<?xml version="1.0" encoding="UTF-8"?><rss version="2.0" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:wfw="http://wellformedweb.org/CommentAPI/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:sy="http://purl.org/rss/1.0/modules/syndication/" xmlns:slash="http://purl.org/rss/1.0/modules/slash/" > <channel> <title>MathEd – SingTeach | Education Research for Teachers | Research within Reach</title> <atom:link href="https://singteach.nie.edu.sg/topic/mathed/feed/" rel="self" type="application/rss+xml" /> <link>https://singteach.nie.edu.sg</link> <description></description> <lastBuildDate>Thu, 23 Sep 2021 08:52:33 +0000</lastBuildDate> <language>en-US</language> <sy:updatePeriod> hourly </sy:updatePeriod> <sy:updateFrequency> 1 </sy:updateFrequency> <generator>https://wordpress.org/?v=6.0</generator> <item> <title>Same Problem, Different Approach</title> <link>https://singteach.nie.edu.sg/2012/11/02/issue39-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue39-mathed</link> <comments>https://singteach.nie.edu.sg/2012/11/02/issue39-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Fri, 02 Nov 2012 00:31:20 +0000</pubDate> <category><![CDATA[issue 39 nov / dec 2012]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Problem solving]]></category> <category><![CDATA[Classroom Perspectives]]></category> <category><![CDATA[School-based curriculum innovation]]></category> <category><![CDATA[Primary school]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[The Big Idea]]></category> <category><![CDATA[Teach Less Learn More]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=93</guid> <description><![CDATA[Primary 4 pupils from Mee Toh School take five whole lessons to solve a couple of non-routine Math […]]]></description> <content:encoded><![CDATA[<p><em><strong>Primary 4 pupils from <a href="https://www.meetoh.moe.edu.sg/" target="_blank" rel="noopener">Mee Toh School</a> take five whole lessons to solve a couple of non-routine Math word problems. It’s not because they don’t know how to. In fact, the Math teachers had specially planned the lessons to be this way. Find out how they went about developing these lessons.</strong></em></p> <div class="message-box-wrapper #ff6600"> <div class="message-box-title">Article highlights</div> <div class="message-box-content"> <ul> <li>Why do some pupils struggle with solving non-routine word problems?</li> <li>How can we help pupils to understand non-routine problems?</li> <li>What can teachers do to improve a problem-solving approach?</li> </ul> </div> </div> <p>When asked if they were “ready for the challenge”, a class of Primary 4 pupils burst out in cheers: “Yeah!” This is something which rarely happens in a typical Math class. The enthusiasm and excitement to learn Math is a result of the work by four passionate teachers who identified the learning patterns of their pupils during Math lessons.</p> <h1>Taking Time to Understand</h1> <p>“Our pupils often encounter difficulties while solving non-routine word problems,” says Mrs Leong Seek Eng, the Head of Department for Math.</p> <p><img loading="lazy" class="alignleft size-full wp-image-180" title="mathed2-for-web" alt="" src="/wp-content/uploads/mathed2-for-web.jpg" width="315" height="238" /></p> <p>The teachers realized that teaching pupils to use Polya’s four-step method of understanding, planning, solving and checking wasn’t sufficient. Pupils were not focusing on the first two steps well enough to help them solve the non-routine problems with greater success.</p> <p>As these pupils do not invest enough time on understanding the question and planning the solution, they tend to be less systematic when approaching a question. When they fail to find the solution and are stuck in a rut, it affects their self-confidence.</p> <p>So Seek Eng, together with Math teachers Mdm Amalina and Mrs Mohana Parthiben and Research Activist Mr Darren Yeo, embarked on a project to get pupils in the habit of understanding a problem first before planning the solution.</p> <h1>Tackling Problems Properly</h1> <p>Rather than dictating that the pupils read and understand the question before attempting to answer it, the team decided to try a different approach.</p> <p>They adopted the STARtUP tool, which stands for “START Understanding and Planning”. STARtUP consists of five components – <em>Given</em>, <em>Find</em>, <em>Picture</em>, <em>Topic(s)</em> and <em>Heuristic(s)</em>. The aim of this framework is to remind pupils not to rush into solving a problem without going through the steps of understanding and planning.</p> <p>“Each session, we cover one component,” shares Amalina. “For example, <em>Given</em> will be covered in one session. The next session, we cover <em>Find</em>.”</p> <p>This approach was adapted from Dr Lee Ngan Hoe’s Problem Wheel. Dr Lee is an Assistant Professor with the Mathematics and Mathematics Education Academic Group in NIE. (Find out more about Dr Lee’s Problem Wheel in “<a title="Teaching this thing called “metacognition”" href="https://singteach.nie.edu.sgissue20-mathed/">Teaching This Thing Called Metacognition</a>“, <em>SingTeach</em>, Issue 20.)</p> <p>Originally designed for secondary students, the team of teachers at Mee Toh modified it for their younger learners.</p> <p>“This project focuses on non-routine problems,” Darren says. “These are challenging problems that pupils often struggle with.”</p> <div class="message-box-wrapper yellow"> <div class="message-box-title">Problem Solving with the STARtUP Tool</div> <div class="message-box-content"> In a typical Primary 4 Math class at Mee Toh School, pupils will take approximately five lessons to complete a couple of word problem sums. One lesson is devoted to each of the five components from the STARtUP tool.</p> <ul> <li><strong><em>Given</em></strong>: Pupils spend some time understanding a non-routine problem. They will identify and list down the key information in the question.</li> <li><strong><em>Find</em></strong>: Pupils identify what information is missing from the question and list down what they are supposed to find to help them solve the problem.</li> <li><strong><em>Picture</em></strong>: To enable the pupils to get a deeper understanding of the question, they will represent the information they have found visually. Pupils may draw a picture or bar model to represent the question.</li> <li><strong><em>Topic</em></strong>: Planning begins here where pupils identify the topics covered in the non-routine problem, such as Factors and Multiples or Fractions. They also write what they know about the identified topic(s).</li> <li><strong><em>Heuristic</em></strong>: The final stage involves pupils coming up with strategies to solve the problem. Some of the heuristics include working backwards, looking for a pattern and making a supposition.</li> </ul> <p>This approach is especially helpful when solving non-routine questions that are almost impossible to solve immediately. An example of such a question is:</p> <p style="padding-left: 30px;"><em>Adam and Dave had a total of 250 marbles. Adam gave 58 marbles to Dave and then Dave gave 45 marbles back to Adam. Both of them then had the same number of marbles in the end. How many marbles did Dave have at first?</em></p> <p>With some guidance from their teachers, pupils are required to understand this question before deciding an appropriate heuristic they can use to solve it. It’s a challenge they gladly welcome.</p> <p>The STARtUP tool facilitates the pupils in approaching the questions systematically without rushing into getting the answers. It promotes metacognition as they would have to understand the questions thoroughly and plan the strategies to solve them. </div> </div> <h1>Problem Solving with Confidence</h1> <p>One important factor to making lessons successful is by asking pupils questions that will stimulate their thoughts. To guide pupils in planning the solution to a problem, the scaffolding questions are carefully planned.</p> <p>“I think it is more on questioning techniques,” says Mohana, a Learning Support teacher for Math. “That’s why we include this when we plan – what kind of questions we want the teachers to ask.”</p> <p><div class="shortcode-block-quote-right" style="color:#999999"> There is a lot of professional development when we discuss our teaching.</p> <p>– <strong>Mrs Leong Seek Eng</strong>,<em> Mee Toh School</em> </div> </p> <p>This method of tackling a problem sum ensures that pupils understand the question enough to solve it at the end of five lessons. A single lesson lasts an hour. Although it does take more time, pupils learn how to properly approach a Math problem, and with this understanding, their attention span improves.</p> <p>With STARtUP, pupils will learn to be independent learners and not be afraid of making mistakes. It helps them overcome their habits of erasing their written work when their answer is different from their classmates.</p> <p>“They should identify what has gone wrong and correct their own solutions,” Amalina says. “This helps to build their confidence in problem solving.”</p> <h1>Sharpening Teaching Skills</h1> <p>The team went through a few stages of planning and development before implementing the framework in a Primary 4 class last year. This year, the team has made additional improvements to the framework.</p> <p><img loading="lazy" class="alignright size-full wp-image-181" title="mathed1-for-web" alt="" src="/wp-content/uploads/mathed1-for-web.jpg" width="315" height="198" /></p> <p>Through in-house training sessions, the teachers sharpen their skills in setting level – appropriate questions for their pupils. They are also able to set questions for pupils of different abilities to ensure a richer learning experience.