<story><title>What is algebra?</title><url>http://profkeithdevlin.org/2011/11/20/what-is-algebra/</url></story><parent_chain><item><author>electrograv</author><text>&lt;i&gt;&amp;gt; ... numbers in general, not particular numbers. And the human brain is not naturally suited to think at that level of abstraction.&lt;/i&gt;&lt;p&gt;This is so wrong (at least as a stereotype).&lt;p&gt;All throughout my early education I &lt;i&gt;HATED&lt;/i&gt; arithmetic, and found almost everything about it mind-numbingly boring and repulsively repetitive. At that point in my life, I hated math. The moment I encountered algebra though, it was &amp;quot;love at first sight&amp;quot;, and ever since I&amp;#x27;ve absolutely been fascinated and engaged with every type of high-level math I encounter (the more abstract, the better). And not just &amp;quot;fascinated&amp;quot; in the &amp;quot;I like it&amp;quot; sense -- math, CS, etc. is more easy&amp;#x2F;natural to me than most humanities subjects, by far.&lt;p&gt;So although I can only speak for myself, I quite disagree with any claim that the brain isn&amp;#x27;t naturally suited to abstract thinking. While I know not all people think the way I do, certainly quite a few do.</text></item></parent_chain><comment><author>B-Con</author><text>His area of expertise is mathematical teaching&amp;#x2F;learning. He was undoubtedly talking about the average person, I doubt it was supposed to be an absolute neurological-level statement. And as a general statement&amp;#x2F;stereotype, there are expected to be exceptions. I doubt he got to be a Stanford math professor without seeing some gifted math students himself. His statement can still stand, despite yourself as a counterexample.&lt;p&gt;A little more about him: His CourseEra course is &amp;quot;Introduction to Mathematical Thinking&amp;quot;. It isn&amp;#x27;t about math, it&amp;#x27;s about how to think mathematically. He commonly talks about the pitfalls people make with basic mathematical approaches. He works with helping them understand approaches to math and how to deal with thinking abstractly and purely logically. Some people pick up all that stuff implicitly with little effort, some people never really master it. Given his position, I think he sees a pretty raw view of the average person&amp;#x27;s &lt;i&gt;approach&lt;/i&gt; toward math.</text></comment>
<story><title>What is algebra?</title><url>http://profkeithdevlin.org/2011/11/20/what-is-algebra/</url></story><parent_chain><item><author>electrograv</author><text>&lt;i&gt;&amp;gt; ... numbers in general, not particular numbers. And the human brain is not naturally suited to think at that level of abstraction.&lt;/i&gt;&lt;p&gt;This is so wrong (at least as a stereotype).&lt;p&gt;All throughout my early education I &lt;i&gt;HATED&lt;/i&gt; arithmetic, and found almost everything about it mind-numbingly boring and repulsively repetitive. At that point in my life, I hated math. The moment I encountered algebra though, it was &amp;quot;love at first sight&amp;quot;, and ever since I&amp;#x27;ve absolutely been fascinated and engaged with every type of high-level math I encounter (the more abstract, the better). And not just &amp;quot;fascinated&amp;quot; in the &amp;quot;I like it&amp;quot; sense -- math, CS, etc. is more easy&amp;#x2F;natural to me than most humanities subjects, by far.&lt;p&gt;So although I can only speak for myself, I quite disagree with any claim that the brain isn&amp;#x27;t naturally suited to abstract thinking. While I know not all people think the way I do, certainly quite a few do.</text></item></parent_chain><comment><author>samatman</author><text>The difference between categorical and analytical modes of thought is not always clear to categorical thinkers, but is usually well-known to the analytical. I&amp;#x27;m heavily in the analytical camp, went straight from high-school level algebra to the theory of formal systems and Godel numbering, and didn&amp;#x27;t &amp;#x27;click&amp;#x27; with my scholastic maths education until linear algebra.&lt;p&gt;Linear algebra was exactly and precisely when I realized that &amp;quot;algebra&amp;quot; was a special case of algebras, which was what I needed to contextualize it. Before that it was a bunch of wasted rote effort.</text></comment>