Teaching Statistics for Sustainability across Contexts: Exploring the Knowledge and Beliefs of Teachers
Abstract
:1. Introduction
2. Theoretical Foundation
2.1. The Mathematics Teacher’s Specialized Knowledge Model
2.2. The MTIA: An Approach for Addressing the Teaching of Statistics in Connection with Sustainability in Primary Education
3. Materials and Methods
3.1. Context and Participants
3.2. Data Collection Techniques and Instruments
 (a)
 Do you think that this itinerary, which includes activities based on a real context, manipulative material, a game, a technological resource, and a graphic resource, can be used to promote education for sustainable development in connection with statistics? Why?
 (b)
 Arrange the different resources provided in the itinerary for teaching statistics in connection with sustainability based on whether you think they can be used to teach sustainable development, where 1 = least suitable and 5 = most suitable (Figure 1. Mark with an “x” only one oval per row. Finally, justify the reasons for your ranking.
 (c)
 What type of resource (everyday situation, manipulative material, games, technological resources, or graphic resources) are you most confident using to teach statistics? Why?
3.3. Analysis Procedure
4. Results
4.1. Specialized Knowledge on the Statistics and Teaching Contexts of the MTIA
4.2. Teachers’ Beliefs Regarding the Teaching of Statistics in Connection with Sustainability Based on Teaching Itineraries
5. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. MTSKStochastic Statistics Questionnaire
Item 1 
A clothes salesman puts up the following sign in his store: “Pants for sale, different prices, average price €25”. Based on this sign, which of the following statements is true and why?

Item 2 
The teacher distributes 30 colored candies per group and asks them to try to fill the table with the number of candies they have based on their color. They are then asked, by group, to try to make a graph according to the different colors that they received to then transfer to paper. Once finished, the teacher asks them: What is the relative frequency of candies of a certain color? And the absolute frequency? Will it be the same for all the groups? Why? Questions:

Item 3 
A Jenga tournament will be held in math class, where each student has to write down how many pieces they were able to move in each game. The dynamic of the game consists of moving blocks from the bottom of the tower to the top without the tower falling. Once eliminated, the student will write down on the board the results obtained (where the value item corresponds to the game and the number of times to the blocks the student was able to move without the tower falling), yielding a table similar to this: Values Number of times
Questions:

Item 4 
John asked his companions if they had any pet dogs or cats. He marked with a bold the pets of each, and collected the following information: 
To complete the table, John got help from some friends. Which of these is correct? 
Once the table is completed, the math teacher asks the students to make a graph using these data. They have to complete it with the Data Grapher applet, and then explain the strategy they used to make the graph and the reason for their choice. 
Questions: 

Item 5 
The math teacher shows them a population pyramid with confirmed COVID19 cases in Galicia through 13 August, sorted by sex and age groups. From this perspective, the teacher asks them: What variables are being represented? What are their values? Secondly, they are asked to identify what percentage of those affected are young people aged 15 to 29, and women aged 70 to 79. Finally, they are asked: What age group has the most cases? What is the difference between the two graphs? 
Questions:

Appendix B. Itinerary for Teaching Statistics in Connection with Sustainability
ACTIVITY 1: Real context 
Activity Discover the arithmetic median present in everyday life situations, in this case, a promotional sign in a business (Figure A1), in order to identify and use the arithmetic median in a dataset. 
Objectives

Materials

Development of the proposal
Based on the sign, which of the following statements is true and why?

Connections to sustainability Work on SDG 1 to end poverty within the framework of working conditions associated with poverty, such as exploitative companies and/or child labor. To this end, based on leading questions, students are invited to reflect on the working conditions in companies that sell their products very cheaply. SDG 12, responsible production and consumption, is presented using the following questions: How often do you think you should buy clothes and/or electronic products? What do you do when your clothes get too small? What is the best way to reduce individual consumption of electronics and/or clothing? This activity promotes, on the one hand, the competence of critical thinking by questioning the practices of some large companies to sell their products cheaper, and at the same time, reflect on their own actions. The students also reflect on the role that each one has in their local community, evaluating the actions they take (competence of selfawareness) in relation to the responsible consumption of products. 
ACTIVITY 2: Manipulatives 
Activity Arrange the candies (Figure A2) in order to identify the relative and absolute frequency of candies of a certain color and compare the results with the different groups. 
Objectives

Content

Materials

Development of the proposal The teacher distributes 30 colored candies per group and asks them to try to fill the table with the number of candies they have based on their color. They are then asked, by group, to try to make a graph according to the different colors that they received to then transfer to paper.

