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	<title>Comments on: Speaking Math</title>
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	<link>http://borderland.northernattitude.org/2008/12/13/speaking-math/</link>
	<description>(bôr&#039;dər-lănd&#039;) n. Located on or near a frontier. An indeterminate area or condition.</description>
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		<title>By: Helen</title>
		<link>http://borderland.northernattitude.org/2008/12/13/speaking-math/comment-page-1/#comment-113589</link>
		<dc:creator>Helen</dc:creator>
		<pubDate>Tue, 23 Dec 2008 07:40:13 +0000</pubDate>
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		<description>Thanks for your comments Doug and Bill. I&#039;m looking forward to more conversations with you soon. In the meantime, I shall leave my air conditioned office and venture out into the sweltering Darwin afternoon, imagining the contours and shadows of an Alaskan mid-winter.</description>
		<content:encoded><![CDATA[<p>Thanks for your comments Doug and Bill. I&#8217;m looking forward to more conversations with you soon. In the meantime, I shall leave my air conditioned office and venture out into the sweltering Darwin afternoon, imagining the contours and shadows of an Alaskan mid-winter.</p>
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		<title>By: Bill Kerr</title>
		<link>http://borderland.northernattitude.org/2008/12/13/speaking-math/comment-page-1/#comment-113583</link>
		<dc:creator>Bill Kerr</dc:creator>
		<pubDate>Tue, 23 Dec 2008 06:00:56 +0000</pubDate>
		<guid isPermaLink="false">http://borderland.northernattitude.org/?p=891#comment-113583</guid>
		<description>Wonderful links (from both of you) and comment from Helen - still reading but thanks in the interim</description>
		<content:encoded><![CDATA[<p>Wonderful links (from both of you) and comment from Helen &#8211; still reading but thanks in the interim</p>
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		<title>By: Doug Noon</title>
		<link>http://borderland.northernattitude.org/2008/12/13/speaking-math/comment-page-1/#comment-113456</link>
		<dc:creator>Doug Noon</dc:creator>
		<pubDate>Sat, 20 Dec 2008 16:11:16 +0000</pubDate>
		<guid isPermaLink="false">http://borderland.northernattitude.org/?p=891#comment-113456</guid>
		<description>Hi Helen. You sound like a person who I could spend some time talking with. 

One of the things that I began doing as a result of this project was something like you suggest. Rather than simply explaining, demonstrating, and so forth, I also began commenting on the classroom discussions. Asking for explanations and justifications, and also offering my own for why I was saying and doing the things I did, making the &#039;talk&#039; of the classroom part of the lesson.

You say, &quot;Then you only ask questions that you know the kids can answer,&quot; which I wish I could say that I consistently do because I understand the wisdom of it. But this is not easy with the curriculum materials we&#039;re using. I&#039;m thinking about how to work around the textbook, and the best idea I have is to create more of my own math problems.

I&#039;ll follow the link you left in your comment. I am very interested. Thank you.</description>
		<content:encoded><![CDATA[<p>Hi Helen. You sound like a person who I could spend some time talking with. </p>
<p>One of the things that I began doing as a result of this project was something like you suggest. Rather than simply explaining, demonstrating, and so forth, I also began commenting on the classroom discussions. Asking for explanations and justifications, and also offering my own for why I was saying and doing the things I did, making the &#8216;talk&#8217; of the classroom part of the lesson.</p>
<p>You say, &#8220;Then you only ask questions that you know the kids can answer,&#8221; which I wish I could say that I consistently do because I understand the wisdom of it. But this is not easy with the curriculum materials we&#8217;re using. I&#8217;m thinking about how to work around the textbook, and the best idea I have is to create more of my own math problems.</p>
<p>I&#8217;ll follow the link you left in your comment. I am very interested. Thank you.</p>
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		<title>By: Helen</title>
		<link>http://borderland.northernattitude.org/2008/12/13/speaking-math/comment-page-1/#comment-113452</link>
		<dc:creator>Helen</dc:creator>
		<pubDate>Sat, 20 Dec 2008 14:50:50 +0000</pubDate>
		<guid isPermaLink="false">http://borderland.northernattitude.org/?p=891#comment-113452</guid>
		<description>Hi Doug,

I live in northern Australia. Part of my job involves helping to train teachers to teach literacy in the bush, and getting them to raise their expectations of low achieving kids. I lurk on your blog occasionally, and have very much enjoyed reading it. 

What you say about Bruner and his contribution to our thinking about classroom discourse resonates very deeply with me and has prompted me to stop just lurking and actually write something. I was particularly interested in what you say about some kids not tuning in to the ‘why’ of school activities.

For Aboriginal kids in the bush (and the whole demographic is currently failing dismally at school), the why of schooling often totally escapes them – why do we read, why do we answer the teacher’s questions, why do we even bother coming. And because teachers aren’t always very reflective on their own culture and its attendant assumptions, it often doesn’t occur to them to even explain why we do the things we do in school. But even when they do think about explaining, the explanation and the activity are often at odds – and as you say, the kids bring things back to the bottom line and to their comfort zone, which often results in very ritualised work.

