Easy and difficult maths problems – and why language matters

Easy and difficult maths problems – and why language matters

by | Emerging Researchers' Group, NW 24 Mathematics Education Research

As soon as we receive a task, we judge it, whether mentally or verbally. Is it interesting, boring, easy, difficult, or worthwhile? In school, teachers and students handle a large number of tasks every day, so it is unsurprising that they do the same.

For example, when  looking at the maths problems below, can you immediately tell which ones you find easy and which you would find more difficult to solve?

Three maths problems are shown. 350 + 120 769 + 858 444 - 111

If you were then asked to sort each addition problem according to its difficulty into the following table, could you solve the task, or would you hesitate?

A piece of paper with a line drawn down the middle. On one side of the line is a simple drawing that resembles a feather or perhaps a stalk of wheat. On the other side of the line is a simple drawing of two circles joined by a line, that resembles a dumbbell.

This sorting task is commonly used in German primary schools. Let’s take a closer look at it, and at the linguistic level of its illustrations. At first glance, the teacher may think this is a simple task, but when considered more closely, it is clear that understanding the task depends on the level of students’ experience, especially those new to the language of instruction, i.e., non-native speakers.  

In this blog post, I’d like to expand on the situational and linguistic factors that influence how a student may perceive the difficulty of a maths problem – beyond their basic mathematical abilities. 

Are there objective or subjective categories in mathematics teaching?

According to mathematics educators, the difficulty of math problems depends on how much effort students have to put into solving each problem, which again depends on their mathematical abilities (Rathgeb-Schnierer & Green 2015), and even diagnoses such as dyscalculia and other learning disabilities.

With this in mind, let’s look again at the maths problems above, how students might perceive them, and how educators might react to students who struggled with the task. Did you find them easy or difficult to solve?

350 + 120 – this task should be easy, given that you understand the decimal place value system. You can add the tens and the hundreds separately without having to carry, and each number is comparatively small.

References in the illustration: Torbeyns&Verschaffel (2013), Baroody (1984), 

Situational factors that affect mathematics understanding

Your judgement of a task’s difficulty might also depend on other factors. Maybe you spent the last weeks working only on subtraction problems, so they seem a little easier right now. Maybe your favourite number is eight, so you enjoy calculating with numbers that contain an eight, which makes the second problem the easiest for you. Perhaps the person next to you received the worksheet earlier, and after watching them calculate, none of the problems are difficult for you anymore. Maybe you want to impress your teacher by showing that you can solve all of the problems, even though they are difficult.

Your mathematical knowledge and familiarity with certain calculation strategies is only one factor that might affect how you solve maths problems. Equally important is your current situation and your relationship with the people you solve the problems with and for.

Whether you use the table to sort the problems as expected also depends on whether the task and the symbols were explained properly.

Linguistic factors that affect mathematics understanding

Whether the table above left you at a loss probably depends on how familiar you are with the German translations of ‘easy’ and ‘difficult’: ‘Leicht’ and ‘schwer’.

These words are often illustrated using drawings in the picture above of a feather and a dumbbell. These symbols are based on a second meaning of the German terms. ‘Leicht’ can also mean ‘light’ in the sense of weight, as illustrated by the feather. ‘Schwer’ can mean ‘heavy’, as illustrated by a dumbbell.

The task is to put the problems you find easy in the left column with the feather and the problems you find difficult in the right column with the dumbbell.

This example of a task observed in a German primary school classroom shows the relevance of language in mathematics classes – and how unexpected it can sometimes be. Without the linguistic explanation, there is no way of logically concluding which column to use for the easy and which for the difficult problems. Trying to find a logical connection between the terms and the symbols might even be misleading.

For example, you might consider the difficulty of a task to be its complexity and apply this to the illustrations. In that case, you might find the dumbbell symbol (which only consists of three lines) a lot less complex than the feather symbol. Consequently, you would sort the easy and difficult problems opposite to the task’s intention. Your only chance to use the table as intended would be to guess. But if you guessed wrong (and you have a 50% chance to do so), that would not be indicative of either your linguistic or mathematical abilities.

Especially when working with a student who is new to the language of instruction, we teachers, teacher assistants, or peers may be quick to assume students’ mistakes are due to a lack of linguistic understanding. We might even believe they didn’t receive proper mathematics education in their previous school.

Conclusion

There is more than mathematics and mathematics learning going on in mathematics lessons. We are often not aware of linguistic aspects, even in tasks and phrases we use every day, that are not explained sufficiently, even by translating.

All students face the challenge of handling these linguistic and situational aspects, but they may be especially confusing to those who have only recently joined a class in a new country, a new language, or a new culture. 

Can you think of an example of ambiguous terms or tasks in your native language? Do you also use the differentiation between ‘easy’ and ‘difficult’ maths problems in your schools? 

