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240 lines
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HTML
240 lines
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<h1 class="center">Learning Mathematics</h1>
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<h2>Why Learn Mathematics?</h2>
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<p>Technology is everywhere around us, and you need mathematics to master it!</p>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/doctor-blood-pressure.jpg" alt="Taking Blood Pressure" width="120" height="169" /><br>
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<br>
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<img src="images/stock-exchange.jpg" alt="stock exchange" width="120" height="112" /></td>
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<td><p>In fact most top-paying jobs need good math skills:</p>
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<ul>
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<li>Doctors</li>
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<li>Vets</li>
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<li>Engineers</li>
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<li>Scientists</li>
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<li>Software Developers</li>
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<li>Marketing Analysts</li>
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<li>Financial Officers</li>
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<li>Investment Managers</li>
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<li>and more ...</li>
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</ul>
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<p> </p> </td>
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<td><img src="images/computer-games.jpg" alt="Computer Games" width="120" height="83" /><br>
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<br>
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<img src="images/skyscraper.jpg" alt="skyscraper" width="120" height="228" /></td>
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</tr>
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</table><br>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="geometry/images/tessellation1.gif" alt="tiles" width="170" height="110" /></p>
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<p>And Mathematics is not just numbers, it is about <a href="geometry/tessellation.html">patterns</a>, too!</p>
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<p>So jobs like fashion and interior design benefit from math skills.</p>
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<p> </p>
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<p>Mathematics is also useful in everyday life:</p>
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<ul>
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<li>Investing money (interest rates, profits, etc)</li>
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<li>Estimating costs</li>
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<li>Shopping (is it really a bargain?)</li>
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<li>Understanding Computers</li>
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<li>Designing rooms and gardens</li>
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<li>Planning trips</li>
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</ul>
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<p>Mathematics also improves our mental ability as it teaches us logical ways of thinking.</p>
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<p>And anyway, it is just plain fun: what other subject is about solving puzzles?</p>
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<h2>How to Be an Expert</h2>
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<p>There are two major steps:</p>
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<table style="border: 0;">
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<tr>
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<td><img src="images/learn-get-use.svg" alt="learn get use" /></td>
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<td> </td>
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<td><p><b>Get</b> the information ... read, listen to a teacher, watch a video.</p>
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<p><b>Use</b> the information ... sketch it, think about it, answer questions.</p></td>
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</tr>
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</table>
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<p><b>Using it</b> is so important! <a href="https://www.mathopolis.com/questions/index.php">Answering questions</a> helps you organize the ideas in your mind*.</p>
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<p>Try to do about 1 hour of practice on your own each day*</p>
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<h2>How to Read Mathematics</h2>
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<p>Mathematics <b>says a lot in a short space</b>.</p>
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<div class="example">
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<p>Example, in English: <b>"We don't know what staplers or trays cost, but we do know that the office manager bought 15 staplers and 11 trays for a total cost of $73"</b></p>
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<p>But in Mathematics: <b>15s + 11t = 73</b></p>
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</div>
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<p>So it is good to re-read, go back and forth and play with the ideas.</p>
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<table style="border: 0; margin:auto;">
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<tr style="text-align:center;">
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<td height="19"><img src="images/reading-math.svg" alt="Reading Math" /></td>
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</tr>
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<tr style="text-align:center;">
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<td height="19">Reading Mathematics is different than reading English</td>
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</tr>
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</table>
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<p>Read it, think about it, read again, write it down or sketch it out, and then use it (by answering questions), that all helps to get the ideas into your mind.</p>
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<div class="example">
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<h3>Example: Converting <a href="temperature-conversion.html">Celsius to Fahrenheit</a></h3>
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<p class="center large">°F = (°C × <span class="frac"><sup>9</sup>/<sub>5</sub></span>) + 32</p>
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<ul>
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<li>Read it once first to see there is <b>°F</b> (which means Fahrenheit) on one side, and <b>°C</b> (Celsius) on the other side, with some calculations.</li>
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<li>Now go over it again and see that <b>°C</b> is multiplied by 9/5 and think "I wonder why that is done? Why 9/5?"</li>
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<li>Then notice that 32 is added ... why is that?</li>
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<li>Maybe you could make a sketch (as shown below)</li>
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<li>Then <b>use it</b> yourself, do a few conversions and see how it works</li>
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</ul>
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</div>
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<h2>Make Sketches</h2>
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<table style="border: 0;">
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<tr>
