# American Institute of Mathematical Sciences

August  2021, 1(3): 141-156. doi: 10.3934/steme.2021011

## Centricities of STEM curriculum frameworks: Variations of the S-T-E-M Quartet

 National Institute of Education, Nanyang Technological University, Singapore; aikling.tan@nie.edu.sg (A.L.T.); yannshiou.ong@nie.edu.sg (Y.S.O.); banheng.choy@nie.edu.sg (B.H.C.)

* Correspondence: tangwee.teo@nie.edu.sg; Tel: +65-790-3830

Received  April 2021 Revised  June 2021 Published  August 2021

This commentary is an extension to the integrated S-T-E-M Quartet Instructional Framework that has been used to guide the design, implementation and evaluation of integrated STEM curriculum. In our discussion of the S-T-E-M Quartet, we have argued for the centrality of complex, persistent and extended problems to reflect the authenticity of real-world issues and hence, the need for integrated, as opposed to monodisciplinary, STEM education. Building upon this earlier work, we propose two additional variationsjsolution-centric and user-centric approachesjto the provision of integrated STEM curricular experiences to afford more opportunities that address the meta-knowledge and humanistic knowledge developments in 21st century learning. These variations to the S-T-E-M Quartet aims to expand the scope and utility of the framework in creating curriculum experiences for diverse profiles of learners, varied contextual conditions, and broad STEM education goals. Collectively, these three approachesjproblem-centric, solution-centric, and user-centricjcan afford more holistic outcomes of STEM education.