Key Messages

  • Beyond the actual learning of mathematics, situational and linguistic aspects are relevant when students are working on a task
  • Any of these aspects can influence whether a maths problem is perceived by the student as easy or difficult. Not understanding the maths problem, therefore, does not unambiguously point to a level of mathematical ability
  • Certain aspects of language can be open to interpretation, such as when using images. We need to be aware of this and take more care when using everyday tasks and phrases that might cause confusion.

Alexandra Dannenberg

Research Assistant and PhD candidate, Kassel University, Germany

Alexandra Dannenberg is currently a research assistant and PhD candidate at Kassel University, Germany, and the graduate school InterFach. She studied primary education in the subjects mathematics, German as a first language, and natural & social sciences. During her studies, she discovered her interest in education research and began her current position in primary education research shortly after graduating. In her doctoral studies, she focuses on the relevance of language in primary school mathematics classroom interactions. Her general research interests are power relations in education, educational disparities, and institutional discrimination.

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References and Further Reading

Baroody (1984): Children’s Difficulties in Subtraction: Some Causes and Cures. In: The Arithmetic Teacher, 32, 3, pp. 14-19. https://www.jstor.org/stable/748349?seq=1&cid=pdf-reference#references_tab_contents

Rathgeb-Schnierer & Green (2015): Cognitive flexibility and reasoning patterns in American and German elementary students when sorting addition and subtraction problems. In: Proceedings of CERME 9 – Ninth Congress of the European Society for Research in Mathematics Education, pp. 339-345. https://hal.science/hal-01281858/document

Torbeyns&Verschaffel (2013): Efficient and flexible strategy use on multidigit sums: a choice/no-choice study. In: Research in Mathematics Education, 15, 2, pp. 129-140. https://doi.org/10.1080/14794802.2013.797745

5 practical tips for maths teachers for the design of emotion-sensitive classrooms

5 practical tips for maths teachers for the design of emotion-sensitive classrooms

by | Emerging Researchers' Group, NW 24 Mathematics Education Research

“If I fill in this survey, will all mathematics classes be removed?”

That was one of the questions the participants asked most often when I was collecting my PhD data, aiming to examine middle school students’ academic emotions in mathematics classes. Many of the students completed the surveys in the hope that they would be excused from all future mathematics classes. The sad truth was that this sentence was a kind of reflection of those students’ feelings.

As described by Rosenberg (1998), emotions are “acute, intense, and typically brief psychophysiological changes that result from a response to a meaningful situation in one’s environment” (p. 250). Students experience such intense feelings during each phase of their academic lives in education, which foregrounds educators’ and researchers’ attention to work on this topical phenomenon. My study findings have motivated my continued interest in researching in this era to determine why students’ emotions matter at schools and what could be done to design emotion-sensitive classrooms.

Academic emotions are important, but why?

Imagine a fourteen-year-old child is taking a mathematics test on algebraic equations. Unfortunately, the questions are not easy, and the child cannot remember the formula. On the other hand, the child recognizes his parents’ expectations about the test, and time is passing. The heart and sweating rate of the child might increase; he might wish to have escaped from taking the test; the test might induce him to experience high stress, and all of these might reflect on his face. In short, the child is experiencing test anxiety.

As described in the given situations, emotion is a complex construct, including affective, cognitive, motivational, expressive, and physiological dimensions (Pekrun, 2006; Pekrun & Linnenbrink-Garcia, 2012, 2014). Based on Pekrun’s (2006) control-value theory of achievement emotions, students might experience various emotions due to achievement activities and achievement outcomes. These emotional experiences of students might exert an influence on their cognitive resources, motivation to learn, learning strategy use, and self-regulated learning, which have a place on their learning and achievement. The most crucial thing is that each element is reciprocally related, so the association between emotions, motivation, and learning-related variables would be dynamic. That foregrounds attention to why both educators and researchers should seek and construe students’ academic emotions.

Mathematics, in particular, has consequential effects on students’ emotions regarding the nature of the discipline, teaching quality, pedagogical knowledge and skills of mathematics teachers, and various student-related factors. Because of the rising focus on 21st-century skills and the “frightening” reputation of math classes, distinct student emotions may stem from their learning activities and outcomes in this discipline. Therefore, my research route specifically addressed students’ achievement emotions in mathematics.

A short glance at students’ mathematics academic emotions in Turkey

My research addressed the antecedents and consequences of the emotional experiences of middle school students (10-14 years of age) in mathematics. In Turkey, where the context of the study was built, mathematics is an often feared subject domain with an increased level of education (Çalık, 2014). Students often fall behind on mathematics competencies regarding Programme for International Student Assessment (PISA) results (OECD, 2010, 2013, 2016, 2019).