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<td><p>It really helps understanding when you <b>sketch</b> what you are learning*.</p>
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<p>Make large and bold sketches with plenty of labels and notes.</p>
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<p>Like this sketch about Celsius and Fahrenheit:</p> </td>
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<td><img src="images/temperature-sketch.svg" alt="Temperature Sketch" /></td>
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</tr>
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</table>
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<p>Sketches are also very helpful when doing questions.</p>
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<h2>Work Neatly</h2>
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<table style="border: 0; margin:auto;">
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<tr>
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<td style="text-align:center;"><img src="images/work-neatly.gif" width="350" height="192" alt="work neatly" /></td>
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</tr>
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<tr>
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<td style="text-align:center;">Working neatly helps you think more clearly<br>
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and also gives you good mental habits.</td>
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</tr>
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</table>
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<p>Have <b>pride</b> in your work, even if nobody else will see it.</p>
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<h2>Take Your Time!</h2>
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<p>Math is not about reading pages ... it is about building <b>concepts</b> in your mind.</p>
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<p>So don't think "I read 2 pages today", instead think "I understand graphs better now".</p>
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<p>It is important to learn about one idea at a time, make sure you understand it, and do plenty of exercises so you become expert.</p>
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<div class="center80">
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<p>Important: If you skip past a section, the rest may not make sense.</p>
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<p>You will get confused, frustrated, and you will begin to hate the subject.</p>
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<p>The cure?</p>
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<ul>
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<li>Go back to where it made sense,</li>
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<li>then move gently forward again,</li>
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<li>do <b>plenty of practical things</b> like solving questions and doing sketches</li>
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</ul>
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<p>And you will soon be "back on track"</p>
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</div>
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<h2>Practice, Practice, Practice</h2>
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<p><b>Do lots of questions.</b></p>
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<p>That is why we developed the <a href="https://www.mathopolis.com/questions/index.php">Mathematics Question Database</a>.</p>
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<p>If you need to pass an exam, find past exams and do them*.</p>
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<h2>Read a Lot</h2>
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<p>Get some books, and read them. Spend time on math websites (like this one!), and join a forum (like the <a href="https://www.mathisfunforum.com/">Math is Fun Forum</a>).</p>
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<h2>Come Up With Your Own Ways</h2>
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<p>You have your <b>own</b> learning style.</p>
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<p class="center">Don't just follow the steps you are shown, try your own ideas!</p>
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<p>Play with the ideas you are learning.</p>
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<p>And try reading about the same subject from different places, you may find some that make a lot more sense to you.</p>
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<div class="center80">
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<p>Your mind is an amazing and unique tool, and you want to use it the best way you know how.</p>
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<p>And studying mathematics is a good way to improve it!</p>
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</div>
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<h2>All About Ideas</h2>
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<p>It is more important to know the <b>ideas</b> than to remember the formulas.</p>
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<p>If you know how things <b>work</b>, you can always re-create the formulas when you need them. And you may also be able to do more clever things with your ideas.</p>
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<p> </p>
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<h3>*Bibliography:</h3>
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<ul>
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<li><b>Drawing 'integral' to science learning</b> https://www.nottingham.ac.uk/news/pressreleases/2011/august/drawing-integral-to-science-learning.aspx</li>
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<li><b>Retrieval Practice Produces More Learning than Elaborative Studying with Concept Mapping</b> (Jeffrey D. Karpicke and Janell R. Blunt)
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Science 20 January 2011: 1199327</li>
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<li><b>Testing Improves Memory</b> https://www.psychologicalscience.org/index.php/news/releases/testing-improves-memory.html</li>
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<li><b>Practice testing protects memory against stress</b><br>
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https://now.tufts.edu/news-releases/practice-testing-protects-memory-against-stress</li>
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<li><b>How Much Math, Science Homework is Too Much?</b><br>
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https://www.apa.org/news/press/releases/2015/03/math-science-homework.aspx</li>
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<li><b>The Worst and The Best Study Tips & Habits based on Psychological Research</b><br>
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https://cognitiontoday.com/2019/04/the-worst-and-the-best-study-tips-habits-from-psychological-research-how-to/</li>
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<li>H. Sigmundsson, R. C. J. Polman, and H. Lorås (2013) <b>Exploring Individual Differences in Children's Mathematical Skills: A Correlational and Dimensional Approach</b>. Psychological Reports: Volume 113, Issue, pp. 23−30. doi: 10.2466/04.10.PR0.113x12z2 https://www.eurekalert.org/pub_releases/2013−12/nuos-nmg121313.php</li>
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</ul>
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<div class="related">
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<a href="mathematics.html">Welcome to Mathematics</a>
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<a href="numbers/evolution-of-numbers.html">Evolution of Numbers</a>
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<a href="mathematics-language.html">The Language of Mathematics</a>
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<a href="mathematics-help-me.html">Help! I Can't Do Mathematics!</a>
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