From the Steam Engine to STEAM Education: An Experience with Pre-Service Mathematics Teachers
Abstract
:1. Introduction
2. Theoretical Context
2.1. STEAM Education
- Trans-disciplinary STEAM content, including humanities (art, history);
- Knowledge construction through a project-based methodology;
- Related to real world problems;
- Contributing to the advancement of key competences, as required in the official curriculum.
2.2. Linkages
- Mechanisms (e.g., historical origins, problems, and applications involved in the development of linkage theory, etc.);
- Mathematics (issues related to the geometric locus achieved by a certain point on a given linkage). We have already included some references dealing with this and the previous item;
- Dynamic geometry (e.g., construction of linkages with dynamic geometry programs, observation of their behavior when dragging some points on the construction);
- STEAM-driven education, with special emphasis on the development of geometric reasoning competences, including the modeling of dynamic geometry artwork (e.g., Theo Jansen’s Strandbeest, see https://www.youtube.com/watch?v=C97kMKwZ2-g, and its GeoGebra implementation at https://www.geogebra.org/m/mNheeHTS (accessed 13 January 2023)).
where we can find, albeit in the context of Secondary Education, an early (recalling the acronym STEM was practically starting to exist at that time, see [5]) antecedent of our pilot study.“Mechanical linkages which occur in many common household items, as well as in ’mathematical machines’ from the past, offer a wealth of geometry appropriate for secondary school mathematics. Dynamic geometry models of these linkages form an interface between the concrete and the theoretical, and create a visually rich environment for students to explore, conjecture and construct geometric proofs,”
3. Research Goals, Context and Methodology
3.1. Research Goals
- Did the participants benefit, in general terms, from the experience?
- Did the participants increase, for their professional development, their network of knowledge concerning the technological/pedagogical/content dimensions (TPACK)?
3.2. Our Experience: Context
3.3. Our Experience: Design and Development
- To fill-in a questionnaire about their perception (in different contexts: personal, professional, etc.) of the taught subject;
- To design and justify some didactic activity using linkages as if they were going to use it in the future as teachers in a secondary education classroom;
- To work in a team with other students, addressing some open-ended activity proposed by the lecturer (a different activity for each group), submitting or presenting the proposed solution.
- Design of the materials for the activity to be developed (authors):
- -
- Lecture preparation including some GeoGebra (www.geogebra.org) and Maple (www.maplesoft.com) (accessed 13 January 2023) files;
- -
- Proposal of seven different open-ended activities related to the lecture to be completed by students in groups; and
- -
- Design of the final questionnaire about some personal data and the evaluation of their experience with the training.
- Synchronous training session (two hours per group) with students via videoconferencing (authors and students):
- -
- One hour lecture; and
- -
- One hour of supervised work on an open-ended activity assigned to each of the four to six student groups.
- Homework (students):
- -
- Completion of the open-ended activity in the group;
- -
- Proposal of a teaching activity inspired in the session (individual);
- -
- Individual feedback by completing the questionnaire.
- Analysis of results (authors):
- The analysis included the student’s profile, feedback during the training session, individual feedback given through the questionnaire, and surveys of the open-ended activities;
- Conclusions and open questions for future work.
3.4. Methodology for the Qualitative Data and Discourse Analysis
and follows:“An account-of describes as objectively as possible by minimizing emotive terms, evaluation, judgments and explanation). (…) By contrast, an account-for introduces explanation, theorising and perhaps judgment and evaluation” [37] (p. 40)
“To account-for something is to offer interpretation, explanation, value-judgment, justification or criticism. To give an account-of is to describe or define something in terms that others who were present (or who might have been present) can recognize” [37] (p. 41).
- The narrative with a low reflection degree or “account-of”, in which the student only describes or refers to anecdotal events of the training sessions and that we could relate, in some way, to a low state of Mason’s “account-of” dimension;
- The narrative with a intermediate reflection degree or “account”, in which the teaching disposition is naive and slightly conscious. Thus, in this case, we consider that their degree of narrative reflection is valued at a midpoint, between a high “account-of” and a low “account-for”, for expressing attempts of interpretation of crucial ideas from training sessions;
- The narrative with a high reflection degree or “account-for”, which already indicates a reflective and personal teaching disposition, with an attempt to conceptualize the key ideas of the sessions and a teaching expectation for the professional future.
4. Analysis of Results
4.1. Students Participation
4.2. Analysis of the Questionnaire
- 1.
- Report two brief-but-vivid moments in the lecture session;
- 2.
- Formulate a question for you, related to the session;
- 3.
- Answer your question in a specific way;
- 4.
- What is not clear to you?
- 5.
- What do you think you have learned?
- (1)
- Classifying the results attending the referred instant of the lecture where the students have set the moments they emphasised in the session (Question 1), or the part of the lecture that it was not clear for him/her (Question 4);
- (2)
- Analyzing the narrative reflection of the responses, attending the three degrees of the TPACK methodology.
4.2.1. Qualitative and Quantitative Analysis by Topics Interest
- I.
- Introduction to the STEAM methodology
- II.
- Linkages: concept. Introduction (Torres Quevedo);
- III.
- Linkages in the context of industrial revolution (end of XVIII century), the search for linkages drawing a straight-line;
- IV.
