Jun 11, 2018 - In addition, Diego was enrolled in a Mathematics Teaching Master ... relationship between Diego's emotional knowledge and his MTSK.
THE EMOTIONAL KNOWLEDGE OF MATHEMATICS TEACHERS María S. García González CRMSE colloquium, June 11, 2018.
Introduction This talk is divided in two parts: In the first part I`ll talk about the relationship between emotional knowledge and Mathematics teacher’s specialized knowledge and in the second part, I`ll talk about some strategies to develop our Emotional Knowledge. I´m going to start by telling you about where I come from. I´m from the state of Guerrero; Chilpancingo is the capital city, where the Autonomous university of Guerrero is located. In this university is the faculty of mathematics. Mathematics is one of the careers that is offered at this university. In this faculty is the Center of research in Mathematics Education, where I work. Our program is Mathematics Education and we have three different levels: Bachelor, Master and PHD. In this center, my research partner whose name is Gustavo Martinez and I are the affective domain team.
PART I: Emotional knowledge and mathematics teachers’ specialized knowledge Theory of the cognitive structure of emotions - OCC theoryIn our research about emotions we are guided by appraisal theories of emotion; appraisal theories propose that people experience emotions according to their appraisals of the specific situation. In particular, we adopted the theory of the cognitive structure of emotions—known as OCC theory for the initials of the surnames of the authors. According to the authors. “[the emotions are] valence reactions to events, agents or objects, with their particular nature being determined by the way in which the eliciting situations is construed” (Ortony et al., 1988, p. 13).
The OCC theory specifies 22 emotion types; here I present just an example from those emotions in Table 1. Table 1. Emotion types. Emotion types according to the OCC theory Type
Definition
Satisfaction
Pleased about the confirmation of the prospect of a desirable event
Relief
Pleased about the disconfirmation of the prospect of an undesirable event
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Disappointment
Displeased about the disconfirmation of the prospect of a desirable event
Fear
Displeased about the prospect of an undesirable event
Use of emotional words in OCC Theory Therefore, we analyzed the emotions of people through their speech. We ask them questions the responses to which should be an emotion; for example, we ask them “How do you feel in a math class?” We let them answer that question openly, and when we analyze their answer, we focus on the emotions and the situations that triggered those emotions. Because of the daily use of words to express emotions, it may happen that one word refers to a number of different types of emotions. We took the situations into account to identify the emotions evoked, just as the OCC theory suggests. For example: Student (male): I feel fine and motivated when I am solving problems.
In this testimony, the student used the emotional phrase “feel fine and motivated” to express his emotional experience triggered by the success of solving a problem. We identified problem-solving capacity as a desirable event for the student. Therefore, the student’s problem-solving capacity triggers an emotional experience of satisfaction defined as being pleased about the confirmation of the prospect of a desirable event. In Table 2, I briefly summarize the results of the research on Mexican students and teachers in two different scholar levels: university and high school. Table 2. Emotions research from Mexican students and teachers STUDENTS TEACHERS Emotions
Goals
Emotions
Goals
Satisfaction
To attend class
Reproach
Disappointment
To participate in class
Distress
To learn
Joy
To be interested in the class
Fear Tedium Interest Joy Distress Pride
To solve problems To pass the exam To pass the course To study at the university To get at job
Liking Anger Pride Gratitude
The students will be able:
To participate in class To pass a course To study at the university
Disappointment
Reproach
Remorse
Self-reproach
Gratification
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Liking
Self-reproach
Disliking Source: Martínez-Sierra & García González, 2017; 2016; 2014; García-González & Martínez-Sierra, 2016)
As you can see in the previous table, the emotions that students and teachers present are set off in terms of their goals, but these goals have different natures. For the students, the goals are the implicit norms of the classroom; for the teachers, their goals are based on how much the students can achieve in the classroom. Considering these results, we reaffirm there is no way that the teachers can evade their emotions or the ones that the students invest in them. We consider that it is important for the mathematics teachers to get to know about their emotions, what we called emotional knowledge or the capacity of knowing your own emotions.
