{"id":11615,"date":"2018-06-25T17:25:36","date_gmt":"2018-06-25T17:25:36","guid":{"rendered":"https:\/\/www.manhattanprep.com\/gre\/?p=11615"},"modified":"2019-08-30T16:40:11","modified_gmt":"2019-08-30T16:40:11","slug":"gre-math-growth-mindset","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gre\/blog\/gre-math-growth-mindset\/","title":{"rendered":"Math and the Growth Mindset"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-11772\" src=\"https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2018\/06\/math-growth-mindset-tom-anderson.png\" alt=\"Manhattan Prep GRE Blog - Math and the Growth Mindset by Tom Anderson\" width=\"1200\" height=\"628\" srcset=\"https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2018\/06\/math-growth-mindset-tom-anderson.png 1200w, https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2018\/06\/math-growth-mindset-tom-anderson-300x157.png 300w, https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2018\/06\/math-growth-mindset-tom-anderson-768x402.png 768w, https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2018\/06\/math-growth-mindset-tom-anderson-1024x536.png 1024w\" sizes=\"auto, (max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Do you consider yourself a \u201cmath person?\u201d<\/span><!--more--><\/p>\n<p><span style=\"font-weight: 400;\"><iframe loading=\"lazy\" src=\"https:\/\/giphy.com\/embed\/BmmfETghGOPrW\" width=\"480\" height=\"206\" frameBorder=\"0\" class=\"giphy-embed\" allowFullScreen><\/iframe><\/p>\n<p><a href=\"https:\/\/giphy.com\/gifs\/reaction-BmmfETghGOPrW\"><\/a><\/p>\n<p><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Actually\u2014hold on a second. Whether you answer yes or no, you\u2019re expressing a potentially harmful thought. Such thoughts reflect a fixed mindset about oneself\u2014a belief that you\u2019re born good at some things and bad at others. Carry that line of thinking a little further:<\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">\u201cMath people\u201d grew up solving quadratic equations in their heads as toddlers. They always just \u201cgot it.\u201d Everyone else had to work hard to get there. \u201cNon-math people\u201d could more easily run 10 miles backwards than calculate a tip at a restaurant. If you\u2019re a \u201cmath person,\u201d congrats on the easy grades and high GRE scores for the rest of your life. If you\u2019re not, then too bad. It\u2019s hopeless.<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">I believe that such thoughts are not just untrue, but downright harmful. There\u2019s a growing body of research on this issue. Many readers of this blog entry will no doubt have heard of Carol Dweck, her book <\/span><a href=\"https:\/\/www.amazon.com\/Mindset-Psychology-Carol-S-Dweck\/dp\/0345472322\" target=\"_blank\" rel=\"noopener\"><i><span style=\"font-weight: 400;\">Mindset<\/span><\/i><\/a><span style=\"font-weight: 400;\">, and her <\/span><a href=\"https:\/\/www.ted.com\/talks\/carol_dweck_the_power_of_believing_that_you_can_improve\" target=\"_blank\" rel=\"noopener\"><span style=\"font-weight: 400;\">TED talk<\/span><\/a><span style=\"font-weight: 400;\">, which currently has over 7 million views. Dweck argues that the way you view yourself has a huge impact on your success. It\u2019s not just those who think they\u2019re \u201cnaturally bad at something\u201d who are at risk, by the way. One of the most negatively-impacted groups seems to be very high-performing students who think it\u2019s all about being \u201cnaturally good at something.\u201d I would encourage you to leave behind those fixed ideas of being a \u201cmath person\u201d and instead adopt a mindset of growth.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In this entry, I\u2019ll share with you a few ideas from research in educational psychology about growth mindsets and what you can do to develop one. In particular, I\u2019ve been reading a book called <\/span><a href=\"https:\/\/www.amazon.com\/Mathematical-Mindsets-Unleashing-Potential-Innovative\/dp\/0470894520\/ref=sr_1_4?s=books&#038;ie=UTF8&#038;qid=1528303782&#038;sr=1-4&#038;keywords=mathematical+mindsets&#038;dpID=51NeyOR3NqL&#038;preST=_SX218_BO1,204,203,200_QL40_&#038;dpSrc=srch\" target=\"_blank\" rel=\"noopener\"><i><span style=\"font-weight: 400;\">Mathematical Mindsets<\/span><\/i><\/a><span style=\"font-weight: 400;\"> by Jo Boaler. I\u2019ll share with you some ideas from this book.<\/span><\/p>\n<h4><b>You Can Rewire Your Brain (to Become a \u201cMath Person\u201d)<\/b><\/h4>\n<p><span style=\"font-weight: 400;\"><iframe loading=\"lazy\" src=\"https:\/\/giphy.com\/embed\/l44QzsOLXxcrigdgI\" width=\"480\" height=\"360\" frameBorder=\"0\" class=\"giphy-embed\" allowFullScreen><\/iframe><\/p>\n<p><a href=\"https:\/\/giphy.com\/gifs\/stupid-smart-l44QzsOLXxcrigdgI\"><\/a><\/p>\n<p><\/span><\/p>\n<p><span style=\"font-weight: 400;\">First of all, know that your brain can be changed. In one intriguing study, researchers looked at the brains of cab drivers in London who had to memorize over 25,000 streets and 20,000 landmarks in order to qualify for their jobs. During the intensive training process, cab drivers showed dramatic growth in the hippocampus\u2014the area of the brain that is used to acquire spatial information. Their brains were so affected by their practice that they showed measurable growth in the very brain matter inside their heads.