teaching:topics:thinking_mathematically:problemsolving:summary
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teaching:topics:thinking_mathematically:problemsolving:summary [2020/06/07 18:28] simon [a summary of the main ideas] |
teaching:topics:thinking_mathematically:problemsolving:summary [2020/08/01 12:40] (current) simon [being systematic about solving problems] |
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| This is relevant from primary school all the way through high school and university and beyond, finding | This is relevant from primary school all the way through high school and university and beyond, finding | ||
| solutions in all kinds of professional tasks --- science, business, design, engineering, computers, policy | solutions in all kinds of professional tasks --- science, business, design, engineering, computers, policy | ||
| - | making and management ... pretty much any field which requires thought and initiative rather than simply | + | making and management --- pretty much any field which requires thought and initiative rather than simply |
| carrying out repetitive set actions. It is one of the ways we analyse and talk about the world. | carrying out repetitive set actions. It is one of the ways we analyse and talk about the world. | ||
| + | == == | ||
| {{blog:mathematics-k-10-org-content.png?direct&75 }}It is also at the centre of the maths syllabus, every year from infants to year 12. | {{blog:mathematics-k-10-org-content.png?direct&75 }}It is also at the centre of the maths syllabus, every year from infants to year 12. | ||
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| * an exact value? --- hence a fraction or surd --- this is the 'default' | * an exact value? --- hence a fraction or surd --- this is the 'default' | ||
| * do you also need an approximate value? --- a decimal --- how accurate is the data given? | * do you also need an approximate value? --- a decimal --- how accurate is the data given? | ||
| - | * give it (them) **a name**, a pronumeral, it is the most important 'unknown'! | + | * give it (them) **a name** --- a pronumeral, it is the most important 'unknown'! |
| * is a diagram, picture or some graphical representation required? | * is a diagram, picture or some graphical representation required? | ||
| * away from the very contrived exam or test context your answer must show the relationships that you found in a form that your audience can read --- maths is very much about communicating particular kinds of abstract ideas. | * away from the very contrived exam or test context your answer must show the relationships that you found in a form that your audience can read --- maths is very much about communicating particular kinds of abstract ideas. | ||
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| ===What facts have you been given?=== | ===What facts have you been given?=== | ||
| * write them down as equations, or draw them | * write them down as equations, or draw them | ||
| - | * **then** recheck, does the equation fit the information given --- is it sensible? | + | * **then** recheck, does what you wrote fit the information given --- is it sensible? |
| * there might be some extra, unimportant, facts given | * there might be some extra, unimportant, facts given | ||
| * as you work on the problem, keep going back to the question | * as you work on the problem, keep going back to the question | ||
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| * label axes, directions and scales | * label axes, directions and scales | ||
| * label lines on graphs with their equations | * label lines on graphs with their equations | ||
| - | * **thoughtfully** and succinctly marking these names and labels will help understand the problem | + | * **thoughtfully** and succinctly marking these names and labels will help understand the problem |
| - | * this step often shows **a path to a solution** | + | * this step often shows **a path to a solution** |
| * draw diagrams, or label the ones given, with any facts you have been told | * draw diagrams, or label the ones given, with any facts you have been told | ||
| * look for geometrical facts connecting the values (known or named) in any diagram | * look for geometrical facts connecting the values (known or named) in any diagram | ||
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| <WRAP tip> | <WRAP tip> | ||
| - | it is all about being systematic --- assembling what you know, remembering some rules, doing a bit of | + | it is all about being systematic --- |
| - | manipulation then giving the answer **to the actual question** --- <wrap em>always in the correct form!</wrap></WRAP> | + | |
| + | assembling what you know, expressing it clearly and succinctly, remembering some rules, doing a bit of | ||
| + | manipulation | ||
| + | |||
| + | then giving an answer **to the actual question** --- <wrap em>always in an appropriate form!</wrap></WRAP> | ||
| - | ===finally - check that your answer is sensible!=== | + | ===finally — check that your answer is sensible!=== |
| * are the values found physically or logically plausible? | * are the values found physically or logically plausible? | ||
| * do the values found actually fit all the given facts? check each phrase! | * do the values found actually fit all the given facts? check each phrase! | ||
| - | remember if the question has lots of parts some information will only be needed for one little part | + | Remember: if the question has lots of parts some information will only be needed for one little part |
| (or not at all). | (or not at all). | ||
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| * if you do not get the full answer you will still get marks for getting half way ... | * if you do not get the full answer you will still get marks for getting half way ... | ||
| * but only if you show clearly that you did at least understand the problem | * but only if you show clearly that you did at least understand the problem | ||
| - | * even better --- show that you are //part of way// to the solution! | + | * even better --- show that you are //part of the way// to the solution! |
| * if you are running out of time ... try outlining the steps you need to take, this can be much faster than working out the details, and it might get most of the marks, but only if very clearly described! | * if you are running out of time ... try outlining the steps you need to take, this can be much faster than working out the details, and it might get most of the marks, but only if very clearly described! | ||
| * if you are stuck and you have written down all facts you see that are relevant | * if you are stuck and you have written down all facts you see that are relevant | ||
teaching/topics/thinking_mathematically/problemsolving/summary.1591518502.txt.gz · Last modified: 2020/06/07 18:28 by simon
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