Connections to sustainability SDG 3 on health and wellbeing is presented by asking how often students eat foods with a lot of sugar, such as candy or sweets. They are asked: What happens if you eat a lot of foods that contain sugar? What diseases can this cause? Are there healthier candies and/or sweets? Regarding the competences for sustainability, the main focus is on the competence of anticipation, since, when investigating the problems associated with the consumption of candy, they have to understand and evaluate future scenarios, such as the effect that excess consumption can have in the medium and long term. 
ACTIVITY 3: Game 
Activity Reinforce the concepts of the mean, mode, median, and range using the game “Jenga”, a game of physical skill in which players take turns removing one block at a time from a tower built using 54 blocks. Each removed block is placed on top of the tower, creating a structure that grows more unstable with each turn (Figure A3). 
Objectives

Content

Materials

Development of the proposal

Connections to Sustainability This activity deals with SDG 11, sustainable cities and communities, by asking about the manipulative material used during the session. In this case, it is the “Jenga” game, made with recycled materials and/or wood. The students are asked to think about the use of this material, inquiring and reflecting on the importance of using recyclable or reusable materials. Specifically, considering that, according to Wikipedia, by the end of 2017, more than 80 million Jenga games had been sold worldwide, equivalent to over 4 billion Jenga blocks, reflect on whether it is better to use blocks of wood or properly recycled material. As far as competences are concerned, this activity primarily develops collaboration, since the fact that it is a game of skill and concentration implies that not all students perform well in this type of situation, which is why it is essential that students learn to engage in collaborative and participatory problem solving. 
ACTIVITY 4: Technological resource 
Activity By manipulating the online version of the Data Grapher applet (Figure A4), discover and identify what graph is best suited to represent the dataset provided by the teacher containing data on local sustainability. 
Objectives

Content

Materials

Development of the proposal

Connections to Sustainability This activity involves all the SDGs by inquiring about the sustainability data of the local community, but it deals particularly with SDG 4, quality education, by promoting learning opportunities for all students by relying on technological resources. Regarding the key competencies for sustainability, this task encourages the competency of anticipation based on good questions about what future scenarios the students expect from the results of the graph. It also works on the selfawareness competency based on the data provided by the teachers. In this regard, the students must be aware of the actions they take and evaluate them to improve local sustainability. 
ACTIVITY 5: Graphic resource 
Activity Observe the data provided by teachers on the effect of COVID19 by age (Figure A5) and analyze them in depth to prompt a dialogue between students, first in pairs and later in a large group. 
Objectives