Citation: Tang Wee Teo, Aik Ling Tan, Yann Shiou Ong, Ban Heng Choy. Centricities of STEM curriculum frameworks: Variations of the S-T-E-M Quartet. STEM Education, 2021, 1 (3) : 141-156. doi: 10.3934/steme.2021011
##### References:
 [1] P.A Asunda, and Mativo, Integrated STEM: A new primer for teaching technology education, Technology and Engineering Teacher, 76 (2016), 14-19. [2] D. Barlex, Young foresight: Handbook for teachers and mentors, Software Production Enterprise, London, 2000. [3] Bryan, L.A., Moore, T.J., Johnson, C.C. and Roehrig, G.H., Integrated STEM Education, in STEM Road Map: A Framework for Integrated STEM Education, C.C. Johnson, E.E. Peters-Burton and T.J. Moore Ed. 2015, pp. 23-37. Taylor & Francis. [4] L. Bucciarelli, Engineering Philosophy, DUP Satellite Press, Delft, The Netherlands, 2003. [5] D. Coghlan and M. Brydon-Miller, The Sage Encyclopedia of Action Research, SAGE, Thousand Oaks, CA, 2014. [6] D.P. Crismond and R.S. Adams, The informed design teaching and learning matrix, Journal of Engineering Education, 101 (2012), 738-797. [7] Y. Doppelt, Assessing creative thinking in design-based learning, International Journal of Technology and Design Education, 19 (2019), 55-65.  doi: 10.1007/s10798-006-9008-y. [8] L.D. English and D.T. King, STEM learning through engineering design: fourth-grade studentso investigations in aerospace, International Journal of STEM Education, 2 (2015), 1-18.  doi: 10.1186/s40594-015-0027-7. [9] L.D English, King D. and Smeed J., Advancing integrated STE learning through engineering design: Sixth-grade studentso design and construction of earthquake resistant buildings, The Journal of Educational Research, 110 (2017), 255-271. [10] J. Gale, M. Alemdar, J. Lingle and S. Newton, Exploring critical components of an integrated STEM curriculum: An application of the innovation implementation framework, International Journal of STEM Education, 7 (2020).  doi: 10.1186/s40594-020-0204-1. [11] A.W. Glancy and T.J. Moore, Theoretical foundations for effective STEM learning environments, School of Engineering Education Working Papers, (2013), Paper 1. [12] M. Hoey, Textual Interaction: An Introduction to Written Discourse Analysis, Psychology Press, Portland, 2001. [13] C. Jacobson and R. Lehrer, Teacher appropriation and student learning of geometry through design, Journal of Research in Mathematics Education, 31 (2000), 71-88. [14] S.J. Jun, S.K. Han and S.H. Kim, Effect of design-based learning on improving computational thinking, Behaviour and Information Technology, 36 (2017), 43-53.  doi: 10.1080/0144929X.2016.1188415. [15] T.R. Kelly and J.G. Knowles, A conceptual framework for integrated STEM education, International Journal of STEM Education, 3 (2016).  doi: 10.1186/s40594-016-0046-z. [16] K. Kereluik, P. Mishra, C. Fahnoe and L. Terry, What knowledge is of most worth, Journal of Digital Learning in Teacher Education, 29 (2013), 127-140.  doi: 10.1080/21532974.2013.10784716. [17] P.A. Kirschner, J. Sweller and R.E. Clark, Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching, Educational Psychologist, 41 (2006), 75-86. [18] J.Q.D. Koh and A.-L. Tan, Students as pharmaceutical engineers: A biology-centric STEM task, Teaching science, 65 (2019), 26-32. [19] M. LaForce, E. Noble and H. King, The eight essential elements of inclusive STEM high schools, International Journal of STEM Education, 3 (2016).  doi: 10.1186/s40594-016-0054-z. [20] K.C. Margot and T. Kettler, Teacherso perception of STEM integration and education: a systematic literature review, International Journal of STEM Education, 6 (2019).  doi: 10.1186/s40594-018-0151-2. [21] R. Mayer, Multi-media Learning, Cambridge University Press, Cambridge, UK, 2001. [22] R. Mayer, Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction, American Psychologist, 59 (2004), 14-19. [23] G. Polya, How to Solve It: A New Aspect of Mathematical Method, Princeton University Press, 1945. [24] Quaye, R.M., Griffin hospital: Insulin pen misuse could have infected patients with diseases. Retrived on December 9, 2020 from https://www.nhregister.com/connecticut/article/Griffin-Hospital-Insulin-pen-misuse-could-have-11724933.php [25] L.M. Rudner and C. Boston, Performance assessment, ERIC Review, 3 (1994), 2-12. [26] J. Sweller, Evolution of human cognitive architecture, The psychology of learning and motivation, 43 (2003), 215-266. [27] J. Sweller, Instructional design consequences of an analogy between evolution by natural selection and human cognitive architecture, Instructional Science, 32 (2004), 9-31. [28] A.-L. Tan, T.W. Teo, B.H. Choy and Y.S. Ong, The S-T-E-M Quartet, Innovation and Education, 1 (2019), 1-14. [29] L. Thibaut, S. Ceuppens and H. De Loof, , Integrated STEM education: A systematic review of instructional practices in secondary education, European Jourrnal of STEM Education, 3 (2018).  doi: 10.20897/ejsteme/85525. [30] U.S. Department of Health and Health Sciences, User-centered Design Basics. 2006. Retrieved on December 9, 2020 from https://www.usability.gov/what-and-why/user-centered-design.html [31] van Eijk, D., van Kuijk, J., Hoolhorst, F., Kim, C., Harkema, C. and Dorrestojn, S., Design for usability: Practice-oriented research for user-centered product design, in IEA 2012: 18th World Congress on Ergonomics – Designing a sustainable future, 2012, 41(1): 1008-1015. [32] J. Wells, PIRPOSAL model of integrative STEM education: Conceptual and pedagogical framework for classroom implementation, Technology and Engineering Teacher, 75 (2016), 12-19. [33] Winter, E.O., Some Aspects of Cohesion in Sentence and Clause in Scientific English. 1968, University College London. [34] D.S. Yeager, C. Romero and D. Paunesku, Using design thinking to improve psychological interventions: The case of the growth mindset during the transition to high school, Journal of Educational Psychology, 108 (2016), 374-391.  doi: 10.1037/edu0000098. [35] P. Zeitz, The Art and Craft of Problem Solving, John Wiley & Sons, New York, NY, 1999. [36] C.B. Zoltowski, W.C. Oakes and M.E. Cardella, Studentso ways of experiencing human-centered design, Journal of Engineering Education, 101 (2013), 25-59.  doi: 10.1002/j.2168-9830.2012.tb00040.x.