In addition, students’ capability judgments towards accomplishing mathematics tasks were below, and their anxiety was above the OECD average (Education Reform Inıtiative, 2013). Those results might signify the changes in intensity and the variety of the experienced emotions in this subject domain across grade levels. As just a small part of my research, the findings indicated that 8th-grade students (13-14 years of age) tended to experience less enjoyment and more anxiety and anger than 7th-graders, which raises the first question of why such a decline occurs. Indeed, a number of student-related, teacher-related, parent-related, instruction-related, and assessment-related factors for this trend (Çalık, 2021) bring the second question to our minds: What could be done in designing emotion-sensitive classrooms?

5 practical tips for maths teachers for the design of emotion-sensitive classrooms

Here are several suggestions for designing emotion-sensitive classrooms regarding the potential sources and consequences of academic emotions based on the control-value theory of achievement emotions (Pekrun, 2006). These five tips might be beneficial for mathematics educators to improve the teaching quality of their classes. Those would also lend themselves to regulating students’ emotional experiences in mathematics.

Make a connection between the subject matter and real-life

As one of the basic process standards of NCTM (National Council of Teachers of Mathematics), students should be able to recognize and apply mathematics in contexts outside of mathematics, which requires the connection between subject matter in mathematics and real life. When maths teachers design authentic learning environments, students in those contexts could easily identify where they might apply the knowledge and skills they have learned in mathematics classes.

In particular, problem-based and project-based learning approaches might be adopted while creating lesson plans. In those cases, students would have the opportunity to learn, apply, and assess the knowledge by dealing with real-life problems, such as teaching how to calculate means or draw bar graphs through a given real-life scenario. Such practices promote the value of learning math and improve learning motivation for mathematics.

Plan the lesson around the student-centered learning activities to contribute to students critical and creative thinking, problem-solving, research, and communications skills

In line with the connection of mathematics with real life, planning mathematics classes around student-centered learning activities would ease students’ understanding of mathematics concepts. Accordingly, constructive learning practices, including problem-based and project-based learning approaches and cooperative learning strategies, would make students active in learning processes and hold them responsible for their learning.

During the teaching process, employing learning technologies, including Web 2.0 tools (e.g., concept mapping tools, assessment tools, interactive presentations, animation and video, Word clouds), dynamic geometry software, and statistical packages, make mathematics learning more enjoyable for students. Those tools captivate learners’ attention by cultivating inquiry, critical and creative thinking skills, and collaboration among learners. Besides, students have the opportunity to express themselves in more than one suggested way and receive immediate feedback from their teachers and peers in mathematics. That might also increase their engagement, motivation to learn, and positive emotions.

Give individual, prompt, and constructive feedback to students

Mathematics teachers may provide process feedback that reveals detailed information about students’ progress on what is expected of them and what they should do to achieve the intended knowledge and skills in mathematics. For instance, rather than comparing the student with his/her peers or telling the child, “Ok! You’re correct!,” for a typical mathematics problem, the mathematics teachers might come up with a statement, such as “I noticed that you came up with an original solution for this problem which you have not tried before, just amazing!”

In other words, teachers might individualize their feedback by highlighting the strengths and weaknesses of the child by relating their previous projects, homework, assignments, performances, etc. However, the weaknesses might be considered “yet to be accomplished sides” rather than deficits. Otherwise, students are more likely to attribute their failure and achievement in mathematics to unstable and uncontrollable situations, which might boost the rate of experiencing negative emotions. In short, individual and constructive process-oriented feedback foregrounds attention on the efforts put in by students, which also contribute to the level of interest in mathematics.

Make students feel successful by adding their mastery experiences

Self-efficacy is one of the strongest allies of positive emotions. In mathematics, students with high self-efficacy experience more positive and less negative emotions, so adding up self-efficacy beliefs might trigger students’ positive emotions in mathematics. Particularly, helping students reach success in mathematics adds to their mastery experiences in this field.

For this aim, mathematics teachers might divide the tasks into smaller chunks and make students form reasonable goals upon completing those chunks rather than at once. For instance, by giving short homework at first, then increasing the intensity and the number, or asking students to write math dairies or journals to see what they have accomplished and learned each day. Each student can learn at their own pace; however, completion of smaller steps would make students experience success and feel more capable, which, in return, would make them more optimistic and less of a ‘math hater’.

Display high enthusiasm for teaching and be sincere while communicating with students

As a last tip to design emotion-sensitive classrooms, teacher emotions are of value. Teaching is an emotion-laden job, so teacher enthusiasm is a key element for designing supportive teaching and learning environments. As well as enthusiasm and motivation, negative emotions, such as anxiety, anger, and boredom, would also be mirrored by students. Students are more likely to integrate the feelings experienced by teachers and experience similar feelings.

Therefore, the experience of high enthusiasm for teaching influences not only teachers but also students in the long term. In order to increase teaching enthusiasm and positive teacher emotions in mathematics, the bond between students and teachers should be so strong that both parties (teacher and student) would enjoy the teaching and learning process. That would be provided by ensuring sincerity during communicating with students. For example, mathematics teachers who make eye contact while talking with students, call students by their names, use humor while teaching math, mind their tone of voice, and are mindful of their body language. Those tips will not only support communication between students and teachers but also reduce the likelihood of experiencing negative emotions.

