Historically, Plato stated that Quadrivium, the core of mathematical knowledge comprising arithmetic, geometry, music, and astronomy, was an essential pre-requisite for understanding philosophy and the greater universe. According to Plato, both Quadrivium and Trivium (grammar, rhetoric, and logic) were necessary for creating a unified idea of our perceived reality.

Our exposure to mathematics, in addition to various parenting styles, plays a significant role in developing our self-beliefs and our capacity to problem-solve.

❓ What’s Self-Efficacy Got to Do with It ❓

Canadian American psychologist, Albert Bandura, defined that belief in capacity within his Theory of Self-Efficacy is the belief people have of themselves and their ability to execute certain behaviors needed to reach a goal. According to Bandura, it’s a key determinant of whether individuals will attempt a given task, the amount of effort they will expend, and their persistence when faced with obstacles.

For instance, you may pick up a musical instrument and learn to play well without extensive music theory knowledge, only to realize that you’ve reached a plateau in your understanding of the music you’re playing. The awareness of this obstacle then presents the scenario mentioned before. It demands a certain level of Self-Efficacy to believe that the following domain of understanding exists and is attainable.

While Self-Efficacy, in general, refers to a multitude of aspirations, let’s take a deeper dive into another concept coined by Bandura called Math Self-Efficacy. 

Its definition mirrors that of the Theory of Self-Efficacy but with a focus on solving mathematical problems. We can connect many areas of study to mathematics, as was illustrated by Quadrivium, and yet, mathematics seems to play a divisive role.

For some of us, learning math may have been a positive and empowering experience leading to confidence in solving math problems and, in turn, high Math Self-Efficacy. 

Reciprocally, learning math may have been a negative experience that led to a lack of confidence and self-doubt, resulting in low Math Self-efficacy. Researchers are beginning to question how we develop high or low levels of Math Self-Efficacy and how this translates to other areas of our lives.

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.

William Paul Thurston

Math Anxiety and Childhood

Self-Efficacy naturally includes our emotional health because we may harbor specific emotions in response to our beliefs about ourselves. Present-day emotion theories agree that emotions are tightly intertwined with personal goals and highlight their essential role in developing coping and adaptation skills.

With the demand for science, technology, engineering, and mathematics (STEM) professionals on the rise, so too are the emotional effects this demand places on today’s students. 

While many institutions have rushed to expand STEM educational programs, very few have prioritized the importance of addressing the fear or apprehension of math, also known as Math Anxiety, that many students experience. According to Pajares & Graham, 1999, Math Anxiety is related to constructs such as Self-Efficacy and indicates that high Math Self-Efficacy can help reduce Math Anxiety.

    child thinking about math

    We can often trace roots of the anxiety we carry into adolescence and adulthood back to our childhoods to the parenting styles we experienced as children. 

    Researchers have shown strong correlations between anxiety, parenting styles, and self-efficacy and that parenting styles specifically affect performance in mathematics and a child’s adaptability to their environment. 

    You may be familiar with the various styles of parenting initially explored by Furnham and Cheng, such as Authoritative, Authoritarian, and Permissive.

    • Authoritative parenting is defined by its controlling and restrictive characteristics, uses logic and rewards rather than punishments.
    • Authoritarian parenting is characterized by similar control and restriction, values punishment rather than rewards.
    • Permissive parenting refers to a style of parenting that demands very little from their children and sets flexible boundaries around their child’s behavior.
    Authoritarian parenting style comic

    Authoritative parenting style comic

    Permissive Parenting Style Comic

    Take a moment to reflect on your own experience and consider what style you experienced as a child or that you may gravitate towards with raising your children. Can you draw any connections between your math self-efficacy and particular parenting styles that show up in your story?

    The results from various studies investigating the relationships between math anxiety, self-efficacy, and parenting styles are surprisingly not surprising. They showed that children raised with unengaged parents (Permissive) or the Authoritarian style obtained low math scores. These low math scores led to more significant math anxiety and lower math self-efficacy.

    The more Authoritative the parenting, the higher the math self-efficacy, while high math self-efficacy leads to lower math anxiety levels. The surprising thing researchers concluded was that males and females with high self-efficacy did not differ in their math anxiety.