- Mathematical issues: algebraic formulation, degrees of freedom/dimension of space of solutions, locus, Thurston’s conjecture, Kapovich–Millson solution (2002) on the universality of linkages, etc.;
- V.
- Linkages as conceptual and methodological antecedents to computers and to computer algebra, in particular;
- VI.
- Linkages in some artistic works (Lopez Binder, Theo Jansen);
- VII.
- Resources for working online with linkages (virtual museums, dynamic geometry tools, automated reasoning…).
- I.
- Introduction to the STEAM methodology;
- II.
- Concept, uses of linkages in the history;
- III.
- Mathematical issues: algebraic formulation, degrees of freedom/dimension of space of solutions, locus, Thurston’s conjecture, Kapovich–Millson solution (2002) on the universality of linkages, etc.;
- IV.
- Modelization, computer algebra (GeoGebra);
- V.
- Maple computation;
- VI.
- Linkages in some artistic works (Lopez Binder, Theo Jansen);
- VII.
- Resources for working on-line with linkages (virtual museums, dynamic geometry tools, automated reasoning…);
- VIII.
- “I understood the whole lecture”;
- IX.
- Problems during the session (classroom management, solving the task in groups, duration of the class,…);
- X.
- “I didn’t understand anything”.
4.2.2. Discursive Analysis
- Question 1: Report two brief-but-vivid moments in the lecture session.
- Account-of: “When trying to make the groups that was a bit chaotic” or “The teacher’s grand handling in GeoGebra” are classified as “account-of”;
- Account: “One of the things that caught my attention that for the speaker of the talk is that, under his criteria, he added to the term STEAM the concept of History and under his explanation, because the relationship was quite logical”, or “Usefulness of the mechanisms developed by Torres Quevedo and their application to models of everyday life”;
- Account-for: “Discovering the topic of algebraic machines, unknown to me until now, which can be perfectly exploited in the creation of projects based on real contexts, involving other disciplines (including Engineering, Physics, Technology, History, Art, and of course Mathematics), allowing collaborative work and requiring research by students”. “The example of the pendulum that was used to find the square roots, seemed to me a very simple example and easy to apply in the classroom, which has motivated me to investigate it on my own”, or “It has been of special interest to know about Jansen’s resources in GeoGebra, which we can take to the mathematics classroom in Secondary Ed”.
- Question 4: What was not clear to you?
- Account-of: “There was very little time to execute with GeoGebra the requested activities since a high knowledge of this tool was assumed”, “The activities are a bit difficult or at least with a lot of time loss to connect in group”;
- Account: “It has been difficult for me to observe Kempes’ theorem, since it is a mixture between Euler’s theorem and conics, so I have searched for more information to understand it better”, and “For which courses are these resources used?”;
- Account-for: “It is clear that, in order to be able to teach my students (and even more so in the times we live in, when information is accessible on the internet to anyone who knows how to look for it) I must become an expert in the subject”, or “It has not been very clear to me how I could explain well to the students the relationship between algebraic machines and computer algebra”.
- Question 5: What do you think you have learned?
- Account-of: “Group work, GeoGebra, more about TEAMS”, “That there is a lot to learn from these mechanisms, which were designed without the need for modern programs”;
- Account: “A very simple way to model mechanisms that can be found in everyday objects or situations. One more tool to give a multidisciplinary (trans-disciplinary) approach to classroom sessions”, “To have another vision of mathematics from the point of view of STEAM methodology”;
- Account-for: “That the resources of mechanisms related to geometry can be a good resource to use in the teaching of mathematics. Additionally, making use of GeoGebra through incomplete exercises can be very interesting, making mathematics a trans-disciplinary subject”, “The use of articulated mechanical models in mathematics class for the generation of ideas and learning of complex concepts is a very effective resource to foster a STEAM educational environment as well as to introduce historical scientific contexts to students. The creation of simulations in environments such as GeoGebra allow the student to better internalize dynamic geometry with tangible and variable objects, becoming a very powerful tool to show complicated geometric concepts and relationships in a simple and intuitive way”, “Another vision of mathematics and how to teach it in a more creative and practical way to call students’ interests”.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Herrero, A.C.; Recio, T.; Tolmos, P.; Vélez, M.P. From the Steam Engine to STEAM Education: An Experience with Pre-Service Mathematics Teachers. Mathematics 2023, 11, 473. https://doi.org/10.3390/math11020473
Herrero AC, Recio T, Tolmos P, Vélez MP. From the Steam Engine to STEAM Education: An Experience with Pre-Service Mathematics Teachers. Mathematics. 2023; 11(2):473. https://doi.org/10.3390/math11020473
Chicago/Turabian StyleHerrero, Angel C., Tomás Recio, Piedad Tolmos, and M. Pilar Vélez. 2023. "From the Steam Engine to STEAM Education: An Experience with Pre-Service Mathematics Teachers" Mathematics 11, no. 2: 473. https://doi.org/10.3390/math11020473
APA StyleHerrero, A. C., Recio, T., Tolmos, P., & Vélez, M. P. (2023). From the Steam Engine to STEAM Education: An Experience with Pre-Service Mathematics Teachers. Mathematics, 11(2), 473. https://doi.org/10.3390/math11020473