kaupae whakapakari mō ngā huatau pāngarau me ngā hāngaitanga ki te ao kikokiko.

Tautoko ai te whakarea i ngā mokopuna kia mārama ki ngā huatau, he pērā me te tāpiritanga tāruarua, me te mahi āwhata, me te whakanao i ngā tau nunui. Waihoki te whakawehe e āwhina atu ana kia otioti ai ngā rapanga e mau ana te tohatoha ōrite, te whakarōpū rānei.

He mea hihira pū ngā paheko nei, ehara mō ngā tātainga taketake noa iho, engari mō ngā kaupapa tuatini ake, he pērā me ngā hautau, me ngā ōwehenga, me ngā pānga riterite, me te taurangi.

Me te mea hoki, whakamahia nuitia te whakarea me te whakawehe i ngā mahi ā-rā, he pērā me te tātaitai utu rānei, te ineine rānei i ngā āpititanga hei taka kai, te whakawehewehe rānei i te wā hei whakaoti mahi.

Ngā Tau Whakahau

Ko te tau whakahau, he tau ka taea te tuhi hei hautanga, arā, he tau whakahau ngā tau.

Hei tauira: ko te 0.25 (1⁄4), ko te 20% (¹/₅), ko te 4 (⁴/₁).

He mea hira pū te ako a ngā mokopuna i ngā tau whakahau i te mea he tūāpapa mō ngā tini huatau pāngarau matua me ngā whakamahinga atu i te ao kikokiko.

Ko ngā tau whakahau, e mau rā ngā hautau, ngā tau ā-ira, ngā ōrautanga, ka putaputa ake i ngā mahi ā-rā, i te whakariterite moni me te taka kai, ki te whakamāori raraunga me te ineine.

Tautoko ai te māramatanga ki ngā tau whakahau kia whanake ake te māramatanga o ngā pānga ā-tau, e mau rā te whakariterite, te tāpiritanga, te tangohanga, te whakawehenga, te whakareatanga me ngā momo tau rerekē.

He hira pū te mātauranga nei kia tatū ai ngā kaupapa pāngarau, he pērā i te taurangi, i ngā tikanga ōwehenga, i te whakaotinga rapanga.

Ngā Waeine me ngā Āwhata

He mea hira te ako a ngā mokopuna i ngā waeine me ngā āwhata i te mea he tūāpapa hei āta whakaahua, hei āta whakariterite i ngā rahinga nō te ao kikokiko.

Ahakoa he inenga roanga rānei, taumaha rānei, wā rānei, kītanga rānei, mahana rānei, mā te whakamahi i ngā waeine e tika ana e mārama ai ngā mokopuna, ā, hei reira ka whai hua te whakawhitiwhiti kōrero mō ngā raraunga.

Mā te māramatanga ki ngā āwhata – he pērā me te pūnaha ngahuru rānei, me te huatau ōwehenga – e āwhinatia ai ngā mokopuna kia whakamāori i ngā inenga hei whakamahi atu i ngā tūāhua kikokiko, arā, hei māramatanga rānei ki ngā tawhiti nō ngā hoahoa whenua, hei tātaitai i ngā tohutohu taka kai rānei, i ngā roanga rānei i haerea ai.

Me te mea hoki, he hira pū te mōhiotanga ki ngā waeine me ngā āwhata i roto i ngā tini peka o te pūtaiao, o te pūhanga, o te hangarau, otirā i ngā peka e matea ai ngā inenga e tika pū ana.

Mā te ako ki te whakawhitiwhiti waeine me te whakamahi i ngā āwhata e tika ana, ka whanake ngā pūkenga o ngā mokopuna hei whakaoti i ngā rapanga huhua o te ao kikokiko me te whakatau tikanga e ai ki ngā raraunga ineine.

Te Mokowā me ngā Āhua

He hira pū te māramatanga o ngā mokopuna me tā rātou torotoro i ngā hanga o te mokowā me ngā āhua i te mea he pūkenga taketake e hāngai ana ki ngā horopaki huhua o te ao kikokiko.

