Tracing physics content knowledge gains using content complexity levels

ABSTRACT

The introductory phase of studying physics poses a wide range of challenging problems to new students. One of them is learning physics on a new, more abstract and highly mathematised level, at high speed, in a lowly regulated learning environment. While several German universities have taken action to mitigate these problems, much knowledge about the problem's core is unavailable, such as information about typical knowledge baselines, probable learning speeds and factors predicting higher or lower individual performance. This study introduces a widely useable test instrument in the context of classical mechanics for a longitudinal study in the first year of study. The analyses presented are based on the psychological, rather than contend-dominated, theory of hierarchical complexity of tasks, which describes the process of learning in an abstract albeit easily testable way. Students are assigned levels that provide information about their general ability to cope with the highly complex presentation of university physics. This framework is then used to obtain a typical starting ability as well as typical patterns of students' development through the level system. As the initial abilities turn out as low as expected, we are able to state the typical learning speed as about one level per year. Further analysis of those students significantly above or below that threshold can be helpful. While high performers can be characterised by high initial mathematical knowledge, low performers are typically less socially integrated with their peers.

KEYWORDS:

• Physics content knowledge
• knowledge acquisition
• introductory study phase
• longitudinal analysis
• hierarchical complexity
• proficiency levels

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 A survey by the German physical society (DPG) (Nienhaus, 2007) shows that virtually all surveyed universities adhere to the curriculum devised by the conference of physics faculties (KFP, Konferenz der Fachbereiche Physik, 2005, 2010). The curricular sequence placing mechanics first is also manifest in most physics textbooks at the university level.

2 A comprehensive derivation of this model can be found in Woitkowski et al. (2011) and Woitkowski (2015).

3 A typical test instrument targeting such knowledge is the force concept inventory (FCI Hestenes et al., 1992).

4 The Rasch model considers an item's difficulty $D_i$ and a person's ability $B_n$. For $B_n=D_i$, the probability of this person solving that item is exactly $P=50\text{\%}$. For $B_n<D_i$ $P<50\text{\%}$ and vice versa (Planinic et al., 2019).

5 Typically, again the item difficulty $D_i$ from the Rasch model is used.

6 This might be backed by the observation that typically about three fourths of the participants handed in their tests early.

7 Those where the items A1a/b, A5, A6, B7a/b, C2, C3, D1, F1, H1b, I2, I4, J1, J3a from the original publication (Woitkowski, 2015).

8 A multifaceted Rasch model or latent class analysis might be suitable in other cases where multiple item characteristics are taken into account (e.g. (Vincent-Ruz & Schunn, 2019)). However, those methods are not guaranteed to exhibit a stacked, level-like structure.

9 Note that other studies require other cutoffs. TIMSS, e.g. requires the much more strict 20% probability difference between thresholds (Mullis, 2012).

10 This is because $-0.85=\log \left(0.3\right)-\log (1-0.3)$ (for the Rasch model equation c.f. Planinic et al., 2019).

11 The first time of testing occurred after the preparatory course.

Additional information

Funding

This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – WO 2181/2-1.