**4.2 Parameters to classify students' unscientific understanding**

Students' unscientific understanding is determined based on students' WAWR combinations. Several parameters and terminologies have been used to determine the level of students' unscientific understanding based on the students' confidence ratings or confidence rating index (CRI) of WAWR. Caleon & Subramaniam [21] employed six scales of confidence ratings and classified unscientific understanding or misconception as to the following. A *genuine* unscientific understanding is an unscientific understanding expressed with a CRI ≥ 3.5. Meanwhile, a *spurious*


#### **Table 1.**

*The parameter to classify unscientific understanding for 5 CRI scales.*

unscientific understanding is an unscientific understanding expressed with a CRI < 3.5. *Genuine* unscientific understanding is further categorized into *moderate* unscientific understanding (those expressed with medium level CRI - between 3.5 and 4.0) and high level of unscientific understanding (those expressed with a high CRI of 4.0 and above). Literature using this scale [1–6] considers 3.5, i.e., the midpoint of unconfident and confidence as the limit of a *genuine* misconception.

The use of this parameter with a decimal number (3.5 as the limit) raises a critique considering that all the CRI scales are in whole numbers. Therefore, the rationale to use the decimal limit is questionable. For this reason, we suggest using the following parameter to classify students' unscientific understanding for a multitier instrument that employs five scales of CRI (**Table 1**).

The example of how to determine students' unscientific understanding is provided from our work in the area of thermochemistry, which is in the press for publication elsewhere. The question in **Figure 8** was intended to investigate students' understanding of the system and surroundings, particularly the difference between open, closed, and isolated systems.

In answering the question in **Figure 8** above, 34.43% of students demonstrated an unscientific understanding that the *drop of water in the bottle's outer wall comes from the bottle's melting ice*. This unscientific understanding was demonstrated by those provided WAWR combination and also CAWR combination. The WAWR combination was with answer A - Reason B, while the CAWR combination was mostly with Answer B - Reason B. To justify that the unscientific understanding is *genuine* or *spurious*, the CRI must be taken into account. If the CRI of whom provided WAWR and/or CAWR combinations is 4.0, it can be declared that the unscientific understanding is *genuine* and fall in the *moderate* category. If the CRI of those provided WAWR and/or CAWR combinations is 3.0, it can be declared that the unscientific understanding is *spurious* and is a result of a *lack of knowledge* rather than a misconception.


#### **Figure 8.**

*Example of a four-tier instrument in thermochemistry [30].*
