# Solving Arithmetic Problems

But if you didn't wanna do it that way, you just do it the old-fashioned way. Negative one times 594 is negative 594, negative one times negative 15 is positive 15.

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Although many different definitions and operationalizations exist in the literature, they converge on two central themes: the knowledge of different solution strategies and the ability to adapt them appropriately when solving a problem (Rathgeb-Schnierer and Green ).

In the current paper, flexibility and adaptivity are used interchangeably as selecting the optimal strategy for a given problem in a given setting for a given person.

Or, one could change the numbers by subtracting 300 instead of 299, and compensating back the 1 subtracted too much.

In contrast to the importance attached to flexibility, adaptivity, and clever strategies, empirical results have shown that primary school students do not use shortcut strategies very frequently in Flanders (e.g., De Smedt et al. The current study aims to extend these results by investigating the use of shortcut strategies in very favorable conditions, that is, by studying older students (with higher levels of conceptual and procedural knowledge) who have received years of reform-based mathematics instruction focusing on fostering adaptivity and clever strategies.

The current study’s results will shed light on the extent to which students use shortcut strategies in these very favorable conditions, making it possible to place previous studies’ findings of limited use of shortcut strategies in a broader perspective.

Moreover, the results may have practical implications for (reform-based) mathematics education striving for adaptive expertise.).

It's going to be 15 minus, you see it's going to be n minus one right here, right when n is four, n minus one is three. It's going to be, and I'll do it in pink, the 100th term in our sequence, I'll continue our table down, is gonna be what? So 99 times six, actually you could do this in your head. So this right here is 594, and then to figure out what 15, so we wanna figure out, we wanna figure out what 15 minus 594 is, and this can sometimes be confusing, but the way I always process this in my head is I say that this is the exact same thing as the negative of 594 minus 15. So that right there is 579, and then we have this negative sign sitting out there.

It's going to be 15 minus 100 minus one, which is 99, times six, right? One, you had a zero here, two, you had a one here, three, you had a two here, 100, you're gonna have a 99 here. You could say that's going to be six less than 100 times six, which is 600, and six less is 594. And if you don't believe me, distribute out this negative sign. So our the 100th term in our sequence will be negative 579.

In reform-oriented mathematics curricula, this striving for adaptive expertise is reflected in the instructional content and approaches, focusing on diversity of solution strategies.

Reform movements throughout the world have identified adaptivity and flexibility of strategy use as an important competence (e.g., Star et al.

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