    Despite the longstanding societal stereotype that females are inferior to males in the STEM fields, this finding suggests that improving female math self-efficacy could lower their math anxiety, leading to increased confidence in excelling in mathematics and improving math scores.

    Our Self-Efficacy

    When diving deeper into understanding how self-efficacy forms, it’s essential to consider the various environments in which we learn. For instance, we learn from our caregivers, in classrooms, at work. Within these settings, we have built perceptions of ourselves through various factors such as curiosity, validation, empowerment, and shame. 

    Different teaching environments have more effective ways of improving self-efficacy for students. Many of us have grown up learning within the Traditional Classroom Model, where the teacher holds all of the knowledge before starting class. Students have very little information about the subject before the class starts. In class, the student then learns the subject matter from the teacher and takes notes.

    Currently, reformations are happening to how we teach the material to students, such as the Flipped Classroom Model (FCM). This teaching approach, indirectly inspired by Alison King in 1993, presents the importance of using class time to construct meaning with students rather than simply transferring information. 

    The FCM requires teachers to instruct the lesson at home with preliminary information (via video, podcast, book, etc.) and have students work in class to develop a deeper understanding of concepts they have previous exposure to and provide support while making new connections. After class, students check their understanding of the concepts and continue their learning at home.

    The FCM allows students to develop autonomy and learn at their own pace by allowing students access to lectures before class to learn individually and bring their understanding and perspectives to class and engage with their peers this way rather than having that be a class activity. Reimagining the classroom using the FCM can improve self-efficacy in students and has been shown to improve academic success and increase self-efficacy.

    For those who no longer find themselves in a “classroom” per se, the FCM is still applicable to our daily lives as working professionals. We may have traded classmates for work colleagues, yet, we continue to work in individual and group settings, either professionally or within personal projects.

    If, for instance, you are an independent contractor, you could practice spending the time needed to collect all of your research or tools before dedicating the time to sit down and work on your task. Using this approach can leave the time allotted to the actual goal of building connections and synthesizing your previous research.

    A similar approach could be conducted in the workplace using the example of a monthly staff meeting. A CEO could prepare topic points to be discussed at the meeting with adequate time for staff to digest them. The staff meeting will then be a space for constructive conversation as staff will have had the time to come to their own opinions and perspectives. The prior preparation allows the meeting to be solely for problem-solving and synthesizing.

    Feeling Down?

    While it’s essential to understand how we may have developed the self-efficacy we have presently, the belief we hold of ourselves is not rigid but rather fluid and malleable. If you feel as though your self-efficacy is high and you don’t suffer from periodic moments of self-doubt, please ignore this next section. 

    If you are human and experience fluctuations between high and low efficacy, remember the following points during moments of low self-efficacy:

    Set simple goals – It may be easy to get carried with the aspirations we have for our lives. Still, with self-efficacy being dependent on feelings of accomplishment, it’s helpful to break down our goals into smaller bite sizes. Some of the most impressive achievements aren’t reached in one significant attempt but instead more minor and tangible steps broken down into realistically achievable tasks.

    Look at the bigger picture – Practicing the skill of looking beyond short-term losses is essential in building self-efficacy. It allows us to preserve the trust we have with ourselves that we will achieve our goals despite our setbacks, not void of the presence of setbacks.

    Reframe Obstacles – How we approach obstacles has a massive influence on our self-efficacy. It’s helpful to practice identifying our barriers or thought blocks and reframing them using positive interventions. Reconstructing how we look at failures, such as the terminology we describe them with, can help build resiliency against the inevitable experience of making mistakes.

    Conclusion

    The beliefs we hold of ourselves are some of the most influential thoughts we possess if not, the most important. Reflecting on how we may have come to our current level of self-efficacy is the first step in understanding how we may either continue to nurture it or build it up from scratch.

    Though we have looked at the concept of self-efficacy in the focus of Math Self-Efficacy, its principles are the same and applicable to many areas of our lives that represent real problem solving or symbolic ones. 

    When we find ourselves in the thick of our interpersonal battles during the low moments, it can be challenging to differentiate a loss from a personal shortcoming. Reaching our goals and succeeding is a beautiful thing, but how we come back from the falls holds far more impact and has the power to send ripples into our behavior for years to come.

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