</p> <p>It took the team many sessions of brainstorming to develop a curriculum that would best meet the needs of their pupils. As part of the teachers’ professional development, they are also required to meet weekly and exchange ideas and experiences.</p> <p>“There is a lot of development going on when we discuss our teaching,” Seek Eng adds. “We hear how other teachers go about teaching <em>Heuristics</em> effectively.”</p> <p>Although a lot of hard work goes into the planning of such a curriculum, it all pays off when they see pupils who were once uninterested in Math now so alive in class when solving problem sums. As Mohana puts it: “We were so impressed!”</p> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2012/11/02/issue39-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>Calculated for Success in Math</title> <link>https://singteach.nie.edu.sg/2012/09/01/issue38-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue38-mathed</link> <comments>https://singteach.nie.edu.sg/2012/09/01/issue38-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Sat, 01 Sep 2012 01:08:43 +0000</pubDate> <category><![CDATA[issue 38 sep / oct 2012]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[Learner anxiety]]></category> <category><![CDATA[Research in Action]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Problem solving]]></category> <category><![CDATA[Differentiated instruction]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=139</guid> <description><![CDATA[Imagine a Math classroom where all students answer freely without fear of being wrong, and where they can […]]]></description> <content:encoded><![CDATA[<p><em><strong>Imagine a Math classroom where all students answer freely without fear of being wrong, and where they can easily relate Math to everyday use. Dr Joseph Yeo tells us how teachers can successfully plan for every student to be engaged during their lessons, regardless of the students’ abilities.</strong></em></p> <div class="message-box-wrapper white"> <div class="message-box-title">Article highlights</div> <div class="message-box-content"> <ul> <li>How can a low-anxiety classroom support diverse learning needs?</li> <li>Can different teaching approaches be used to meet the same instructional objective?</li> <li>What are some ways to make Math meaningful for all learners?</li> </ul> </div> </div> <p>A subject of formulas and methods, one would think Math should be taught with mechanical precision. Every step is drilled into the student, no matter the individual’s learning needs.</p> <p>But our classrooms are not made up of just one type of students. More often than not, it’s a room of mixed-ability learners. Because of this, Math teachers also face the challenge of understanding different student needs and how to address them.</p> <p>Dr Joseph Yeo, who has been teaching since 1988, knows this from experience and learning theories.</p> <p>“You need to pay special attention to diverse learners and differentiate the students according to their abilities. You need to understand that different students learn differently and learn at different pace.”</p> <h1>Creating a Low-anxiety Classroom</h1> <p>To support all your learners, Joseph suggests creating a low-anxiety classroom.</p> <p><img loading="lazy" class="alignright size-full wp-image-488" title="mathed-for-web1" src="https://singteach.nie.edu.sg/wp-content/uploads/mathed-for-web1.jpg" alt="" width="315" height="204" />“Diverse learners not only have different learning styles but they will have different affective domains. Some students have Math anxiety or dislike Math. That’s where the Math teacher needs to create a low-anxiety environment to engage the students.”</p> <p>To do this, he celebrates the “little successes”. It is not, however, just about rewarding students when they get the right answer.</p> <p>“While we point out the students’ errors and we correct their misconceptions, we should not belittle the students,” Joseph says. “You praise the attempt and recognize the effort.”</p> <p>In so doing, you are creating a space where students feel comfortable participating actively and are not afraid of being penalized for the wrong answer.</p> <h1>One Objective, Different Methods</h1> <p>Another way to create a low-anxiety classroom is to plan your lessons with a clear objective, and one that <em>all</em> learners can reach, rather than to “teach to the middle level of a class”.</p> <p><div class="shortcode-block-quote-left" style="color:#999999"> You need to understand that different students learn differently and learn at different pace.</p> <p>– <strong>Joseph Yeo</strong>,<em> Mathematics and Mathematics Education Academic Group</em> </div> <p> “Don’t plan without instructional objectives,” Joseph reminds us. “Although it is for diverse learners, the objective given must be specific. And it is important that it is made clear to the students at the outset. Your specific instructional objective must always be on your mind.”</p> <p>Though there may be one specific instructional objective, the method of instruction and the types of resources used could be varied to cater to diverse learners. This objective guides the choice of teaching strategy.</p> <p>For example, a mathematical concept could be represented in various forms. “It can be concrete, pictorial, or symbolic,” says Joseph. “Some students prefer to act out, some prefer to be engaged in activity, some prefer to hear it, and some prefer to draw.”</p> <p>Classroom activities can also be varied to engage them. “The activity that I give them can be differentiated. Different students will do different activities in the class but at the end point they achieve the same instructional objective.”</p> <div class="message-box-wrapper yellow"> <div class="message-box-title">Understanding the How and Why of Math</div> <div class="message-box-content"> <p>“Math teaching involves not just instrumental understanding but relational understanding,” says Joseph.</p> <p>He distinguishes between the two: Instrumental understanding is the how-to-do. Relational understanding refers to the why.</p> <p>Due to the constraints of the classroom, some teachers tend to focus on the procedural aspects of Math. They give instructions for students to follow. But to make learning Math meaningful, we also need to pay attention to the reasons behind the procedures.</p> <p>For example, the formula for finding the area of a rectangle is <em>length</em> x <em>breadth</em>. To get students to understand why this is so, they can do an activity to derive the results and verify the formula. This way, we can create conceptual understanding before teaching procedural understanding.</p> <p>Knowing how to do is one thing, but knowing why will help students in the longer term. “If I know how to do but I do not know the reason why, I won’t be able to transfer the knowledge to the next topic.”</p> <p>“In a way, you also encourage the learners to understand,” notes Joseph. “If learners know the how-to-do and the reasons for doing it, then they will be eager to participate.”</p> </div> </div> <h1>Putting Math into Context</h1> <p>A simple way to reach out to every student is to put what they are learning into a familiar context. He uses everyday situations that students can easily relate to so that they can understand the mathematical concept better.</p> <p>“I vary my activities. I give a context that is meaningful to them, something they have experienced in their lives,” explains Joseph.</p> <p><img loading="lazy" class="size-full wp-image-489 alignright" title="mathed-for-web3" src="https://singteach.nie.edu.sg/wp-content/uploads/mathed-for-web3.jpg" alt="" width="315" height="209" /></p> <p>For example, when teaching percentage to learners, one of the teaching tools we could use is dining receipts. Asking each student where he or she would like to eat at, Joseph produces a receipt corresponding to the student’s choice – much to the student’s delight.</p> <p>At this point, the student is already involved in the activity. All that is left to do is to explain how the 7% GST and 10% service charge add to the bill.</p> <p>Other than using familiar resources, Joseph gets his students to talk about how they experience mathematics in their lives.</p> <p>“When teaching speed, teachers can’t make the students run around in the classroom, but they could get them to narrate the experiences that they have encountered in their lives. When they talk about it, it becomes meaningful to them.”</p> <p>Teaching mathematics to diverse learners need not be procedural. It’s about purposefully planning for it to be meaningful. And because mathematics is all around us, we do not have to worry about running out of ideas.</p> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2012/09/01/issue38-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>Problem Finding and Mathematical Thinking</title> <link>https://singteach.nie.edu.sg/2012/06/30/issue37-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue37-mathed</link> <comments>https://singteach.nie.edu.sg/2012/06/30/issue37-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Fri, 29 Jun 2012 21:14:46 +0000</pubDate> <category><![CDATA[issue 37 jul / aug 2012]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Problem solving]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[Problem finding]]></category> <category><![CDATA[Inventive thinking]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=526</guid> <description><![CDATA[Many people believe creativity begins with finding many solutions to a problem. What if that’s actually at the […]]]></description> <content:encoded><![CDATA[<p><strong>Many people believe creativity begins with finding many solutions to a problem. What if that’s actually at the end of the process? Dr Manu Kapur is turning the creative thinking process on its head and exploring the mechanics of problem finding – and we believe he’s on to something!