“So a brachistochrone has some other cool properties. What’s the primary thing we know about the brachistochrone?”<\/span><\/p>\nInstruction not working.\u00a0<\/strong> If you watch instruction where the term and the concept have been taught simultaneously, confusion ensues when the teacher uses the term.\u00a0 You’ll see students looking away as they try to bring up the explanation of that weird new term in their memory (see the pictured example?).\u00a0 Sometimes the teacher will notice this and give a thumbnail definition or example of the term, and the students will then remember.\u00a0 However, the teacher should then realize that the concept was not connected to the new vocabulary term.<\/p>\nMath teaching strategies: Teach new concepts using a common sense term at first.\u00a0\u00a0<\/span><\/h2>\nWhen a new vocabulary term is used to introduce a new concept, students will need a lot of practice with recalling the term and the definition before it can be used in instruction.\u00a0\u00a0<\/span>On the other hand, students can quickly understand and use new concepts and ideas in math if they don’t have to learn a new word for it.\u00a0 Using a common sense term<\/strong>, the idea or concept can be worked with, the implications studied and it can be applied to real world problems almost immediately.\u00a0 Students can later quite easily learn proper vocabulary terms for concepts they understand and recognize.\u00a0 Here’s an example.\u00a0<\/span><\/p>\nThe “shortest time curve.”<\/strong>\u00a0 It is more efficient and effective to teach the concept first and use a common sense term for it.\u00a0 I would call a brachistochrone the “shortest time curve.”**\u00a0 Instruction would proceed with the, “Do you remember that ‘shortest time curve’ we talked about last week?”\u00a0 Students would easily be able to remember it.\u00a0 Instruction would go like this:\u00a0“So ‘the shortest time curve’ has some other cool properties. What’s the primary thing we know about the ‘shortest time curve’?”\u00a0 <\/span>Students would easily be able to answer this question.<\/p>\nThen after students have worked with the concept of “the shortest time curve” for a couple of weeks, you can add the vocabulary term to it. “By the way, the proper mathematical name for “the shortest time curve” is called a brachistochrone. Isn’t that cool?”<\/span>\u00a0 Students will want to learn its proper name as a point of pride about knowing this fancy term for a concept they already “own,” rather than a point of confusion.<\/p>\n**Actually that’s what brachistochrone means in Greek: brakhistos, meaning shortest and khronos meaning time.<\/p>\n
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Here’s an example of the problem.\u00a0 \u00a0A brachistochrone (pictured above)\u00a0is\u00a0a curve between two points along which a body can move under gravity in a shorter time than for any other curve. It is the same curve as a cycloid, but just hanging downward.\u00a0 \u00a0A cycloid is the path traced by a point on a […]<\/p>\n","protected":false},"author":837,"featured_media":38459,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"pmpro_default_level":0},"categories":[101],"tags":[35,43,120,122,52,119,38],"_links":{"self":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/38460"}],"collection":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/users\/837"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/comments?post=38460"}],"version-history":[{"count":5,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/38460\/revisions"}],"predecessor-version":[{"id":38486,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/38460\/revisions\/38486"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/media\/38459"}],"wp:attachment":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/media?parent=38460"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/categories?post=38460"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/tags?post=38460"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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<\/a>Introducing this concept and the term brachistochrone at the same time would be designed so the teacher can use brachistochrone and its concept in instruction.\u00a0 However, because the term is new and the concept is also new, when the teacher uses the new term during later instruction, the students will have difficulty bringing the concept into their minds.