Emotional knowledge: background The background for emotional knowledge comes from two references in educational research. Michalinos Zembylas defines emotional knowledge as the “Teacher’s knowledge that comes from his or her emotional experiences with respect to one’s self, others (e.g. students, colleagues), and the wider social and political context in which teaching and learning takes place” (Zembylas, 2007, p. 356). Rafael Bisquerra talks about emotional knowledge when he refers to emotional awareness, that is, the knowledge of one’s emotions and the emotions of others. The others can be the students in this case. We define the emotional knowledge of the mathematics teacher as the capacity of teachers to know their emotions and those of their students during the teaching of mathematics. Have emotional knowledge implies being aware of the emotions that we experience in the classroom and knowing what set them off.
What knowledge do we need to teach math? After having researched teacher emotions, now our purpose of study is the relationship between emotional knowledge and the teaching of mathematics. For that reason, we begin
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by rethinking a question similar to the one answered by Deborah Ball and Lee Shulman: What knowledge do we need to teach mathematics? The group of José Carrillo from the University of Huelva in Spain gives one answer. They point out that the mathematics teacher requires specialized knowledge, and they created the Mathematics Teacher’s Specialised Knowledge (MTSK) model (Carrillo, Climent, Contreras & Muñoz-Catalán, 2013; Carrillo et al., 2018), which describes two large groups of knowledge that a mathematics teacher needs. The MTSK model is formed by two domains (Figure 1). In the mathematical knowledge domain we can find three subdomains: the knowledge of mathematics topics, the knowledge of the structure of mathematics, and the knowledge of practices in mathematics. In terms of pedagogical content knowledge, we can find three subdomains: the knowledge of mathematics teaching, the knowledge of features of learning mathematics, and the knowledge of mathematics learning standards. In the center we can see beliefs; they are present in all MTSK model. Those beliefs are about mathematics and mathematics teaching and learning.
Figure 1. MTSK model
Personally, I think that the MTSK is not enough for teaching math; we also need emotional knowledge. For this reason I asked for help from my research partners Isabel Pascual and José Carrillo (from the University of Huelva) and Gustavo Martínez (from University of Guerrero) in order to study the relationship between MTSK and Emotional Knowledge.
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Together, we all formulated this research question: What role does emotional knowledge play in the MTSK of a novice mathematics teacher? We decided to study the case of a novice math teacher, because it had been reported that novice teachers felt high levels of stress, anxiety and confusion. However, over time teachers’ negative emotions seem to decrease (Mevarech & Maskit 2014).
The case: Diego Our case study is Diego (this is a pseudonym), a novice mathematics teacher; I met him in the Mathematics Teaching Master program where I teach. I talked to Diego and I told him about our research project; he decided to participate in the research. He agreed that his case could be publicized, to help other teachers in the same situation. Diego is an architect and was 39 years old in 2017, when the research began. He began to teach math in 2015, because he had the profile to be a teacher of mathematics. In Mexico we don`t have academic training to be a mathematics teacher specializing in middle education; generally to be a mathematics teacher in middle school the teacher has to have a bachelor`s degree in mathematics or some area related to mathematics such as architecture, engineering or accounting. In addition, Diego was enrolled in a Mathematics Teaching Master program. Data gathering procedure For data collection, we used three instruments: a) Observation of Diego´s classes. Diego recorded and observed his math classes during 3 months. b) A semi-structured interview to delve into Diego's story as a teacher of mathematics and the emotions he experienced while teaching. c) A semi-structured interview to delve into Diego's emotions in the master-Guerrero classes. Data analysis The data analysis focused on identifying from Diego’s MTSK what emotions Diego feels when he is teaching math and the situations which trigger those emotions based on OCC theory. Next, I present two examples of emotions related to Diego's MTSK, to illustrate the relationship between Diego's emotional knowledge and his MTSK. 5
Diego feels distressed because of his poor knowledge of some mathematical topics
The first is the emotion distress; Diego feels distressed because his poor knowledge of some mathematical topics. Diego: When I started to teaching math, as my knowledge of mathematics was very little I felt frustrated for not being able to teach more ... In my case the ignorance of something scares me, that fear makes me feel overwhelmed, and that showed in the class with my students because I was upset, irritable, I wasn't focused on giving lessons. In this piece of evidence, we can note that Diego is aware of the emotions he experiences while teaching mathematics; he can give them a name, speaks of frustration, fear, being overwhelmed, and knows the situations that trigger those emotions, in this case, his limited mathematical knowledge of the subjects that he will teach. Analyzing these data in the light of the OCC theory, we see that Diego experiences distress. Based on the MTSK of Diego, we find that particularly the knowledge of the mathematical topics (KoT) is the trigger of the distress; in addition, this emotion that he experiences has consequences in his teaching, since he argues he cannot concentrate on the subjects that he has to teach.
