Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ - Original copyright The Open University
This unit is aimed at teachers who wish to review how they go about the practice of teaching mathematics, those who are considering becoming mathematics teachers, or those who are studying mathematics courses and would like to understand more about the teaching and learning process.<link rel="canonical" href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0" /> First published on Thu, 17 Oct 2013 as <a href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0">Working mathematically</a>. To find out more visit The Open University's <a href="http://www.open.edu/openlearn/ole-home-page">Openlearn</a> website. Creative-Commons 2013
This free course, Working mathematically, is aimed at teachers who wish to review how they go about the practice of teaching mathematics, those who are considering becoming mathematics teachers, or those who are studying mathematics courses and would like to understand more about the teaching and learning process.<link rel="canonical" href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0" /> First published on Wed, 22 May 2013 as <a href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0">Working mathematically</a>. To find out more visit The Open University's <a href="http://www.open.edu/openlearn/ole-home-page">Openlearn</a> website. Creative-Commons 2013
This unit is aimed at teachers who wish to review how they go about the practice of teaching mathematics, those who are considering becoming mathematics teachers, or those who are studying mathematics courses and would like to understand more about the teaching and learning process.<link rel="canonical" href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0" /> First published on Wed, 22 May 2013 as <a href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0">Working mathematically</a>. To find out more visit The Open University's <a href="http://www.open.edu/openlearn/ole-home-page">Openlearn</a> website. Creative-Commons 2013
<p>In this course you will explore a number of major issues in mathematics education. For example, when you think about mathematics, do you see it mainly as a collection of topics (mathematical content) or as a way of thinking (mathematical process)? Later in the course you will be asked to consider further the distinction between content and process in mathematics. You will also be asked to consider a particular organising framework for thinking about your teaching. It is referred to as the <i>do–talk–record</i> (DTR) framework. You will also be asked to work on some mathematics yourself and then reflect on what you have done. The mathematical context used in this course is Möbius strips. This context has been chosen to give you the opportunity to work on some mathematics at your own level. After you have completed several mathematical activities relating to Möbius strips, you will be expected to select parts of these activities, adapting them as necessary, to try out with your learners (or others). This work with learners will give you the opportunity to apply the DTR framework to your own teaching.</p><p>But first, take a little time to reflect on your own feelings about your aims for this course. What do <i>you</i> want to work on with regard to the learning and teaching of mathematics and what is of most concern to <i>you</i>? Activity 1 will help you engage with these and related questions.</p><div class=" oucontent-activity oucontent-s-heavybox1 oucontent-s-box "><div class="oucontent-outer-box"><h3 class="oucontent-h3 oucontent-heading oucontent-nonumber">Activity 1  Hopes and fears</h3><div class="oucontent-inner-box"><div class="oucontent-saq-question"><p>In your notebook, complete the following sentences. You may have one overwhelming response to each prompt or it may be appropriate to list three or four responses to each.</p><ul class="oucontent-unnumbered"><li>I expect this course to include work on …</li><li>I personally would like to work on …</li><li>An anxiety that I have about the course is …</li></ul></div>
<div class="oucontent-saq-discussion"><h4 class="oucontent-h4 oucontent-discussionhasalias">Comment</h4><p>Clearly the degree of flexibility of this course is limited by the fixed nature of the course materials. It is important to stress that what you bring to the course is at least as important as the course materials. Awareness of your needs and hopes will help you choose which activities to focus on and which personal examples of your own to stress as you progress through the units. </p></div></div></div></div><p>This OpenLearn course is an adapted extract from the Open University course <span class="oucontent-linkwithtip"><a class="oucontent-hyperlink" href="http://www3.open.ac.uk/study/undergraduate/course/me620.htm?LKCAMPAIGN=ebook_&MEDIA=ol">ME620 <i>Mathematical thinking in schools</i></a></span>.</p><p/>
<p>In this unit you will explore a number of major issues in mathematics education. For example, when you think about mathematics, do you see it mainly as a collection of topics (mathematical content) or as a way of thinking (mathematical process)? Later in the unit you will be asked to consider further the distinction between content and process in mathematics. You will also be asked to consider a particular organising framework for thinking about your teaching. It is referred to as the <i>do–talk–record</i> (DTR) framework. You will also be asked to work on some mathematics yourself and then reflect on what you have done. The mathematical context used in this unit is Möbius strips. This context has been chosen to give you the opportunity to work on some mathematics at your own level. After you have completed several mathematical activities relating to Möbius strips, you will be expected to select parts of these activities, adapting them as necessary, to try out with your learners (or others). This work with learners will give you the opportunity to apply the DTR<i> </i>framework to your own teaching.</p><p>But first, take a little time to reflect on your own feelings about your aims for this unit. What do <i>you</i> want to work on with regard to the learning and teaching of mathematics and what is of most concern to <i>you</i>? Activity 1 will help you engage with these and related questions.</p><div class=" oucontent-activity oucontent-s-heavybox1 oucontent-s-box "><div class="oucontent-outer-box"><h3 class="oucontent-h3 oucontent-nonumber">Activity 1  Hopes and fears</h3><div class="oucontent-inner-box"><div class="oucontent-saq-question"><p>In your notebook, complete the following sentences. You may have one overwhelming response to each prompt or it may be appropriate to list three or four responses to each.</p><ul class="oucontent-unnumbered"><li>I expect this unit to include work on …</li><li>I personally would like to work on …</li><li>An anxiety that I have about the unit is …</li></ul></div>
<div class="oucontent-saq-discussion"><h4 class="oucontent-h4 oucontent-discussionhasalias">Comment</h4><p>Clearly the degree of flexibility of this unit is limited by the fixed nature of the unit materials. It is important to stress that what you bring to the unit is at least as important as the unit materials. Awareness of your needs and hopes will help you choose which activities to focus on and which personal examples of your own to stress as you progress through the units. </p></div></div></div></div><p>This unit is an adapted extract from the Open University course <span class="oucontent-linkwithtip"><a class="oucontent-hyperlink" href="http://www3.open.ac.uk/study/undergraduate/course/me620.htm">ME620, Mathematical thinking in schools</a></span>.</p><p/>
This free course, Working mathematically, is aimed at teachers who wish to review how they go about the practice of teaching mathematics, those who are considering becoming mathematics teachers, or those who are studying mathematics courses and would like to understand more about the teaching and learning process.
<link rel="canonical" href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0" /> First published on Wed, 22 May 2013 as <a href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0">Working mathematically</a>. To find out more visit The Open University's <a href="http://www.open.edu/openlearn/ole-home-page">Openlearn</a> website. Creative-Commons 2013
This free course, Working mathematically, is aimed at teachers who wish to review how they go about the practice of teaching mathematics, those who are considering becoming mathematics teachers, or those who are studying mathematics courses and would like to understand more about the teaching and learning process.<link rel="canonical" href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0" /> First published on Mon, 22 Feb 2016 as <a href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/working-mathematically/content-section-0">Working mathematically</a>. To find out more visit The Open University's <a href="http://www.open.edu/openlearn/ole-home-page">Openlearn</a> website. Creative-Commons 2016