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This concept that the brain can change and adapt in dramatic ways is called <\/span><b>neuroplasticity<\/b><span style=\"font-weight: 400;\">. There are abundant examples of it. Stroke victims can sometimes regain their speech by rewiring a new region of their brain. People paralyzed in accidents can sometimes regain their movement; in one extreme case, an individual even lost the entire left hemisphere of her brain and was then able to regrow its functions in the remaining right hemisphere.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Aside from these extreme examples, we all experience neuroplasticity when we learn. <\/span><b>Your brain is more like a muscle that can grow with exercise than like a computer that\u2019s stuck with the processor it was built with.<\/b><\/p>\n<h4><b>Mistakes Matter<\/b><\/h4>\n<p><span style=\"font-weight: 400;\"><iframe loading=\"lazy\" src=\"https:\/\/giphy.com\/embed\/xUPGczg032OXCUb4Iw\" width=\"480\" height=\"261\" frameBorder=\"0\" class=\"giphy-embed\" allowFullScreen><\/iframe><\/p>\n<p><a href=\"https:\/\/giphy.com\/gifs\/antmvh1-premiere-antm-xUPGczg032OXCUb4Iw\"><\/a><\/p>\n<p><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Take a few minutes and watch <\/span><a href=\"https:\/\/www.bbc.com\/news\/av\/world-europe-44333446\/the-swiss-master-watchmaker-running-out-of-time\" target=\"_blank\" rel=\"noopener\"><span style=\"font-weight: 400;\">this video of a Swiss watchmaker<\/span><\/a><span style=\"font-weight: 400;\"> who has been making watches by hand for 50 years. He tells us, \u201cIt\u2019s not easy because you learn all your life. Even at my age, I learn every day and very often by making mistakes.\u201d An expert in nearly any field will tell you the same thing: they\u2019ve made their most significant learning through mistakes rather than successes.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The research backs them up. Not only do experts learn from making an incredible number of mistakes, <\/span><i><span style=\"font-weight: 400;\">they seem to learn more when making mistakes than when doing something correctly.<\/span><\/i><span style=\"font-weight: 400;\"> Jo Boaler summarizes some research on the issue:<\/span><\/p>\n<p style=\"padding-left: 30px;\"><span style=\"font-weight: 400;\">\u201cStudents\u2019 brains reacted with greater [\u2026] electrical activity when they made mistakes than when their answers were correct. Second [&#8230;] brain activity was greater following mistakes for individuals with a growth mindset than for individuals with a fixed mindset. The study also found that individuals with a growth mindset had a greater awareness of errors than individuals with a fixed mindset, so they were more likely to go back and correct errors.\u201d <\/span><i><span style=\"font-weight: 400;\">Mathematical Mindsets<\/span><\/i><span style=\"font-weight: 400;\"> (p.12)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">It may not always feel this way, but mistakes are not something that should make you cringe. They\u2019re probably the most worthwhile tidbits from any study session. And they\u2019re even better for you if you open yourself up to growth, log them, and go back to correct them.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Think of it this way: your brain grows a synapse every time you make a mistake. A good practice session shouldn\u2019t be easy. Get out there and start making some mistakes!<\/span><\/p>\n<h4><b>Process > Product<\/b><\/h4>\n<p><span style=\"font-weight: 400;\"><iframe loading=\"lazy\" src=\"https:\/\/giphy.com\/embed\/eP00VsF12Bbfq\" width=\"480\" height=\"270\" frameBorder=\"0\" class=\"giphy-embed\" allowFullScreen><\/iframe><\/p>\n<p><a href=\"https:\/\/giphy.com\/gifs\/lightbulb-eP00VsF12Bbfq\"><\/a><\/p>\n<p><\/span><\/p>\n<p><span style=\"font-weight: 400;\">A good teacher will make it clear: the route to a right answer is much more important than the right answer itself. Of course, on an exam like the GRE, you want to get as many points as possible. But you get those points by carefully thinking about the problem in front of you and the solution paths it beckons you to use.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In the same way that you don\u2019t improve your free throws by focusing on the \u201cwhoosh\u201d a basketball makes when it goes through the net, you shouldn\u2019t try to improve your problem-solving process by going straight to an answer key. Instead, focus on the steps to get there.