Over the past few years I’ve been fortunate to be able to watch lots of teachers teaching, and to talk with them about what they do. What you say about kids who don’t ‘get’ school is very true of kids here too. Which brings me to a comment on your reading of Bruner – we have found that the difference between middle class kids and kids from low-literate  backgrounds is not so much a question of language, as a question of ‘orientation’ to the text or the activity. So, for example, middle class kids from literate families know that when the teacher asks a question about the story they have just read, they are expected to find the answer in the text of the story. Kids who don’t come from literate backgrounds often don’t know this, and so they look for answers in their own experience. Similarly, kids who understand the purpose of schooling will look for answers to math questions from within the logic of the mathematics; kids who don’t really know where it’s all going invent their own logic, which is often ‘please the teacher so she leaves me alone’ or ‘get through this lesson and get out to lunch’. Or if that fails, ‘disrupt the lesson and get kicked out, or at least buy some time not to have to do the math, or the writing, or whatever’. 

One strategy we use as a way of giving kids the orientation that we want them to have is a strategy called ‘preformulation’ (the term comes from Courtney Cazden, but she might have got it from someone else), where you basically tell the kids what you want them to know before you ask any questions about it. Then you only ask questions that you know the kids can answer. No more ‘guess what’s in the teacher’s head’. It sounds a bit daft, but it provides a strong scaffold for kids who may not otherwise know where you are coming from. Lots of teachers use this strategy intuitively anyway – but it’s interesting to become conscious of, and plan it into each lesson. The follow up to preformulation is ‘reconceptualisation’, where you take up from the answer to your question and elaborate on it, and talk about its significance. The idea is that as you work through a cycle of lessons, you have less and less need to preformulate, and you will be able to ask more open questions about your topic, because the kids share your orientation to it and know where you’re coming from. The craft of course is to know when to stop preformulating. Teachers who are good at the technique get the kids to take on the reconceptualising too.

I don’t know if I’ve made any sense here; I got a little carried away as your study struck so many chords for me. Anyway, if you’re interested, you can read something about our project here: http://www.nalp.edu.au/whatisal.html</description>
		<content:encoded><![CDATA[<p>Hi Doug,</p>
<p>I live in northern Australia. Part of my job involves helping to train teachers to teach literacy in the bush, and getting them to raise their expectations of low achieving kids. I lurk on your blog occasionally, and have very much enjoyed reading it. </p>
<p>What you say about Bruner and his contribution to our thinking about classroom discourse resonates very deeply with me and has prompted me to stop just lurking and actually write something. I was particularly interested in what you say about some kids not tuning in to the ‘why’ of school activities.</p>
<p>For Aboriginal kids in the bush (and the whole demographic is currently failing dismally at school), the why of schooling often totally escapes them – why do we read, why do we answer the teacher’s questions, why do we even bother coming. And because teachers aren’t always very reflective on their own culture and its attendant assumptions, it often doesn’t occur to them to even explain why we do the things we do in school. But even when they do think about explaining, the explanation and the activity are often at odds – and as you say, the kids bring things back to the bottom line and to their comfort zone, which often results in very ritualised work.</p>
<p>Over the past few years I’ve been fortunate to be able to watch lots of teachers teaching, and to talk with them about what they do. What you say about kids who don’t ‘get’ school is very true of kids here too. Which brings me to a comment on your reading of Bruner – we have found that the difference between middle class kids and kids from low-literate  backgrounds is not so much a question of language, as a question of ‘orientation’ to the text or the activity. So, for example, middle class kids from literate families know that when the teacher asks a question about the story they have just read, they are expected to find the answer in the text of the story. Kids who don’t come from literate backgrounds often don’t know this, and so they look for answers in their own experience. Similarly, kids who understand the purpose of schooling will look for answers to math questions from within the logic of the mathematics; kids who don’t really know where it’s all going invent their own logic, which is often ‘please the teacher so she leaves me alone’ or ‘get through this lesson and get out to lunch’. Or if that fails, ‘disrupt the lesson and get kicked out, or at least buy some time not to have to do the math, or the writing, or whatever’. </p>
<p>One strategy we use as a way of giving kids the orientation that we want them to have is a strategy called ‘preformulation’ (the term comes from Courtney Cazden, but she might have got it from someone else), where you basically tell the kids what you want them to know before you ask any questions about it. Then you only ask questions that you know the kids can answer. No more ‘guess what’s in the teacher’s head’. It sounds a bit daft, but it provides a strong scaffold for kids who may not otherwise know where you are coming from. Lots of teachers use this strategy intuitively anyway – but it’s interesting to become conscious of, and plan it into each lesson. The follow up to preformulation is ‘reconceptualisation’, where you take up from the answer to your question and elaborate on it, and talk about its significance. The idea is that as you work through a cycle of lessons, you have less and less need to preformulate, and you will be able to ask more open questions about your topic, because the kids share your orientation to it and know where you’re coming from. The craft of course is to know when to stop preformulating. Teachers who are good at the technique get the kids to take on the reconceptualising too.</p>
<p>I don’t know if I’ve made any sense here; I got a little carried away as your study struck so many chords for me. Anyway, if you’re interested, you can read something about our project here: <a href="http://www.nalp.edu.au/whatisal.html" rel="nofollow">http://www.nalp.edu.au/whatisal.html</a></p>
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