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Number Sense = Mathematical Skills?


We were finishing up the school term with some last minute marking and writing of student reports. I was also lamenting the inability of many students to know the difference between perimeter, area and volume (more on this in H3 later). Despite a range of teaching techniques (some involving practical measuring of outdoor objects and spaces) it was obvious that there is some sort of cognitive disconnect happening with some students, and they have a poor sense of space and numbers. Which led to this interesting article, which showed that “we have an inborn, intuitive grasp of numbers that varies from one person to the next and is closely linked to advanced math skills, according to a study. In experiments with teenagers in the United States, scientists discovered that children whose “approximate number system” (ANS) was highly developed were also good in school-taught mathematics from an early age. 64 14-year-olds were shown a series of images containing between 10 and 32 dots that were either blue or yellow.

beansIn some images – flashed for only one-fifth of a second – there were twice as many dots of one colour.

In other images, however, the ratio was closer to parity with, for example, seven yellow dots and eight blue, and thus much harder to discern.

The results showed a wide variation in the capacity to pick the colour with the most dots at least 75% of the time, suggesting that some people are simply much better at such lightning-fast “guesstimates.”

Even more unexpected, however, was the extent to which the two distinct kinds of number-crunching cognition – ANS and learned mathematics – are linked.

Now here is the interesting mathematical link – students who performed best in the image test were also those who scored the highest in standard math achievement tests, going back almost 10 years to kindergarten.”

H3 Note: This research is of a very small sample group and is still not conclusive! Check out the full article here.

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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