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">When you practice on your own, try thinking of your answer keys and explanations less like the finish line and more like consultants to whom you can turn for feedback along the way. Rather than just checking the right answer, peek at the explanation to see if the work you\u2019ve done is on the right track. If so, continue onward. If not, go back and revise. Try to lead yourself to the correct answer rather than just reading what it is.<\/span><\/p>\n<h4><b>Believing You Can Grow is Part of the Recipe for Growth <\/b><\/h4>\n<p><span style=\"font-weight: 400;\"><iframe loading=\"lazy\" src=\"https:\/\/giphy.com\/embed\/B2zrUu1Q4HKeSO1brl\" width=\"480\" height=\"269\" frameBorder=\"0\" class=\"giphy-embed\" allowFullScreen><\/iframe><\/p>\n<p><a href=\"https:\/\/giphy.com\/gifs\/rupaulsdragrace-episode-1-rupauls-drag-race-B2zrUu1Q4HKeSO1brl\"><\/a><\/p>\n<p><\/span><\/p>\n<p><span style=\"font-weight: 400;\">On the first day of my GRE class, I often ask my students a similar question to the one I asked at the beginning of this blog entry\u2014I ask them to raise their hand if they\u2019ve come into my classroom with an idea floating around in their subconscious that they are \u201cbad at math.\u201d Every time I ask this question, a few reluctant hands pop into the air, followed by an avalanche of others, until a huge majority of hands silently confess this belief.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">It\u2019s easy for me to believe that there is no such thing as being \u201cbad at math\u201d\u2014for years, I\u2019ve seen my students bring up their GRE Math scores, sometimes to levels they never thought possible. That said, I\u2019m well aware many folks have been traumatized by math in their prior education. Even many well-meaning teachers may have conveyed the notion that math is a gift, and either you have it or you don\u2019t. Take heart and do what you can to throw out these \u201cfixed\u201d notions that may be rummaging around in your brain. Just like your math ability can be changed, so can your mindset.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Believing that you can get smarter is part of the process in doing so. ?<\/span><\/p>\n<hr \/>\n<p><b><i>Want more guidance from our GRE gurus? You can attend the first session of any of our online or in-person GRE courses absolutely free! We\u2019re not kidding.\u00a0<\/i><\/b><a id=\"bloglink\" href=\"https:\/\/www.manhattanprep.com\/gre\/classes\/\" target=\"_blank\" rel=\"noopener\"><b><i>Check out our upcoming courses here<\/i><\/b><\/a><b><i>.<\/i><\/b><\/p>\n<hr \/>\n<p><em><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-10555 size-thumbnail\" src=\"https:\/\/d27gmszdzgfpo3.cloudfront.net\/gre\/wp-content\/uploads\/sites\/19\/2017\/08\/tom-anderson-150x150.png\" alt=\"tom-anderson\" width=\"150\" height=\"150\" \/><a id=\"bloglink\" href=\"https:\/\/www.manhattanprep.com\/instructors\/tom-anderson\/\" target=\"_blank\" rel=\"noopener\">Tom Anderson<\/a>\u00a0is a Manhattan Prep instructor based in New York, NY.<\/strong>\u00a0He has a B.A. in English and a master\u2019s degree in education. Tom has long possessed an understanding of the power of standardized tests in propelling one\u2019s education and career, and he hopes he can help his students see through the intimidating veneer of the GRE.\u00a0<a id=\"bloglink\" href=\"https:\/\/www.manhattanprep.com\/gre\/classes\/#instructor\/53\" target=\"_blank\" rel=\"noopener\">Check out Tom\u2019s upcoming GRE courses here<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do you consider yourself a \u201cmath person?\u201d<\/p>\n","protected":false},"author":173,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[474284,6,7,636674,449765,733451,9,733445],"tags":[1362572,1362573],"yst_prominent_words":[],"class_list":["post-11615","post","type-post","status-publish","format-standard","hentry","category-current-studiers","category-gre-strategies","category-how-to-study","category-in-the-news","category-learning-science","category-life-hacks","category-math-gre-strategies","category-study-tips-2","tag-growth-mindset","tag-math-person"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/11615","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/users\/173"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/comments?post=11615"}],"version-history":[{"count":2,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/11615\/revisions"}],"predecessor-version":[{"id":11773,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/11615\/revisions\/11773"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/media?parent=11615"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/categories?post=11615"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/tags?post=11615"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/yst_prominent_words?post=11615"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}