{"id":303,"date":"2016-03-14T13:23:51","date_gmt":"2016-03-14T13:23:51","guid":{"rendered":"http:\/\/samizdatmath.com\/?p=303"},"modified":"2016-03-17T14:46:24","modified_gmt":"2016-03-17T14:46:24","slug":"enough-with-fractions-already","status":"publish","type":"post","link":"http:\/\/samizdatmath.com\/?p=303","title":{"rendered":"Enough with fractions, already&#8230;."},"content":{"rendered":"<p>Robert is an occasional reader of our hometown paper, The New York Times, and usually rolls his eyes whenever one of the cub reporters attempts to make sense of mathematics education. Every once in a while, however, the editors manage to slip up and allow someone with an ounce of common sense to write about his chosen field of expertise.<\/p>\n<p>Such was the case when a reporter covered Andrew Hacker and\u00a0his\u00a0<a href=\"http:\/\/www.nytimes.com\/2016\/02\/07\/education\/edlife\/who-needs-advanced-math-not-everybody.html?_r=0\" target=\"_blank\">very convincing case<\/a> for eliminating the traditional &#8220;advanced math&#8221; curriculum. We all know this as the algebra-geometry-trigonometry-advanced algebra, yadda, yadda, yadda forced march that\u00a0college and capital accumulation bound high schoolers must march through. This sequence\u00a0allegedly prepares\u00a0the few students who actually understand this stuff for brilliant careers in art history, restaurant management and human resource development. It&#8217;s not that Hacker dislikes mathematics or wants to dumb it down; rather, he suggests that maybe a more thoughtful approach focusing on &#8220;real life&#8221; uses of mathematics would actually achieve the goals we have\u00a0set out: prepare our students to participate\u00a0in our quasi-capitalistic\u00a0economic life and pseudo-democratic political system.<\/p>\n<p>While we&#8217;re at it, Robert\u00a0wishes Hacker would also take a more courageous stand, and push back against the teaching of fractions in the elementary grades. Talk about a waste of time: while fractions were a useful thing to know if you were a working class\u00a0Sumerian over 5 millennia ago, today they&#8217;re just that like\u00a0that unwelcome uncle who pops up at the Thanksgiving dinner table each year: nobody knows why he&#8217;s there, and everybody would digest much easier if he just stayed in his cardboard box.<\/p>\n<p><img loading=\"lazy\" class=\"alignleft wp-image-314\" src=\"http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/Screenshot-2016-03-14-09.35.35-300x294.jpg\" alt=\"Screenshot 2016-03-14 09.35.35\" width=\"223\" height=\"218\" srcset=\"http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/Screenshot-2016-03-14-09.35.35-300x294.jpg 300w, http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/Screenshot-2016-03-14-09.35.35.jpg 337w\" sizes=\"(max-width: 223px) 100vw, 223px\" \/>As Robert tells it,\u00a0fractions had a good run, and with a 5,000+ year history, they&#8217;ve outlived every fad imaginable, including paisley togas and virgin\u00a0sacrifices. Fractions began their long run with the Egyptians, who utilized them to divide up plots of land and levy taxes.\u00a0The ancient Sumerians loved fractions so much that they invented the 24 hour day, the 60 minute hour and the 360 degree circle just so they could divide them\u00a0up into equal pieces really easily: a 24 hour day can be divided into halves, thirds, quarters, sixths, 8ths, 12ths and 24ths (don&#8217;t get me started on how easy it is to divide 60 and 360&#8230;.) You just can&#8217;t do that with 10 or 100.<\/p>\n<p>But\u00a0Robert maintains,\u00a0fractions are pretty much dead so far as common usage goes, and you can blame that on the French. Yes, those Jerry Lewis and croissant beurre loving eggheads are to blame for the downfall of fractions and the rise of its bitter opponent, the easy and convenient (and mostly sanitary) decimal notation. <em>Quelle barbe!\u00a0<\/em><\/p>\n<div id=\"attachment_307\" style=\"width: 201px\" class=\"wp-caption alignleft\"><img aria-describedby=\"caption-attachment-307\" loading=\"lazy\" class=\" wp-image-307\" src=\"http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/frenchguy-240x300.jpg\" alt=\"Typical French citizen holding 300 ml glass of wine with 1 meter long baguette and smoking 100 mm cigarette. He'll probably live to be 100 years old....\" width=\"191\" height=\"239\" srcset=\"http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/frenchguy-240x300.jpg 240w, http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/frenchguy.jpg 400w\" sizes=\"(max-width: 191px) 100vw, 191px\" \/><p id=\"caption-attachment-307\" class=\"wp-caption-text\">Typical French citizen holding 300 ml glass of wine with 1 meter long baguette and smoking 100 mm cigarette. He&#8217;ll probably live to be 100 years old&#8230;.<\/p><\/div>\n<p>Whatever your feelings for the French, which can be determined by what you call fried potatoes served with ketchup, you&#8217;ll have to admit they were on to something by inventing and then adopting the metric system: it&#8217;s soooo easy to use!\u00a0No one who has ever worked with\u00a0kilograms, meters or liters (as well as newtons, joules and candela) has ever had to struggle finding a common denominator, convert to a mixed number or inverting and multiplying. Is it any wonder that 99.9% of all the countries in the world use decimal units of measurement?