</strong></p> <div class="message-box-wrapper white"> <div class="message-box-title">Article highlights</div> <div class="message-box-content"> <ul> <li>How is problem finding different from problem solving?</li> <li>Why is problem finding an important skill to develop?</li> <li>How can problem finding develop mathematical thinking?</li> </ul> </div> </div> <p>Philosophers and scientists alike have claimed that problem finding is important but in truth, we don’t really understand what the process looks like.</p> <p>That’s a gap Associate Professor Manu Kapur, Head of NIE’s Learning Sciences Lab, hopes to plug – both in terms of our understanding of the problem-finding process as well as the practice of Math in schools.</p> <p><img loading="lazy" class="alignnone size-full wp-image-529" title="mathed-for-web" src="https://singteach.nie.edu.sg/wp-content/uploads/mathed-for-web.jpg" alt="" width="620" height="193" /></p> <h1>So What’s the Problem?</h1> <p>In traditional problem-solving situations in schools, the Math problem is either fully specified or known to a great degree. The assumption is that students have sufficient knowledge to solve these problems because they have been taught and the goal is specified.</p> <p>With problem finding, however, the problem itself is not known. We may not even have enough knowledge to solve the problem, which is the case in many of the challenges we encounter in life.</p> <p>“We have a very good sense of the processes of problem solving, but we don’t quite have a theory or an understanding of what the process of finding a good problem looks like,” says Manu.</p> <p>So instead of giving students a set of data and asking them to calculate something definite, we give them the data and say: What problems can we generate based on this data? He gives the example of soccer league tables. Instead of asking them to invent various measures to determine who the best team is, students can ask and answer mathematical questions of their own.</p> <p>“That’s a very different enterprise, where students have to use whatever knowledge they have, both formal and informal knowledge, to really start thinking.” This, says Manu, provides a huge opportunity for developing mathematical thinking and invention.</p> <p>“The mere act of defining the problem, even though you’re asking students to invent multiple solutions, constrains mathematical thinking,” he explains. “You would be surprised by how many important problems you could define just given the data, which you would miss if you just gave students a problem and asked them to solve it.”</p> <h1>The Process of Problem Finding</h1> <p>So what does this process of problem finding look like? And what implications does it have for schooling and education? That’s the area of research that Manu wants to start looking into.</p> <p><div class="shortcode-block-quote-right" style="color:#999999">We have a very good sense of the processes of problem solving, but we don’t quite have a theory or an understanding of what the process of finding a good problem looks like.</p> <p>– <strong>Manu Kapur</strong>, <em>Learning Sciences Lab</em> </div> </p> <p>We know a lot about the processes of problem solving in the cognitive and the learning sciences, but not about problem finding, says Manu. Yet every time we talk about innovation, inventiveness, or breakthroughs, people say it’s thinking about a problem to solve that’s more important than actually solving the problem.</p> <p>“If you look at the history of scientific revolution, or the history of innovation, invariably it’s about finding a good problem to solve, and yet we don’t have an understanding of that process,” explains Manu.</p> <p>Interestingly, the process of solving a problem is much easier than finding a useful problem to solve. Problem finding is a very long, divergent and iterative process – you don’t know until you try many things, until you finally stumble upon a good problem to solve.</p> <p>“Once you’ve defined a good problem to solve, it’s easy to solve the problem!” Not that solving a problem is not difficult, Manu qualifies. But it’s not as difficult as finding an inventive, original and meaningful problem to solve.</p> <h1>Developing Inventive Thinkers</h1> <p>“There’s a lot of rhetoric around creating students who are inventive, entrepreneurial, innovative, creative,” notes Manu. “I think the more we understand this process, the more we will learn about how to use this process more effectively for education.”</p> <p>He differentiates between inventing your own problems and inventing multiple solutions to given problems. The latter is good and necessary to train people to solve problems – we need workers like that in the workforce.</p> <p>“But if you want the leaders and the innovators, then you want these people to think of important problems to solve, so that as a society we move higher up in the value chain.”</p> <p>While it is still early days, Manu is hopeful that addressing <em>this </em>problem will not only help students learn Math better, but also help develop the dispositions of creativity and inventive thinking. For the moment, he is working on designing problem-finding activities that can help develop this skill.</p> <p>“This is really about inventing your own problems and then developing the skill to see which problems are better than others. If we can develop this skill in our students, then they will be much better prepared for the 21st century.”</p> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2012/06/30/issue37-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>New Ways to Learn</title> <link>https://singteach.nie.edu.sg/2012/02/20/issue35-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue35-mathed</link> <comments>https://singteach.nie.edu.sg/2012/02/20/issue35-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Mon, 20 Feb 2012 03:00:34 +0000</pubDate> <category><![CDATA[issue 35 mar / apr 2012]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Professional development]]></category> <category><![CDATA[Technology]]></category> <category><![CDATA[Student engagement]]></category> <category><![CDATA[Scaffolding]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[Self-directed learning]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=7479</guid> <description><![CDATA[Clear delivery of content used to be equated with good teaching. The teachers of today, though, are going […]]]></description> <content:encoded><![CDATA[<p dir="ltr" data-font-name="g_font_p0_22" data-canvas-width="445.85746014022845"><strong><em>Clear delivery of content used to be equated with good teaching. The teachers of today, though, are going beyond that to engage their students in the Math classroom. Master Teacher Cynthia Seto points the way.</em></strong></p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="54.523639974594126">When Cynthia started teaching in 1979, she used vanguard sheets to create charts for her Math classes. Teachers now can easily do much more using computer software.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="152.36510099983218">Resources are not the only difference between then and now. On pedagogy, she notes: “The emphasis was on clear delivery to the children, with very explicit examples. I’m not saying those are no good but now we need to go beyond that to engage them in learning.”</p> <h1 dir="ltr" data-font-name="g_font_p0_6" data-canvas-width="125.91127430725095">Engaging Students<img loading="lazy" class="size-full wp-image-7508 alignright" alt="" src="https://singteach.nie.edu.sg/wp-content/uploads/2013/10/MathEd-for-web.jpg" width="315" height="336" /></h1> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="482.9367592563629">As Master Teacher, Cynthia mentors fellow Math teachers. She also seeks to promote teacher leadership and ownership of their professional development through networked learning.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="184.88292133522037">As she sees it, “going beyond” the clear delivery of content means the role of the teacher has expanded. “Not only do we need to be good teachers, we also need to be facilitators and co-learners.”</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="459.88366682052623">This means teachers have the opportunity to interact and learn with their students. And even though we want students to be self-directed learners, teachers should observe the students and know when and how to step in to guide them along.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="207.76583194160463">“When to scaffold and when to let go a little bit for students to explore, to make sense of their learning, and when to give the right amount of practice, which is very important in Math,” she elaborates.</p> <h1 dir="ltr" data-font-name="g_font_p0_6" data-canvas-width="144.34472908401492">Engaging Technology</h1> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="477.4647588939667">Another way to engage students is to make use of what they like – technology. “Those children, when you give them computers and technology, their eyes will sparkle!”</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="141.7745548439026">Teachers are encouraged to tap on information and communications technology (ICT) to enhance students’ learning. Cynthia gives an example of how she would teach the concept of π (pi) to a Math class today.