{"id":38447,"date":"2019-01-17T11:20:22","date_gmt":"2019-01-17T19:20:22","guid":{"rendered":"https:\/\/www.rocketmath.com\/?p=38447"},"modified":"2019-12-23T12:47:54","modified_gmt":"2019-12-23T20:47:54","slug":"math-misteaching-5-teaching-two-similar-new-concepts-at-the-same-time","status":"publish","type":"post","link":"https:\/\/www.rocketmath.com\/stagingserver\/math-misteaching-5-teaching-two-similar-new-concepts-at-the-same-time\/","title":{"rendered":"Math Teaching strategies #5: Separate the introduction of similar concepts"},"content":{"rendered":"

Teaching two similar concepts and their vocabulary terms at the same time creates confusion.<\/h3>\n

The classic example is teaching parallel and perpendicular on the same day.\u00a0 The two concepts have to do with orientation of lines and the new vocabulary terms for them are similar.\u00a0 So teaching them at the same time means some or many students will have the two terms confused for a long time.\u00a0 That is known as a chronic confusion–possibly permanent.\u00a0 They will know that orientation of lines is one of those two terms, possibly, but will be confused about which is which.\u00a0 The predictable conversation with the teacher goes thusly:<\/p>\n

\"\"<\/a>Teacher:\u00a0 See these two lines lines.\u00a0 Are they parallel or perpendicular?<\/p>\n

Student: I think they’re perpendicular.<\/p>\n

Teacher: Well…<\/p>\n

Student: No, wait! I know.\u00a0 They’re parallel.<\/p>\n

Teacher: Yes, you’re right.\u00a0 I’m glad you’ve learned that.<\/p>\n

In case you missed it, the above student did NOT know the correct term.\u00a0 The student just knew it was one of two terms, but unsure as to which one.\u00a0 So the student picked one and as soon as there wasn’t confirmation by the teacher, switched to the other term.\u00a0 When you’re busy teaching it is easy to get fooled by that kind of response into assuming the students really did learn it.<\/em><\/p>\n

Other examples abound in math.\u00a0 Teaching numerator and denominator in the same lesson is common.\u00a0 Teaching the terms proper fractions and improper fractions on the same day is another example.\u00a0 Acute and obtuse angles are yet another pair of chronically confused concepts that are introduced simultaneously.<\/p>\n

Math teaching strategies: Separate the introduction of similar concepts in time.<\/strong><\/h2>\n

\"\"<\/a>If you teach one concept and only one of the pair, there’s no cause for confusion.\u00a0 It will still take a lot of repetition and practice for it to be cemented into memory, but students will be clear.\u00a0 If they use the term, for example parallel a lot of times in conjunction with examples they will soon (in a couple of weeks) be able to recall.\u00a0 However, you should pair the concept with non-examples of the concept.\u00a0 Not the opposite necessarily but just not an example of the concept.<\/p>\n

For example: For the picture to the right you would ask the students.<\/p>\n

A “Are the two lines in item A parallel or not parallel?”\u00a0 \u00a0Ans: Not parallel<\/em>.<\/p>\n

B “Are the two lines in item B parallel or not parallel?”\u00a0 \u00a0Ans: Parallel<\/em>.<\/p>\n

C “Are the two lines in item C parallel or not parallel?”\u00a0 \u00a0Ans: Not parallel<\/em>.<\/p>\n

Then after a couple of weeks you could introduce perpendicular.\u00a0 Again teach it on its own and then contrasted with non-examples until the vocabulary was clear. Probably for a couple of weeks.\u00a0 \u00a0Only then can you combine both terms in the same lesson.<\/p>\n

Another advantage of this approach is that you have avoided the other common mistake.\u00a0 Students sometimes come to the conclusion that all pairs of lines are either parallel or perpendicular.\u00a0 This method of introducing the concepts helps them realize that there are non-examples of each concept, parallel lines and ones that aren’t as well as perpendicular lines and ones that aren’t as well.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Teaching two similar concepts and their vocabulary terms at the same time creates confusion. The classic example is teaching parallel and perpendicular on the same day.\u00a0 The two concepts have to do with orientation of lines and the new vocabulary terms for them are similar.\u00a0 So teaching them at the same time means some or […]<\/p>\n","protected":false},"author":837,"featured_media":38444,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"pmpro_default_level":0},"categories":[101],"tags":[35,37,43,120,122,52,119,38],"_links":{"self":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/38447"}],"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=38447"}],"version-history":[{"count":4,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/38447\/revisions"}],"predecessor-version":[{"id":40278,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/38447\/revisions\/40278"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/media\/38444"}],"wp:attachment":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/media?parent=38447"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/categories?post=38447"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/tags?post=38447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}