<\/p>\n<p>But here in the United States, we love our fractions, which means that it is the only place on earth (well, toss in Liberia and Myanmar) where fractions have to be taken seriously. Open a cookbook and what do you find? Fractions of a pound, fractions of a cup, fractions, fractions, fractions! Robert\u00a0believes cooking is a pretty pleasurable experience, up there with consensual sex, open-water swimming and playing the concertina, but when you mix in fractions, well, you&#8217;re just asking for trouble. Robert\u00a0wagers\u00a0that\u00a0there is a significant fraction of the American population which hates to cook because they&#8217;re scared of fumbling with quarter cups and half-pounds.<\/p>\n<div id=\"attachment_308\" style=\"width: 204px\" class=\"wp-caption alignright\"><img aria-describedby=\"caption-attachment-308\" loading=\"lazy\" class=\" wp-image-308\" src=\"http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/cookierecipe.jpg\" alt=\"Sorry, kids, no cupcakes today! Daddy doesn't like baking with fractions...\" width=\"194\" height=\"162\" \/><p id=\"caption-attachment-308\" class=\"wp-caption-text\">Sorry, daughter, no cupcakes for your birthday:\u00a0daddy doesn&#8217;t like baking with fractions&#8230;<\/p><\/div>\n<p>Open a cookbook anywhere else in the world, and there will be nary a fraction in sight: everything will be measured in grams, kilograms and liters, which makes life quite a bit easier. Don&#8217;t need an entire kilogram? Just put a decimal point on it, baby!\u00a0Need to\u00a0increase a\u00a0recipe by ten times? Push those digits\u00a0one place to the left and move on! You just can&#8217;t do any of that with half-tablespoons of vanilla&#8230;..<\/p>\n<p>And this just has to do with cooking; the prevalence of fractions in American life, from our use of 8 1\/2 x 11&#8243; sheets of paper for correspondences to road signs which tell us our exit is 3\/4 of a mile away is just <span style=\"text-decoration: underline;\">so<\/span> pass\u00e9. I agree: I know decimals will take some getting used to when it comes to our everyday life, but can&#8217;t we give it chance?<\/p>\n<div style=\"width: 131px\" class=\"wp-caption alignleft\"><a href=\"https:\/\/www.teacherspayteachers.com\/Product\/Fractions-Youre-Teaching-Them-Wrong-15-Concrete-Recommendations-1110811\"><img loading=\"lazy\" class=\"\" src=\"https:\/\/ecdn1.teacherspayteachers.com\/thumbitem\/Fractions-Youre-Teaching-It-Wrong-10-Concrete-Recommendations-1110811\/original-1110811-1.jpg\" alt=\"\" width=\"121\" height=\"157\" \/><\/a><p class=\"wp-caption-text\">My best seller!<\/p><\/div>\n<p>Truthfully, Robert\u00a0loves teaching fractions,\u00a0and even makes a pretty good living off of them, seeing as how 4 of \u00a0the top 5 bestsellers at his\u00a0online store are about&#8230; fractions! Even I\u00a0think they have some important uses, especially when it comes to algebraic notation, and they can be rather fun when done in a playful and non-threatening way.<\/p>\n<div id=\"attachment_309\" style=\"width: 240px\" class=\"wp-caption alignright\"><img aria-describedby=\"caption-attachment-309\" loading=\"lazy\" class=\" wp-image-309\" src=\"http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/goldengrahamssmoresad-264x300.jpg\" alt=\"I really don't think this is going to fix the problem...\" width=\"230\" height=\"261\" srcset=\"http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/goldengrahamssmoresad-264x300.jpg 264w, http:\/\/samizdatmath.com\/wp-content\/uploads\/2016\/03\/goldengrahamssmoresad.jpg 570w\" sizes=\"(max-width: 230px) 100vw, 230px\" \/><p id=\"caption-attachment-309\" class=\"wp-caption-text\">I really don&#8217;t think this is going to fix the problem&#8230;<\/p><\/div>\n<p>However, in an era of high-stakes testing and curriculum standardization, maybe\u00a0it&#8217;s time we reconsider the teaching of fractions in elementary school. Fractions prevent our students\u00a0from solidifying more important concepts and mastering developing\u00a0skills. They are confusing and have limited uses, yet we persist in teaching them to children who are just not equipped to understand them. Can we agree to delay them until 5th, 6th or 7th grade, when kids are more able to comprehend them, and can be covered in 1\/4 the time?<\/p>\n<p>I would wager that 93\/95\u00a0of the American population would agree with me.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Robert is an occasional reader of our hometown paper, The New York Times, and usually rolls his eyes whenever one of the cub reporters attempts to make sense of mathematics education. Every once in a while, however, the editors manage &hellip; <a href=\"http:\/\/samizdatmath.com\/?p=303\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[7,8],"tags":[10,9],"_links":{"self":[{"href":"http:\/\/samizdatmath.com\/index.php?rest_route=\/wp\/v2\/posts\/303"}],"collection":[{"href":"http:\/\/samizdatmath.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/samizdatmath.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/samizdatmath.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/samizdatmath.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=303"}],"version-history":[{"count":9,"href":"http:\/\/samizdatmath.com\/index.php?rest_route=\/wp\/v2\/posts\/303\/revisions"}],"predecessor-version":[{"id":317,"href":"http:\/\/samizdatmath.com\/index.php?rest_route=\/wp\/v2\/posts\/303\/revisions\/317"}],"wp:attachment":[{"href":"http:\/\/samizdatmath.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/samizdatmath.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=303"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/samizdatmath.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}