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="427.0778464660648">Give each student a string to measure the circumference and diameter of a circular object, such as a coaster. Then get them to divide the circumference by the diameter, and enter the data into an ICT platform that allows real-time sharing of information and facilitates the analysis of the underlying mathematical relationships.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="316.27638458251965">“With technology, it enables the children to have access to others’ data. When you have multiple data, it helps them to be able to see different perspectives and patterns, to come to a conclusion, and to generalize.”</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="343.88511368370064">“We want to engage the students in this way because we want them to develop this kind of thinking, to identify patterns and see relationships,” Cynthia explains. “These are important skills they need to have in the 21st century.”</p> <h1 dir="ltr" data-font-name="g_font_p0_6" data-canvas-width="204.99272984504708">Learning the Language of Math</h1> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="249.77456199645994">In the 21st century classroom, we also want our students to be able to justify their solutions, besides giving the correct answers. They should be able to solve the Math problem and explain how they did it, explains Cynthia.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="330.100385498047"> <div class="shortcode-block-quote-right" style="color:#999999"> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="186.81018738555912">Have conversations with like-minded people, so that you can exchange ideas and know what’s happening.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="237.31200707244875">– <strong><em>Cynthia Seto</em></strong><em></em>, on how to become a better teacher</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="330.100385498047"></div> </p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="55.989821889877334">Students also need to communicate their thought processes, especially for problem sums. To achieve this, teachers need to help them learn the language of Math.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="491.13166888999945">Getting students to be peer assessors can help them become effective communicators.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="425.72948274040243">For example, the teacher can get one student to pose a Math problem. The rest of the class then uploads their solutions using an ICT-sharing platform. The first student then acts as a teacher and explains why each answer is right or wrong.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="435.4429379291535">“We want children to have this disciplinary thinking in Math, to see situations and generalize, and to summarize what they have learned. At the same time, we also want children to be able to communicate Math effectively to one another.”</p> <h1 dir="ltr" data-font-name="g_font_p0_6" data-canvas-width="168.16727483749398">Engaging Other Teachers</h1> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="117.94909872055055">What makes a good teacher? And what advice would she give to fellow teachers who want to teach well?</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="484.63857755088804">“Number one, you need to read up,” says Cynthia. “Read not only about pedagogy, but in terms of your own content knowledge. Content knowledge is a non-negotiable.”</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="244.89165258216858">Besides having strong subject mastery, teachers need to have a good understanding of the learners and the learning environment. That means understanding the social, psychological and pedagogical contexts in which learning occurs and how these affect student achievement and attitudes.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="288.4189281921387">“The other important thing is to have conversations with like-minded people, so that you can exchange ideas and know what’s happening,” recommends Cynthia. One of the best ways to do so is to engage in research.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="58.17600385284425">Research can “sharpen your senses, and develop ‘eyes’ to see what is happening in the classroom”. In this way, teachers will not just be able to deliver a lesson clearly, but also develop a clear vision of how various teaching strategies can benefit their students.</p> <p dir="ltr" data-font-name="g_font_p0_1" data-canvas-width="316.27638458251965">With these in mind, teachers will be able to ensure that they are teaching to the needs of the students and to make sure they are ready for the world beyond the classroom.</p> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2012/02/20/issue35-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>Formula for a Good Math Teacher</title> <link>https://singteach.nie.edu.sg/2012/01/20/issue34-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue34-mathed</link> <comments>https://singteach.nie.edu.sg/2012/01/20/issue34-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Fri, 20 Jan 2012 02:40:37 +0000</pubDate> <category><![CDATA[issue 34 jan / feb 2012]]></category> <category><![CDATA[Values education]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Professional development]]></category> <category><![CDATA[21st century competencies]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[Teacher professionalism]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=698</guid> <description><![CDATA[If technology can replace the human teacher, does that make the teacher obsolete? Certainly not, says Dr Ang […]]]></description> <content:encoded><![CDATA[<p><strong>If technology can replace the human teacher, does that make the teacher obsolete? Certainly not, says Dr Ang Keng Cheng, who believes that being a good Math teacher is more than just functions and formulae.</strong></p> <div class="message-box-wrapper white"> <div class="message-box-title">Article highlights</div> <div class="message-box-content"> <ul> <li>Is the Math classroom very different today?</li> <li>How can Math teachers impart values?</li> <li>What is required of Math teachers in the 21st century?</li> </ul> </div> </div> <p>“Love Math and love teaching Math”. That is what makes a good Math teacher, according to Associate Professor Ang Keng Cheng, who heads NIE’s Mathematics and Mathematics Education (MME) Academic Group.</p> <h1>Living Math</h1> <p><img loading="lazy" class="alignright size-full wp-image-700" title="mathed-for-web (1)" src="https://singteach.nie.edu.sg/wp-content/uploads/mathed-for-web-1.jpg" alt="" width="315" height="243" />It goes without saying that we expect our Math teachers to have mastery of mathematical content knowledge. But content alone is not enough, says Dr Ang. A good teacher needs good “pedagogical sense”.</p> <p>“Teachers need to balance content mastery with the craft skills in pedagogy. Having the pedagogical skills to go with the content mastery will add a lot more value to a classroom teacher.”</p> <p>Adding value to students’ lives remains fundamental, despite the many new challenges we’ve seen in the classroom. One of the challenges has come in the form of technology, which has also made students more savvy in many ways.</p> <p>But Dr Ang reminds us that the role of the teacher hasn’t changed: It is always to facilitate and motivate learning. While technology has made it easier for students to access information on their own, it has also reinforced the need for teachers.</p> <p>“The fact that the technology can deliver the content doesn’t mean that the learner can learn,” he says. “Learning can be, at times, a complex and dynamic process.”</p> <p>“For different people, learning is different. The teacher is in a better position to assess these differences, compared to any form of technology. It is difficult to have a one-size-fits-all computer software to facilitate learning.”</p> <h1>Valuing Math</h1> <p>For Dr Ang, who started out as a Math teacher in the 1980s, there is more to teaching Math. For him, what intrigued him to teach was the way Math could be applied to solve real-life problems.</p> <p><div class="shortcode-block-quote-right" style="color:#999999"> In a classroom, we have to deliver well. But it is not enough to be successful as a professional. A teacher has to go beyond the classroom.</p> <p><em>– <strong>Assoc Prof Ang Keng Cheng</strong>, Mathematics and Mathematics Education Academic Group</em> </div> </p> <p>“It has always been my personal wish to see teachers not only talk about formulae, algorithms and methods, but to also explain mathematical concepts, and how they can be used in real life.”</p> <p>Making Math come alive has become all the more relevant to 21st century teaching. These days, a teacher has to do more than just teach content knowledge – we need to impart values and skills.</p> <p>And there are a lot of values in the teaching of Math, says Dr Ang. He calls this a “hidden curriculum” in the training of Math teachers.</p> <p>“We have been doing these things, for example, building character and developing perseverance. We put our trainees in a situation where they have to solve problems, and it takes time. This builds perseverance. This is part of the value system a person has to have in order to be successful in doing Math.”</p> <h1>Success Factors</h1> <p>For all pre-service teachers, MME’s aim is to make sure our Math teachers are “functional” and able to “hit the ground running” from the day they step into a classroom.