Key Messages

  1. Teachers should design authentic learning environments in which students are provided with learning opportunities to apply their knowledge and skills in different disciplines and real life.
  2. The mathematics lessons should be designed around student-centered learning activities that cultivate the 21st-century skills of students.
  3. The feedback given to students should be individual, prompt, and constructive.
  4. The increase in mastery experiences could make students feel successful and foster students’ self-efficacy beliefs so they may experience more positive emotions.
  5. Teaching enthusiasm is also critical for students’ emotions, so the student-teacher interaction is of value.
Dr. Başak Çalık

Dr. Başak Çalık

Assistant Professor in the Educational Sciences Department of Istanbul Medeniyet University, Turkey & Postdoctoral Research Scholar in the Educational Psychology Department of City University of New York, Graduate Center, US

Dr. Başak Çalık is an Assistant Professor in the Educational Sciences Department of Istanbul Medeniyet University, Turkey & Postdoctoral Research Scholar in the Educational Psychology Department of City University of New York, Graduate Center, US. She holds a doctorate in Curriculum and Instruction from Middle East Technical University, Ankara, Turkey.

Her doctoral dissertation was supported by the Turkish National Science Foundation International Research Fellowship Program and the Middle East Technical University Academic Research Projects Grant. The dissertation study entitled “Investigation Of Middle School Mathematics Teacher Emotions And Their Students’ Mathematics Achievement Emotions: A Mixed-Methods Study” received the METU Outstanding Dissertation Award. Dr. Çalık received the Turkish National Science Foundation International Postdoctoral Research Fellowship to continue her studies at the City University of New York, Graduate Center. Her research interests include affective aspects in the teaching and learning process, academic emotions of teachers and students, self-efficacy, and teaching quality.

Profile in Researchgate: https://www.researchgate.net/profile/Basak-Calik

Profile in Linkedin: https://www.linkedin.com/in/ba%C5%9Fak-%C3%A7al%C4%B1k-57a23687/

University Profile: https://avesis.medeniyet.edu.tr/basak.calik

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References and Further Reading

Çalık, B. (2014). The relationship between mathematics achievement emotions, mathematics self-efficacy, and self-regulated learning strategies among middle school students. (Unpublished Master Thesis). Middle East Technical University, Ankara.

Çalık, B. (2021). Investigation of middle school mathematics teacher emotions and their students’ mathematics achievement emotions: a mixed-methods study. (Unpublished Doctoral Dissertation). Middle East Technical University, Ankara.

 Education Reform Initiative (2013). Türkiye PISA 2012 analizi:Matematikte öğrenci motivasyonu, özyeterlik kaygı ve başarısızlık algısı [Turkey PISA 2012 analysis: Student motivation, self-efficacy, anxiety and failure perception]. Retrieved from http://erg.sabanciuniv.edu/sites/erg.sabanciuniv.edu.

Organization for Economic Co-operation and Development (OECD) (2010). PISA 2009 results: What students know and can do – Student Performance in reading, mathematics and science (Volume I). Retrieved from https://www.oecd.org/pisa/pisaproducts/48852548.pdf 289

Organization for Economic Co-operation and Development (OECD) (2013). PISA 2012 results in focus: What 15-year-olds know and what they can do with what they know. Retrieved from https://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf

 Organization for Economic Co-operation and Development (OECD) (2016). PISA 2015 results in focus. Retrieved from https://www.oecd.org/pisa/pisa-2015-results-in-focus.pdf

 Organization for Economic Co-operation and Development (OECD) (2019). PISA 2019: Insights and interpretations. Retrieved from https://www.oecd.org/pisa/PISA%202018%20Insights%20and%20Interpretations%20FINAL%20PDF.pdf

 Pekrun, R. (2006). The control-value theory of achievement emotions: Assumptions, corollaries, and implications for educational research and practice. Educational Psychology Review, 18, 315–341. https://doi.org/10.1007/s10648-006-9029-9

 Pekrun, R., & Linnenbrink-Garcia, L. (2012). Academic emotions and student engagement. In S.L. Christenson et al. (eds.), Handbook of research on student engagement (pp. 259-282). Springer.

Pekrun, R. & Linnenbrick-Garcia, L. (2014). Introduction to emotions in education.

In R. Pekrun & L. Linnenbrick-Garcia (Eds), International handbook of emotions in education (pp. 1-109). New York and London: Routledge.

 Rosenberg, E. L. (1998). Levels of analysis and the organization of affect. Review of

General Psychology, 2, 247–270. https://psycnet.apa.org/doi/10.1037/1089-2680.2.3.247

Is the self-efficacy of maths teachers related to teaching competency?

