Data analysis – why isn’t there any significance!?!

Mood: hug me 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 glass-box seems to have low maths explanations and high real explanations).

I do think I just need to double-check 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 real-life 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 real-life 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 real-life explanation.

Hmm … wonder what the criteria would be for real-life 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; 40-20 = 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. 

Real-Life Explanations

Mathematical explanations were somewhat easy to define – let’s see if I could do a real-life explanations – it seems to me my idea of real-life explanations tend to be the obscure explanations but explanations that seem to draw from life-experiences. Ok, real-life 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 real-life 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 real-life explanations (based on the rubric) – but what is so real-life 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 real-life 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 real-life. 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 real-life 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 real-life 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 real-life explanations rubric.

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