Content

Materials

Development of the proposal

Connections to sustainability This activity emphasizes SDG 1, end to poverty, and SDG 10, reduced inequalities, by prompting a dialogue with questions such as: Do you think that the poor were more affected by COVID? Or has it affected everyone equally? In addition, with regard to SDG 3, good health and wellbeing, students have to investigate and remember what behavioral routines they had during the time of COVID19 and their opinion about them. Regarding the key competencies, this activity deals with regulations by reflecting on the norms and actions in place during the time of COVID19. The students are also asked if they believe that a pandemic, such as COVID19, will happen again and, if so, what actions they would take to deal with the potential risks. 
References
 Rocard, M. (Ed.) Science Education Now: A Renewed Pedagogy for the Future of Europe; European Communities: Brussels, Belgium, 2007. [Google Scholar]
 Morin, E. La Cabeza Bien Puesta: Repensar la Reforma, Reformar el Pensamiento; Ediciones Nueva Visión: Buenos Aires, Argentina, 1999. [Google Scholar]
 UNESCO. Guidelines for Inclusion: Ensuring Acces to Education for All; UNESCO: Paris, France, 2005. [Google Scholar]
 Bonil, J.; Junyent, M.; Pujol, R.M. Educación para la sostenibilidad desde la perspectiva de la complejidad. J. Eureka Sobre Enseñanza Y Divulg. De Las Cienc. 2010, 7, 198–215. [Google Scholar] [CrossRef]
 OECD. OECD Future of Education and Skills 2030: OECD Learning Compass 2030. 2019. OECD: Paris, France. Available online: http://www.oecd.org/education/2030project/teachingandlearning/learning/corefoundations/Core_Foundations_for_2030_concept_note.pdf (accessed on 10 October 2023).
 Batanero, C.; Borovcnik, M. Statistics and Probability in High School; Sense Publishers: Rotterdam, The Netherlands, 2016. [Google Scholar]
 BenZvi, D.; Makar, K.; Garfield, J. (Eds.) International Handbook of Research in Statistics Education; Springer: Cham, Switzerland, 2018. [Google Scholar]
 Begg, A. Some emerging influences underpinning assessment in statistics. In The Assessment Challenge in Statistics Education; Gal, I., Garfield, J., Eds.; IOS Press: Amsterdam, The Netherlands, 1997. [Google Scholar]
 Arteaga, P. Evaluación de Conocimientos Sobre Gráficos Estadísticos y Conocimientos Didácticos de Futuros Profesores. Ph.D. Thesis, Universidad de Granada, Granada, Spain, 2011. [Google Scholar]
 Moore, D.; Cobb, G. Mathematics, Statistics, and Teaching. Am. Math. Mon. 1997, 104, 801–823. [Google Scholar]
 Bargagliotti, B.; Franklin, C.; Arnold, P.; Gould, R.; Jhonson, R.; Perez, L.; Spangles, D.A. (Eds.) PreK–12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II); American Statistical Association: Alexandria, VA, USA, 2020. [Google Scholar]
 Hahn, C. Linking academic knowledge and professional experience in using statistics: A design experiment for business school students. Educ. Stud. Math. 2014, 86, 239–251. [Google Scholar] [CrossRef]
 Wild, C.J.; Pfannkuch, M. Statistical thinking in empirical enquiry. Int. Stat. Rev. 1999, 67, 223–248. [Google Scholar] [CrossRef]
 Gal, I. Understanding statistical literacy: About knowledge of contexts and models. In Proceedings of the Third International Virtual Congress of Statistics Education, Virtual, 21–24 February 2019; Contreras, J.M., Gea, M.M., LópezMartín, M.M., MolinaPortillo, E., Eds.; University of Granada: Granada, Spain, 2019. [Google Scholar]
 Bakker, A.; Cai, J.; Zenger, L. Future themes of mathematics education research: An international survey before and during the pandemic. Educ. Stud. Math. 2021, 107, 1–24. [Google Scholar] [CrossRef] [PubMed]
 Batanero, C. La comprensión de la probabilidad en los niños. ¿Qué podemos aprender de la investigación? In Atas do III Encontro de Probabilidades e Estatítica na Escola; Fernandes, J.A., Correia, P.F., Martinho, M.H., Viseu, F., Eds.; Centro de Investigação em Educação, Universidade Do Minho: Braga, Portugal, 2013. [Google Scholar]
 Bryant, P.; Nunes, T. Children’s Understanding of Probability. A Literature Review; Nuffield Foundation: London, UK, 2012. [Google Scholar]
 Frye, D.; Baroody, A.J.; Burchinal, M.; Carver, S.M.; Jordan, N.C.; McDowell, J. Teaching Math to Young Children: A Practice Guide (NCEE 20144005); National Center for Education, Evaluation and Regional Assistance: Washington, DC, USA; Institute of Education Sciences: Washington, DC, USA; U.S. Department of Education: Washington, DC, USA, 2013. [Google Scholar]
