Could points be taken off for not factoring?

[C5F8576]

Would a professor in a linear algebra, another upper-level math course, or an upper-level physics course take off points if I don't show steps when factoring an equation expression?

 

[C5F8576]

I am not taking a particular math course this semester so it's difficult to ask a specific professor. I'm just preparing for future math courses so I wanted a general sense of what a professor would do. In the past, my physics professors haven't taken points off for not fleshing out each mathematical step while my CS high school teachers and college professors, and high school math teachers have.

 

[fresh_42]

Would a professor in a linear algebra, another upper-level math course, or an upper-level physics course take off points if I don't show steps when factoring an equation?

The answer to this question depends on so many circumstances that it is not easy to answer. It depends on the person, the task, the kind of teaching, sympathy, application, difficulty level, etc.

Here is a list of my personal experiences:

• I lost points for drawing a line at $y=6.5$ instead of $y=7$ and we both knew it was only a miscount.
• I had fewer points than my neighbor who copied my text, and to disguise it, he added a little comment.
• I saw a girl who knew everything (eidetic memory) but apparently did not understand things and thus got bad grades.
• I had a professor arguing about someone's dissertation that had a very severe error: "I don't care. The result is right anyway!" without saying how this "anyway" would be proven.
• I heard about an exam in which the student had better grades than deserved because: "... and greetings to your father!"

These are a variety of possibilities of only those I do remember, and I am absolutely sure that they did happen. If you still want an absolute answer to a question depending on so many constraints, then it is: Yes, absolutely!

 

[Mark44]

Would a professor in a linear algebra, another upper-level math course, or an upper-level physics course take off points if I don't show steps when factoring an equation?

I'm not sure what you mean by "showing steps when factoring an equation." If you have a matrix equation like $A^2 - 2A = 0$, there aren't any steps between that equation and $A(A - 2I) = 0$. Are you thinking about a slightly more complicated equation in which you would need to use, say, the quadratic formula?

BTW, you don't "factor an equation." You can factor expressions that appear on one or both sides of an equation.

 

[C5F8576]

I'm not sure what you mean by "showing steps when factoring an equation." If you have a matrix equation like $A^2 - 2A = 0$, there aren't any steps between that equation and $A(A - 2I) = 0$. Are you thinking about a slightly more complicated equation in which you would need to use, say, the quadratic formula?

BTW, you don't "factor an equation." You can factor expressions that appear on one or both sides of an equation.

Hi,

I mean factoring an expression, e.g. $\lim_{x\to-2}\frac{x^3-x^2-6x}{x^2+2x}$
into $=\lim_{x\to-2}\frac{(x+2)(x-3)}{(x+2)}$ and ultimately $=\lim_{x\to-2}(x-3)$.

 

[Mark44]

Hi,

I mean factoring an expression, e.g. $\lim_{x\to-2}\frac{x^3-x^2-6x}{x^2+2x}$
into $=\lim_{x\to-2}\frac{(x+2)(x-3)}{(x+2)}$ and ultimately $=\lim_{x\to-2}(x-3)$.

That's exactly the point of my uncertainty. There aren't any steps between $\frac{x^3-x^2-6x}{x^2+2x}$ and $\frac{(x+2)(x-3)}{(x+2)}$. If you went directly from $\frac{x^3-x^2-6x}{x^2+2x}$ to $x - 3$ without showing the factorization of $x^3-x^2-6x$, taking points off would probably be reasonable.

 

[vela]

What I tell my physics students is that their primary goal is to demonstrate they know what they're doing in solving a problem. I also assume they know how to do basic algebra, trig, and calculus. If they can omit steps yet communicate to me they know what they're doing, leaving those steps out is perfectly fine as far as I'm concerned. It actually makes their work easier to read and follow.

Some students, however, go too far and leave out too much. If, as the grader, I look at their work and wonder, "where did this come from?", it's not going to be good for their grades even if it's correct. Did they figure it out themselves or did they happen to copy it off their neighbor's test? From my perspective, I can't tell the difference based on what they wrote.

So it's a bit of a balancing act. It all boils down to "know your audience." Just like when you're writing an essay, you need to include enough details so the reader can follow your reasoning, but you don't want to obscure the points you're trying to get across by burying them in a lot of unnecessary verbiage.

A good mindset to have is to see your role as the teacher. You don't want to omit too many steps and confuse your students but also don't muddy your exposition with a bunch of pedantic details.

 

[symbolipoint]

I am not taking a particular math course this semester so it's difficult to ask a specific professor. I'm just preparing for future math courses so I wanted a general sense of what a professor would do. In the past, my physics professors haven't taken points off for not fleshing out each mathematical step while my CS high school teachers and college professors, and high school math teachers have.

That's an interesting contrast. The less advanced the course, the more attention needs to be placed on what the students show for the skills and concepts. For the more advanced courses, maybe professor is less concerned with the less advanced but still extremely important skills, and is less worried about good sequences of solution steps being shown in students' works.

SHOW YOUR STEPS! You and others need to trace what you do in solving exercises/problems.

 

[berkeman]

Funny story -- Back in undergrad, I was a TA in a 2nd year EE class (I was 3rd year and had done very well in the class the previous year). Part of my duties included grading homework and exams, and in general the policy was to require that a fair amount of work was shown in order to be sure the student was understanding the material and hadn't just copied the answer from somewhere.

But I knew one of the best students in the class fairly well, and he was one of the most intelligent people I'd ever met. He had been entering (and winning) advanced math competitions since he was in high school, and had already built an FM radio and a small computer from scratch (using discrete transistors and SSI gates). This was back in the late 1970s.

Dan often did most of the work in his head, and rarely needed to write down the intermediate steps. Since the professor and I knew Dan, it was agreed that we did not need to grade him down if there was very little work shown on his homework or exams. Of course, he was an exceptional exception.

Dan and I worked at Tektronix in Beaverton Oregon together that summer, and he went on to work full-time for them after he got his MSEE. Pretty amazing guy.

https://ieeexplore.ieee.org/author/37662433900

 

[Choppy]

My advice would be to get in the habit of showing your work.

You never really know who's going to be marking your work. The professor may or may not mark it. A lot of marking gets delegated to teaching assistants. And even though efforts are made to make sure that marking is generally consistent, you will still encounter different people who apply different standards. And if you get an answer wrong, you get specific feedback on where you made the error.