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# Mathematics Matters Lesson Accounts 27 - Extrapolating New Knowledge from Old

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Created on 28 May 2008 by ncetm_administrator
Updated on 16 June 2008 by ncetm_administrator
 Mathematics Matters Lesson Accounts A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

# Lesson Account 27 - Extrapolating New Knowledge from Old

 Written by P Lacey Organisation Unknown Age/Ability Range Unknown

Extrapolating new knowledge from old is an engine for exploring and charting the territory of mathematics. In this exercise learners are expected to apply their understanding of fundamental concepts and principles (inverse, equivalence etc) in order to “map” and extend their knowledge.

(a) What was the mathematical task(s)?
What else do you know (and why) if you know that 5 + 3 = 8? The statement is written in the middle of a board visible to a whole class. Initially whole class responses. For example: 500 + 300 = 800. This is written on the board with an arrow to it from the original statement. A ‘mind-map’ is generated with answers to the why bit of the question determining the connections. Lead on to groups/pairs with eventual ‘composite’ mind map. Discussing the why proves productive.

(b) What learning culture was created?
How was this achieved? Learners in control. No perceived limit. Genuine sharing of personal understandings.

(c) How could you tell that the task(s) achieved the intended purposes? Do you have any evidence?
I think the activity actually altered the views of some of the learners on what mathematics actually is. Certainly challenged the ‘quantum’ view of mathematics as isolated facts.

Reported in ‘Mathematics Teaching’ 187 June 2004 as a special conference insert, after being included in an ATM annual conference presentation

(e) Can you say why you chose this example? What criteria were in your mind?
Simple and accessible start – almost trivial; but deep in its engagement. Explicit and shared discussions on personal maps of understanding have a sense of deep learning.

## Values & Principles

 Conceptual understanding and interpretations for representations Builds on the knowledge learners already have Encourages reasoning rather than ‘answer getting’ Creates connections between topics both within and beyond mathematics and with the real world

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