 Jones, G.A. (Ed.) Exploring Probability in School. Challenges for Teaching and Learning; Springer: Berlin/Heidelberg, Germany, 2005. [Google Scholar]
 NCTM. Principios y Estándares Para la Educación Matemática; Thales: La Défense, France, 2003. [Google Scholar]
 Nunes, T.; Bryant, P.; Evans, D.; Gottardis, L.; Terlektsi, M.E. Teaching Mathematical Reasoning: Probability and Problem Solving in Primary School; University of Oxford: Oxford, UK, 2015. [Google Scholar]
 Batanero, C.; Álvarez, Á.; Hernández, L.; Gea, M. El inicio del razonamiento probabilístico en educación infantil. PNA 2021, 15, 267–288. [Google Scholar] [CrossRef]
 Vásquez, C.; Alsina, Á.; Seckel, M.J.; GarcíaAlonso, I. Integrating sustainability in mathematics education and statistics education: A systematic review. Eurasia J. Math. Sci. Technol. Educ. 2023, 19, em2357. [Google Scholar] [CrossRef]
 Semiz, G.K.; Baykal, I.I. Middle school pre service mathematics teachers’ opinions related to mathematics education for sustainability. Eurasian J. Educ. Res. 2020, 20, 111–136. [Google Scholar] [CrossRef]
 Alsina, Á.; Mulà, I. Advancing towards a transformational professional competence model through reflective learning and sustainability: The case of mathematics teacher education. Sustainability 2019, 11, 4039. [Google Scholar] [CrossRef]
 Carrillo, J.; Climent, N.; Montes, M.; Contreras, L.; Flores, E.; Escudero, D.; Vasco, D.; Rojas, N.; Flores, P.; AguilarGonzález, Á.; et al. The mathematics teacher’s specialised knowledge (MTSK) model. Res. Math. Educ. 2018, 20, 236–253. [Google Scholar] [CrossRef]
 Alsina, Á. A Abordagem dos Itinerários do Ensino da Matemática: Por quê?, Por quê? E como aplicálo na sala de aula? TANGRAMRev. De Educ. Matemática 2020, 3, 127–158. [Google Scholar] [CrossRef]
 Shulman, L. Those Who Understand: Knowledge Growth in Teaching. Educ. Res. 1986, 15, 4–14. [Google Scholar] [CrossRef]
 Ball, D.; Thames, M.H.; Phelps, G. Content knowledge for teaching: What makes it special? J. Teach. Educ. 2008, 59, 389–407. [Google Scholar] [CrossRef]
 Godino, J.D.; Giacomone, B.; Batanero, C.; Font, V. Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas. Bolema Bol. De Educ. Matemática 2017, 31, 90–113. [Google Scholar] [CrossRef]
 Carrillo, J.; Climent, N.; Contreras, L.C.; Catalán, M.C. Determining Specialised Knowledge for Mathematics. In Proceedings of the Eighth Congress of European Research in Mathematics Education, Antalya, Turkey, 6–10 February 2013; Ubuz, B., Haser, Ç., Mariotti, M., Eds.; Middle East Technical University and ERME: Ankara, Turkey, 2013; pp. 2985–2994. [Google Scholar]
 Escudero, D.; Flores, E.; Carrillo, J. El conocimiento especializado del profesor de matemáticas. In Report of the 15th Winter School in Educational Mathematics; Landy, S., Eddie, A., Flor, R., Eds.; Ciudad de México: Red Cimates: Hague, The Netherlands, 2012; pp. 35–42. [Google Scholar]
 FloresMedrano, E.; EscuderoAvila, D.I.; AguilarGonzález, Á. Oportunidades que brindan algunos escenarios para mostrar evidencias del MTSK. In Investigación en Educación Matemática XVII; Berciano, A., Gutie, G., Estepay, A., Climent, N., Eds.; SEIEM: Santiago Tlaxomulco, Mexico, 2013; pp. 275–282. [Google Scholar]
 Montes, M.A.; Contreras, L.C.; Carrillo, J. Conocimiento del profesor de matemáticas: Enfoques del MKT y del MTSK. In Investigación en Educación Matemática XVII; Berciano, A., Gutie, G., Estepa, A., Climent, N., Eds.; SEIEM: Santiago Tlaxomulco, Mexico, 2013; pp. 403–410. [Google Scholar] [CrossRef]
 Carrillo, J.; Montes, M.A.; Contreras, L.C.; Climent, N. Les connaissances du professeur dans une perspective basée sur leur spécialisation: MTSK. Ann. Didact. Sci. Cogn. 2017, 22, 185–205. [Google Scholar] [CrossRef]
 Clark, L.M.; DePiper, J.N.; Frank, T.J.; Nishio, M.; Campbell, P.F.; Smith, T.M.; Griffin, M.J.; Rust, A.H.; Conant, D.L.; Choi, Y. Teacher characteristics associated with mathematics teachers’ beliefs and awareness of their students’ mathematical dispositions. J. Res. Math. Educ. 2014, 45, 246–284. [Google Scholar] [CrossRef]
 Vygotsky, L.S. Mind in Society. In The Development of Higher Psychological Processes; Harvard University Press: Cambridge, MA, USA, 1978. [Google Scholar]
 Tigchelaar, A.; Melief, K.; Van Rijswijk, M.; Korthagen, K. Elementos de una posible estructura del aprendizaje realista en la formación inicial y permanente del profesorado. In Creando mi Profesión. Una Propuesta Para el Desarrollo Profesional del Profesorado; Esteve, O., Melief, K., Alsina, Á., Eds.; Octaedro: Barcelona, Spain, 2010; pp. 39–64. [Google Scholar]
