{"id":43651,"date":"2010-12-12T16:05:21","date_gmt":"2010-12-12T16:05:21","guid":{"rendered":"http:\/\/mast.thomasjpitts.co.uk\/?p=94"},"modified":"2010-12-12T16:05:21","modified_gmt":"2010-12-12T16:05:21","slug":"mitchelmore-white-reading","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2010\/12\/12\/mitchelmore-white-reading\/","title":{"rendered":"Mitchelmore & White Reading"},"content":{"rendered":"
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\"Angle<\/a><\/dt>\n
Image via Wikipedia<\/a><\/dd>\n<\/dl>\n<\/div>\n<\/div>\n

The main reading for this study block (linked below) is a tricky and detailed account of current teaching relating to angles. It’s main findings are that not enough is done to develop the concept<\/a> of ‘turn’ with children<\/a> – that an angle<\/a> can be defined at the amount of\u00a0turn\u00a0from one position to another, and that, if it is taught, the main focus is on right angled turns.<\/p>\n

Beebots and roamers could be used in school to investigate the idea of turn, but why not use the school grounds? Create obstacle courses in the playground for children to be directed around – making sure that the turns aren’t always at right angles.<\/p>\n

Mitchelmore and White state that children need to experience a wider range of angle concepts. They believe that teacher move too quickly on to the abstract idea of an angle – as shown here.<\/p>\n

Their research looked at whether children could represent the movement of objects such as a door, or wheel<\/a> in terms of diagrams and still understand what was happening – whether they could move from the physical to the abstract in one move.<\/p>\n

For instance, the angle shown here could represent the movement of the blades of a pair of scissors, or the opening of a handheld fan, things that children could see happening, and represent in a diagram like this. However, children\u00a0referred\u00a0to these movements as ‘opening’, not ‘turning’.<\/p>\n

Children were asked to represent the angles using bendy straws to\u00a0demonstrate\u00a0the\u00a0movement and the associated angles. If children could see the angle of movement, and explain what was happening, the researchers were happy.<\/p>\n

The researchers also looked at children’s ideas of slope<\/a>, with the idea that this is an area that is overlooked in schools. I would consider this to be the case simply because of the difficulty of\u00a0representing it as well as not always being able to see the angle that a hill slopes at, for instance.<\/p>\n

…most students<\/a> had\u00a0some global concept of slope but that many did not quantify it by relating\u00a0the sloping line to a fixed reference line. Unlike the wheel and door, where\u00a0the second line may be suggested by the initial position and there is a\u00a0global movement which can be copied, there is in fact very little to help a\u00a0na\u00efve student interpret a slope in terms of a standard angle.<\/p>\n

We conjecture that many students\u00a0have a global conception of slope as a single line and do not conceive it\u00a0in terms of angles. Had the physical model of the hill consisted simply of a sloping plane without any supporting edges, it is likely that far fewer\u00a0students would have indicated a standard angle interpretation.<\/div>\n<\/blockquote>\n

Mitchelmore and White discuss how children find it easier to see the turns, angles and slopes when both elements are easily visible (the scissors, fan, etc.) and this is likely to be because it fits more\u00a0readily\u00a0to the idea of an angle as drawn above – something they are likely to encounter in class. They go on to say that,\u00a0“the fact that the standard angle was used\u00a0more frequently for the door and hill (where one arm must be constructed)\u00a0than the wheel (where both arms must be constructed) supports the view\u00a0that the crucial factor accounting for the rate of use of standard angles is\u00a0the physical presence of the angle arms…\u00a088% of the students used standard angle modelling when\u00a0both lines were visible, 55% when only one was visible, and 36% when\u00a0no line was visible.”<\/p>\n

There are three main findings to this piece of research.<\/p>\n

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  1. That angle work can be related to the everyday concepts\u00a0of corner, slope and turn.<\/li>\n
  2. The fewer arms that are present\u00a0in a particular angle context, the more that has to be constructed to bring\u00a0it into relation to other angle contexts and, therefore, the more difficult\u00a0it is to recognise the standard angle. It is only in exceptional cases that\u00a0the relevant line has to be discovered. In most cases, it has to be invented\u00a0through conscious mental activity.<\/li>\n
  3. That many children form a standard angle concept early, but that this concept is likely to be limited to situations\u00a0where both arms of the angle are visible. If the concept\u00a0is to develop into a general abstract angle concept, children will need more\u00a0help than is presently given to identify angles in slope, turn and other\u00a0contexts where one or both arms of the angle are not visible. The slope\u00a0and turn domains are particularly important for the secondary mathematics\u00a0curriculum, the former because of the frequency of angles of inclination in\u00a0trigonometrical applications and the latter because it provides a valuable\u00a0aid in teaching angle measurement.<\/li>\n<\/ol>\n

    Again, the more hands on practice children have at experiencing \u00a0the different elements of angle, the stronger their\u00a0knowledge\u00a0is likely to be.<\/p>\n

    Link<\/strong>:\u00a0Mitchelmore, M., C & White (2000), “Development of angle concept by progressive abstraction and generalisation.” Educational Studies in Mathematics, 209-238.<\/a><\/div>\n
    \"\"<\/div>\n","protected":false},"excerpt":{"rendered":"

    Image via Wikipedia The main reading for this study block (linked below) is a tricky and detailed account of current teaching relating to angles. It’s main findings are that not enough is done to develop the concept of ‘turn’ with children – that an angle can be defined at the amount of\u00a0turn\u00a0from one position to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4438,4439,4441],"tags":[73,244,4461,660,4486,4487,1015,4489,1909,4545,4547,4550,4584,4592,2884,4597,4614],"class_list":["post-43651","post","type-post","status-publish","format-standard","hentry","category-recommended-reading","category-reflections","category-study-block-2-measures","tag-73","tag-angle","tag-angle-concept","tag-child","tag-development","tag-development-of-angle-concept-by-progressive-abstraction-and-generalisation","tag-education","tag-educational-studies-in-mathematics","tag-math","tag-measure","tag-measures","tag-mitchelmore","tag-right-angle","tag-slope","tag-student","tag-study-block-2","tag-white","has-post-title","has-post-date","has-post-category","has-post-tag","has-post-comment","has-post-author",""],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6OeSW-bm3","jetpack-related-posts":[],"builder_content":"","_links":{"self":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/43651","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/comments?post=43651"}],"version-history":[{"count":0,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/43651\/revisions"}],"wp:attachment":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=43651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=43651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=43651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}