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Mathematics

Mathematics. NISPLAN Day 2 Afternoon Session. "The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver." I . N. Herstein. “It’s not how many answers students know. It’s how they behave when they

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Mathematics

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  1. Mathematics NISPLAN Day 2 Afternoon Session

  2. "The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver." I. N. Herstein

  3. “It’s not how • many answers students know. • It’s how they • behave when they • don’t know that counts.” • Alistair Smith (2003) • Leading Learning

  4. Challenge How would you do the following questions?

  5. 5 – 2.37 b) 5hrs 37mins – 2hrs 45mins • 2 + 3 + 5 b) 7 ÷ 4 x 12 • 4 x 6 b) 37.6 x 5 • 4.99 x 16 b) 3 x 5 • 428 ÷ 6 b) x = √23 • 25 x 8 b) 320 x 25 a) 2 + 5 b) 0.75 x 0.25

  6. Counting on / back Re -ordering • 5 – 2.37 b) 5hrs 37mins – 2hrs 45mins • 2 + 3 + 5 b) 7 ÷ 4 x 12 • 4 x 6 b) 37.6 x 5 • 4.99 x 16 b) 3 x 5 • 428 ÷ 6 b) x = √23 • 25 x 8 b) 320 x 25 a) 2 + 5 b) 0.75 x 0.25 Partitioning Rounding & adjusting Inverse operations Factors Equivalence

  7. Mathematical concepts are made up of three components:

  8. Mathematical Language What words do you use? Sometimes words sound the same but have different meanings

  9. Working in pairs try to list as many definitions of ‘right’ you can think of. • Right angle • Turn right or right-hand side • Right meaning correct • Right meaning good or OK • Right in terms of health • Right wing or right-handed • Right meaning deserved • ‘Write’ down using a pen or pencil

  10. What can you do to help a pupil’s understanding?

  11. Pupils, their parents and teachers should be aware that there can be a number of valid ways to arrive at an answer. It is important that pupils are given the opportunity to explore and share different strategies for calculating, and through discussion, to conclude that some are more efficient than others. Such sharing of thinking is essential to consolidate understanding. For all pupils, reflecting on and explaining how a calculation has been worked out is a powerful way of learning. The teacher’s role is to encourage thinking, discussion and explanation in order to foster in pupils a willingness to listen to the strategies used by their peers, and consequently to evaluate their own strategies.

  12. To help learners to adopt more active approaches towards learning Engage learners in discussing and explaining ideas, Challenging and teaching one another, Creating and solving each other's questions Working collaboratively to share methods and results.

  13. One day the teacher was reading the story of Chicken Little to her class. She came to the part where the chicken warns the farmer . “ … and Chicken Little went up to the farmer and said, “The sky is falling!” The teacher then asked the class. “And what do you think the farmer said?” One little girl raised her hand and said, I think he said: “Holy Sh*t a talking chicken!” The teacher was unable to teach for the next 10 minutes

  14. Multiplication http://www.teachertube.com/viewVideo.php?video_id=46231

  15. Application Abstract Pictorial The wall of maths mastery Mahesh Sharma Communication Concrete Intuitive Linguistic Conceptual Procedural

  16. Application Abstract Pictorial Text Book The wall of maths mastery No layers above so what supports further building? No solid foundation below so what’s going to happen?

  17. Developing Cognitive Strategies Use a great deal of concrete experiences Ask a considerable number of questions

  18. Concrete Multiplication

  19. 600 150 120 30 900 Pictorial Multiplication 25 x 36 20 5 150 30 600 30 120 6

  20. Algebra … Abstract?? Have you tried Algebra Tiles to keep the area model going?

  21. Using your Algebra TilesShow 3(x + 1) = 3x + 3

  22. Using your Algebra TilesShow (x + 2)(x + 3) equals x² + 5x + 6

  23. Procedural What is eleven hours and thirty minutes take away four hours and forty-five minutes? As the number of minutes to be subtracted is bigger. (You have to subtract 45 mins which is bigger than 30 mins)Convert both times into minutes      11 hours 30 minutes   is    11 x 60    +   30   =   690 minutes      4 hours 45 minutes   is    4 x 60    +    45   =   285 minutesSubtracting them gives      690 - 285 = 405 minutesTo change this into hours divide by 60      405 ÷ 60 = 6      with 45 left overThe answer is 6 hours and 45 minutes.

  24. Procedural What is eleven hours and thirty minutes take away four hours and forty-five minutes? - 15 mins - 30 mins - 4 hrs 6.45 7.00 7.30 11.30

  25. http://nlvm.usu.edu/en/nav/vlibrary.html

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