tag:theconversation.com,2011:/nz/topics/calculators-19318/articlesCalculators – The Conversation2019-10-31T18:53:28Ztag:theconversation.com,2011:article/1260272019-10-31T18:53:28Z2019-10-31T18:53:28ZWould you notice if your calculator was lying to you? The research says probably not<figure><img src="https://images.theconversation.com/files/299628/original/file-20191031-187903-hakehj.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C2700%2C1782&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">As our worlds are become increasingly digitised, we're starting to rely more on machines and devices for everyday tasks. But in an age when even pacemakers can be hacked, how do we know when and who to trust?</span> <span class="attribution"><span class="source">SHUTTERSTOCK</span></span></figcaption></figure><p>These days, it’s hard to know whom to <a href="https://www.routledge.com/Truth-Lies-and-Trust-on-the-Internet-1st-Edition/Whitty-Joinson/p/book/9780203938942">trust</a> online, and how to discern genuine content from fakery.</p>
<p>Some degree of trust in our devices is necessary, if we’re to embrace the growing number of technologies that could potentially enhance our lives. How many of us, however, bother trying to confirm the truth, and how many blindly approach their online communications?</p>
<p>In a <a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0223736">study published this week</a>, Texas Tech University researchers tested how university students reacted when unknowingly given incorrect calculator outputs. Some students were presented with an onscreen calculator that was programmed to give the wrong answers, whereas a second group was given a properly functioning calculator. </p>
<p>Participants could also opt not to use the calculator, but most chose to use it - even if they had good numeracy skills. Researchers found most participants raised few or no suspicions when presented with wrong answers, until the answers were quite wrong. In addition, those with higher numeracy skills were, unsurprisingly, more suspicious of incorrect answers than others.</p>
<h2>Do the math</h2>
<p>To understand these results, we need to acknowledge calculators were created to make our lives easier, by reducing our mental burden. Also, there were no real consequences for participants who did not realise they were being duped. </p>
<p>Perhaps if they were completing their income tax forms, or applying for a loan, they may have been more thorough in checking their results. More importantly, there’s no reason an individual ought to feel suspicious about a calculator, so the participants were acting in accord with what we might expect.</p>
<p>People can’t spend their time deciding if they should trust every tool they use. This would consume too much time and energy. This study, however, was carried out with university students in a lab. What are the consequences of this in the real world, when much more is at stake? </p>
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Read more:
<a href="https://theconversation.com/lie-detectors-and-the-lying-liars-who-use-them-28167">Lie detectors and the lying liars who use them</a>
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<p>The Internet and digital technologies have changed our lives for the better in so many ways. We can access information at super speeds, communicate regularly (and in fun ways) with our friends and family, and carry out mundane tasks such as banking and shopping with ease. </p>
<p>However, new technologies pose new challenges. Is the person you’re talking to online a real person or a <a href="https://www.aaai.org/ocs/index.php/ICWSM/ICWSM17/paper/viewPaper/15587">bot</a>? Are you developing a real romantic relationship on your dating app, or being conned in a <a href="https://academic.oup.com/bjc/article-abstract/53/4/665/396759">romance scam</a>? </p>
<p>To what extent do people blindly accept their technologies are safe, and that everyone online is who they claim to be?</p>
<h2>Hackers are often phishing for data</h2>
<p>The <a href="https://www.forbes.com/sites/jacobmorgan/2014/05/13/simple-explanation-internet-things-that-anyone-can-understand/#5e48e2931d09">Internet of Things</a> is already changing our lives in and outside the home. At home, there’s the constant threat that we’re being listened to and watched through our devices. In August, Apple publicly apologised for allowing contractors to <a href="https://www.theguardian.com/technology/2019/aug/29/apple-apologises-listen-siri-recordings">listen to voice recordings</a> of Siri users. </p>
<p>Similarly, as autonomous vehicles become the norm, they too <a href="https://ieeexplore.ieee.org/abstract/document/8038391">pose ethical concerns</a>. Not only do we need to be worried about the programmed moral choices on whom to harm if an accident becomes inevitable, but also whether criminals can hack into these vehicles and alter programmed decisions. </p>
<p>Also, there have been reports of benign-looking USB cables being rigged with small WiFi-enabled implants which, when plugged into a computer, let a nearby hacker run commands. We even need to think about the safety of health devices, such as pacemakers, which can <a href="https://www.wired.com/story/pacemaker-hack-malware-black-hat/">now be hacked</a>.</p>
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Read more:
<a href="https://theconversation.com/with-usb-c-even-plugging-in-can-set-you-up-to-be-hacked-102296">With USB-C, even plugging in can set you up to be hacked</a>
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<p>A major problem organisations and governments are trying to solve is stopping individuals from falling victim to phishing. A phish is an email or text which is made to appear authentic and trustworthy, but isn’t. </p>
