“At the high and low joint angles the control group scored more than the experimental group. At the middle angles the control group scored lower than the experimental group. Therefore, the stretch intervention makes the muscle stronger at the middle joint angles, but weaker at the end joint angles.” (Representation of a typical student statement)
The above quote represents a typical biomechanics student’s statement made within their second year biomechanics laboratory report. The report focuses on answering the question “does stretching effect muscular strength?”. The study is set up so that the duration of stretching does not cause any change in muscular strength (stretching for longer than 60 seconds continuously has been consistently shown to reduce muscular strength; in no circumstances has it increased muscular strength). As such, any “change” measured in muscular strength following stretching is due to variability of the data i.e. when performing three muscular contractions under the same state, the score will be different every time. The slight fluctuations in the measurement are interpreted by the student as a difference, despite these being within the error of the measurement. The above representative statement highlights the student’s inability to acknowledge this uncertainty aspect of science.
Uncertainty as a threshold concept
The uncertainty aspect of science has previously been described as a concept theory (Kirkup, 2009). Within science, we are taught at school that science is exact. It is objective and void of emotions and subjective thought. This causes problems later on when the individual is confronted with the latest theory and research. They are not happy with accepting that there are some unknowns; that not everything is as clear-cut as they were led to believe. This uncertainty may also take the form of accuracy in measurements, as in the example above. There are errors in all measurements, and as such all results need to be taken with a “pinch of salt”.
To be able to fully comprehend the uncertainty within science, one needs to be critical. We need to take a watchful eye, to step back and see the complete picture, and not to take anything as gospel. This requires an understanding of the area, but most importantly of the testing/research environment. It is not so much what the student knows, but what they understand and fully comprehend (Cousin, 2006).
For a student to fully grasp a threshold concept, they have to travel through the liminal space (Cousin, 2006; Perkins, 2010). It is this that teachers strive to aid the student in achieving. Students do not achieve the completion of this journey at the same rate, nor do they achieve it using the same pathway (Perkins, 2010), as such it is a very personal journey. It is an ongoing challenge for research within this subject to develop efficient, and effective, teaching strategies for aiding the student to navigate through the liminal space to achieve understanding of the threshold concept.
One key component of a threshold concept is that it is likely to involve forms of troublesome knowledge. The student needs to reverse the current understanding, which can prove difficult and uncomfortable for the student (Cousin, 2006). A belief of science being “perfect” and without uncertainty is one that is held throughout the student’s education. With the student being relatively young, it is something that has been embedded in their perceived understanding for the majority of their life. As such, overcoming this pre-held belief of certainty is challenging. As a lecturer, we are perceived by the new student to be the source of knowledge on the subject. It is not thought that we will not be able to answer a question with a precise answer; this is not through lack of knowing the latest knowledge, but through a lack of the human race not knowing the answer. As such, it is not appropriate for the lecturer purely to respond to questions with phrases such as “we/I don’t know this”. Instead, an explanation needs to be given. One in which the student understands why we don’t know this.
To begin with, the student needs to understand where we get our knowledge from i.e. research, and that this is a development within itself. When focusing on a topic, the current picture of the area should not be presented immediately. Instead, a journey is taken through how we, as the human race, came to acquire the current knowledge we have of this area. This also includes times when contradictions were shown within research. Due to development of technology, our ability to investigate certain topics improves in parallel. As such, with more advanced imaging tools, and more powerful computers, we are able to get more detail. This provides more information, with which we are able to produce a more thorough hypothesis on what is happening. As an example, it was not until the mid 1900s that the sliding filament theory of skeletal muscular contraction was presented (A. F. Huxley & Niedergerke, 1954; H. Huxley & Hanson, 1954) . This was possible only with new technology allowing more detailed imaging. Prior to this, various theories were proposed, including muscles crimpling to produce shortening, and even spirits travelling from the brain to the muscle to fill it and cause the contraction. In presenting this journey of knowledge within the different areas, the student gains an insight into a vast array of examples of when science was wrong i.e. uncertain. Including examples of both past and present informs the student that occurrences of uncertainty still occurs. The inclusion of the uncertainty concept into the assignment (see above) allows the student to experience this first hand. It is the student collecting, processing, and analysing the data. As such, they are involved throughout the process, gaining confidence in the procedures undertaken.
Textbooks, the starting point provided to students for further learning, do not focus on uncertainty. Instead, they provide the current knowledge without a mention for the uncertainty. However, a few textbooks do take on the uncertainty of science i.e. recently published Lieber (2009). The author, a world-leader on the topic, does not take an all-knowing approach. Instead, he is just as interested, and enthusiastic, in addressing what we don’t know, as well as what we do know. He provides reasoning as to why we don’t yet know certain things, or why we are unsure about other things. Having this addressed in a textbook helps students think about the concept of uncertainty more regularly; it is the textbook they will be using in their own study time, more so than the tutor.
A multidisciplinary approach?
It is important to provide an array of examples from different areas of expertise (Land & Meyer, 2010). A threshold concept is something that is more a way of thinking than a specific piece of knowledge. As such, it is important to provide the student with an array of examples and applications. This allows the student to concentrate on the specific examples when they are the focus, but over time they will develop their understanding of the concept as a secondary action. The teachings do not need to be based solely on the threshold concept. There may be times when the threshold concept plays a small part in the current topic. However, having the student experience the threshold concept on regular occasions, linked to different fields of thought/topics, will aid them in travelling to a position of understanding.
Some students just want to pass
It is important to acknowledge that not all students will achieve mastery of a threshold concept. Those students employing a rote learning methodology, in order to “just pass” will be very unlikely to achieve mastery. This is a shame as threshold concepts are normally very applicable to other areas, especially the threshold concept of uncertainty.
Cousin, G. (2006). An introduction to threshold concepts. Planet, 17, 4-5.
Huxley, A. F., & Niedergerke, R. (1954). Structural changes in muscle during contraction; interference microscopy of living muscle fibres. Nature, 173(4412), 971-973.
Huxley, H., & Hanson, J. (1954). Changes in the cross-striations of muscle during contraction and stretch and their structural interpretation. Nature, 173(4412), 973-976.
Kirkup, L. (2009). The how and the why of uncertainty in measurement. Physics Competitions, 11(1), 36-41.
Land, R., & Meyer, J. (2010, July). Threshold concepts and interdiciplinarity. Paper presented at the 3rd International Threshold Concepts Symposium, Sydney.
Lieber, R. L. (2009). Skeletal Muscle Structure, Function, and Plasticity (3rd ed.): Lippincott Williams and Wilkins.
Perkins, D. (2010, July). Threshold experiences: developing concepts from object to tool to frame. Paper presented at the 3rd International Threshold Concepts Symposium, Sydney.
 Extraordinarily, these two lead authors are different researchers working in different labs, unbeknown to the other that they were examining the same phenomenon. There approaches were using two very different methodologies. Despite this being a huge advancement of knowledge within the muscle physiology subject area, the two groups were happy to publish their findings in the same journal at the same time; this was probably made easier with the reference being the same i.e. Huxley 1954!
Heading photo credit: francisrowland