Is the self-efficacy of maths teachers related to teaching competency?

by | Emerging Researchers' Group, NW 24 Mathematics Education Research

The role of teachers is one of the essential elements that ensure the proper functioning of the education system and the world for students’ benefit.  In addition to guiding them academically, teachers can influence children’s future, making them better human beings. A teacher can instill content knowledge, life skills, good dispositions, traditional values, and modern-day issues to students.

Teaching mathematics goes beyond the knowledge capacity of teachers and pre-service teachers. In other words, equipping students with different 21st-century skills and attitudes is the main goal of teaching mathematics, rather than transferring content knowledge. The confidence teachers have in their planning and implementation skills affects their teaching and learning objectives in online education. A number of problems can arise in the classroom if the teacher is lacking in confidence. A teacher may have comprehensive mathematical knowledge and skills yet have low self-confidence while lecturing. They may not be able to use their expertise and abilities adequately in the classroom teaching process, leading them to perform their profession poorly. The self-confidence of the teacher is important in terms of providing more effective teaching to their students.

 What is the meaning of maths self-efficacy?

As defined by Bandura (1997), mathematics self-efficacy is one’s beliefs or perceptions concerning their abilities in mathematics education. Mathematics self-efficacy is operationalized as a belief which should be internalized by teachers and pre-service teachers. On the other hand, teaching competencies can be defined as the knowledge and skills that they must perform in their profession effectively and efficiently. Without sufficient knowledge, enthusiasm, and self-efficacy in these areas, it is unlikely that future elementary teachers will be able to provide effective instruction (Battista 1986; Stevens & Wenner, 1996; Tosun, 2000).

Mathematics self-efficacy is different from teachers’ mathematics competencies. Teacher competencies refer to a teacher’s professional knowledge and expertise, while teacher self-efficacy is tied to a more general concept. Teacher self-efficacy is more than having technical experience and skills; it also includes confidence that one has in putting this knowledge and competencies into practice. Having this confidence helps to provide an effective teaching environment in the classroom and to manage the negativities that may be encountered in classroom management by strengthening the student-teacher relationship. Gavora (2010) pointed out that a teacher’s high self-efficacy enables them to use their professional knowledge and skills successfully. Students learn more from teachers who have high self-efficacy (Zuya et al., 2016).

In line with Küçükalioğlu and Tuluk (2021), mathematics teachers with high self-efficacy were observed to have a positive effect on students’ mathematical achievement. Therefore, the self-efficacy of mathematics teachers seems to be the determining factor in their way of teaching and behaviour in class. According to Bandura (1995), teachers with low self-efficacy tend to create an environment that has an adverse effect on students’ mathematical achievement. I would add that if a teacher does not attend their lesson prepared for the misconceptions about the related content that students may encounter, they may not notice the student’s current misconception, which may lead to the student’s learning based on faulty thinking and understanding.

The association between mathematics education, self-efficacy, and teaching competency

The question of how the mathematics competencies and self-efficacy of teacher candidates who grew up with technological advancements (i.e. the flipped learning approach) have been a matter of curiosity. What are the teaching competencies and self-efficacy of elementary mathematics pre-service teachers in teacher education at a foundation university?

When we look at the studies carried out to date in general, we can say that most of the studies (e.g., Çakıroğlu & Işıksal (2009); Gülten (2013)) examining the variables focused on gender, age, and grade level were conducted on pre-service teachers and teachers as study groups. Reviewing the previous studies, we observed that most of them were carried out in state universities, and that teacher education programs involved preservice mathematics teachers who were exposed to insufficient practicum. Having analyzed the literature, there was no research carried out on pre-service teachers who have been educated in a foundation university in Istanbul!

 Considering that practicum courses attended by freshmen years were intensively included in the internship in order to improve pre-service teachers’ mathematics self-efficacy and mathematics teaching competencies, examining the relationship between mathematics self-efficacy and mathematics teaching competencies aims to bring a different perspective to the related literature.

Our research into self-efficacy and mathematics

We conducted a study with second, third, and fourth-grade teacher candidates at the department of Middle School Mathematics Teaching at MEF University in Istanbul, Turkey, in the 2021-2022 academic year. When we analyze the scores obtained through the questionnaires (Özgen & Bindak, 2008 for self-efficacy;  Esendemir et al., 2015 for teaching competency), we can say that the self-efficacy of pre-service mathematics teachers is higher than their competence in teaching mathematics. There is a relationship between pre-service mathematics teachers’ mathematics self-efficacy and mathematics teaching competency. The results revealed that there is a statistically significant and positive relationship between the pre-service mathematics teachers’ self-efficacy and their teaching competencies. This result means that as mathematics teacher candidates’ teaching competencies increase, their self-efficacy also increases (Check for the full manuscript of the graduation thesis).