<p>Cybercriminals use them to trick users into revealing secret information, such as bank account details, or clicking on a link that downloads malicious software onto their computer. This software can then steal passwords and other important personal data. </p>
<p>Clicking on a phishing message can have long-lasting detrimental effects on an individual or an organisation, as was the case with an Australian National University <a href="https://www.anu.edu.au/news/all-news/anu-releases-detailed-account-of-data-breach">data breach</a> last year.</p>
<p>We’re yet to effectively train people to recognise a phish. This is partly because because they’re often realistic and difficult to identify. However, it’s also because, as illustrated in the Texas Tech University study, people tend to place undue trust in technology and devices, without pausing to check the facts.</p>
<h2>Knowledge is power, and safety</h2>
<p>It’s incredibly difficult to have the right balance between scepticism and trust in the digital age. Individuals need to function in the world, and the mental effort required to constantly check all information is perhaps more than what we can expect of people. </p>
<p>That said, one positive takeaway from the calculator study is that training is critical if we want to improve people’s cybersecurity practices. This includes training individuals on what to do as online users, how to do it, and why it’s important. </p>
<p>As with all learning, this needs to be repetitive and the individual needs to be motivated to learn. Without effective learning methods, end-users, organisations, and state nations will remain vulnerable to cybercriminals.</p>
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Read more:
<a href="https://theconversation.com/payid-data-breaches-show-australias-banks-need-to-be-more-vigilant-to-hacking-123529">PayID data breaches show Australia's banks need to be more vigilant to hacking</a>
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<img src="https://counter.theconversation.com/content/126027/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Monica Whitty does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Research shows we’re pretty gullible as it is. And our increasing reliance on machines for completing everyday tasks makes us all-the-more vulnerable to being exploited.Monica Whitty, Chair in Human Factors in Cyber Security, The University of MelbourneLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/834312017-09-05T20:11:20Z2017-09-05T20:11:20ZTechnology in the classroom can improve primary mathematics<figure><img src="https://images.theconversation.com/files/184656/original/file-20170905-28074-1wx7i8h.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">There’s much more to mathematics than computation, and that’s where more contemporary technologies can improve primary mathematics.</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>Many parents are beginning to demand less technology use in the primary classroom due to the amount of screen time children have at home. This raises questions about whether technology in the classroom helps or hinders learning, and whether it should be used to teach maths.</p>
<h2>Blaming the calculator for poor results</h2>
<p>We often hear complaints that children have lost the ability to carry out simple computations because of the reliance on calculators in primary schools. This is not the case. In fact, there has been very little research conducted on the use of calculators in classrooms since the 80’s and 90’s because they are not a significant feature of primary school maths lessons. When calculators are used in primary classrooms, it’s usually to help children develop number sense, to investigate number patterns and relationships, or to check the accuracy of mental or written computation. </p>
<p>There is also <a href="http://files.eric.ed.gov/fulltext/ED373963.pdf">evidence</a> that children become more flexible in the way they compute through the use of calculators. It allows them to apply their knowledge of place value and other number related concepts rather than using a traditional algorithm. </p>
<p>The <a href="https://www.australiancurriculum.edu.au/">Australian Curriculum</a> promotes a strong focus on the development of <a href="https://www.australiancurriculum.edu.au/media/1077/general-capabilities-numeracy-learning-continuum.pdf">numeracy</a>, including the development of estimation and mental computation. These are skills that children need in order to use calculators and other technologies efficiently. </p>
<p>The curriculum also promotes the thinking and doing of mathematics (referred to as <a href="http://v7-5.australiancurriculum.edu.au/mathematics/content-structure">“proficiencies”</a>) rather than just the mechanics. There’s much more to mathematics than computation. That’s where more contemporary technologies can improve primary mathematics.</p>
<h2>The importance of technology in learning maths</h2>
<p>The use of digital technologies in the primary mathematics classroom is not an option. The Australian Curriculum and Reporting Authority (<a href="https://www.australiancurriculum.edu.au/">ACARA</a>) has made it mandatory for teachers to incorporate technologies in all subject areas. Fortunately, schools have access to more powerful, affordable devices than ever before. Importantly, these are the same devices that many children already have access to at home, providing an opportunity to bridge the gap between the mathematics at school and their lives outside the classroom.</p>