show all references

##### References:
 [1] P.A Asunda, and Mativo, Integrated STEM: A new primer for teaching technology education, Technology and Engineering Teacher, 76 (2016), 14-19. [2] D. Barlex, Young foresight: Handbook for teachers and mentors, Software Production Enterprise, London, 2000. [3] Bryan, L.A., Moore, T.J., Johnson, C.C. and Roehrig, G.H., Integrated STEM Education, in STEM Road Map: A Framework for Integrated STEM Education, C.C. Johnson, E.E. Peters-Burton and T.J. Moore Ed. 2015, pp. 23-37. Taylor & Francis. [4] L. Bucciarelli, Engineering Philosophy, DUP Satellite Press, Delft, The Netherlands, 2003. [5] D. Coghlan and M. Brydon-Miller, The Sage Encyclopedia of Action Research, SAGE, Thousand Oaks, CA, 2014. [6] D.P. Crismond and R.S. Adams, The informed design teaching and learning matrix, Journal of Engineering Education, 101 (2012), 738-797. [7] Y. Doppelt, Assessing creative thinking in design-based learning, International Journal of Technology and Design Education, 19 (2019), 55-65.  doi: 10.1007/s10798-006-9008-y. [8] L.D. English and D.T. King, STEM learning through engineering design: fourth-grade studentso investigations in aerospace, International Journal of STEM Education, 2 (2015), 1-18.  doi: 10.1186/s40594-015-0027-7. [9] L.D English, King D. and Smeed J., Advancing integrated STE learning through engineering design: Sixth-grade studentso design and construction of earthquake resistant buildings, The Journal of Educational Research, 110 (2017), 255-271. [10] J. Gale, M. Alemdar, J. Lingle and S. Newton, Exploring critical components of an integrated STEM curriculum: An application of the innovation implementation framework, International Journal of STEM Education, 7 (2020).  doi: 10.1186/s40594-020-0204-1. [11] A.W. Glancy and T.J. Moore, Theoretical foundations for effective STEM learning environments, School of Engineering Education Working Papers, (2013), Paper 1. [12] M. Hoey, Textual Interaction: An Introduction to Written Discourse Analysis, Psychology Press, Portland, 2001. [13] C. Jacobson and R. Lehrer, Teacher appropriation and student learning of geometry through design, Journal of Research in Mathematics Education, 31 (2000), 71-88. [14] S.J. Jun, S.K. Han and S.H. Kim, Effect of design-based learning on improving computational thinking, Behaviour and Information Technology, 36 (2017), 43-53.  doi: 10.1080/0144929X.2016.1188415. [15] T.R. Kelly and J.G. Knowles, A conceptual framework for integrated STEM education, International Journal of STEM Education, 3 (2016).  doi: 10.1186/s40594-016-0046-z. [16] K. Kereluik, P. Mishra, C. Fahnoe and L. Terry, What knowledge is of most worth, Journal of Digital Learning in Teacher Education, 29 (2013), 127-140.  doi: 10.1080/21532974.2013.10784716. [17] P.A. Kirschner, J. Sweller and R.E. Clark, Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching, Educational Psychologist, 41 (2006), 75-86. [18] J.Q.D. Koh and A.-L. Tan, Students as pharmaceutical engineers: A biology-centric STEM task, Teaching science, 65 (2019), 26-32. [19] M. LaForce, E. Noble and H. King, The eight essential elements of inclusive STEM high schools, International Journal of STEM Education, 3 (2016).  doi: 10.1186/s40594-016-0054-z. [20] K.C. Margot and T. Kettler, Teacherso perception of STEM integration and education: a systematic literature review, International Journal of STEM Education, 6 (2019).  doi: 10.1186/s40594-018-0151-2. [21] R. Mayer, Multi-media Learning, Cambridge University Press, Cambridge, UK, 2001. [22] R. Mayer, Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction, American Psychologist, 59 (2004), 14-19. [23] G. Polya, How to Solve It: A New Aspect of Mathematical Method, Princeton University Press, 1945. [24] Quaye, R.M., Griffin hospital: Insulin pen misuse could have infected patients with diseases. Retrived on December 9, 2020 from https://www.nhregister.com/connecticut/article/Griffin-Hospital-Insulin-pen-misuse-could-have-11724933.php [25] L.M. Rudner and C. Boston, Performance assessment, ERIC Review, 3 (1994), 2-12. [26] J. Sweller, Evolution of human cognitive architecture, The psychology of learning and motivation, 43 (2003), 215-266. [27] J. Sweller, Instructional design consequences of an analogy between evolution by natural selection and human cognitive architecture, Instructional Science, 32 (2004), 9-31. [28] A.