Mā te whakawhanake i ngā pūkenga hei whakamāori, hei whakanao i ngā āhua me ngā pānga mokowā, e mārama ake ai ngā mokopuna ki ngā take me ngā pāhekohekotanga o ngā mea me ngā hanganga i te ao kikokiko, arā, i ngā horopaki ahu-rua, ahu-toru hoki.

He mea hihira pū ngā pūkenga nei, ehara noa iho mō ngā mahi ā-rā – he pērā me te whai hoahoa whenua, me te whakatū hanganga – engari mō ngā mahi tuatini hoki – he pērā me te pūhanga, me te hoahoa whare, me te waihanga, me te mahi hoahoa.

Mā te ako i ngā huatau nei e whai ai ngā mokopuna ki ngā pūkenga hei torotoro ā-hinengaro, ā-tinana hoki i ō rātou ao, hei whakaata tika i ngā taiao kikokiko, hei whakamahi atu hoki i aua pūkenga nei i roto o ngā kaupapa me ngā marau huhua.

Te Tātari Raraunga

He hira pū te wāhanga tātaritari raraunga o te tūhura tauanga amio i te mea ka taurima i ngā āheinga o te mokopuna ki te torotoro, ki te whakamārama, ki te taukumekume whai take i ngā raraunga.

Mā te whakahaere me te whakariterite whai hua i ngā raraunga e āhei ai ngā mokopuna ki te tautohutohu i ngā hanga matua, he pērā me ngā ritenga nui rawa, me ngā ritenga iti rawa, me ngā tānuitanga, me ngā tauira, ā, hei reira āwhina atu ai i a rātou kia whiriwhiri i ngā āwhata mō ngā kauwhata.

Ko te whakamanawa i ngā mokopuna kia hanga i ā rātou ake kauwhata – kei whaiwhai kau i ngā tohutohu – hei taunaki i te mana o te tukanga tūhuratanga, hei taurima i te whakaroaro arohaehae, o te taukumekume whai take i ngā raraunga.

Ko te aronga ringapā nei, ehara noa iho i te whakawhanake i te māramatanga ki ngā momo tikanga whakariterite kauwhata, engari ka whakaako i ngā mokopuna kia kitekite atu i ngā pānga i waenga i ngā raraunga, i ngā tūtohi, i ngā kauwhata, ā, kia mārama hoki te whakawhitiwhiti kōrero i ā rātou kitenga.

Pāngarau Programme
Assessment for Learning
Ngā Pātai Auau

Pāngarau Programme

While focusing on the Mata Ako, it is important that the programme integrates with the rest of the pāngarau curriculum. To achieve this, consider the following strategies:

Curriculum Mapping: Map the Mata Ako against the Wāhanga Ako: Pāngarau content across the different year levels (Years 1–8). Ensure the programme is balanced and structured to introduce new concepts each year while revisiting and consolidating previous learning.
Spiraling Approach: Use a spiraling curriculum design, where foundational concepts are revisited and built upon in increasingly complex ways. For example, uara tū concepts introduced in Years 1–2 should be revisited and extended in Years 3–4 and beyond
Integration with Local Contexts: Adapt the pāngarau programme to reflect local contexts, and the lived experiences of students.
Contextual Relevance: Ensure that the programme connects abstract mathematical ideas to students’ lived experiences. For example, use Māori measurement systems or local geography to teach geometry and measurement, or integrate data from local surveys or community events for statistics.

Assessment for Learning

Assessment for learning is an essential part of any pāngarau programme, particularly in identifying student progress and diagnosing areas of difficulty. The focus should be on using assessment to guide instruction and provide feedback that supports students' learning.

