1 / 21

Welcome

Welcome. PGCE Core 2 Using and Applying Mathematics. Is it magic?. Roll a die and make a note of the number Double the number Add three Multiply by 5 Roll again and make note of the number Add your new number Add 6 Multiply by 10 Roll again Add to the total Tell me the final answer.

neron
Télécharger la présentation

Welcome

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Welcome PGCE Core 2 Using and Applying Mathematics

  2. Is it magic? • Roll a die and make a note of the number • Double the number • Add three • Multiply by 5 • Roll again and make note of the number • Add your new number • Add 6 • Multiply by 10 • Roll again • Add to the total Tell me the final answer

  3. No it is mathematics!

  4. Classifying Problems - 1 As thinking skills (National Curriculum, 1999:p.22) • Information processing skills • Reasoning skills • Enquiry skills • Creative thinking skills • Evaluation skills

  5. Classifying Problems - 2 Key features Orton and Frobisher( 1996) Insights into Teaching Mathematics A mathematics problem can be said to be a situation in which an individual student • Recognizes or believes that there exists a mathematical goal to be achieved • Accepts the challenge to perform some mathematical task in order to reach the goal • Has no readily recallable mathematical procedure available to enable the goal to be attained directly ‘It would appear that the distinction between a problem and an investigation is the existence of the clear goal specified in the statement of the activity’ (p.32)

  6. Pupils need to be introduced to a wide range of problem solving situations • Standard problems: stories requiring translation into mathematical operations • Non-standard problems: situations for which the problem solver will not have a set routine or procedure for solving the problem • Real world problems: situations where the pupil will have to select the relevant information and set up a mathematical model that simplifies the situation • Puzzles: Problems depending upon ,luck, insight or unusual strategies Askew, M and Wiliam, D. (1995) Recent research in mathematical education, London, HMSO

  7. Standard problems Start unknown The initial quantity has to be found Mrs Green put some apples into bags. She ended up with 6 bags of apples, each containing five apples. How many apples did she start with? ? ÷ 5 = 6 , possibly calculated as 5 x 6 = ? Change unknown The second quantity has to be found. Jo baked 20 currant buns. Someone sneaked down in the night and ate some. The next morning Jo found there were only 15 in the tine. How many were eaten? 20 - ? = 15, possibly calculated as 15 + ? = 20 Result unknown The final quantity has to be found Jo baked 12 lemon buns and 14 cherry buns. How many buns did she bake altogether? 12 + 12 = ?

  8. Problems and investigations • Convergent • Divergent A range of structures/models to support progress 2/11

  9. JMcC 2/10

  10. JMcC 2/10

  11. JMcC 2/10

  12. Problem solving models JMcC 2/10

  13. JMcC 2/10

  14. Read Understand Choose Solve Answer Check JMcC 2/11

  15. Would you rather solve problems on your own or with others? Does it depend on anything?

  16. Collaboration in mathematics promotes opportunities for; • discussion • justification of ideas • justification of the answer • communication of ideas • reflecting on learning • …..

  17. Anthony, G. and Walshaw, M. (2009) ‘Effective Pedagogy in Mathematics.’. Educational Practices Series 19

  18. DCFS (2008) ‘Effective Teacher-Pupil Dialogue in Key Stages 2 and 3 Mathematics’. Full document available at: https://www.education.gov.uk/publications/RSG/Subjects/Page6/DCSF-EPPI-02-08FR(E) • Initiate (teacher) Response (pupil) Feedback (teacher). • Focusing attention on mathematics rather than ‘getting the answer right’ • Working collaboratively with pupils • Transformative listening • Scaffolding

  19. http://www.collaborativelearning.org/basketballscores.pdf

  20. Today’s schedule

  21. Independent Study Task • Haylock, D and Thangata, F (2007) Key Concepts in Teaching Primary Mathematics London: Sage • DCFS (2008) ‘Effective Teacher-Pupil Dialogue in Key Stages 2 and 3 Mathematics’. Full document available at: https://www.education.gov.uk/publications/RSG/Subjects/Page6/DCSF-EPPI-02-08FR(E) • DCFS (2006) Guidance Paper – Using and Applying Mathematics. Available at: http://www.teachfind.com/national-strategies/guidance-paper-using-and-applying-mathematics-0(E)

More Related