-L. Tan, T.W. Teo, B.H. Choy and Y.S. Ong, The S-T-E-M Quartet, Innovation and Education, 1 (2019), 1-14. [29] L. Thibaut, S. Ceuppens and H. De Loof, , Integrated STEM education: A systematic review of instructional practices in secondary education, European Jourrnal of STEM Education, 3 (2018).  doi: 10.20897/ejsteme/85525. [30] U.S. Department of Health and Health Sciences, User-centered Design Basics. 2006. Retrieved on December 9, 2020 from https://www.usability.gov/what-and-why/user-centered-design.html [31] van Eijk, D., van Kuijk, J., Hoolhorst, F., Kim, C., Harkema, C. and Dorrestojn, S., Design for usability: Practice-oriented research for user-centered product design, in IEA 2012: 18th World Congress on Ergonomics – Designing a sustainable future, 2012, 41(1): 1008-1015. [32] J. Wells, PIRPOSAL model of integrative STEM education: Conceptual and pedagogical framework for classroom implementation, Technology and Engineering Teacher, 75 (2016), 12-19. [33] Winter, E.O., Some Aspects of Cohesion in Sentence and Clause in Scientific English. 1968, University College London. [34] D.S. Yeager, C. Romero and D. Paunesku, Using design thinking to improve psychological interventions: The case of the growth mindset during the transition to high school, Journal of Educational Psychology, 108 (2016), 374-391.  doi: 10.1037/edu0000098. [35] P. Zeitz, The Art and Craft of Problem Solving, John Wiley & Sons, New York, NY, 1999. [36] C.B. Zoltowski, W.C. Oakes and M.E. Cardella, Studentso ways of experiencing human-centered design, Journal of Engineering Education, 101 (2013), 25-59.  doi: 10.1002/j.2168-9830.2012.tb00040.x.
Problem-centric integrated STEM instructional framework [taken from 28]
Solution-centric integrated STEM instructional framework
User-centric integrated STEM instructional framework
Summary of STEM curriculum frameworks
 Entry No. Articles on STEM Curriculum Frameworks Brief Description of Integration Centrality of STEM F#1 Thibaut, L., Ceuppens, S., De Loof, H., De Meester, J., Goovaerts, L., Struyf, A., Boeve-de Pauw, J., et al. [29] Integration of STEM content, problem-centered learning, inquiry-based learning, design-based learning, cooperative learning Not mentioned F#2 Wells, J. G. [32] PIRPOSAL Model based on engineering design PIRPOSAL is the acronym for: ●   Problem Identification ●   Ideation ●   Research ●   Potential solutions ●   Optimization ●   Solution evaluation ●   Alterations ●   Learned outcomes Questioning - to initiate the engineering design processes, promoting convergent and divergent thinking F#3 English, L. D., King, D., & Smeed, J. [9] Framework based on engineering design STEM disciplinary knowledge from each STEM domain F#4 Asunda, P. A., & Mativo, J. [1] Problem-based learning, pragmatism, and four theoretical constructs (systems thinking, situated learning theory, constructivism, and goal orientation theory) that blend together to accentuate Pedagogical Content Knowledge (PCK) Problem-based learning F#5 Kelley, T. R., & Knowles, J. G. [15] Connections between situated learning, engineering design, scientific inquiry, technological literacy and mathematical thinking Context F#6 Glancy, A. W., & Moore, T. J. [11] STEM Translation Model that proposes engaging the unique ways of thinking within each discipline and applying it to solve problems in another disciplines Disciplinary thinking F#7 Gale, J., Alemdar, M., Lingle, J., & Newton, S. [10] Innovation Implementation Framework identifies the critical component of innovation and uses it for evaluating innovation implementation Structural and interactional innovation components F#8 Tan, Teo, Choy, & Ong [28] S-T-E-M Quartet Instructional Framework on vertical and horizontal integrations within and across disciplines to solve authentic problems Complex, extended and persistent problems
