1. Embedding threshold concepts Embedding Threshold Concepts etc Diagrams, economic modeling and learning Jean Mangan

2. Embedding threshold concepts Embedding Threshold Concepts etc has pointed to the difficulties that students have in reproducing graphs Cohn and Cohn (2003), Strober and Cook (1992) considers what this is linked to Dynan & Rowse (1997), Hill & Stegner (2003) questioned whether graphs are actually useful in promoting learning Cohn et al (2001). The Literature

3. Embedding threshold concepts Embedding Threshold Concepts etc Modelling Thresholds The ETC project has suggested a threefold distinction between types of conceptual change: basic, threshold discipline and threshold modelling Modelling concepts as enablers without which students cannot achieve a deep level understanding of the discipline concepts and so are integrative and transformative. Learning how to select, amend and test economic models is a central part of learning to think like an economist. At undergraduate level, on many courses, the modelling is portrayed graphically. Difficulty with understanding the modelling process may lead to students treating graphs as isolated objects of learning.

4. Embedding threshold concepts Embedding Threshold Concepts etc What are our diagrams for? Just for visual aid I suppose.Student B1 Yeah… yeah found it sort of sometimes when you just read a textbook so it just washes over you and you think yeah I understand it and then you get to the exam and its like wow, whats going on but if you like try and sort of see whats happening within sort of your model and like how changes like affect the model then and you sort of get a better sort of grasp of the idea, of whats going on. Student D8

5. Embedding threshold concepts Embedding Threshold Concepts etc The passage of time It was at AS level. I never really encountered it before say it just seems really difficult in the first year with all these diagrams and its just really confusing. For the first few months it really was confusing. It got really hard …but then it got easier as it goes along. The more you learn it gets easier, because it all links together. Student C2 Maybe like….around beginning of the year. Well, when I actually got … when I actually got a chance sit down and actually look at the diagrams properly and read about them and stuff and then I started to understand it, and then it started to make more sense. You cant really understand it all in one go, you have to kind of sit down and take time out and actually look at them and see why it has….why that curve moves here and there and stuff like that. And then once you understand it then its easy.Student A3

6. Embedding threshold concepts Embedding Threshold Concepts etc Graphs as representations of data ……..when people draw them just like in theory and stuff, not like obviously if you are going to plot a graph, you are going to apply it properly with data and stuff, but the way people just plot trends and they just like in the middle of the graph and that. I dont know, I tend not to believe things like that unless I see it, which is probably why Ive been searching, why I have searched for like data and things, just to see that that actually happens and things and it is just the way that graphs conflict… Finding …we did the Phillips curve a while back, which I really liked, because the Phillips curve is like the only think Ive come up Ive come across in economics that is actually based on historical data. I think it is that one, anyway. Is this that one? Where it is actually based on something that means something. Like you can actually go out onto the internet and you can look it up and find all that employment data and you can plot it and it looks just like that. Which is lovely, I like that, it is nice. Student B9

7. Embedding threshold concepts Embedding Threshold Concepts etc Abstraction Some students did not accept abstraction. However, there were others that seemed happy to accept abstraction, but want to put numbers on the axis as part of their learning process Student: Not all of them no, the first one you draw has no numbers, just what it is really and then obviously afterwards then you start to make changes and stuff and see what, its easier to see what happens when you have numbers rather than when you dont because the line change. You dont really know where its going like, it moves up and how much it affects it, whereas if you have a number and it has an increase by a percentage… Student D8

8. Embedding threshold concepts Embedding Threshold Concepts etc Student: Marginal, marginal thinking is really important in microeconomics and in macro it should be probably equilibrium, equilibrium is one of the most important in macroeconomics. Student D9 And asked why: Because without marginal thinking you cant fully, fully really understand all this…..whats behind the graphs, what is behind the course module, course module, you know. In microeconomics its all about really this…..a few curves and if you think about macroeconomics its… Appreciating Threshold Concepts

9. Embedding threshold concepts Embedding Threshold Concepts etc Discussion The majority of students in our interviews were seeing graphs as both essential and useful in their learning. There indication that some students were beginning to integrate ideas and appreciate the role of modelling in this, but also suggestions of continuing problems with others. Revisiting the concepts is important in understanding. We cannot expect students to fully grasp the full implications of our assumptions and need to try and stop them developing misconceptions. Providing labels with numbers may help some students in the initial stages.