</p> <p>But unlike their subject, there is no standard formula that determines success for Math teachers. Dr Ang goes back to the basics: “A good Math teacher should have passion for both the subject and for teaching children.”</p> <p>Dr Ang stresses the importance of continual learning and hard work in all this. “If one were to just sit down, do routine work and the bare minimum, there is little hope that one will do well.”</p> <p>“If you think you are lacking in some areas, you will make the effort to make up for it if you are really passionate about it,” he adds. “When you are passionate about teaching, you would want to do well and other things will naturally fall into place.”</p> <p>Looking on the bright side, Dr Ang says, “It is exciting in a sense, that the teachers’ job is no longer routine. That may be the perception in the past, but not anymore.”</p> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2012/01/20/issue34-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>Understanding Students’ Misconceptions in Learning</title> <link>https://singteach.nie.edu.sg/2011/09/01/issue32-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue32-mathed</link> <comments>https://singteach.nie.edu.sg/2011/09/01/issue32-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Thu, 01 Sep 2011 07:14:39 +0000</pubDate> <category><![CDATA[issue 32 sep / oct 2011]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Secondary school]]></category> <category><![CDATA[Action research]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[Lesson study]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=764</guid> <description><![CDATA[by Choy Chan Hong, Irving Quah, Tan Wen Dee and Toh Pui Yhing If we want our students […]]]></description> <content:encoded><![CDATA[<p class="content-body"><strong>by Choy Chan Hong, Irving Quah, Tan Wen Dee and Toh Pui Yhing</strong></p> <p class="content-body"><strong>If we want our students to learn from us, we may have to start learning from them. Through the lesson study process, our focus shifts from how we teach to how they learn, and a culture of observation and discussion is created.</strong></p> <div class="message-box-wrapper white"> <div class="message-box-title">Article highlights</div> <div class="message-box-content"> <ul> <li>How can we find out how learning is taking place in the minds of students?</li> <li>How can we plan the lesson to ensure our students learn better?</li> <li>How can we promote lesson study as a tool for professional learning?</li> </ul> </div> </div> <p>Do our students really understand what they have learned? Are they able to transfer the knowledge and apply it to new situations? What difficulties do students face and how can we help them? As teachers, we need to be aware of our students’ learning behaviours. If they are not able to apply their learning correctly, it could be due to misconceptions (Carpenter & Lehrer, 1999). This awareness can help us adapt our teaching strategies to better impact our students’ learning.</p> <h1>“Seeing” Our Students Learn</h1> <p>In 2008, the Math Department at Clementi Town Secondary School adopted lesson study in our professional learning teams. Lesson study has taught us to understand our students’ misconceptions, the reasons behind these misconceptions, their physical and verbal responses during lessons, the quality of their work, their attitudes as well as how they interacted with their classmates.</p> <p><img loading="lazy" class="alignright wp-image-767" title="mathed2-for-web" src="https://singteach.nie.edu.sg/wp-content/uploads/mathed2-for-web1.jpg" alt="" width="284" height="212" />In our research lessons, we usually start off with a recapitulation activity to draw out any misconceptions of basic concepts. We address these before introducing new ones.</p> <p>For example, in one of the research lessons, we used a cuboid tank and planes made from acrylic as a trigger activity to help the students visualize a trigonometry problem. Through the lesson observation and post-lesson discussions, we received immediate and valuable feedback that helped us to understand the students’ misconceptions and learning behaviours.</p> <p>Based on this feedback, we revised our worksheet to provide clearer instructions for future lessons. The teacher who taught the lesson also made a conscious effort to guide the students through the activity by using probing questions.</p> <h1>Guiding Our Students’ Learning</h1> <p>From our ongoing journey in lesson study, we have gained some important insights on preparing effective lessons. We have found that it is important to:</p> <ul> <li>delineate the lesson objectives explicitly so that the students know what they are going to learn;</li> <li>plan the lesson with proper scaffolding from one section to another to optimize time and the learning process;</li> <li>consider the dynamics of the class so that you can group the students effectively for collaborative learning; and</li> <li>ensure instructions are clear and, if needed, model the lesson activities for students.</li> </ul> <p><img loading="lazy" class="alignleft size-full wp-image-769" title="mathed1-for-web" src="https://singteach.nie.edu.sg/wp-content/uploads/mathed1-for-web1.jpg" alt="" width="315" height="176" />We also found that we need to enhance our students’ inquiry skills (the type and frequency of questions asked) to promote deep thinking. This would help students make sense of their learning and connect their learning to pre-existing knowledge (Piaget, 1964, 1969).</p> <p>Guided by the learning points we had gleaned through lesson study, we have been able to enhance our teaching practices to improve students’ understanding of the lessons and achieve the lesson goals.</p> <h1>Strengthening Teacher Learning</h1> <p>Over the years, strong collegial bonds have been forged between the teachers. Through the lesson study process, we have begun to establish a classroom culture of observing our students closely in order to improve student learning.</p> <p><div class="shortcode-block-quote-center" style="color:#999999"> As teachers, we need to be aware of our students’ learning behaviours…<br /> This awareness can help us adapt our teaching strategies to better impact our students’ learning.</p> <p><em>– <strong>Math teachers</strong>, Clementi Town Secondary School</em> </div> </p> <p>Having benefited from the process of lesson study, we wanted to share our experience with fellow educators and allow them to have a first-hand experience of observing a public research lesson. We successfully implemented the first public research lesson in March 2011 with a Secondary 5 Normal (Academic) Math class.</p> <p>The public lesson was attended by more than 50 participants, including school leaders and teachers from other schools. They had the opportunity to analyse the students’ behaviours in an authentic, real-time classroom setting, and discuss ways to further improve the instructional plan through an evidence-based and structured approach.</p> <p>The post-lesson conferences are especially useful in sharpening our classroom instruction collectively in a non-intrusive manner. For this event, we had two eminent Japanese educators present, who provided rich insights for all participants. We hope more fellow educators can learn about lesson study through experiencing it themselves.</p> <p><strong>References</strong><br /> Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), <em>Mathematics classrooms that promote understanding</em> (pp. 19-32). Mahwah, NJ: Lawrence Erlbaum Associates.</p> <p>Piaget, J. (1964). Development and learning. In R. Ripple & V. Rockcastle (Eds.), <em>Piaget rediscovered</em> (pp. 78-119). Washington, DC: U.S. Office of Education, National Science Foundation. Piaget, J. (1969). <em>Science of education and the psychology of the child</em>. New York: Viking.</p> <p><strong>Related article</strong><br /> Read a previous article about <a title="Lesson Study in Action" href="https://singteach.nie.edu.sgissue29-teachered/">“Lesson Study in Action”</a> in <a href="https://singteach.nie.edu.sgcategory/issues/issue29-mar-apr2011/"><em>SingTeach</em> Issue 29</a>.</p> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2011/09/01/issue32-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>Helping Low Attainers to Keep Up</title> <link>https://singteach.nie.edu.sg/2011/07/01/issue31-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue31-mathed</link> <comments>https://singteach.nie.edu.sg/2011/07/01/issue31-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Fri, 01 Jul 2011 08:24:55 +0000</pubDate> <category><![CDATA[issue 31 jul / aug 2011]]></category> <category><![CDATA[Motivation]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[Redesigning Pedagogy Conference]]></category> <category><![CDATA[Self-belief]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Low attainers]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=802</guid> <description><![CDATA[Singapore pupils ace Math in international studies so often that it’s easy to forget there are some who […]]]></description> <content:encoded><![CDATA[<p class="content-body"><strong>Singapore pupils ace Math in international studies so often that it’s easy to forget there are some who struggle with the subject. How we can make their experiences in learning Math more positive for them?<br /> </strong></p> <div class="message-box-wrapper white"> <div class="message-box-title">Article highlights</div> <div class="message-box-content"> <ul> <li>Why do some pupils struggle with Math?</li> <li>How do low attainers feel about learning Math?</li> <li>How can we motivate them to learn better?