 Entry No. Articles on STEM Curriculum Frameworks Brief Description of Integration Centrality of STEM F#1 Thibaut, L., Ceuppens, S., De Loof, H., De Meester, J., Goovaerts, L., Struyf, A., Boeve-de Pauw, J., et al. [29] Integration of STEM content, problem-centered learning, inquiry-based learning, design-based learning, cooperative learning Not mentioned F#2 Wells, J. G. [32] PIRPOSAL Model based on engineering design PIRPOSAL is the acronym for: ●   Problem Identification ●   Ideation ●   Research ●   Potential solutions ●   Optimization ●   Solution evaluation ●   Alterations ●   Learned outcomes Questioning - to initiate the engineering design processes, promoting convergent and divergent thinking F#3 English, L. D., King, D., & Smeed, J. [9] Framework based on engineering design STEM disciplinary knowledge from each STEM domain F#4 Asunda, P. A., & Mativo, J. [1] Problem-based learning, pragmatism, and four theoretical constructs (systems thinking, situated learning theory, constructivism, and goal orientation theory) that blend together to accentuate Pedagogical Content Knowledge (PCK) Problem-based learning F#5 Kelley, T. R., & Knowles, J. G. [15] Connections between situated learning, engineering design, scientific inquiry, technological literacy and mathematical thinking Context F#6 Glancy, A. W., & Moore, T. J. [11] STEM Translation Model that proposes engaging the unique ways of thinking within each discipline and applying it to solve problems in another disciplines Disciplinary thinking F#7 Gale, J., Alemdar, M., Lingle, J., & Newton, S. [10] Innovation Implementation Framework identifies the critical component of innovation and uses it for evaluating innovation implementation Structural and interactional innovation components F#8 Tan, Teo, Choy, & Ong [28] S-T-E-M Quartet Instructional Framework on vertical and horizontal integrations within and across disciplines to solve authentic problems Complex, extended and persistent problems
Comparison of the problem-, solution- and user-centric S-T-E-M Quartets
 Problem-Centric Solution-Centric User-Centric Focus Complex, extended, and persistent problem An existing solution to (part) of a complex, extended, and persistent problem The existing and potential users of the outputs of the STEM solution Types of knowledge prioritised in 21CC framework Meta Knowledge: Students may think creatively on different ways to solve the problem collaboratively Foundational Knowledge: The solution may be well-defined and core content knowledge and cross-disciplinary knowledge are pre-identified (e.g., use of technology as a requirement). Humanistic Knowledge: Development of empathy in designers can be an outcome of the process. Beneficiaries of the outcomes and outputs of engaging each model The learners get to explore alternatives and develop a range of solutions for people to choose from. The process is systematic, and resources may be sourced and provided to systematically test the feasibility of the idea. The product is based on what users want, need or can use. They are not forced to change their behaviour and expectations to accommodate the product. Their needs are better met. Limitations of the outcomes/outputs of engaging the various models Wide range of solutions may be derived that may not be pragmatic unless tested and evaluated The solution or approach may become too well-defined and limits creativity and innovation. Individual needs are diverse hence, the product may not meet the needs of a large group of beneficiaries.
 Problem-Centric Solution-Centric User-Centric Focus Complex, extended, and persistent problem An existing solution to (part) of a complex, extended, and persistent problem The existing and potential users of the outputs of the STEM solution Types of knowledge prioritised in 21CC framework Meta Knowledge: Students may think creatively on different ways to solve the problem collaboratively Foundational Knowledge: The solution may be well-defined and core content knowledge and cross-disciplinary knowledge are pre-identified (e.g., use of technology as a requirement). Humanistic Knowledge: Development of empathy in designers can be an outcome of the process. Beneficiaries of the outcomes and outputs of engaging each model The learners get to explore alternatives and develop a range of solutions for people to choose from. The process is systematic, and resources may be sourced and provided to systematically test the feasibility of the idea. The product is based on what users want, need or can use. They are not forced to change their behaviour and expectations to accommodate the product. Their needs are better met. Limitations of the outcomes/outputs of engaging the various models Wide range of solutions may be derived that may not be pragmatic unless tested and evaluated The solution or approach may become too well-defined and limits creativity and innovation. Individual needs are diverse hence, the product may not meet the needs of a large group of beneficiaries.
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