 Freudenthal, H. Revisiting Mathematics Education; Kluwer Academic Publishers: Norwell, MA, USA, 1991. [Google Scholar]
 Comisión Mundial del Medio Ambiente y del Desarrollo. CMMAD. In Nuestro Futuro Común; Alianza: Pleasant Grove, UT, USA, 1987. [Google Scholar]
 UNESCO. Educación Para los Objetivos de Desarrollo Sostenible: Objetivos de Aprendizaje; United Nations Educational, Scientific and Cultural Organization: Paris, France, 2017. [Google Scholar]
 Stibbe, A. The Handbook of Sustainability Literacy: Skills for a Changing World; Green Books: Newark, NJ, USA, 2009. [Google Scholar]
 Creswell, J.W. Research Design: Qualitative, Quantitative, and Mixed Methods Approaches, 4th ed.; Sage Publications: Thousand Oaks, CA, USA, 2014. [Google Scholar]
 Franco, J.; Alsina, Á. Evaluando el conocimiento especializado para enseñar estadística y probabilidad: Elaboración y validación del Cuestionario MTSKestocástico. Uniciencia 2023, 37, 84–105. [Google Scholar] [CrossRef]
 Korthagen, F.A. Linking practice and theory. In The Pedagogy of Realistic Teacher Education; Lawrence Erlbaum Associates: Mahwah, NJ, USA, 2001. [Google Scholar]
 Gal, I. Adults’ Statistical literacy: Meanings, components, responsibilities. Int. Stat. Rev. 2002, 70, 1–25. [Google Scholar] [CrossRef]
 Batanero, C. Retos para la formación estadística de los profesores. II Encontro de Probabilidade e Estatística na Scola 2009, 1–24. Available online: https://www.researchgate.net/publication/257295767_retos_para_la_formacion_estadistica_de_los_profesores (accessed on 6 October 2023).
 Batanero, C.; Díaz, C.; Contreras, J.M.; Arteaga, P. Enseñanza de la estadística a través de proyectos. In Estadística con Proyectos; Universidad de Granada: Granada, Spain, 2011; pp. 9–46. Available online: https://www.ugr.es/~batanero/pages/ARTICULOS/Libroproyectos.pdf (accessed on 3 October 2023).
 Hahn, C. La recherche internationale en éducation statistique: État des lieux et questions vives. Statistique et Enseignement 2015, 6, 25–39. [Google Scholar]
 Pratt, D.; Davies, N.; Connor, N. The role of technology in teaching and learning statistics. In Teaching Statistics in School MathematicsChallenges for Teaching and Teacher Education; Batanero, C., Burrill, G., Reading, C., Eds.; Springer: Berlin/Heidelberg, Germany, 2011; pp. 97–107. [Google Scholar]
 Nolan, V.T.; Swart, A.J. Undergraduate student perceptions regarding the use of educational technology—A case study in a statistics service course. Eurasia J. Math. Sci. Technol. Educ. 2015, 11, 505–513. [Google Scholar]
 Batanero, C. Thirty years of stochastics education research: Reflections and Challenges. In Proceedings of the Third International Virtual Congress on Statistical Education; Contreras, J.M., Gea, M., LópezMartín, M.M., MolinaPortillo, E., Eds.; 2019; pp. 1–15. Available online: https://www.ugr.es/~fqm126/civeest/ponencias/batanero_ing.pdf (accessed on 5 October 2023).
 Franklin, C.; Mewborn, D. The statistical education of PreK12 teachers: A shared responsibility. In NCTM 2006 Yearbook: Thinking and Reasoning with Data and Chance; Burrill, G., Ed.; NCTM: Reston, VA, USA, 2006; pp. 335–344. [Google Scholar]
 Ruiz, B.; Arteaga, P.; Batanero, C. Comparación de distribuciones, Una actividad sencilla para los futuros profesores. In Paper Presented at the II Encontro de Probabilidade e Estadística na Escola; Universidade do Minho: Braga, Portugal, 2009. [Google Scholar]
 Batanero, C. Didáctica de la Estadística; Grupo de Investigación en Educación Estadística, 2001. Available online: http://www.ugr.es/local/batanero (accessed on 7 October 2023).
 Gómez, E.; Ortiz, J.J.; Batanero, C.; Contreras, J.M. El lenguaje de probabilidad en los libros de texto de Educación Primaria. UNIÓN. Rev. Iberoam. De Educ. Matemática 2013, 35, 75–91. [Google Scholar]
 SánchezCobo, F.T. Análisis de la Exposición Teórica y de Los Ejercicios de Correlación y Regresión en Los Textos de Bachillerato; Third Cycle Report; Universidad de Granada: Granada, Spain, 1996. [Google Scholar]
 Ortiz de Haro, J.J. Significado de Conceptos Probabilísticos en los Textos de Bachillerato. Ph.D. Thesis, Departamento de Didáctica de la Matemática, Universidad de Granada, Granada, Spain, 1999. [Google Scholar]
Contexts/ Subdomains  Real Contexts  Manipulatives  Games  Technological Resources  Graphical Resources 

