Introduction
A mathematics classroom is a collaborative classroom. However, this means that some of the learners within the classroom are equipped with similar communication classifications. There are two types of learners that a teacher encounters inside a classroom. Introverts and extroverts are classified by their personalities. Moreover, while extroverts can present a fair share of challenges in teaching and learning mathematics, introverts present the main challenge. Learners are classified as extroverts or introverts based on their consistent traits, habits, and responses to real-life situations. Introverts, for instance, are considered to be more careful and critical but less fast when compared to extroverts (Burtăverde and Mihaila, 2011). I agree that mathematics is a subject that is best learned in an active environment, and this has posed a challenge for introverted students who cannot wholly thrive in a highly active collaborative classroom (Burtăverde and Mihaila, 2011). Learners can’t claim mastery of crucial mathematics concepts without verbal expressions. However, based on the classification of introverts, it is evident that this group of students learns best in solitude. History presents that most of the best mathematicians, scientists, historians, and psychologists were introverts because introverts are generally creative and critical thinkers, the two most essential qualities of a good learner. Therefore, teachers are responsible for identifying their learners by characterization and helping maximize their skills through appropriate learning strategies.
Learning and Teaching Mathematics (Introvert’s Perceptive)
Mathematics has been considered a complex subject by most students, and therefore there has been a lot of anxiety associated with teaching and learning mathematics. While this assumption has room for argument, I agree with this assessment in this context. I have witnessed that in a classroom setting. At the same time, teachers stress the best ways of changing the attitudes of young mathematics learners; students are anxious about mastery of the subject (Hwang et al., 2007). However, introverts’ primary anxiety is not in learning mathematics but communicating their creative ideas to their peers. There are five main objectives of learning mathematics. These learning objectives have been associated with developing communication skills amongst young learners, mainly in lower and middle school. The aim of learning mathematics includes:
- Mathematical communication. All learners are expected to be able to communicate the concepts that they learn in a mathematics classroom. Therefore, introverted learners must master the courage to communicate what they have learned in the classroom verbally. Communication involves both written and verbal. In mathematics, learners are taught how to use written communication to explain mathematical ideas, which can ultimately be used to interpret numerical and symbolic algebra. Since these are the core symbols used in communication, introverts find it easy to communicate their ideas since communication is one of the significant challenges for introverts.
- Mathematical reasoning: this objective aims to enhance the learner’s critical thinking skills. Introverts are natural critical thinkers. Therefore, this explains why introverts love mathematics as a subject. In reasoning, learners can improve their vocabulary and speaking skills before they enhance their writing skills.
- Mathematical problem-solving. Most mathematics concepts initiate problem-solving skills. Learning mathematics enhances the problem-solving skills of a student. To solve most mathematics concepts, a learner must be creative and innovative to analyze the questions and realize the demands of the mathematics problems (Hwang et al., 2007). The problem-solving process is associated with psychological development.
- Mathematical connections: every mathematics learner must be able to associate different mathematics ideas to establish a mathematical solution.
- Creating a positive attitude towards learning mathematics. While most introverts have positive attitudes toward mathematics, ensuring that all mathematics learners develop a positive attitude towards mathematics is one of the top objectives when teaching mathematics.
Challenges of Teaching Mathematics to Introverts
Introverts are socially quiet, and most have been linked to social anxiety, especially when communicating with their peers or teachers (Burtăverde and Mihaila, 2011). I concur with this evaluation of introverts as presented by the authors Burtăverde and Mihaila. Therefore, I think this anxiety makes it quite difficult for them to perform efficiently when asked questions within a class setting and makes it quite hard for them to establish connections with their peers. This makes it very hard for teachers to understand their classroom needs and efficiently satisfy them. However, writing is considered the most preferred communication method for introverts, forcing teachers to pay more attention to the written solutions, which might be time-consuming, especially for lessons that require a lot of time to teach. For instance, according to Sussane Prediger (2009) in her article ” How to develop a mathematics for teaching and understanding: the case of meanings of the equal signs,” one of the constituents of diagnostic competence is interest in student thinking. She emphasizes that they can’t teach efficiently unless the teacher understands how their student is thinking. However, teachers have a hard time understanding what introverts think due to a difference in personalities, which poses a challenge in teaching introverted learners mathematics.
I have realized that naturally, teachers are prone to pay more attention to the participative and active learners in class. This makes it relatively easy to neglect introverted learners. For instance, when analyzing the attitude of mathematics learners, it was established that while extroverts find the subject challenging and uninteresting, they were more prone to asking the teacher direct questions whenever they did not understand the concepts than introverts. By asking questions, the teacher can identify the areas that need more emphasis and know the areas that have been well understood. On the other hand, introverts tend to find answers in books whenever they encounter challenges during learning. This makes it impossible for teachers to generate a one-on-one relationship with the learners, making the teacher-learner relationship more strained and complicated. This might raise speculations of favoritism and bias within the classroom.