Diego feels satisfaction when he understands the topics and explains them to his students
When Diego achieved understanding of the topics he taught, the emotion of distress disappeared; instead of that, the emotion of satisfaction appeared, so we found a connection between the two MTSK´s subdomains: Mathematical Knowledge and Pedagogical content Knowledge. Diego: When I was teaching resolution of equations a year ago I remember that I said: - it jumped to the other side of equality- [laughs], I did not know the properties that were being fulfilled, but now I know it and I like to know it and share it in this way they can learn as I learnt it. In Diego´s speech, we identify the emotion of satisfaction when Diego said “I like” and when he mentioned that now he has understood the resolution of equations and he wants to share it with his students.
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I can now say that Diego is able to explain to his students the resolution of equations step by step and he also emphasizes the use of the additive and multiplicative inverse as a result of his master classes. Based on Diego´s MTSK, the emotion of satisfaction that he presents is due to the understanding of the mathematic topic and this has good consequences when he is giving lessons. Answering the research question stated before, we found that Diego's MTSK triggers Diego's emotions; in particular, the lack of mathematical knowledge (KoT) triggered his emotions, and this had implications for Diego's teaching. We think that this result is because of his academic training. In Picture 1 (Diego is teaching the resolution of equation, he authorized us to show his picture), if you observe carefully, you can see he is teaching the resolution of equations step by step; this is his own way to resolve equations and he feels comfortable with it, because he understands it better.
Picture 1. Diego and the resolution of equations
From Diego's case we can learn what emotional knowledge implies...
To recognize how we feel, because emotions are part of our human nature.
To name the emotion, to know the emotional word that clearly represents what we feel.
To recognize what situation triggers what we feel.
To manage the emotions we experience, that means, to be able to act in consequence of emotions.
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To be able to help others to get to know each other emotionally, for example, our students.
PART II: Activities to develop the emotional knowledge of the mathematics teachers To conclude, I would like to share with you some activities to develop the emotional knowledge of the mathematics teachers.
Do I know myself emotionally? As mathematics teachers, can you answer the following question: Do I know myself emotionally? I have asked this question of some teachers. Their answers lead me to say that we do not have genuine emotional knowledge. For example, when I ask the question "What emotions have you experienced in the classroom?” some teachers respond with emotional words such as fear, pride, relief, sadness or distress. But it is common for others to say I feel good or I feel bad, which shows that some teachers are not able to put a specific name to what they feel; this is one of the skills that should be developed for them to have emotional knowledge, as I mentioned before. Here I share with you two activities that I implemented with math teachers in order to develop their emotional knowledge, mainly to give name to the emotion that is experienced and to identify the situation that triggers it; these activities have been taken from the literature. It is important that they be done collectively, but modifications can be made to be done individually.
Drawing One of them is the drawing; according to Sam, 2002: “Images are associated with affective elements such as emotions and feelings,” so the instruction for the teacher is to draw an emotion experienced in the classroom, without including emotional words, then show it to the rest of the teachers. People who see the drawing have to guess the emotion that is expressed.
