{"id":445,"date":"2015-09-13T16:42:49","date_gmt":"2015-09-13T20:42:49","guid":{"rendered":"http:\/\/sundogpetservices.ca\/?p=445"},"modified":"2015-09-13T19:32:59","modified_gmt":"2015-09-13T23:32:59","slug":"calculus","status":"publish","type":"post","link":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/2015\/09\/calculus\/","title":{"rendered":"Calculus"},"content":{"rendered":"

How Calculus is Taught<\/h3>\n

Ca\"\\int_a^blculus is taught,\u00a0 at the earliest, in high school (in Canada).\u00a0\u00a0 How is calculus taught?\u00a0 In kindergarten (or preschool) we learn numbers, and perhaps to add and subtract (1+1 = ?).\u00a0 By Grade 6 or 7 we’ve learned more complex math; division, multiplication, some algebra, geometry and maybe basic trigonometry (SOH-CAH-TOA anyone?).\u00a0 By Grade 10 or 11, we’ve learned algebra, probably Trig (y=x^2 + 4x + 4; y = sinx).\u00a0 Calculus in Grade 12.\u00a0 Understanding algebra and trig\u00a0 is essential to learning calculus.\u00a0 Hence the slow progression of learning (12 years!!!).<\/p>\n

How Calculus isn’t taught<\/h3>\n

Once learning numbers and reciting them once, we don’t immediately start adding and subtracting.\u00a0 Once succeeding in adding and subtracting once, we don’t move immediately move to multiplication and division.\u00a0 Once succeeding once in multiplication and division, we don’t proceed to algebra.\u00a0 Once succeeding once with geometry, we don’t proceed to trig.\u00a0 Once succeeding once with algebra and trig, we don’t move right to Calculus.<\/p>\n

Put another way.\u00a0 Once learning the basics of a chosen field (say Biology) one doesn’t move right to polymerase chain reactions (replicating DNA in a lab).\u00a0 Understanding basic units of Cells doesn’t immediately mean DNA replication is understood.\u00a0 “But you know about DNA!”<\/p>\n

We wouldn’t teach children, or even adults this way.\u00a0 Yet….<\/p>\n

What Does This Mean for Dog Training?<\/h3>\n

Going too fast. I have been guilty of asking for too much too quickly (I\u2019m sure most professional trainers would also agree too). Humans are in a hurry. We want results NOW (even more so in the last century). Dogs have a different schedule and a different mindset \u2013\u201cWhat do you want me to do?” (Do I have the skills to do that right now?) and\/or “*Why* should I do this now? (\u201cAm I getting paid, and\/or is what I\u2019m already doing better?\u201d)<\/span><\/span><\/p>\n

“What do you want me to do?”<\/h5>\n

Teaching what you want away from distractions first is essential.\u00a0 Before complexity, basic behaviour is needed.<\/p>\n

“But he knows how to sit!”<\/strong>\u00a0\u00a0 — could you do your job in the middle of the Superbowl (or The Grey Cup, for people who like real football<\/strong>\u00a0 -3 downs, 110yardsx65 yards and bigger balls – I’m not biased….)<\/em>.\u00a0 Probably not, or at least not well (unless you’re a professional football player or mascot).<\/p>\n

Dogs are asked to do this… a LOT.\u00a0 When there are many distractions around, focus becomes difficult.\u00a0 Most dogs who fail likely don’t have the skill set yet to deal with the distractions.\u00a0 Teaching them to work around the distractions is part of building complexity and “proofing”.\u00a0 To work in the real world, dogs need to know how to work around the different aspects of the real world.\u00a0 Understanding what a carburetor is doesn’t mean you can rebuild one.\u00a0 Some dogs though may have appropriate skill sets and may not participate for other reasons.<\/p>\n

“Why should I do it?”<\/h5>\n

Let’s say you could<\/em> do your job in the middle of the Superbowl; you paid $250 for these seats\u00a0 by the way.\u00a0 Now someone puts your work in front of you.\u00a0 You’re watching the game, why should you do it now?\u00a0 Not much motivation to do it for free.\u00a0 Now they offer you $1000 dollars.\u00a0 Motivated now; still only $750 and you will miss the game?\u00a0 How about $10,000 if $1000 didn’t work?<\/p>\n

A hungry teenager isn’t likely going to pay attention in class (want of food > want of Emily Dickinson).\u00a0 An overly full party goer isn’t going to be tempted by a plate of nachos but might enjoy a nap (Sleep > Food).\u00a0 A rampaging, happy tummy toddler isn’t going to care about a sandwich or a nap when the swing set is waiting (Fun > Food or Sleep)!<\/p>\n

Dogs require appropriate pay\u00a0 as well,\u00a0 Once proficient around distractions payments may not need to be as valuable, but in order to maintain their desire to do a behaviour they need practice and at least occasional payment.<\/strong><\/p>\n

And this means…?<\/h5>\n

Training to fluency could look like this sequence:<\/p>\n

    \n
  1. Learn Sit in the House<\/li>\n
  2. Learn Sit in the Backyard<\/li>\n
  3. Practice Sit in the Backyard when the squirrels are running around on the fence<\/li>\n
  4. Practice Sit in the Park when no dogs are around<\/li>\n
  5. Practice Sit in the Park around other dogs\/people<\/li>\n
  6. Practice Sit in the Park, after play with other dogs<\/li>\n
  7. Practice Sit in the Park, right before playing with other dogs<\/li>\n<\/ol>\n

    Sit could easily be replaced with Recall etc.<\/p>\n

    I’ve been guilty in the past of “assumption of knowledge”.\u00a0 Consider the following sequence:<\/p>\n

      \n
    1. Learn Recall in the House\/yard<\/li>\n
    2. Ask for a Recall in the park, during dog play<\/li>\n<\/ol>\n

      This is very much like asking that 5 year old to solve the area under a curve.<\/p>\n

      The Paradox<\/h5>\n

      Before we teach our dogs Calculus, they need to learn the steps involved from learning numbers through addition, multiplication, algebra and trig.\u00a0 Training is faster if we follow steps in increments rather the equivalent of going from constructing paper airplanes to designing the Concord.<\/p>\n","protected":false},"excerpt":{"rendered":"

      How Calculus is Taught Calculus is taught,\u00a0 at the earliest, in high school (in Canada).\u00a0\u00a0 How is calculus taught?\u00a0 In kindergarten (or preschool) we learn numbers, and perhaps to add and subtract (1+1 = ?).\u00a0 By Grade 6 or 7 we’ve learned more complex math; division, multiplication, some algebra, geometry and maybe basic trigonometry (SOH-CAH-TOA … Continue reading Calculus<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,19],"tags":[],"class_list":["post-445","post","type-post","status-publish","format-standard","hentry","category-learningtheory","category-philosophical-dog-discussions"],"_links":{"self":[{"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/posts\/445","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/comments?post=445"}],"version-history":[{"count":4,"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/posts\/445\/revisions"}],"predecessor-version":[{"id":449,"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/posts\/445\/revisions\/449"}],"wp:attachment":[{"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/media?parent=445"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/categories?post=445"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sundogpetservices.ca\/wordpress\/index.php\/wp-json\/wp\/v2\/tags?post=445"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}