Advantages of Teaching Introverts
I agree that introverts are critical thinkers, which gives teachers an easy time in teaching mathematical concepts (Burtăverde and Mihaila, 2011). This characterization of introverts, unlike extroverts, makes them interested in mathematics. Extroverts have been known to develop mathematics anxiety from quite an early age, making it almost impossible for teachers to change their attitudes. However, introverts are associated with extreme enthusiasm for learning mathematics, which makes the teacher’s work simple and helps to achieve the objectives of learning mathematics. The complexity of mathematics appeals to introverts who want to solve problems using formulated creative ideas, enhancing the mastery of complex concepts.
Introverts pay attention to details, which helps them understand complex mathematics problems (Burtăverde and Mihaila, 2011). Through this characterization, introverts are prone to manage their time better than extroverts and hence solve mathematical problems articulately. When introverts are presented with adequate learning materials, they require less supervision from teachers than students. For instance, introverts, compared to extroverts, usually accurately answer questions directly lifted from learning materials. Their love for details makes them intrigued enough to learn outside the classroom setting. This makes the teacher’s work in the class more manageable and helps create time for learners experiencing difficulties.
Strategies for Teaching Introverts
Incorporation of technology. We live in an era where most children are thrilled with social media and technology. I concur with the academic evaluation that implies that access to a virtual academic world has allowed introverts to have a platform to post their creative ideas with maximum flexibility (Ke and Clark, 2020). Lucky for teachers, different software applications have been developed to help teach additional subjects, mathematics included. For instance, there are polling applications with features that allow every child with the application to provide an answer simultaneously. The main challenge with introverted students is communication. However, studies have shown that during a teaching and learning session, young students, mainly in kindergarten and middle school, master more concepts when verbally responding and communicating in class. This explains why math teachers have mastered allowing learners to repeat essential concepts such as the multiplication table (Hwang et al., 2007).
Careful selection of learners during question-answer sessions: I agree with the careful selection of learners during question responses. When teaching mathematics, teachers, especially primary school learners, have to ask questions at the beginning and the end of the session and sometimes during the learning session to ascertain that learners have understood the concepts taught (Lee et al., 2018). While introverts are usually anxious about raising their hands, it is essential to note that they also articulately prepare their answers before raising their hands compared to more spontaneous extroverts. Introverts can easily feel disappointed and discouraged if they are not selected; therefore, teachers must find the best solution. For instance, a teacher can allow all the learners to shout their answers and then ask an introverted student to provide a detailed explanation of the solution. This will encourage the learner to communicate with other learners while motivating them to participate actively in the classroom.
Rewarding. In most classroom settings, teachers can award learners based on performance and character. However, it is essential to encourage the efforts of introverted learners by rewarding them for mastery. Introverts may lack social skills such as empathy, courage, persistence, and other related social skills (Ke and Clark, 2020). However, they excel in the mastery of concepts. Therefore, they strategically provide a platform for introverted learners to display their mastery of complex or critical mathematical concepts and issue awards to enhance this skill. This can be through techniques such as setting aside time for deliberate practice and allowing learners to show others how they have navigated challenging concepts.
Create groups: introverts get very tired when exposed to extreme social settings. This implies that introverts tend to grow tired by sitting and participating in an active classroom for a few hours. Introverts are also prone to be anxious in spaces with high volume. Therefore, a teacher should help minimize the classroom volume, especially if the class has a few introverts, or create manageable groups during mathematics and put all introverts in one group to create a comfortable learning environment for them.
Conclusion
In conclusion, it has been established that teaching mathematics to introverted learners can be both challenging and advantageous. I concur with this evaluation. However, introvert teaching has been simplified with the improved strategies introduced in the academic world, including virtual learning and technology to enhance learning. Introverts’ mastery and understanding of mathematics concepts have been established to be relatively easy. However, for teaching to be efficient, teachers must communicate with the learners, and the barrier in communication between a teacher and an introverted learner makes the process challenging.
References
Burtăverde, V., and Mihaila, T. (2011). Significant Differences Between Introvert and Extrovert People’s Simple Reaction Time in Conflict Situations. Romanian Journal of Experimental Applied Psychology, 2(3), pp18–24.
Hwang, W.-Y., Chen, N.-S., Dung, J.-J., and Yang, Y.-L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving using a Multimedia Whiteboard System. Educational Technology & Society, 10(2), pp191–212. https://www.jstor.org/stable/jeductechsoci.10.2.191.
Ke, F., and Clark, K. M. (2020). Game-based multimodal representations and mathematical problem-solving. International Journal of Science and Mathematics Education, 18(1), pp103–122. https://doi.org/10.1007/s10763-018-9938-3.
Lee, Y., Capraro, R. M., and Capraro, M. M. (2018). Mathematics Teachers’ Subject Matter Knowledge and Pedagogical Content Knowledge in Problem Posing. International Electronic Journal of Mathematics Education, 13(2), pp75–90. https://doi.org/10.12973/iejme/2698.
Prediger, S. (2009). How to develop a mathematics for teaching and understanding: the case of the meanings of the equal signs.Springer Science +Business Media B.V. pp. 74-93. https://doi.org/10.1007/s10857-009-919-y
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