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The challenge in this activity is to express what you feel; it doesn’t matter that you are not a great draftsman, the important thing is to communicate the emotion experienced and what triggers it. In Figure 2, on the left a female teacher expresses the emotion of joy when her student understands her explanation of the subject; on the right, she expresses sadness (the tears in her eyes can be observed) because her student is bored (the letters z by the student indicate boredom).
Figure 2. Emotions expressed in drawings
Picture 2 is from a workshop with teachers in Peru, where they are implementing a drawing strategy for expressing their emotions.
Picture 2. Emotions expressed in drawings
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Narrative The second strategy is narrative, because the humans are storytelling organisms. The instruction is to ask the teachers to take time off in their free time to write their history as mathematics teachers. After that, ask them to read for themselves and they have to identify emotions, as well as the situations that trigger them. This strategy also works if instead of writing the story it is told to another; for example in the interviews with Diego we used narrative, and he was able to express his emotional knowledge as has been evidenced before.
To end I would like to finish with a reflection on the MTSK and emotional knowledge in the classroom. Look closely at picture 3, and respond accordingly: What does the image suggest?
Picture 3. Dear Fish, You have an island on your back (Erik Johansson).
For me this image suggests a metaphor for MTSK and emotional knowledge: Sometimes the emotions that we experience in the classroom are the fish under water. References Bisquerra, R. (2005). La educación emocional en la formación del profesorado. Revista Interuniversitaria de Formación del Profesorado, 19(3), (2005), 95-114 Carrillo, J., Climent, N., Contreras, L.C., & Muñoz-Catalán, M.C. (2013).Determining Specialized Knowledge for Mathematics Teaching. In B. Ubuz, C. Haser, & M.A. Mariotti (Eds.),
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Proceedings of the VIII Congress of the European Society for Research in Mathematics Education (CERME 8) (pp. 2985-2994). Antalya, Turquía: Middle East Technical University, Ankara. ISBN 978-975-429-315-9 Carrillo, J., Climent, N., Montes, M., Contreras, L.C., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M., & Muñoz-Catalán, M.C. (2018, to appear). The Mathematics Teacher’s Specialised Knowledge (MTSK) model. Research in Mathematics Education. ISSN: 1479-4802. DOI 10.1080/14794802.2018.1479981 Connelly, M. & Clandinin, J. (1900). Stories of experience and narrative inquiry. Educational Researcher 19 (5), 2–14. García-González, M. & Martínez-Sierra, G. (2016). Emociones en profesores de matemáticas: un estudio exploratorio. En J. A. Macías, A. Jiménez, J. L. González, M. T. Sánchez, P. Hernández, C. Fernández, F. J. Ruiz, T. Fernández y A. Berciano (Eds.), Investigación en Educación Matemática XX (pp. 247-252). Málaga: SEIEM. García, M. & Pascual, M. (2017). De la congoja a la satisfacción: el conocimiento emocional del profesor de matemáticas. IE Revista de Investigación Educativa de la Rediech, 8(15), 133148. Martínez-Sierra, G. y García González, M.D.S. (2014). High school students’ emotional experiences in mathematics classes. Research in Mathematics Education, 16(3), 234-250. http://doi.org/10.1080/14794802.2014. 895676. Martínez-Sierra, G. y García-González, M.S. (2016). Undergraduate Mathematics Students’ Emotional Experiences in Linear Algebra. Educational Studies in Mathematics, 91(1), 87106. http://doi.org/10.1007/s10649-015- 9634-y Martínez-Sierra, G. y García-González, M.S. (2017). Students’ emotions in the high school mathematics classroom: The appraisals in terms of a structure of goals. International Journal of Science and Mathematics Education, 15(2), 349-369. Ortony, A., Clore, G.L. & Collins, A. (1988). The cognitive structure of emotions. Cambridge, UK: Cambridge University Press. Sam, L.C. (2002). Public images of mathematics. Philosophy of Mathematics Education Journal, 15. Retrieved from http://people.exeter.ac.uk/PErnest/pome15/public_images.htm Zembylas, M. (2007). Emotional ecology: The intersection of emotional knowledge and pedagogical content knowledge in teaching. Teaching and Teacher Education, 23(4), 355-367.
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