experimental math model
数 学 实 验 模 型
SAT math tests assess on the foundational skills in numbers, algebra, geometry and data analysis areas. These areas include operations of linear/quadratic/cubic expressions, equations and functions, geometric relations of lines, triangles, quadrilaterals and circles, and data analysis of one or two-variable datasets. The high school math classes teach the rules and ways in solving such problems. However, all problems can be solved by applying mind2learn's Experimental Math Model. Simple! Let’s go!
Experimental Math Model (EMM) regards each math problem as an experiment. To us, math is an abstract framework to find the best (often exact) solutions for real-life problems. Instead of driving for abstract mathematical answers, we can always solve it with experiments as scientists do in real world.
Start with the student-produced-response example below.
Experimental Math Model (EMM) regards each math problem as an experiment. To us, math is an abstract framework to find the best (often exact) solutions for real-life problems. Instead of driving for abstract mathematical answers, we can always solve it with experiments as scientists do in real world.
Start with the student-produced-response example below.
This example illustrates a general experiment for the quadratic problems in SAT, of which the experiments on P1 and P2 for (Y = c) can always lead to the solution. And P1 can always be (0, c). If you can remember, P2 is (-b/2, c).
Take another example in data analysis. This one is a multiple-choice question.
Take another example in data analysis. This one is a multiple-choice question.
This example also illustrates the general experiment for a problem category, data/regression. For any linear data problems, experiments can always be conducted on the left and right ends (or towards the minimum and maximum) of the horizontal variable range.
Up to here, you might have suspected that EMM looks a lot like the plug-in strategy. These two are similar in that they both use a plug-in mechanism. However, EMM spells a general experiment in which two special data points are tested, whereas plug-in requires to test more than two-some times all four choices are tested. Plug-in strategy may be impossible in certain problem settings, whereas EMM will be always possible. Therefore, EMM can be regarded a one-size-fit-all strategy. It is a very powerful tool for your test, specially on the few hard questions. Like the strategies you learnt elsewhere, mind2learn's EMM only augments but not replaces what you have learnt from the school.
Try to define your own general experiments for each category of math problems. Download the document below for a list of math categories in SAT, SAT Math 1 and 2. It will be fun.
Up to here, you might have suspected that EMM looks a lot like the plug-in strategy. These two are similar in that they both use a plug-in mechanism. However, EMM spells a general experiment in which two special data points are tested, whereas plug-in requires to test more than two-some times all four choices are tested. Plug-in strategy may be impossible in certain problem settings, whereas EMM will be always possible. Therefore, EMM can be regarded a one-size-fit-all strategy. It is a very powerful tool for your test, specially on the few hard questions. Like the strategies you learnt elsewhere, mind2learn's EMM only augments but not replaces what you have learnt from the school.
Try to define your own general experiments for each category of math problems. Download the document below for a list of math categories in SAT, SAT Math 1 and 2. It will be fun.
| sat_math_-_subject_math_1_-_math_2_compared.pdf |