KoT  1(a)  3(a)  4(a)  5(b)  
KSM  1(a) y 1(d)  3(a) y 3(d)  4(a)  5(b)  
KMT  1(c)  2(b)  3(c)  4(d)  5(d) 
KFLM  1(b)  2(a)  3(a) y 3(b)  4(a) y 4(b)  5(a) y 5(c) 
KMLS  1(a), 1(c) y 1(d)  2(c)  3(d) y 3(e)  4(c)  5(e) 
Coefficients ^{a}  

Standardized Coefficients Beta  Sig.  
Real_contexts  0.220  <0.001 
Manipulatives_resources  0.239  <0.001 
Games  0.444  <0.001 
Technology_resources  0.336  <0.001 
Graphic_resources  0.421  <0.001 
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Franco Seguí, J.; Alsina, Á.; Vásquez, C. Teaching Statistics for Sustainability across Contexts: Exploring the Knowledge and Beliefs of Teachers. Sustainability 2024, 16, 692. https://doi.org/10.3390/su16020692
Franco Seguí J, Alsina Á, Vásquez C. Teaching Statistics for Sustainability across Contexts: Exploring the Knowledge and Beliefs of Teachers. Sustainability. 2024; 16(2):692. https://doi.org/10.3390/su16020692
Chicago/Turabian StyleFranco Seguí, Joan, Ángel Alsina, and Claudia Vásquez. 2024. "Teaching Statistics for Sustainability across Contexts: Exploring the Knowledge and Beliefs of Teachers" Sustainability 16, no. 2: 692. https://doi.org/10.3390/su16020692