Mood: hug me
Now Playing: Nothin’ but the Wheel (Patty Loveless)
I have been bogged down (or trapped) in doing my quantitative data analysis. I can’t find anything special or significant about anything really. So, that is a bit depressing.
When I check overall statistical differences at a higher level (multivariate analysis) – I can’t find anything of real interest (well when I say anything of real interest I mean with respect to the boxes). When I look at the mean scores in terms of explanations that is being elicited for the boxes there seems to be a difference but when I run an ANOVA there isn’t any (the glassbox seems to have low maths explanations and high real explanations).
I do think I just need to doublecheck my consistency in scoring explanations for the answers given – because when I was doing it I didn’t have a rubric as I did when I was scoring the marks. Since I scored the explanations on about 3 separate occasions with some weeks apart I just want to make sure there is some consistency. I think I need to develop a rubric and determine what I mean by reallife explanations and what I mean by mathematical explanation and what can be scored or not because I remember when I was scoring I did change the scores for some students I did previously which implies to me I don’t have a clear idea what it should be. Probably I should do it now since I’m in a writing frame of mind. Although the truth is in scoring these two explanations I do get confused for example one of the students (Participant 2) said for Problem 1C:
“More soldiers would be sold as this means that the price of trains would have increased and the company would now have to make more soldiers“
I mean this implies to me they’re explaining this from reallife since their explanation was definitely not based on any maths they previously calculated but using the word ‘increase‘ implies that is also mathematically motivated in some ways. I guess I’ll be turning to discourse analysis – I need to make clear how to categorize these or I would end up in a lot of trouble. In this particular case, I had only classify it as a reallife explanation.
Hmm … wonder what the criteria would be for reallife explanations and mathematical explanations – I know sometimes an answer can be scored as both but just want to make sure I have it clear in my mind. Ok – let me make a rubric now.
Mathematical Explanations
For mathematical explanations I think the following should hold true, the student has to have:

Written a mathematical equation e.g. 2x + 3y = 20

Used inequalities or equalities to help the explanation e.g. x<=20; y =5; x is greater than y. That is they must say something like “Since x<=20 and y=5 then ….” – in other words an argument has to be ensued from writing it in this way

Calculated a value or some indication of calculating a value e.g. z will be negative; 4020 = 20; x approaches infinity; no change to x and y

Cannot be when student’s rewrite numbers that have been previously calculated e.g. number of chairs produced = 20

Cannot be counted as a mathematical explanation when they explored except when it is written in the answer sheet to indicate they have explored and give an explanation as one of the above.
RealLife Explanations
Mathematical explanations were somewhat easy to define – let’s see if I could do a reallife explanations – it seems to me my idea of reallife explanations tend to be the obscure explanations but explanations that seem to draw from lifeexperiences. Ok, reallife explanations are when:

Not based on any explicit maths such as numbers or equations but using rules of thumb or heuristics that is commonplace such as “increasing production would increase profit”

Drawing to conclusions without testing any maths but rather what they ‘feel’ might be true e.g. “the demand is too low to have any production”

Drawing from their own feelings or experience on how the manufacturing world works e.g. “this would not be economical”
Additional thoughts
Problems can only be coded into maths or reallife explanations in the part where students were asked to elaborate or give and explanation not when answering the question where they are required to regurgitate numbers. I am not certain if all explanations should be coded into these two categories, I mean I think I could leave some explanations as not coded. But is that right?
I think I’m still a bit uncertain about my rubric – I am having a hard time trying to code the following (Participant 8, P2B):
“It does not change what will be manufactured because the other variables or constraints have not been changed.”
I initially coded it as a mathematical explanation but doesn’t fit quite so nicely into my mathematical explanations rubric. However, the way it is written implies to me it fits into the reallife explanations (based on the rubric) – but what is so reallife about this explanation? I get the feeling it is more mathematically oriented. I have sust it out in my mind and I think this should be relegated to a reallife explanation – now that I think more of it it feels as if someone sort of realised their amount of resources did not change which is not quite mathematical but more reallife. But perhaps it could be both since “no change” is a mathematical way of writing things that is the difference is equal to zero – I should add that onto the list.
I guess in this case, this explanation can be both a reallife and mathematical? My mind keeps changing – but the participant says the “variables or constraints have not been changed” is that the same as saying no change? Why am I quibbling about this – I hate this part of qualitative data. I don’t think this sentence means ‘no change’ as I’ve just written in the list. I’ve spun it through my head again and I’m going with this being a reallife explanation as there is no explicit reference to a constraint or variable and “have not been changed“; implies to mean a look at all resources and knowing that they have not changed and this perhaps would influence the results and thus aligns with the second point on the reallife explanations rubric.