Conclusion

We mentioned that instructors have responsibilities such as educating learners, conveying their knowledge, guiding students’ futures, and preparing learners for life. We have proven that the effective provision of this environment is related to teachers’ self-efficacy and mathematics teaching competencies. So, what can we do to create this environment?
We suggest that various activities and practices related to self-efficacy beliefs and teaching competency should be included in teacher training programs so that teacher candidates can use their teaching skills effectively in the classroom. So, what various activities can encourage the efficient use of our skills in the classroom? For example, it may be beneficial for pre-service teachers to create awareness by preparing a presentation on mathematics teaching competency, especially for the “Methods” course, which is one of the field courses, before starting their professional life.
In order to increase the awareness level of elementary school mathematics teacher candidates studying in education faculties, seminars can be organized about the perception of mathematics self-efficacy and mathematics teaching competency as an important factor in success.                   

Key Messages

  • Teachers’ self-confidence and self-efficacy skills are significant factors in providing more effective teaching to their students.
  • Pre-service mathematics teachers’ self-efficacy was higher than their mathematics teaching competencies.
  • Mathematics teachers’ self-efficacy seems to be the determining factor in their teaching styles and behaviour in the classroom and affects their teaching quality.
  • There was a significant and positive relationship between the pre-service mathematics teachers’ self-efficacy and their teaching competencies.
  • Teachers’ self-efficacy and teaching competencies should be sufficient for teaching in order for them to begin their professional careers properly.

Other blog posts on similar topics:

Büşra Uysal

Büşra Uysal

Büşra Uysal is a mathematics teacher. She graduated from MEF University, Istanbul. She gained teaching experience in both systems including face-to-face and online systems intensively. She received a Mentoring Certificate (2020-2021) and has been a supervisor for university students. In the scope of the “University within School” project, she did tutoring lessons with students. Her professional interests are to provide students with mathematical thinking skills and to create effective classroom environments where students can discover information and share their ideas freely.

She worked as a volunteer teacher at the Youth Education Center (Sarıyer Gençlik Eğitim Merkezi, Istanbul) within the “Social Responsibility Project” scope. In 2022, she conducted research on Pre-service Elementary Teachers’ Self-Efficacy for Teaching Mathematics & Teaching  Competency and presented at MEF University International Educational Sciences Student Conference (MEFEDUCON, 2022)

Dr Bengi Birgili

Dr Bengi Birgili

Research Assistant in the Mathematics Education Department at MEF University, Istanbul.

Dr Birgili is a research assistant in the Mathematics Education Department at MEF University, Istanbul. She experienced in research at the University of Vienna. Her research interests focus on curriculum development and evaluation, instructional design, in-class assessment. She received the Emerging Researchers Bursary Winners award at ECER 2017 for her paper titled “A Metacognitive Perspective to Open-Ended Questions vs. Multiple-Choice.”

In 2020, a co-authored research became one of the four accepted studies among Early-Career Scholars awarded by the International Testing Commission (ITC) Young Scholar Committee in the UK [Postponed to 2021 Colloquium due to COVID-19].

In Jan 2020, she completed the Elements of AI certification offered by the University of Helsinki.

Researchgate:https://www.researchgate.net/profile/Bengi-Birgili-2

Twitter: @bengibirgili

Linkedin: https://www.linkedin.com/in/bengibirgili/

ORCID:https://orcid.org/0000-0002-2990-6717

Medium: https://bengibirgili.medium.com

References and Further Reading

Bandura, A. (1995). Self-efficacy in changing societies. https://doi.org/10.1017/CBO9780511527692. 

Bandura, A. (1997). Self-efficacy: The exercise of control. Freeman and Company Press.

Battista, M. T. (1986). The relationship of mathematics anxiety and mathematical knowledge to the learning of mathematical pedagogy by preservice elementary teachers. School Science and Mathematics, 86(1), 10–19. https://doi.org/10.1111/j.1949-8594.1986.tb11580.x 

Çakıroğlu, E., & Işıksal, M. (2009). Preservice elementary teachers’ attitudes and self-efficacy beliefs toward mathematics. Education and Science, 34, 151. https://hdl.handle.net/11511/52775

Esendemir, Ö., Çırak, S., & Samancıoglu, M. (2015). Pre-service elementary math teachers’ opinions about mathematics teaching competencies. Gaziantep University Journal of Social Sciences, 14(1), 217–239.https://doi.org/10.21547/jss.256787

Gavora, P. (2010). Slovak pre-service teacher self-efficacy: Theoretical and research considerations. The New Educational Review, 21(2), 17–30. https://www.researchgate.net/publication/287424468_Slovak_Pre-Service_Teacher_Self-Efficacy_Theoretical_and_Research_Considerations 

Gülten, D. Ç. (2013). An investigation of pre-service primary mathematics teachers’ math literacy self-efficacy beliefs in terms of certain variables. International Online Journal of Educational Sciences, 5(2), 393–408. https://iojes.net/?mod=makale_tr_ozet&makale_id=41128 

