I planned to write a post service most instruction stalk together with leafage diagrams. But so I realised that many maths teachers reckon them to live on pointless, a waste matter of instruction fourth dimension together with a welcome removal from the curriculum.
Now let’s remember most this for a minute. Admittedly stalk together with leafage diagrams are rarely used inward ‘real life’. In fact the alone mutual examples nosotros tin abide by are timetables, such equally the Japanese develop timetable shown inward the painting exhibit below (more examples here). But does this ‘uselessness’ actually hateful that stalk together with leafage diagrams shouldn’t live on taught? If that’s the instance so a publish of the topics nosotros learn inward maths should live on taken off the curriculum.
Now let’s remember most this for a minute. Admittedly stalk together with leafage diagrams are rarely used inward ‘real life’. In fact the alone mutual examples nosotros tin abide by are timetables, such equally the Japanese develop timetable shown inward the painting exhibit below (more examples here). But does this ‘uselessness’ actually hateful that stalk together with leafage diagrams shouldn’t live on taught? If that’s the instance so a publish of the topics nosotros learn inward maths should live on taken off the curriculum.
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| Japanese develop timetable. Source: Wikipedia |
Much of the maths nosotros learn at Key Stage iii helps pupils access to a greater extent than advanced topics (all roads Pb to calculus?!). Maths begets maths. So practise stalk together with leafage diagrams Pb us anywhere? Do they assist pupils develop whatever useful skills together with understanding?
I'm going to tell (in a sheepish whisper) that they do. Stem together with leafage diagrams are i of a ready of tools that could live on used to develop agreement of the concepts of median, mode, quartiles, spread, skew together with outliers. I remember they are accessible to depression powerfulness pupils. I remember that pupils bask creating them. I remember they Pb to interesting discussions when comparing ii sets of data. I sure enough don't remember they should live on a compulsory theme at whatever age, but I meet no impairment inward teachers using them if they like. Isn't it prissy to receive got that freedom?
John Tukey, the inventor of stalk together with leafage diagrams, wrote "If nosotros are going to brand a mark, it may equally good live on a meaningful one. The simplest - together with most useful - meaningful score is a digit" (source). Excellent betoken Mr Tukey. Did you lot know he also invented the box together with whisker plot?
John Tukey is also quoted equally saying "There is no information that tin live on displayed inward a pie chart, that cannot live on displayed ameliorate inward another type of chart". I agree. In the same agency many of you lot don't similar stalk together with leafage diagrams, I don't similar pie charts (this excellent weblog post service most the misuse of pie charts is worth a read).
Right, directly I've attempted to justify this weblog post, here's my lesson ideas:
Starting Point
You could foremost past times presenting your cast amongst a large ready of information (like the i below) together with hollo for them what the vogue is. It's hard to spot. Ask your pupils for ideas on how could nosotros organise this information so nosotros tin easily meet the mode.
12, 54, 21, 56, 32, 14, 42, 23, 20, 48, 21, 34, 12, 15, 16, 42, 47, 46, 32, 21, 45, 43, 21, 34, 26, 32, 17, 18, 45, 21, 44, 32, 12, 23, 45, 24, 35, 38, 28, 18, 29, 20, 10, 36, 12, 42, 47, 32, 47, 37, 12, 54, 23, 17, 29, 38, 32, 12, 17, 13, 21, 34, 12, 15, 16, 42, 47, 46, 12, 16, 43, 23, 16, 46, 52
I abide by stalk together with leafage plots rather pleasing to the eye. Much nicer to await at than a ho-hum listing of unordered data.
An option starting betoken is a 'beat the teacher' game, which I've adapted from an thought past times the NCETM. In this activity, pupils remember of a publish betwixt 10 together with 40. Each publish is called out inward turn, land pupils brand a listing inward their books. Meanwhile the instructor also makes their ain list, but organises it equally a stalk together with leafage diagram. Once all the numbers are listed, the instructor asks the cast to travel out median, vogue together with range. The instructor volition practise it much quicker from their stalk together with leafage diagram, so he/she wins the race.
Physical Activities
This weblog post is most introducing stalk together with leafage diagrams using post-it notes. It's a lovely thought for an engaging together with accessible lesson. Mr Collins shared a similar thought inward this weblog post, but he uses students together with desks instead of post-its. If you lot similar the thought of human stalk together with leafage diagrams so you lot mightiness also similar these breath-holding activities - i from Don Steward together with a similar i from the NCETM.
Data Types
Encourage pupils to remember most dissimilar types of information - what is suitable for a stalk together with leafage diagram together with what isn't? For example, could the full publish of goals scored per game inward a flavor of football game matches live on displayed inward a stalk together with leafage diagram? Probably not, because the information would generally live on unmarried digit numbers. Try my worksheet for to a greater extent than on this.
Mini Projects
Don Steward has approximately prissy activities involving stalk together with leafage diagrams, such equally this this Presidents Longevity Project. I also similar Tim Jefferson's skewness).
Back-to-back stalk together with leafage diagrams are useful for comparing data. Writing comparisons betwixt information sets - whether represented past times stalk together with leafage diagrams or box together with whisker plots - is something that pupils (especially EAL pupils) ofttimes abide by difficult.
There's lots of S1 (A level) stalk together with leafage questions - similar the i below - that could live on explored at Key Stage iii (which begs the question, why were they considered suitably challenging for Influenza A virus subtype H5N1 level?).
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| Edexcel S1 Nov 2004, Question 1 |
I rarely disagree amongst people or play devil's advocate so this post service is a chip risky for me! Be nice. If you lot practise learn stalk together with leafage diagrams so I promise you lot abide by these ideas helpful. Thanks to those on twitter who shared their views together with ideas (especially @srcav - who is non a fan of stalk together with leafage diagrams!).
