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

Academic Editor: Christopher Tisdell

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.   Google Scholar

[2] D. Barlex, Young foresight: Handbook for teachers and mentors, Software Production Enterprise, London, 2000.   Google Scholar
[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. Google Scholar

[4] L. Bucciarelli, Engineering Philosophy, DUP Satellite Press, Delft, The Netherlands, 2003.   Google Scholar
[5] D. Coghlan and M. Brydon-Miller, The Sage Encyclopedia of Action Research, SAGE, Thousand Oaks, CA, 2014.   Google Scholar
[6]

D.P. Crismond and R.S. Adams, The informed design teaching and learning matrix, Journal of Engineering Education, 101 (2012), 738-797.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[10]

J. GaleM. AlemdarJ. 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.  Google Scholar

[11]

A.W. Glancy and T.J. Moore, Theoretical foundations for effective STEM learning environments, School of Engineering Education Working Papers, (2013), Paper 1.   Google Scholar

[12] M. Hoey, Textual Interaction: An Introduction to Written Discourse Analysis, Psychology Press, Portland, 2001.   Google Scholar
[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.   Google Scholar

[14]

S.J. JunS.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.  Google Scholar

[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.  Google Scholar

[16]

K. KereluikP. MishraC. 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.  Google Scholar

[17]

P.A. KirschnerJ. 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.   Google Scholar

[18]

J.Q.D. Koh and A.-L. Tan, Students as pharmaceutical engineers: A biology-centric STEM task, Teaching science, 65 (2019), 26-32.   Google Scholar

[19]

M. LaForceE. 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.  Google Scholar

[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.  Google Scholar

[21] R. Mayer, Multi-media Learning, Cambridge University Press, Cambridge, UK, 2001.   Google Scholar
[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.   Google Scholar

[23] G. Polya, How to Solve It: A New Aspect of Mathematical Method, Princeton University Press, 1945.   Google Scholar
[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 Google Scholar

[25]

L.M. Rudner and C. Boston, Performance assessment, ERIC Review, 3 (1994), 2-12.   Google Scholar

[26]

J. Sweller, Evolution of human cognitive architecture, The psychology of learning and motivation, 43 (2003), 215-266.   Google Scholar

[27]

J. Sweller, Instructional design consequences of an analogy between evolution by natural selection and human cognitive architecture, Instructional Science, 32 (2004), 9-31.   Google Scholar

[28]

A.-L. TanT.W. TeoB.H. Choy and Y.S. Ong, The S-T-E-M Quartet, Innovation and Education, 1 (2019), 1-14.   Google Scholar

[29]

L. ThibautS. 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.  Google Scholar

[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 Google Scholar

[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. Google Scholar

[32]

J. Wells, PIRPOSAL model of integrative STEM education: Conceptual and pedagogical framework for classroom implementation, Technology and Engineering Teacher, 75 (2016), 12-19.   Google Scholar

[33]

Winter, E.O., Some Aspects of Cohesion in Sentence and Clause in Scientific English. 1968, University College London. Google Scholar

[34]

D.S. YeagerC. 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.  Google Scholar

[35] P. Zeitz, The Art and Craft of Problem Solving, John Wiley & Sons, New York, NY, 1999.   Google Scholar
[36]

C.B. ZoltowskiW.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.  Google Scholar

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.   Google Scholar

[2] D. Barlex, Young foresight: Handbook for teachers and mentors, Software Production Enterprise, London, 2000.   Google Scholar
[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. Google Scholar

[4] L. Bucciarelli, Engineering Philosophy, DUP Satellite Press, Delft, The Netherlands, 2003.   Google Scholar
[5] D. Coghlan and M. Brydon-Miller, The Sage Encyclopedia of Action Research, SAGE, Thousand Oaks, CA, 2014.   Google Scholar
[6]

D.P. Crismond and R.S. Adams, The informed design teaching and learning matrix, Journal of Engineering Education, 101 (2012), 738-797.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[10]

J. GaleM. AlemdarJ. 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.  Google Scholar

[11]

A.W. Glancy and T.J. Moore, Theoretical foundations for effective STEM learning environments, School of Engineering Education Working Papers, (2013), Paper 1.   Google Scholar

[12] M. Hoey, Textual Interaction: An Introduction to Written Discourse Analysis, Psychology Press, Portland, 2001.   Google Scholar
[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.   Google Scholar

[14]

S.J. JunS.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.  Google Scholar

[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.  Google Scholar

[16]

K. KereluikP. MishraC. 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.  Google Scholar

[17]

P.A. KirschnerJ. 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.   Google Scholar

[18]

J.Q.D. Koh and A.-L. Tan, Students as pharmaceutical engineers: A biology-centric STEM task, Teaching science, 65 (2019), 26-32.   Google Scholar

[19]

M. LaForceE. 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.  Google Scholar

[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.  Google Scholar

[21] R. Mayer, Multi-media Learning, Cambridge University Press, Cambridge, UK, 2001.   Google Scholar
[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.   Google Scholar

[23] G. Polya, How to Solve It: A New Aspect of Mathematical Method, Princeton University Press, 1945.   Google Scholar
[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 Google Scholar

[25]

L.M. Rudner and C. Boston, Performance assessment, ERIC Review, 3 (1994), 2-12.   Google Scholar

[26]

J. Sweller, Evolution of human cognitive architecture, The psychology of learning and motivation, 43 (2003), 215-266.   Google Scholar

[27]

J. Sweller, Instructional design consequences of an analogy between evolution by natural selection and human cognitive architecture, Instructional Science, 32 (2004), 9-31.   Google Scholar

[28]

A.-L. TanT.W. TeoB.H. Choy and Y.S. Ong, The S-T-E-M Quartet, Innovation and Education, 1 (2019), 1-14.   Google Scholar

[29]

L. ThibautS. 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.  Google Scholar

[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 Google Scholar

[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. Google Scholar

[32]

J. Wells, PIRPOSAL model of integrative STEM education: Conceptual and pedagogical framework for classroom implementation, Technology and Engineering Teacher, 75 (2016), 12-19.   Google Scholar

[33]

Winter, E.O., Some Aspects of Cohesion in Sentence and Clause in Scientific English. 1968, University College London. Google Scholar

[34]

D.S. YeagerC. 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.  Google Scholar

[35] P. Zeitz, The Art and Craft of Problem Solving, John Wiley & Sons, New York, NY, 1999.   Google Scholar
[36]

C.B. ZoltowskiW.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.  Google Scholar

28]">Figure 1.  Problem-centric integrated STEM instructional framework [taken from 28]
Figure 2.  Solution-centric integrated STEM instructional framework
Figure 3.  User-centric integrated STEM instructional framework
Table 1.  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
Table 2.  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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