Karen+Knarston

PLC Learning 2009 Karen-Numeracy PLC 2009 –Geoff Woolford ** “__one loses the opportunity to think if you suggest what strategy you are teaching at the beginning of the lesson using a problem to suggest a strategy is more productive__. “ **  · ** Selected the hexagon – asked what other shapes could be used to make that shape. ** · ** 2 factors always make a shape ** · ** The equipment indicates what strategy they will use. ** · ** He used Cuisenaire rods to image 23x15 getting bigger starting with smallest rectangle and moving to largest- image it getting bigger ** Can you have a 1/4 bigger than a 1/2? Meaning of a whole - talk about the whole as being the complete thing. Use appropriate language to get across fractions such as one part of the whole or two parts of the whole. Use of 100 bead snake - imaging – another 100 bed snake- fractions and decimals had chn recite 1/10 or 0.1, 2/10 or 0.2… Using shapes particulaly a hexagon - one yellow shape, two red to make one yellow, six green to make a whole yellow, three green plus one red make a whole. Three blue make a whole yellow. Used this shape to illustrate that one cannot add things if they do not have the same name 1/6 + 4/6 + 2/6 = 7/6 more than one whole Clarify the meaning of a decimal point –shows where the ones column is – called it a ‘oneth’ **
 * __ 25th March __**
 * First presentation from Geoff. What clarity of thinking when it comes to explaining maths concepts, no cluttering it up with unnecessary explanations-questions are the key. **
 * Using Gloss assessment –take the optimistic approach and look for the best effort. The strategy they use to solve a question, even if answer incorrect, determines their stage. **
 * Wording the learning intention for the strategy is at variance to general class lessons. His attitude in maths is don’t give a specific learning outcome of the strategy which you are planning to introduce. **
 * His questioning method encourages children to work out alternatives **
 * ** ‘What is going on? **
 * ** Can you think of a way you could do this problem? **
 * ** What can you do to solve this problem without using this method? **
 * By using knowledge they already know you can direct them towards developing alternative strategies. **
 * __ 8th June 2009 __**
 * __ Observation: __**** Stephanie’s Yr 5 class (Stage 5/6) **
 * Geoff demonstrated meaning of multiplication ‘groups of’ **
 * **Chn given oblong array and had them decide on what made up the rectangle-named these as __factors__ after chn identified.**
 * **Chn asked to __imagine__ they were ‘cut and pasting a new bigger rectangle’**
 * **Posed harder problem that they weren’t supposed to be able to work out but they used what they had just learnt in the cut and paste exercise. It was a very effective imaging technique.**
 * **Gave the L/O: To solve a 2 digit multiplication problem by easiest way possible – they were using doubling strategy without being aware. __Illustrated his belief that way you present the problem will show the strategy.__**
 * __ 4th Aug __**
 * __ Multiplication/Division __**
 * Start with division –prepares them for equal groups for multiplication **
 * **‘How many’ aspect as opposed to ‘sharing’**
 * Bringing together of sets **
 * Using language ‘sets of’ ‘groups of’ ‘piles of’ **
 * Used geometric shapes and identified the properties of 2D shapes to link it to tables. It gave a clear visual picture. **
 * __ 14th Sept __**
 * Observation in Room 8 with Geoff Woolford **
 * __ Fractions/decimals( Stage 6) __****
 * Mistake children often make -Never put the decimal point in its own column. **
 * Every number has a decimal –we just don’t always put it in. Shows us the ones column and you need to work out all the rest. **


 * __ 20th Oct __**
 * __ Decimals/Fractions __**
 * Need to be pedantic about words to clarify understanding of fractions and decimals **
 * **Asked if ¼ could be larger than a ½ - depends on what a quarter is**
 * **Do you ever know what how big is a ½ ? Need to make sure you now the whole first**
 * **Why is it a half? Cut into 2 equal pieces.**
 * **Why ½ = It is 1 of 2 equal pieces that make a whole.**
 * **Used a hexagon shape – what can be used to make another…**
 * **Need to use a square/circle as experientially too hard to find 1/3 of a rectangular shape.**
 * **Shape of whole can reflect difficulty of fraction**
 * **He used 100 bead snake to introduce decimals 0.1 or 1/10 chn took turns to count on 1/10, 0.1, 2/10, 0.2…**
 * **Jumping over 1 is a major issue eg 11/10, 1.20**
 * **To illustrate the question :Why don’t we add the bottom numbers? Eg 3 dogs and 3 cats-need to rename before you can add**
 * **Don’t show equivalent fractions in ascending order-encourages them to go up in algebraic pattern**
 * **Decimal point’s job is to point out where the ones column is-your job to work out everything yourself.**
 * **Never put decimal point in a column on its own –it overlaps on a line 1/1-the oneth column**


 * __ 2nd Nov : __**** Missed demonstration for Geoff absent as sick **


 * __ What I have learnt from working and observing Geoff. __**
 * Skilled questioning is a key element of Geoff’s effectiveness and clarity in teaching and introducing maths strategies. He knows what to ask and when and how to draw on chn’s existing knowledge and how to transfer that into a new strategy that they are using logically. It seems a seamless transition with him. **
 * I have seen new uses of concrete materials (simple 2D shapes) that bring the children’s thinking into the higher level strategy learning but in an effective visual method. **
 * His use of cut and pasting imaging is an effective way to extend the concepts. **
 * Most importantly his lack of directives when taking a lesson -not how they are to be taught a strategy- instead drawing it out of them with his questions. He doesn’t tell them the strategy until they have discovered it for themselves. He sets tasks to solve that lead to it. **
 * Use of the number problems that are specifically designed to allow this exploration. See numeracy planning on nzmaths site-they have designed them in appropriate stages of difficulty. **
 * What I need to continue with in my maths teaching is developing the skilful questioning and simplify the concepts around their existing knowledge base. **