Mathematical Inquiry for Engaging Lessons in Culturally Responsive Education

1. Getting a great start to every lesson Robin Averill

2. Kia ora e te whānau. Ko te Herenga Waka tōku marae. Ko te whānau o ako pai ki te ūpoko o te ika a Māui tōku whānau. Ko te akoanga pāngarau toku mahi. My research is in culturally responsive and culturally sustaining education. Ko Robin Averill ahau.

3. Kei hoputōuringakite aka tāepa, engarikiamaukite aka matua.

4. Focus areas: • Quick investigative questions to stimulate mathematical thinking and discussion • Being strategic in selection of mathematical focus • Making personal connections to nurture classroom community • Exploring real life links and applications to stimulate engagement and interest • Linking to Tātaiako and Tapasā

5. Quick investigative questions to stimulate mathematical thinking and discussion Examples: Sometimes.... find a true example and a false example. Explore, generalise where possible. A polygon has exactly two mirror lines.1/2 + 1/x > 1 If p < r, than pq < qr x2– k can be factorised. The graph of y = 3x + b passes through quadrants 1, 2 and 3.

6. Quick investigative questions to stimulate mathematical thinking and discussion Examples: How do you know that...? How do you know that 43 = 26?How do you know that 100>10? How do you know that the points (4, 7), (0, -5), (-1, -8) lie on the same straight line? How do you know that a traingle with sides 5, 6, and 10 cm has an obtuse angle? How do you know that a cubic equation with real coefficients must have at least one real root?

7. Quick investigative questions to stimulate mathematical thinking and discussion Examples: What if? What happens to the line y = 3x + k as k increases? What happens to the series a + ar + ar2 + ... if IrI < 1? What happens to the sum of an arithmetic series if each term is doubled? What happens to the area of a sector if you double the size of the central angle and double the length of the radius?

8. Quick investigative questions to stimulate mathematical thinking and discussion Examples: For each set, which one doesn’t belong? Why?

9. Exploring real life links and applications to stimulate engagement and interest Examples: Choosing contexts that link to students’ interests and experiences (school-based and out-of-school) Choosing contexts that show the usefulness of content e.g., curve fitting for ski design, surfboard design, tennis racket design, etc – YouTube videos can show these types of application in action Choosing contexts that develop their sense of citizenship and of mathematics and statistics as powerful tools for advancing understanding and equity

10. Being strategic in selection of mathematical focus Examples: Reactiviating prior learning necessary for new learning Reminders of prior learning to aid retention Asking questions to stimulate curiosity about content of the next topic

11. Making personal connections to nurture classroom community Examples: Greeting students individualy as they arrive and leave the classroom using their names and showing you know them Reminding students of the learning and activities of the last time you were all together Referring to own, school and community activities as contexts for maths ideas to build sense of community Starting with a cooperative game focussed on new learning, (e.g., SKUNK) Showing care for students and their learning and goals Involving student creativity and enable student humour in lesson starter questions and discussion

12. Links to T ātaiako and Tapasā Now let’s consider links between the ideas discussed and the cultural competencies of Tātaiako and the Turu of Tapasā.

13. Focus areas: • Quick investigative questions to stimulate mathematical thinking and discussion • Being strategic in selection of mathematical focus • Making personal connections to nurture classroom community • Exploring real life links and applications to stimulate engagement and interest • Linking to Tātaiako and Tapasā