Küçükalioğlu, T., & Tuluk, G. (2021). The effect of mathematics teachers’ self-efficacy and leadership styles on students’ mathematical achievement and attitudes. Athens Journal of Education, 8(3), 221–238. https://doi.org/10.30958/aje.8-3-1 

Özgen, K., & Bindak, R. (2008). The development of a self-efficacy scale for mathematics literacy. Kastamonu Education Journal, 16(2), 517–528. https://doi.org/10.24106/kefdergi.413386

Stevens, C., & Wenner, G. (1996). Elementary preservice teachers’ knowledge and beliefs regarding science and mathematics. School Science and Mathematics, 96(1), 2–9. https://doi.org/10.1111/j.1949-8594.1996.tb10204.x 

Tosun, T. (2000). The beliefs of preservice elementary teachers toward science and science teaching. School Science and Mathematics, 100(7), 374–379. https://doi.org/10.1111/j.1949-8594.2000.tb18179.x

Zuya, H, E., Kwalat, S, K., & Attah, B, G. (2016). Pre-service teachers’ mathematics self-efficacy and mathematics teaching self-efficacy. Journal of Education and Practice, 7(14), 93–98. https://www.researchgate.net/publication/303723566_Pre-service_Teachers%27_Mathematics_Self-efficacy_and_Mathematics_Teaching_Self-efficacy 

How Broadening Horizons leads to the Development of Intercultural Competences

How Broadening Horizons leads to the Development of Intercultural Competences

by | Emerging Researchers' Group, NW 24 Mathematics Education Research

I would like this post to inspire emerging educational researchers. That’s why I’m going to include a lot of my own experiences.

Currently, in Poland, intercultural competences are developed only during philological studies. While learning a foreign language, we can understand what these competences are and how they are supposed to work. What about the rest of society? Should only foreign language students be ‘citizens of the world’? There are Erasmus type programs that allow all students to study abroad. However, not everyone knows how to take advantage of them.

From an early age, children should be accustomed to diversity and taught that nothing is better or worse. Everyone deserves respect and love. We all have similar needs, despite the colour of our skin. Meanwhile, there is still not enough content like this in the educational programs for the youngest students. When it appears in older classes, it is associated only with the culture of the country whose language they are currently learning.

Beginning my intercultural journey

I started my adventure with interculturalism by volunteering in Vietnam in the small village of Sapa. I taught English there and conducted art classes. A young Vietnamese Hmong couple ran the Homestay. In exchange for working with the local children, I spent quality time with their family, participated in all celebrations, and had meals with them. I met people from different countries and even continents every day. It was an extraordinary and fascinating experience for me.

After a month’s stay, I returned to Warsaw. Nothing was the same as it was before I had left. Even the tea lost its flavour. I felt a huge thirst for travel, and I was hungry to discover, taste and admire new things. I felt a terrible hunger for knowledge. Only then did I understand how much we lose by closing doors and surrounding ourselves with people from the same cultural circle. If it weren’t for this trip, I would not have realized how diligent and hungry for knowledge these children are and how much they care about learning. They can truly appreciate it. Unfortunately, the region lacks English teachers with intercultural experience. The teachers I encountered had little awareness of the use of English in different cultural contexts.

Thanks to my stay in Vietnam (apart from trying durian, drinking fresh coconut juice, making my own spring rolls), I experienced Milton Benett’s Developmental Model of Intercultural Sensitivity myself. I have gone through all the phases, from Denial (Ethnocentric stages) to Integration (Ethnorelative stages). I believe that I will remember this process for the rest of my life.

Exploring the Concept of Intercultural Sensitivity 

It was the beginning of my doctoral studies, and I was eager to explore this concept. So I started looking for universities that interested me in terms of the research they conduct, hoping to complete a short internship or a study trip.

I was able to find a university that not only suited my needs scientifically but was also willing to accept me for a short stay – the first Center for Cultural Psychology in Europe, which was then at the University of Aalborg in Denmark.

The stay in Denmark exceeded my expectations. I cooperated with scientists from all over the world in meetings, seminars, conferences and workshops, which provided a lot of inspiration. At that time, I also had the opportunity to communicate in English on a higher level than before. I met people not only from Europe but also from South America, Asia and the United States. Every Wednesday, a ‘kitchen seminar’ was organized. That was the name of the meetings of scientists from around the world where we discussed one given topic every day. 

Imagine discussing one specific scientific topic from different cultural perspectives. This experience enriched me​​ scientifically. I am still very grateful to the scientists who are developing this Center, who took me under their wings. I think that was a milestone in my scientific development.

ECER and the Emerging Researchers’ Group

Shortly after defending my doctoral dissertation, I learned about the opportunity to participate in the European Educational Research Association Conference (ECER). The Emerging Researcher group was of particular interest to me. I imagined how wonderful it would be to be among young scientists from all over the world. Those are the young people who want to change the educational space. They are brave, and they look at the world with trust and openness. They have broad horizons, and they want to keep learning and improving.