<p>Literature around digital technologies and mathematics suggest new technologies have potentially changed teaching and learning, providing opportunities for a shift of focus from a traditional view to a more problem-solving approach. This notion is supported by <a href="http://www.tandfonline.com/doi/abs/10.1080/09669760.2010.494426">research</a> that claims the traditional view of mathematics that was focused on memorisation and rote learning is now replaced with one that has purpose and application.</p>
<p>When used well, technology <a href="http://researchdirect.westernsydney.edu.au/islandora/object/uws%3A29162/">can improve student engagement</a> with mathematics and assists in improving their understanding of mathematical concepts. </p>
<p>In a recent <a href="http://researchdirect.westernsydney.edu.au/islandora/object/uws:37189">research evaluation</a> of the Matific digital resources, the findings were positive. The students found that they enjoyed using the digital resource on iPads and computers, and went from thinking about mathematics as something to be tolerated or endured to something that is fun to learn. An added bonus was that the children voluntarily started to use their screen time at home to do maths. Pre- and post-test data also indicated that the use of the technology contributed to improved mathematics results.</p>
<h2>How technology is used in the classroom</h2>
<p>Many would consider that the use of mobile devices in maths would consist of simple game playing. A search of the App Store reveals tens of thousands of supposedly educational maths games, creating a potential <a href="https://engagingmaths.co/2015/06/02/technology-and-mathematics-have-you-fallen-into-the-app-trap/">app trap</a> for teachers who might spend hours searching through many low- quality apps. Although playing games can have benefits in terms of building fluency, they don’t usually help children learn new concepts. Luckily, there’s much that teachers can and are doing with technology. </p>
<p>The following are some of the different ways teachers are using technology:</p>
<p>– <a href="https://www.researchgate.net/publication/285620177_Showing_and_telling_using_tablet_technology_to_engage_students_in_mathematics">Show and tell apps</a>, such as Explain Everything, <a href="https://www.educreations.com/lesson/view/maths-work/10191743/?s=oChXE1&ref=appemail">EduCreations</a> or ShowMe, allow students to show and explain the solution to a mathematical problem using voice and images</p>
<p>– Flipped learning, where teachers use the technology to replace traditional classroom instruction. YouTube videos or apps that provide an explanation of mathematical concepts are accessed by students anywhere and anytime</p>
<p>– Subscription based resource packages such as Matific which provide interactive, game-based learning activities, allow the teacher to set activities for individual students and keep track of student achievement</p>
<p>– Generic apps (camera, Google Earth, Google Maps, Geocaching) that allow students to explore mathematics outside the classroom.</p>
<p>Just as the world has changed, the mathematics classroom has also changed. Although technology is an integral part of our lives, it shouldn’t be the only resource used to teach maths. When it comes to technology in the classroom, it’s all about balance.</p><img src="https://counter.theconversation.com/content/83431/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>In 2016 Catherine Attard received funding from Slate Science, who produce the Matific digital resources. </span></em></p>Many parents are demanding less technology use in the classroom due to the amount of screen time children get at home. This story explores whether maths education and technology go hand in hand.Catherine Attard, Associate Professor, Mathematics Education, Western Sydney UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/449002015-08-09T20:34:50Z2015-08-09T20:34:50ZWeapons of maths destruction: are calculators killing our ability to work it out in our head?<figure><img src="https://images.theconversation.com/files/91101/original/image-20150807-9952-vo72z3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">from www.shutterstock.com.au</span></span></figcaption></figure><p>Since the 1980s we have had access to calculators of various types. Today, we can include computers and smartphones – which are attached to our hip 24/7. So does this ubiquitous access to calculators affect our ability to do maths in our heads like we used to?</p>
<p>Thirty years ago calculators promised immense opportunity – opportunity, alas, that brought considerable controversy. The sceptics predicted students would not be able to compute even simple calculations mentally or on paper. Multiplication, basic facts, knowledge would disappear. Calculators would become a crutch. </p>
<p>The controversy has not dissipated over time. As recently as 2012, the UK government announced it <a href="http://connection.ebscohost.com/c/opinions/83406522/does-maths-add-up">intended</a> to ban calculators from primary classrooms on the grounds that students use them too much and too soon.</p>
<p>Research conducted in response to this <a href="http://thenferblog.org/2014/11/12/subtracting-calculators-from-maths-tests-doesnt-add-up/">found little difference</a> in performance tests whether students used calculators or not. An earlier US study had <a href="http://www.jstor.org/stable/42802150?seq=1#page_scan_tab_contents">found the same</a>: the calculator had no positive or negative effects on the attainment of basic maths skills.</p>
<p>Researchers recommended moving the conversation on. What types of tasks and activities suit calculators? How can calculators complement and reinforce mental and written methods of arithmetic in maths?</p>