</li> </ul> </div> </div> <p>In every school, there is a small group of pupils who frequently fail their Math assessments. They may be slow learners, less able or under-performing. Whatever the case, if not attended to, these “low attainers” will continue to fall further and further behind their peers.</p> <p><a href="https://www.nie.edu.sg/profile/berinderjeet-kaur" target="_blank" rel="noopener">Professor Berinderjeet Kaur</a> and her research team set out to study the characteristics of these pupils and their experiences in learning Math. They also wanted to know how schools identify such low attainers and address their learning needs.</p> <h1>Problems with Math Learning</h1> <p>The team asked the Primary 4 pupils in their study to journal how they feel about learning Math. These were some of the common responses:</p> <p style="padding-left: 30px;"><em>“I hate Maths. I found that it was very difficult because Maths needs a lot of thinking.”<br /> “I love Mathematics when I understand, like when I first started whole numbers.”<br /> “I feel sad about mathematics because I don’t know how to use a protractor.”<br /> “When I am learning mathematics, I feel confused…because Maths is hard for me to learn. Problem sums is the hardest.”<br /> </em></p> <p>They found that most of these pupils actually enjoy the subject initially. Math is easy and fun when they can understand the topic. But as it gets more advanced, they cannot keep up. Boredom, stress and even sadness are mentioned in their journal entries as they begin to find the subject more difficult.</p> <p>The teachers also noted that most of them are easily distracted during Math lessons. Only a third are always on-task and able to complete class work on time, and the rest are unable to cope due to their difficulties in understanding the lesson.</p> <h1>Motivation to Learn</h1> <p>The team found that pupils’ belief in their own ability is a good predictor of how well they’ll do in Math. (See related article in Issue 29:<em> Strong Links Between Self-Confidence and Math Performance</em>.)</p> <p>This group of low attainers is often not confident of doing well. When asked if they think they are good at Math, more than half said no, while most of the rest said it depends:</p> <p style="padding-left: 30px;"><em>“50–50, my family tells me I am good in maths, but I always make careless mistakes.”<br /> “Sometimes. Maths is very hard and I make careless mistakes.”<br /> “Sometimes. Doing word problem I am no good.”<br /> </em></p> <p>They are, however, eager to do well in the subject. When asked if they can do better in Math, pupils were optimistic despite their past failures. Most of them felt they could improve if they put in more time and hard work:</p> <p style="padding-left: 30px;"><em>“Yes, focus during math lessons and not talk to friends.”<br /> “Yes. Studying hard and not play games. Do more problem sums.”<br /> “Yes, by asking my parents to buy assessment books and revise everyday at home.”<br /> </em></p> <p>The Math teachers, the team observed, were very positive towards the pupils. They were generous with their praise and did not reprimand the pupils even if the answer was wrong.</p> <p>The teachers were similarly positive when asked whether these pupils were motivated to learn: a majority of them thought the pupils were trying their best to learn and were capable of improving.</p> <p>Despite this, only 15% of the pupils always sought help from the teacher when they were in doubt; more than 40% seldom or never did. It’s also hard for teachers to tell which students are having difficulties as they often elicit choral responses from the whole class during the lesson.</p> <h1>Meeting Pupils’ Learning Needs</h1> <p><img loading="lazy" class="size-full wp-image-803 alignright" title="math-group-for-web-with-names" src="https://singteach.nie.edu.sg/wp-content/uploads/math-group-for-web-with-names.jpg" alt="" width="315" height="207" /></p> <p>Pupils may not be paying attention in class because of a mismatch between how teachers teach and how learners learn.</p> <p>When asked how they would like to learn Math, many of the pupils said they’d prefer to do activities in groups, rather than individual work. Such collaborative learning allows them to consult their peers when they feel unsure.</p> <p>However, teachers tended to use direct instruction most of the time. It was observed that teachers didn’t spend enough time consolidating the learning. This is important to ensure that pupils have understood the lesson before moving on to a new task.</p> <p><div class="shortcode-block-quote-right" style="color:#999999"> Pupils’ belief in their own ability is a good predictor of how well they’ll do in Math.</p> <p><em>– <strong>Berinderjeet Kaur</strong>, Mathematics and Mathematics Education Academic Group</em> </div> </p> <p>The findings also suggest a need to rethink the way Math assessments are designed. The team found that teachers tend to set repetitive and procedural questions, which heightens the pupils’ sense of failure.</p> <p>“If the pupils cannot do one question, there are 10 other questions they cannot do as it’s the same type of question over and over again,” notes Research Assistant Masura Bte Mohamed Ghani. “They would be making the same mistake 10 times.”</p> <p>It only requires a little bit of extra effort to make learning Math more manageable for our low-attaining pupils. If we can be mindful of how they learn and take their needs into consideration, success in Math will soon be within their reach.</p> <div class="message-box-wrapper white"> <div class="message-box-title"></div> <div class="message-box-content">This article draws on findings from a research project led by <a href="https://www.nie.edu.sg/profile/berinderjeet-kaur" target="_blank" rel="noopener">Professor Berinderjeet Kaur </a>entitled An Exploratory Study of Low Attainers in Primary Mathematics.</div> </div> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2011/07/01/issue31-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>Transforming Math Lessons with New Technology</title> <link>https://singteach.nie.edu.sg/2011/05/01/issue30-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue30-mathed</link> <comments>https://singteach.nie.edu.sg/2011/05/01/issue30-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Sun, 01 May 2011 08:51:54 +0000</pubDate> <category><![CDATA[issue 30 may / jun 2011]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Technology]]></category> <category><![CDATA[Curriculum design]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[Classroom interactions]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=833</guid> <description><![CDATA[Traditional math classrooms typically see students quietly working hard at solving problems as the teacher makes her rounds […]]]></description> <content:encoded><![CDATA[<p class="content-body"><strong>Traditional math classrooms typically see students quietly working hard at solving problems as the teacher makes her rounds to check that they are on task. What happens when we do away with the problem solving and start with the solutions instead?<br /> </strong></p> <div class="message-box-wrapper white"> <div class="message-box-title">Article highlights</div> <div class="message-box-content"> <ul> <li>How is technology changing classroom interactions?</li> <li>How does technology influence math learning?</li> <li>How can teachers respond to teaching with technology?</li> </ul> </div> </div> <p>Technology is part and parcel of the daily school life for students at the School of Science and Technology (SST). But it isn’t just the technology that is transforming the way they learn.</p> <p>A team from NIE’s <a href="https://www.nie.edu.sg/research/research-offices/office-of-education-research/learning-sciences-lab" target="_blank" rel="noopener">Learning Sciences Lab </a>(LSL), led by Research Scientist <a href="https://www.lsl.nie.edu.sg/people/researchers/sarah-margaret-davis" target="_blank" rel="noopener">Sarah Davis</a>, has been exploring how we can foster critical thinking and deep understanding of math concepts with the support of highly collaborative technologies.</p> <p><img loading="lazy" class="size-full wp-image-835 alignright" title="saradavis-for-web" src="https://singteach.nie.edu.sg/wp-content/uploads/saradavis-for-web.jpg" alt="" width="315" height="236" />They are particularly interested in seeing how interactions between the teacher and students change with the use of new technology.</p> <p>“What we are focusing on are the types of activities that teachers can leverage to improve students’ talk and dialogue, communication and critical thinking, and what the classrooms will start to look like when technologies are being used,” says Sarah.</p> <h1>Dynamic Math Learning</h1> <p>Sarah has introduced the use of a program called <em>NetLogo</em> for teaching Math at SST. The use of<em> NetLogo</em> enables teachers to transform Math classes into dynamic learning platforms through networked classroom activities.</p> <p>The software is currently being applied to graphing type activities. It also has the ability to produce real-time synchronous feedback and interactions between teachers and their students.</p> <p>With <em>NetLogo</em>, students can now generate their own graphs with ease and produce immediate visual representations. It has simplified the process of computation, and allowed students to focus on the mathematical explanations behind the calculation.</p> <h1>Changing Classroom Culture</h1> <p>While still in its pilot phase, the math teachers at SST are already seeing how technology can change classroom interactions. One of the most significant changes is a shift in the classroom culture.