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I read pages of the book "Elementary and Middle School Mathematics: Teaching Developmentally" by John A. Van de Walle, Late of Virginia Commonwealth University Karen S. Karp, Johns Hopkins University Jennifer M. Bay-Williams, University of Louisville

Reading this extract:

enter image description here I remember an idea that I still don´t use, so... I would like to use it in this starting week,... but the library where I read the book does not have access to the online company resources (where I suppose that any activity pages about this issue are available)

The question is:

1.- Do you have any activity pages with the strategy "find the error" about this issue (powers, and fraction operations)?

and secondarily,

2.- Do you know papers about this strategy "Find the error"

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    $\begingroup$ I'm developing a college course in which I'd like to use this sort of exercise daily. I will be interested in what others have to offer. $\endgroup$ – Sue VanHattum Nov 7 '17 at 20:15
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    $\begingroup$ @SueVanHattum Do you think this is actually good for students? I'm not saying it's necessarily not good, but I would be worried that they reinforce the errors as acceptable by seeing them. The main problem I've seen at the lower university level was a complete lack of understanding that math is not like law. In law if it's not forbidden it's allowed in math if it's not allowed it's forbidden. But I would see way too much random guessing which I think these kinds of exercise might just reinforce since it feels way too much like there are just some things which are wrong. Instead of almost all. $\endgroup$ – DRF Nov 13 '17 at 20:20
  • $\begingroup$ Interesting comparison! I will keep that in mind! We want to work with beginning algebra students on recognizing what sorts of steps make sense, and which don't, and understanding why. $\endgroup$ – Sue VanHattum Nov 14 '17 at 22:55
  • $\begingroup$ My experience with using find the error questions this semester is that they have added nothing to the assessment and confused students into making the same errors presented when asked to do the problem later. I would oppose this question type. $\endgroup$ – Alexander Gruber Nov 25 '17 at 4:51
  • $\begingroup$ Exercises in this spirit are standard in traditional introductory computer programming classes. One gives students code and asks them to find the errors (or to describe the output). Such exercises can be useful when first learning syntax (essentially the issue in the examples given). The potential pitfall of such exercises is that they could reinforce the student's idea (perhaps less incorrect in the programming context) that everything is just a formal game with incomprehensible rules that need to be memorized and applied (rather than understood). $\endgroup$ – Dan Fox May 8 '18 at 16:11
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As to question 1: I do have a german speaking background, so please excuse the source actually is in german: There is a really nice journal called Wurzel, the german word for "square root". In there, Attila Furdek has a section called "Schlaue Leute werden durch die Fehler von anderen klug" (trans. "Clever people become wise through the mistakes of others"). The structure of the tasks is always the same: The Problem is posed, along with two or more answers, all getting to a different conclusion. The question then is, which solution is correct and why. Sample problems can be accessed online, Attila Furdek also collected the problems along with solutions in a book.

The way to get these questions is similar to the way distractors for multiple choice questions are generated: Furdek would collect his students work to a problem. If there are different solutions among them, he would pick two or three different solutions ans give them back to the class, together with the question which one would be the correct one and why.

This way, the different alternatives are actual mistakes, which makes the problems very authentic.

I used translations of the book in my own classes, but more over, collected my students solutions in order to use the same style of task.

On question 2: I have to admit, I haven't "Google scholared" this topic as I should. My experiential knowledge is, that this type of task, put right, can be a great learning opportunity. Similar to tasks using concept cartoons, it stimulates classroom discussions not only about the "what" and the "how", but also the "why" of a solution. This way, I've the impression my students were less relying on "solutions from the book" and went towards more confidence in their answers. Opposite of the worries of DRF (see comments), in my experience this tasks did not reinforce wrong procedures, to the contrary, they helped my students a lot in "making sense" of what they do.

Much in the sense of a saying by Groucho Marx: "Learn from the mistakes of others. You can never live long enough to make them all yourself."

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