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<span class="caption">Studies have found the use of calculators doesn’t reduce the ability to compute in our heads.</span>
<span class="attribution"><span class="source">from www.shutterstock.com</span></span>
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<h2>Using calculators to extend maths</h2>
<p>Teachers had high hopes that calculators would be used in enhancing and extending the learning of mathematics. While standard procedures for the four operations (+, -, x, ÷) would still be taught and the basic facts of arithmetic would still need to be mastered, calculators could facilitate the study of number patterns and the absence of tedious calculations would free students up to pose, model and solve interesting and relevant problems.</p>
<p>Rather than replacing mental computation, calculators actually make calculating more efficient. Even the simple four-function calculator is a powerful instrument for investigating a range of concepts that previously were not so easily accessed by young children independently. </p>
<p>Counting, skip counting, negative numbers, relationships between common and decimal fractions and other number patterns all open up. The calculator lets students investigate and generalise patterns in numbers that they have previously not had access to. </p>
<p>The “constant” function means young children can explore numbers to infinity, if they fancy, without being restricted to charts or number lines. Skip-counting is also possible using the constant function. </p>
<p>Multiplication tables are no longer limited to 12 x 12. In the diagram below the child is exploring the pattern made by entering 11+11 and continuing to press the Equals sign to see what happens to the pattern once you count beyond 99 by elevens.</p>
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<span class="caption">Lots of number patterns are possible.</span>
<span class="attribution"><span class="license">Author provided</span></span>
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<p>Calculators have great potential in concept development. For example, what happens when you multiply or divide a number by 10 or 100? These generalisations are spectacularly demonstrated and discovered with a calculator, which frees students to ask more questions about number patterns.</p>
<p><a href="http://search.informit.com.au/documentSummary;dn=462445434680297;res=IELHSS">In a 1997 review</a> of the extent to which calculators were being used in schools, numerous studies were examined that indicated the use of calculators at primary levels had no detrimental effects on students’ arithmetic abilities.</p>
<p>Unfortunately, the research indicated that calculators were still being used for trivial things like checking answers and were making little difference in mathematics education. </p>
<p>Although teachers indicated their support for the use of calculators across all levels of primary school, there was little evidence that these ideas were being taken up and implemented. Parental disapproval of the use of calculators was cited as a possible cause of the limited take-up.</p>
<h2>Calculators’ potential is not being achieved</h2>
<p><a href="http://espace.library.uq.edu.au/view/UQ:176139">In a 2008 study</a> this finding was reiterated. Researchers reported that despite educators’ high hopes for digital technologies to transform maths education, the uptake, both internationally and in Australia, had been disappointing. </p>
<p>Influential in this has been the lack of professional development to assist teachers in planning and implementing teaching approaches that take advantage of the technology. British technologist Conrad Wolfram said in his <a href="http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers?language=en">TED talk</a>:</p>
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<p>From rockets to stock markets, many of humanity’s most thrilling creations are powered by math. So why do kids lose interest in it?</p>
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<span class="caption">We’re not harnessing calculators’ full potential.</span>
<span class="attribution"><a class="source" href="https://www.flickr.com/photos/dominicspics/3915942881/">Dominic Alves/Flickr</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
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<p>Wolfram pointed out that students in mathematics classes across the globe spend up to 80% of their time learning and practising mathematical procedures. This time could be spent more productively if the digital technology already in the classrooms was used more effectively and efficiently. </p>
<p>While mathematics is popular, challenging and useful in the real world, kids are rapidly losing interest in the subject in schools. Wolfram blames teaching that focuses on calculation by hand: it’s tedious and mostly irrelevant to real mathematics and the real world.</p>
<p>Sadly, the potential for calculators to transform school mathematics and enhance our facility with mental arithmetic is not being achieved. We are not being provided with opportunities to solve real and interesting mathematical problems in the most effective ways. </p>
<p>So to answer whether calculators are affecting our mental arithmetic: not as much as we would like them to.</p><img src="https://counter.theconversation.com/content/44900/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jeanne Carroll does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Smartphones double as calculators and are attached to our hip 24/7. Does the ubiquitous access to calculators affect our ability to do maths in our heads like we used to?Jeanne Carroll, Senior Lecturer, College of Education, Victoria UniversityLicensed as Creative Commons – attribution, no derivatives.