</p> <p><div class="shortcode-block-quote-right" style="color:#999999">I have yet to go into a classroom without any questions raised.</p> <p>–<em> <strong>Jason Ingham</strong>, Subject Head of Mathematics, School of Science and Technology</em> </div> </p> <p>Jason Ingham, Subject Head of Mathematics, has noticed that his students now ask more questions – and he is glad for this.</p> <p>“I have yet to go into a classroom without any questions raised. A lot of time is spent on discussing math concepts and reinforcing one another. Students get to reinforce their understanding of math concepts by spending time talking about it,” notes Jason.</p> <p>Fellow math teacher Edmund Ng has also observed this in his classes. He notes that the quality of the interactions among the students has heightened.</p> <p>“Often, in a conventional classroom, you will find it very difficult to engage your students in interactions because of the classroom size and the amount of control you want to exert over the class,” explains Edmund. “Using the network tools and activities, you could have simultaneous interactions at the same time.”</p> <h1>Changing Learning Habits</h1> <p>Such a shift in classroom culture has been possible because the use of technology drastically cuts down on the time needed for tedious and repetitive work. This includes plotting graphs and drawing representations, which Jason describes as procedural.</p> <p>“The emphasis of the lesson can now be on the analysis of the graph rather than plotting it so a lot more time will actually be spent on looking at the conceptual aspect of things rather than the repetitive work of getting the graph right,” says Edmund. “So technology really helps with this.”</p> <p>And because students have more time to explore, experiment and learn by themselves, they are able to pick up concepts by themselves. Jason notes, “Technology helps my students and me to look at math concepts from the high level first before moving down to the details.”</p> <h1>Learning with Purpose</h1> <p>In addition to saving on time and gaining on understanding, Edmund says students need to find purpose in their learning, where they can relate math learning to the real world. Today’s technology makes it easy to bring up practical examples to interest and excite the students.</p> <p>Technology can also be extremely powerful in improving students’ math learning because of the sense of ownership students have over their work.</p> <p>“To them, this is something that they have created rather than forced on by their teachers. They see a purpose in using the product that they have created,” explains Edmund. “This part is important for them to really progress in their learning.”</p> <p><div class="shortcode-block-quote-center" style="color:#999999"> The key to improving learning in a math classroom still boils down to the pedagogy, how teachers orchestrate their classes, and the types of questions they ask their students.</p> <p><em>– <strong>Sarah Davis</strong>, Learning Sciences Lab</em> </div> </p> <h1>New Pedagogy for New Technology?</h1> <p>Math lessons have never been so exciting. Technology offers choices for content and pedagogy never experienced before. But while software like <em>NetLogo</em> allows us to save a lot of precious lesson time, offering more opportunities for spontaneous conversations and activities, we have to remember it is also just a tool.</p> <p>Sarah says that the key to improving learning in a Math classroom still boils down to the pedagogy, how teachers orchestrate their classes, and the types of questions they ask their students.</p> <p>“Technology is more like a scaffolding and directing tool,” says Jason. “You can introduce ICT into your math lessons but you can also do it didactically, so it is down to the questioning techniques. Are the teachers able to know what to ask? When and how to ask questions in a way that scaffolds learning?”</p> <p>So while the technology may be new, the goal of learning really hasn’t changed. Students need to feel that they can ask any question with no shame, say Jason and Edmund – technology has only helped to make this a little easier.</p> <div class="message-box-wrapper white"> <div class="message-box-title"></div> <div class="message-box-content">The research featured here is part of the <a href="https://www.lsl.nie.edu.sg/projects/gensing-2-pedagogy-content-and-teacher-tools-generative-classroom-gensing-project" target="_blank" rel="noopener">GenSing project </a>led by Sarah Davis, a Research Scientist with the <a href="https://www.nie.edu.sg/research/research-offices/office-of-education-research/learning-sciences-lab" target="_blank" rel="noopener">Learning Sciences Lab </a>at NIE. The project seeks to broaden curricular activities, applications and classroom management tools in the Singaporean school system, affording powerful methods for teachers to enhance math understanding.</div> </div> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2011/05/01/issue30-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>Strong Links between Self-Confidence and Math Performance</title> <link>https://singteach.nie.edu.sg/2011/03/01/issue29-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue29-mathed</link> <comments>https://singteach.nie.edu.sg/2011/03/01/issue29-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Tue, 01 Mar 2011 10:18:43 +0000</pubDate> <category><![CDATA[issue 29 mar / apr 2011]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[MathEd]]></category> <category><![CDATA[Self-belief]]></category> <category><![CDATA[Learner anxiety]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=862</guid> <description><![CDATA[Many studies have shown that there is a strong relationship between students’ self-belief and their academic performance. How […]]]></description> <content:encoded><![CDATA[<p class="content-body"><strong>Many studies have shown that there is a strong relationship between students’ self-belief and their academic performance. How can this understanding help us in the Math classroom?<br /> </strong></p> <div class="message-box-wrapper white"> <div class="message-box-title">Article highlights</div> <div class="message-box-content"> <ul> <li>What is the relationship between self-belief and math performance?</li> <li>What role does self-confidence play in learning math?</li> <li>Why is self-confidence important for math learning?</div> </div> </li> </ul> <p>An NIE study conducted by Professor Lazar Stankov, Dr Suzanne Morony and Dr Lee Yim Ping investigates self-beliefs and metacognition in mathematics students. They found that students who think they are good in math tend to perform well in math tests. What sets these students apart?</p> <h1>More about Self-belief</h1> <p>Lazar and his team suggest that students’ beliefs in their own ability are of particular importance to their math performance. He identifies four kinds of self-belief:</p> <ul> <li><strong>Self-concept</strong> refers to a student’s belief in his ability in a particular subject.<br /> <em>E.g., “I have always believed that Math is one of my best subjects.”</em></li> <li><strong>Anxiety</strong> is the apprehension a student experiences when learning math.<br /> <em>E.g., “I get very nervous doing math problems.”</em></li> <li><strong>Self-efficacy</strong> is the belief that he is capable of producing some future outcome.<br /> <em>E.g., “Even if the work in math is hard, I can learn it.”</em></li> <li><strong>Self-confidence</strong> has to do with how sure the student is about his abilities.<br /> <em>E.g., “I am confident that I have solved the math problem correctly.”</em></li> </ul> <p>“There is plenty of evidence indicating that the first three of these self-beliefs are among the best predictors of how well a child does in school,” says Lazar. “Few studies, however, investigate the role of confidence.”</p> <h1>Exploring Self-confidence in Math</h1> <p>Findings from the study show that our students are conscious of what they are capable of and can determine quite accurately what they know and what they do not know – perhaps better than students in many other countries.</p> <p>Collecting data from more than 600 Secondary 3 students in 5 schools, this is the first project in Singapore that focuses on measuring self-confidence.</p> <p><img loading="lazy" class="size-full wp-image-864 alignleft" title="lazar-and-team" src="https://singteach.nie.edu.sg/wp-content/uploads/lazar-and-team.jpg" alt="" width="315" height="236" />“From this study, we know that confidence is a much better predictor of students’ achievements than any other non-cognitive measure,” notes Lazar. “In fact, it acts in a way that it overcomes everything else; so confidence is very important.”</p> <p>“We measure students’ self-confidence by asking them to do a math test. After each item in the test, we ask how confident they are that their answers are correct,” he explains.</p> <p>Using this method, Lazar and his team calculate the students’ confidence rating. It is then compared to their percentage of correct answers. The difference between students’ confidence rating and percentage of accurate answers yields a bias score, which indicates how aware students are with regard to their math abilities.</p> <h1>Assessment for Math Learning</h1> <p>Lazar believes these confidence tests would benefit both learning and teaching. “If students strongly endorse an incorrect answer to a question, then this indicates that something has gone wrong either in the learning or teaching process.” This has important implications in the area of assessment for learning.