 I learnt that there was an opportunity to receive a conference scholarship. I decided to apply. I was happy to find out that my application was accepted and that I could go to Hamburg!

The organization of the entire conference was excellent, starting with critical, interesting comments that I had the opportunity to hear, to various workshops and events that were organized to fill the time fruitfully. Everything was arranged on a world-class level. During the ERG and EERA conference, I had the opportunity to meet fantastic people from all over the world. We were all one big family.

One of the most interesting events for me was the exchange of personal experiences with women of my age in a similar scientific situation (facilitated by the ERG). Long conversations about our experiences during meals or while sightseeing around the city provided an excellent opportunity to reflect on our lives and goals. The exchange of scientific understanding is always invaluable. Communicating with people so culturally different teaches us humility and greater self-awareness.

It also allows you to understand your location on the map of the world and in space. Finally, it teaches that what is objectively good is not always good in reality. And what’s bad is not only bad. Indeed, there is more than just gray.

 

Forging lasting friendships through intercultural experiences 

What is the result of all these experiences? First, I teach Intercultural Competences at my university, The Maria Grzegorzewska University in Warsaw. It is in the form of workshops and is aimed at students of education of all years and nationalities.

Apart from fruitful intercultural cooperation, I have gained unforgettable experiences and friendships. I discovered that there is more than a Polish educational space, that dumplings are not only eaten in Poland because they can also be eaten in Argentina (as Empanadas). The concept of marriage can vary between continents and countries, and collective memory has become an inspiring research topic. 

It is impossible to develop intercultural competences without experience with OTHERS. We will never know who we truly are without exposure to foreign cultures. We will never appreciate our country and culture without knowing others. If you want to be an outstanding teacher or scientist, you must have intercultural experience.

Developing intercultural competences through communing with others is a beautiful relationship. Maybe a bit turbulent at first and bringing a bit of fear, but in the end, giving a great sense of satisfaction, security, and fulfilment.

Other blog posts on similar topics:

Dr Maja Wenderlich

Dr Maja Wenderlich

Assistant Professor in the Department of Supporting Human Development and Education, The Maria Grzegorzewska University, Warsaw, Poland

References and Further Reading

What is Erasmus+? European Commission: https://ec.europa.eu/programmes/erasmus-plus/about_en  (05.06.2021)

Curriculum for Primary School in Poland: https://podstawaprogramowa.pl/files/D2017000035601.pdf   (09.06.2021) 

R. Flowers, Ethnic minority education in Viet Nam: challenges and opportunities during COVID-19 outbreak, https://www.unicef.org/vietnam/stories/ethnic-minority-education-viet-nam-challenges-and-opportunities-during-covid-19-outbreak (04.06.2021)

E. Pachina, My Vietnamese Experience: Challenges for English Learners in Vietnam,

https://www.teflcourse.net/blog/my-vietnamese-experience-challenges-for-english-learners-in-vietnam-ittt-tefl-blog/ (05.06.2021).

M. J. Bennett, 1986, 1993, 2002, 2005, 2011, A Developmental Model of Intercultural Sensitivity, The Intercultural Development  Research Institute: https://www.idrinstitute.org/wp-content/uploads/2018/02/FILE_Documento_Bennett_DMIS_12pp_quotes_rev_2011.pdf  (05.06.2021).

AAlborg Univeristy, Denamark: https://www.ccp.aau.dk/ (05.06.2021).

Promoting Emerging Researchers:  https://eera-ecer.de/about-eera/promoting-emerging-researchers/ecer-conference-bursaries/ (05.06.2021)

M. J. Bennett, Becoming interculturally competent. (In): J.S. Wurzel (Ed.), Toward Multiculturalism: A Reader in Multicultural Education. Newton, MA: Intercultural Resource Corporation, 2004.

Gu, Intercultural Experience and Teacher Professional Development, (in:) RELC Journal; Volume 36, Issue 1, April 2005, pp. 5–22.

Further Reading

Bennett, M. J., & Wiseman, R. (2003). Measuring intercultural sensitivity: The Intercultural Development Inventory. International Journal of Intercultural Relations, 27(4), 421-443.

Koester, J., & Lustig, M. W. (2015). Intercultural communication competence: Theory, measurement, and application. International Journal of Intercultural Relations, 48, 20-21

Martin, J. N. (2015). Revisiting intercultural communication competence: Where to go from here. International Journal of Intercultural Relations, 48, 6-8.

Minzaripov R. G., Fakhrutdinova  A. V.,  ,Mardakhaev  L. V., Volenko O. I., ,Varlamova E. Y. (2020) Multicultural Educational Approach Influence on Student’s Development.  International Journal of Criminology and Sociology, 9, 1-5.

Savicki V. (2008). Developing Intercultural Competence and Transformation: Theory, Research, and Application in International Education, Stylus Publishing; Illustrated edition.