Key Steps

Ongoing Formative Assessment: Use frequent and varied formative assessments (e.g., quizzes, group work, observations, one-on-one conferences, written tasks, etc.) to gauge student understanding and inform teaching. These assessments should be closely tied to the whāinga and putanga ako of each lesson or unit.
Diagnostic Tools: Utilise diagnostic assessments (such as Poutama Tau) to identify areas where students may be struggling. These can help determine which foundational concepts need to be revisited or where additional support may be required.
Progress Monitoring: Track student progress regularly using tools such as learning journals, digital portfolios, or assessment rubrics. This allows teachers to monitor how students are progressing with the Mata Ako and whether they are ready to move on to more complex material.
Data-Driven Instruction: Use assessment data to make informed decisions about when to provide additional support or differentiation for students who need it. This ensures that no student is left behind and all have the opportunity to master foundational concepts before moving on to more advanced topics.
Student Self-Assessment and Reflection: Encourage students to reflect on their own learning, set goals, and assess their own progress. This helps develop metacognitive skills and a sense of ownership over their learning journey.

Design and Sequence the Programme

Using student assessment data, the structured mathematics programme should be designed with a clear progression of learning, starting with foundational concepts and building towards more complex mathematical understanding

Whānau Involvement

Engage with whānau and caregivers to support students' mathematical learning at home. Provide resources and guidance for parents to reinforce foundational skills, and encourage involvement in school-based learning activities (e.g., pāngarau evenings, whānau workshops).

Ngā Pātai Auau

Pāngarau (Programme and resources)

What supports can I expect to receive with the resources?

Guidance materials, resources and professional development will be available to support implementation. 
More information, including how to access this PLD can be found here: https://pld.education.govt.nz/

How do I get more resources?

Hard copies can be ordered from Down the Back of the Chair. 
Use the MOE number provided with the print or online versions (Tāhūrangi) to identify the resource in Down the Back of the Chair (DTBOTC) in the ‘Search’ button.

Why do the Poutama Pāngarau books only have one akoranga per mata ako, per tau?

The first set of Poutama Pāngarau books are to provide initial guidance and examples for teaching scope, sequence and pace in Pāngarau and to provide support for planning. The full set of Poutama Pāngarau books will be delivered in Term 2 and will have multiple examples of akoranga per mata ako, per tau. These resources will also be available online.

Is Poutama Pāngarau informed by the science of learning?

Poutama Pāngarau draws from cognitive neuroscience (specifically how the brain processes language for kōrero, pānui and tuhituhi), linguistics as it applies to te reo Māori, language acquisition theory and practice, research carried out in classrooms where learning is through te reo Māori and the experience of educators who teach through te reo Māori. The science of learning combines ideas from psychology, neuroscience, education, and more to understand how we learn and retain knowledge. In pāngarau, this science helps create teaching strategies that match how the brain processes pāngarau, improving both skill retention and deeper understanding. It’s important, however, to include learning approaches that recognise the social and cultural factors that shape how students learn. This ensures that pāngarau education is both effective and inclusive, connecting with students’ cultural backgrounds and real-life experiences.

Is there any local professional learning and development (PLD) available for using this resource?

Information, including how to access this PLD can be found here: https://pld.education.govt.nz/

How do I integrate this into my Pāngarau programme?

The rauemi derives from the key concepts of the pāngarau curriculum and is designed to support your existing pāngarau programme. The content will be familiar and align with what is already being taught in your classroom. The resource provides the scope, sequence and pace of key foundational pāngarau concepts should be explicitly taught. These resources are designed to enhance and support your existing lessons.

How does the content in Poutama Pāngarau differ from Maths textbooks used for English-medium? 

Poutama Pāngarau is aligned with Te Marautanga o Aotearoa and draws from cognitive neuroscience and linguistics that are tailored to support learners in te reo Māori.

Where can I find further information about the curriculum resources and Poutama Pāngarau?

Go to Tāhūrangi and search under Pāngarau.

Are there any other Pāngarau resources coming?

A timeline will be on Tāhūrangi showing you when additional Pāngarau curriculum resources will be delivered to your kura.

Mō te rauemi

Wāhanga Ako: Pāngarau
Tūārere: Tūārere 1, Tūārere 2, Tūārere 3

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