2. Methodology
Both quantitative and qualitative methods were used to conduct this study. Since the two main stakeholders involved in the teaching and learning of post-secondary Physics are AM Physics teachers and students, the views of both of these cohorts were taken into consideration in this study. This was decided in order to determine which factors, if any, contribute to having underprepared Physics students in post-secondary institutions.
In order to obtain feedback about AM Physics from past students, quantitative methods were used as opposed to qualitative ones, due to the large sample being considered. In this way, results could be generalized to the entire population of Maltese students. An online questionnaire was designed and completed by students who applied for the AM Physics examination between 2011 and 2018. Out of 3430 students who applied for the examination within this period, the questionnaire was completed by 200. This implies that using a 95% confidence level, the statistical inferences of the questionnaire have a margin of error of 6.73%.
The questionnaire was divided into four main parts. The first part of the questionnaire consisted of seven questions designed to provide information on demographics. The information obtained through this section included: gender, the type of school which students attended, the year in which they sat for their SEC and AM Physics exam, other academic subjects which students studied at advanced level apart from Physics, and the grades obtained in both SEC and AM Physics.
The second part of the questionnaire then consisted of seven more questions designed to obtain the general perception of students towards the SEC and AM Physics syllabi. These questions determined the overall level of difficulty of the material studied in both SEC and AM Physics according to students. Students were also asked to comment on the amount of content taught in both SEC and AM Physics as well as on the overall disparity between the two levels. Student opinions on the amount of Mathematics involved in SEC Physics were also obtained along with students’ perceptions of what “direct proportionality” means.
The SEC and AM Physics syllabi were compared to understand what students need to know at Advanced level and what grounding the SEC material provides. Recent SEC and AM Physics examiners’ reports were then analyzed in order to identify common areas in which students struggle. These areas involved knowledge and skills which were supposed to be mastered at SEC level but were still lacking at A-level. For the third part of the questionnaire, students were asked six questions about how well they believe that the SEC Physics syllabus prepared them for parts of the AM examinations in which marks are commonly lost.
For the final part of the questionnaire, the AM Physics syllabus was split up into small sections. Students were given four questions in which to express their opinion on each individual part of the syllabus.
The views of post-secondary Physics teachers were also taken into consideration by means of qualitative methods in order to gain a more profound insight on the situation. Seven teachers from six different post-secondary institutions participated in semi-structured interviews and generated data about the challenges faced by Maltese students when studying AM Physics. The interviews consisted of two main parts. The introductory part consisted of five questions designed to acquire basic information about the teachers, such as the amount of experience teaching SEC and AM Physics.
The core part consisted of sixteen questions which gave teachers the opportunity to express their opinions on AM Physics and how well they feel that SEC Physics prepares students. Some of the questions were designed to confirm whether or not teachers agree with what students responded in the questionnaire. After conducting all seven interviews, their recordings were transcribed in order to be compared and contrasted. Content analysis was then performed by summarizing and categorizing the transcribed data.
3. Results and Discussion
3.2. Mathematics and Problem-Solving
Students at the secondary level lack problem-solving skills and thus struggle with mathematical calculations and higher order thinking skills [
9]. Furthermore, it is difficult for students to succeed in Physics without a strong mathematical background [
10]. If students are not being prepared well mathematically at SEC level, it will be harder for them to succeed at a level which is more mathematically demanding and requires the application of Mathematics to solve complex and unfamiliar problems [
11]. All interviewed teachers agreed that while SEC Physics prepares students well to be able to recall and work out simple mathematical problems, it does not prepare them to think critically, apply what they know to unfamiliar situations, or solve complex, multi-step problems. One of these teachers elaborated that this may be due to:
Students being too young to have sufficient problem-solving skills;
Teachers avoiding problem-solving and opting to teach students to memorize;
Exam questions asked encourage students to memorize and recall rather than think critically.
In response to this, teachers claimed that compulsory Physics needs to shift its focus from simply presenting content to teaching higher order thinking skills. This would mean that it is not just the syllabus which requires change, but also the teaching pedagogy. Furthermore, five out of the seven interviewed teachers agreed that students tend to be poorly prepared in Mathematics and struggle to understand the mathematical relationships found in AM Physics. These teachers elaborated that students especially struggle to comprehend aspects which should have been mastered at SEC level such as indices, algebra and simultaneous equations.
Two teachers noticed that the mathematical content of SEC Physics was being reduced. This was detrimental to students studying Physics as it gave them the impression that they do not need Mathematics to study Physics. Similarly, another two teachers mentioned that when there are problem-solving tasks, students coach themselves into working out enough examples to be able to recall the method used. This results in students having the false impression that they have good problem-solving skills. Two other teachers observed that students struggle to choose the right equation or deconstruct a problem in order to tackle it.
Another teacher suggested increasing the amount of Mathematics at SEC level so as to significantly challenge students in problem-solving and asking them to back qualitative answers mathematically in order for students to understand the links between Physics and Mathematics. Three teachers believe that exam questions asked in SEC Physics should push students to use algebra and solve challenging problems which involve multiple steps in order for students to be better prepared mathematically for further studies in the subject. These teachers remarked that this lack of experience in dealing with challenging mathematical situations leads to students struggling in topics which involve a greater deal of mathematical calculations such as ‘Mechanics’ and ‘Electricity. In response to this, a teacher suggested splitting up the SEC Physics syllabus so that students who wish to further their studies in Physics can study higher levels of Mathematics at SEC level. These students would be challenged to solve complex problems in order to be well-prepared for A-level Physics.