</p> <p><div class="shortcode-block-quote-right" style="color:#999999"> If students strongly endorse an incorrect answer to a question, then this indicates that something has gone wrong either in the learning or teaching process.</p> <p>– <em><strong>Lazar Stankov</strong>, Centre for Research in Pedagogy and Practice</em> </div> </p> <p>The scores from the self-confidence tests provide students with insights into the topics they are weak in. Students who <em>think</em> they have given a correct answer to a question but are proven otherwise may gain the necessary knowledge of the kind of math topics they are weak in.</p> <p>This could encourage self-reflection in students and motivate them to pay more attention to these weaker topics. “It teaches students to really think about what type of math questions they struggle with and which questions they thought were easy,” says Suzanne.</p> <p>For teachers, this information could guide them in effectively modifying instructions to cater to students’ learning needs. “This could suggest to the teachers to explore alternative approaches to help the student access that particular knowledge, and to the students to devote more study time to this topic,” observes Lazar.</p> <h1>Enhancing Learning</h1> <p>“When we went to share the findings with the schools, teachers were very interested to know their students’ bias scores. They wanted to know how correct their students’ answers were and how confident the students were about their responses being correct,” says Yim Ping.</p> <p>Some of the findings enabled to the teachers to sharpen their selection of specific strategies to increase their students’ confidence. “They realized they could leverage on certain topics to explore enhancing students’ self-confidence and interest,” she adds.</p> <p>By understanding the link between confidence and students’ academic performance, we can better build on the firm foundation we have in math learning, to make our competent learners also confident learners.</p> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2011/03/01/issue29-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> <item> <title>Through the Lens of Research</title> <link>https://singteach.nie.edu.sg/2011/01/01/issue28-mathed/?utm_source=rss&utm_medium=rss&utm_campaign=issue28-mathed</link> <comments>https://singteach.nie.edu.sg/2011/01/01/issue28-mathed/#respond</comments> <dc:creator><![CDATA[singteach]]></dc:creator> <pubDate>Sat, 01 Jan 2011 10:40:09 +0000</pubDate> <category><![CDATA[issue 28 jan / feb 2011]]></category> <category><![CDATA[Education research]]></category> <category><![CDATA[Mathematics]]></category> <category><![CDATA[Professional development]]></category> <category><![CDATA[Technology]]></category> <category><![CDATA[Action research]]></category> <category><![CDATA[MathEd]]></category> <guid isPermaLink="false">https://singteach.nie.edu.sg?p=891</guid> <description><![CDATA[Teaching Fellow Tan Liang Soon is always looking for possibilities. How can learning be improved? How can teaching […]]]></description> <content:encoded><![CDATA[<p><strong>Teaching Fellow Tan Liang Soon is always looking for possibilities. How can learning be improved? How can teaching be done differently? What else can we do? For Liang Soon, “research” is just another word for the exploration that he is constantly engaged in.<br /> </strong><br /> Even as a teacher, Liang Soon was always seeking ways and means to combine theory and knowledge with teaching practice and learning.</p> <p><img loading="lazy" class="size-full wp-image-893 alignleft" src="https://singteach.nie.edu.sg/wp-content/uploads/stiss28_liangsoon_2.jpg" alt="" width="228" height="170" />His explorations – in schools and in the Educational Technology Division (ETD) at the Ministry of Education (MOE) – have led to some innovative developments to benefit learning both within and beyond his field of Math.</p> <p>When asked to describe the role of research in relation to teaching, one word says it all for him: <em>Significant</em>.</p> <p>Through the lens of research, he can more clearly see what is and what can be – myriad possibilities that can significantly impact practices today and influence the future of learning.</p> <p>Liang Soon has found some of his answers through integrating research and practice. His present secondment to teach Math at NIE has opened up new opportunities to bridge theory and practice.</p> <h1>Q: Tell us about some of the innovations you developed when you were teaching.</h1> <p><strong>A</strong>: One aspect I was looking at was how we can integrate ICT meaningfully into learning and teaching. I think ICT has potential for developing certain skills in pupils. However, it needs to be undergirded by pedagogy.</p> <p>In the school where I was teaching, we were exploring how collaborative learning can take place by leveraging on ICT. Because we were trying an integrated curriculum approach, we worked with different departments.</p> <p>We wanted students to be engaged in collaborative problem solving across the Chemistry and Biology domains. We designed a problem task situated in a “detective game” setting. Students had to go around the school to investigate this “murder” case and, at the same time, collaborate through a virtual platform. We also created an e-Portfolio system for developing and showcasing students’ learning dispositions.</p> <h1>Q: Would you say your experience as a teacher influenced your research?</h1> <p><strong>A</strong>: Definitely. It has helped to augment that iterative process between theory and practice in the translation research that I’ve done as an attempt to improve practice.</p> <p>I’ve been involved in small-scale action research back in school, with the e-Portfolio project, which is practice-based. That was back in 2006/2007. I shared the idea at one of the CPDD seminars, and I believe the e-Portfolio team in NIE is now working with MOE to try this out. I’m encouraged to see that it is moving forward.</p> <p>I was also doing programme-level research when I was in ETD, to evaluate the FutureSchools programme. We looked at various aspects, like how the ICT-enabled learning and teaching was designed and developed on a school-wide level, and the influence of school-level and environmental factors. This research was very important in informing the next phase of the FutureSchools programme.</p> <h1>Q: What do you think is the place of research in the classroom?</h1> <p><strong>A</strong>: I feel it boils down to practice-based research. Especially when you talk about “teaching less, learning more” – teaching for understanding, effective teaching, engaged learning for the students.</p> <p>If teachers at the classroom level believe in and want to work towards such meaningful and engaged learning, they really ought to see their students – whom they interact with constantly – as the best mirror of their teaching.</p> <p>But in order to do so, you need to have some kind of systemic or structured approach. I’m alluding to some type of action research.</p> <h1>Q: You mean, teachers have a role to play in bridging research and practice?</h1> <p><div class="shortcode-block-quote-right" style="color:#999999"> It’s a two-way thing. Because when you are teaching, you understand the unique sort of challenges that practitioners face in class.</p> <p><em><strong>– Tan Liang Soon, </strong>Mathematics and Mathematics Education Academic Group</em> </div> </p> <p><strong>A</strong>: It’s a two-way thing. Because when you are teaching, you understand the unique sort of challenges that practitioners face in class.</p> <p>But teachers can’t do it alone. And researchers can’t work in silos; they have to engage continually with teachers in schools. If practitioners can have that constant conversation with researchers, this will help both parties to understand each other.</p> <p>Back in ETD, this was common practice. We worked with researchers to do design-based research in schools, where the researchers were really engaged with teachers on the ground, to better understand the learning and teaching needs and difficulties.</p> <p>At the same time, the interaction allows teachers to better appreciate the theoretical basis that researchers come with. The teachers will see that they can learn something new if the researchers share their perspective, and they are able to link what they are doing with what the empirical evidence shows.</p> <h1>Q: How do you think teachers can benefit from research?</h1> <p><strong>A</strong>: I think it really all boils down to teachers as reflective practitioners. It has helped me as a teacher, to reflect on my practice as a teacher. It has also helped me to view things at a macro level, like in how the FutureSchools programme was being implemented.</p> <p>I am now doing an exploratory study on the mathematical modelling (MM) experiences of secondary school pre-service teachers. MM is a key component of the new Math syllabus but it is pretty new in its implementation and teachers still lack the confidence to do it. So I’m doing this study to find out how I can structure my course to impact pre-service teachers’ confidence and competence in carrying out MM with their students.</p> <p>So from action research in schools, to programme-level evaluation, and here with my teaching and exploratory study, I would say the whole experience has been significant.</p> ]]></content:encoded> <wfw:commentRss>https://singteach.nie.edu.sg/2011/01/01/issue28-mathed/feed/</wfw:commentRss> <slash:comments>0</slash:comments> </item> </channel> </rss> <!-- Performance optimized by W3 Total Cache. 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