I read a post last week by “Mathy McMatherson”, talking about students in his math “intervention” classes (which is the current euphemism for remedial math):

A Student with an Answer-Getting Mentality will:

Blurt Out 1-2 Word Answersbecause eventually I’ll say the right thing and the teacher will acknowledge it and then move on with the lesson and I can stop paying attention. If the teacher asks me why, I can just say “I don’t know” and they’ll explain it or just call on someone else. It’s easy for me to give a quick answer and be wrong. It’s hard for me to admit I struggle with this and need time to work it through knowing that it’ll probably be wrong anyway.

Assignments are Turned In On-Time but are Incomplete or Incorrectbecause I just want to be done with the problems as soon as I can so we can move on to the next thing. Once it’s done, it’s done and I don’t want to think about it again. I’ll get it back tomorrow with a grade so my teacher knows I did it, but I already forgot what the problems were about anyway.

Take notes and do problems with the teacher, but becomes disruptive during those ‘investigations’ they make us do every once in a while.When we take notes, I know what I need to write down. When we do problems, I know what the answer looks like—I just look at the examples we just did. But when we do investigations, I never know what they want us to do. Most of the time we don’t even finish—what’s the point? And the next day they just tell us what we were supposed to do anyway. Just tell me how to do it so I can move on.

Avoid Showing Workbecause the answer keys just have the answers on them, so I guess I should just do as much as I can in my head. This makes it easier for me to copy too, since I don’t have to worry about all that scratch work. But, deep down, I know I don’t show my work because I’m not confident in all of the steps that lead up to the answer and I don’t want to admit that by trying to put it down on paper and letting other people see my mistakes. Mistakes are bad, right?

“I’ll do it because the teacher told me” mentality.All I want is for the teacher to not bother me and let me sit here and think about other things. If I turn in my work, they’ll leave me alone.

These behaviors are not, of course, unique to remedial students. I see versions of the behaviors even in quite good college students, continuing into grad school. Disruptive behavior is rare (college students just don’t bother showing up if they don’t want to participate), but avoiding showing work, forgetting a problem as soon as it is “done”, doing things only because the teacher requires it, turning in incomplete or incorrect work, blurting out random guesses—those I certainly see.

Of course, recognizing the ubiquity of a problem, or even its cause, does not necessarily lead to a solution. I still don’t know how to budge the students off their answer-getting mindset. Unfortunately the blog post does not furnish much in the way of suggestions, ending with

One of the things I’ve realized is that any intervention strategy has to address both this Answer-Getting mindset (which, as I write this post, I guess I could also call a Failure-Avoidance mindset) as well as any missing mathematical skills. This Answer-Getting mindset acts as a wall between my classroom and any long-term understanding—before any real learning can occur, I need to break these habits. As long as a student lives in fear of failure, they’ll never be able to learn as effectively as they could be. My very first goal in any intervention needs to be breaking down this wall and creating some kind of intrinsic motivation and self-worth.

So breaking down the answer-getting mindset is important, but how does one do that?

I try to combat the answer-getting mentality by requiring students to write up design reports that describe how they arrived at the design they came up with, and grading them primarily on the accuracy of their description and process, rather than the quality of the final design (though serious errors in the design or any errors in the schematic will result in a “REDO”). Most of my design problems don’t have a single “correct” answer, and the only way I can tell whether the design is any good is by following their chain of reasoning in creating it. As I mentioned in my previous post, some students are beginning to do a careful job of describing their design methods, while others appear to be just pulling numbers out of the air (there may be method in their designs, but they keep it well hidden).

To reduce “failure avoidance”, I try to keep any one assignment from having huge weight (I don’t have exams, for example, but only quizzes with the same weight as for weekly design reports, and with the same redo policy).

To reduce dawdling until the problem goes away, I commit to staying in the lab until every group has completed a working project.

None of these measures are enough, by themselves or together, to eliminate answer-getting mindset, but I think I’m making a little progress. Does anyone have suggestions for other strategies I can try?

I am a 20-year veteran high school math teacher; next year I’m going to try something new: instead of taking points *off* on tests, I’m going to mark where I *give* points. I will announce that correct answers are worth something, but the ideas that lead there are worth more. I hope this will encourage more emphasis on communication of ideas and prevent students from just leaving a problem blank if they get stuck…try *something* useful!!

Comment by Jason — 2014 May 13 @ 07:18 |

Tests and quizzes seem to me too short a format for expressing “ideas that lead there”. Only short one-step or two-step problems are suitable for tests, and they don’t need much if any explanation. Students should be getting them right not just having a vauge idea how to do them (but see the post on students doing poorly on the first quiz in the circuits class). I desire explanation not on routine test problems, but on more challenging multistep design problems (or in computer programs, when those are assigned).

I’m not looking so much for students to “try something”, as they are almost all capable of putting down something random that has a vague connection to the problem, as I am for students to organize their thinking and give sentences explaining what their computations

mean. For a pure math class, there may be no real-world meaning, so the best thing math teachers could do to help me is not to have them write more, but to give them multistep problems, where they have to put together chains of 6–10 simple steps, rather than only ever giving 1-step and 2-step problems where the method is obvious from what unit you are in.Physicsteachers could help by having students write more, particularly about unit conversions and converting different types of units (like converting pressure into force, by explicitly invoking the area over which the pressure is applied).But I can’t change the math and physics instructions my students have already had. I need strategies for getting the students able to explain multistep designs despite their previous inexperience with either explanation or multistep problems. I don’t think that a sleight-of-hand with quiz grading would have any useful effect.

Comment by gasstationwithoutpumps — 2014 May 13 @ 08:00 |

Well, I see your point for most math classes at most schools, but this is a very strong school, and indeed, many test problems are indeed multi-step problems that use cumulative knowledge and not just obvious processes from the chapter. It’s what we practice in class, and it’s what I insist on for tests.

Comment by Jason — 2014 May 13 @ 08:25 |

I’m glad to hear of a math class using multistep problems! It seems that the students I get in bioengineering classes are unfamiliar with them, despite having had calculus and (usually) ODE.

If you are giving multistep problems, it may not be necessary to give points for “ideas that lead there” expressed in English, unless there are so many different routes to a solution that you want an explanation of which one they have taken. (I see the more need for English in a class that involves proof than one that just manipulates trig identities, for example.)

The design problems I give are a bit different from math problems, in that there are some arbitrary choices to be made that lead to different answers. I need the students to tell me when they make an arbitrary choice (like what power supply voltage to use, when the only obvious constraint is that it be ≤6v), or what calculation they used to determine a value from some previous choice. Very few math problems allow students to make arbitrary choices, so only the calculation needs to be explained. I would, in many cases, be satisfied with students simply showing all the steps of their calculation from the numbers on the spec sheet to the component values in their designs, but they omit huge chunks of the calculation, apparently having copied an intermediate result from somewhere else (another student, an explanation on the whiteboard, …) without explanation.

Comment by gasstationwithoutpumps — 2014 May 13 @ 08:56 |

[…] but they don’t record the meaning of each step or even what the sequence of steps is, and the “answer-getting” mentality causes them to flush the process from their minds as soon as they have a […]

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[…] learn how to design and debug—to ask their own questions and figure out how to answer them. (See Answer getting for more on what change I’m trying to invoke.) Some of the top students are already on […]

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[…] students who see their role as answer getting are easily convinced to grab one of the good designs so readily available on the Internet and […]

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