On the other hand, 49.5% of students believe that they were well-prepared to be able to apply what they know to unfamiliar situations while only 30% disagreed with this. In this study, most student participants believe that SEC Physics prepared them well mathematically when it comes to plotting graphs (74%) and interpreting graphs (68.5%), converting numerical values depending on the units being used (88.5%) and relating graphical information to equations (64.5%). That being said, 79.5% of student stated that the use of Mathematics should be better emphasized in SEC Physics. Results also indicate that 60.5% of student respondents were incorrectly taught that two variables are directly proportional if “one value increases as the other increases”. In reality, this is an oversimplified explanation which gives an incorrect meaning to a fundamental relationship.
While challenging compulsory Physics students in Mathematics may lead to having better prepared students at A-level, two teachers expressed that students end up memorising content if Physics is taught through equations rather than concepts. One of these teachers elaborated that students immediately think of equations whenever ‘Newton’s Second Law’ or ‘Ohm’s Law’ are mentioned. Without any deeper thought, students think that these laws are about inputting values in order to obtain an answer.
Another teacher stated that students have misconceptions in graphs and gave the example that in velocity—time graphs, some students think that a straight horizontal line means that the object is at rest. This may also indicate that students memorize velocity-time and displacement-time graphs rather than understand what they represent, which results in mistaking one graph for the other. This further emphasizes the importance of using good pedagogies as while the Physics syllabus does well to ensure that students are familiar with both types of graphs, teachers must ensure that students are taught to reason out graphs.
Two teachers mentioned that some students learn how to change subject of the formula by remembering images such as
Figure 2. This tool works in such a way that when students want to make Force subject of the formula, they cover ‘F’ and remember that the equation would be equal to the pressure multiplied by the area. In this way, students are being trained to recall rather than understand algebra and the Physics behind the equation. While both teachers agree that tools such as this would be a good idea to use with low-achievers, it should not be used with everyone. Thus, once again, it is emphasized that teachers must ensure that their end-goal is to teach students to think and understand rather than memorize and recall. Furthermore, this triangle hinders future learning because students cannot apply it to harder equations.
3.5. Proper Grounding
Six interviewed teachers confirmed that when students have a good grounding at SEC level in a particular topic, students find new concepts related to the topic easier to grasp and are more participative and confident. Four of these teachers also observed that they cover material quicker and encounter fewer problems when there is good grounding. One of these teachers stated that in familiar topics, some students may be overconfident and are shocked once they see the level of detail which there is at A-level, especially compared to what is asked of the students at SEC level. Furthermore, even though students seem to understand the theory faster, they still struggle to apply it because the questions being asked at A-level which are related to these topics tend to be much harder. In response to this, a teacher believes that while familiarity makes students more comfortable and thus makes it easier for them to understand, it is important to get students out of their comfort zone so that they become used to applying what they know to unfamiliar situations.
In an open question on how to better prepare students for AM Physics, thirteen students suggested that compulsory Physics should cover the basic concepts of every area of Advanced level Physics, even ‘Quantum Physics’, in order to make learning less strenuous at post-secondary level. In relation to this, another teacher argued that when a topic is covered at SEC level, students are more likely to have misconceptions. In order to reduce the number of underprepared students, teachers in SEC education should therefore be aware of common misconceptions in order to be careful not to instil them in students and to tackle them should they arise.
Five interviewees believe that misconceptions hinder students from understanding and that it is harder for students to unlearn and adjust previously learned information than it is to learn something completely new. Students often recall information as it was taught to them at SEC level, even if this information is improved upon at A-level. For example, at SEC level, acceleration due to gravity is taken to be 10 m/s2 while at A-level, it is taken to be 9.81 m/s2. Students often continue to make use of the value used at SEC level even at A-level and end up losing marks as a result. In fact, the majority of respondents (85%) agree that it would be beneficial to consider the acceleration due to gravity to be 9.81 m/s2 at even compulsory level. Similarly, a teacher mentioned that since only the elastic limit is mentioned when covering Hooke’s Law at SEC level, students often disregard the limit of proportionality at A-level and end up losing marks by stating that Hooke’s law is obeyed up to the elastic limit.
Two teachers mentioned that A-level students struggle to comprehend vectors due to the lack of emphasis on the directional properties of vectors at SEC level which results in misconceptions. Three teachers commented that students also have significant misconceptions regarding what ‘Voltage’, ‘Current’, ‘Heat’ and ‘Temperature’ are. One of these teachers also mentioned that students have vague ideas about what ‘Potential Energy’ really is and that since only ‘Gravitational Potential Energy’ is thoroughly covered at the SEC level, students struggle to understand that there are other types of ‘Potential Energy’. Therefore, SEC compulsory education should not teach specific ideas such as ‘Gravitational Potential Energy’ or ‘Magnetic Fields’ without first covering the general concepts, ‘Potential Energy’ and ‘Fields’, from which those ideas arise as it gives students the wrong impression.
Two teachers stated that misconceptions result from students memorizing and learning for exam purposes rather than properly understanding concepts. To tackle this issue, these teachers suggest moving away from a teaching-centered mentality to teaching Physics in the laboratory using experiments and discussing the results obtained. Another two teachers suggested using discussions and probing questions to ensure that concepts are properly understood by students rather than memorized. These comments indicate that misconceptions can be tackled both by tweaking the syllabi and also by using the right pedagogy.
One of these teachers elaborated that compulsory Physics should not be about content but rather about teaching students how to think and how to learn. In order to do so, the interviewee suggested getting students to design experiments and solve complex problems rather than recall. Another teacher stated that at the SEC level, students “skim through a lot of things but they don’t go into any detail” as students know a number of concepts but do not know the reasoning behind them.
A teacher stated that students with a poor Chemistry background struggle to understand concepts such as ‘Semiconductors’ and ‘Nuclear Physics’. Although time is an issue, teaching the basics of the atom in SEC Physics as learned though Chemistry would provide better grounding, even for concepts which are taught in SEC Physics such as ‘Electrostatics’.