Reaching Our Goals

How do math and parenting styles impact our self-beliefs and our capacity to problem-solve?

Our exposure to mathematics, in addition to various parenting styles, plays an important role in developing our self-belief and problem-solving abilities.

Plato once stated that the Quadrivium, the core of mathematical knowledge consisting of arithmetic, geometry, music, and astronomy, was a necessary pre-requisite for understanding philosophy and the larger universe. He believed that the Quadrivium and Trivium (grammar, rhetoric, and logic) were both necessary for developing a unified concept of our perceived reality.

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

Canadian American psychologist, Albert Bandura, defined self-efficacy as the belief people have in themselves and their ability to execute certain behaviors needed to reach a goal. According to Bandura, self-efficacy is 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. To move beyod this pleateau demands a certain level of Self-Efficacy to believe a new understanding exists and is attainable.

While self-efficacy can refer to a variety of goals, let's take a closer look at another concept coined by Bandura called Math Self-Efficacy.

Its definition is similar to that of the Theory of Self-Efficacy, but with a focus on mathematical problem solving. Many fields of study can be linked to mathematics, as demonstrated by the Quadrivium, but mathematics appears to be divisive.

For many, learning math is a positive and empowering experience, leading to confidence in solving math problems and, as a result, high math self-efficacy. On the other hand, learning math may have been a negative experience that resulted in a lack of confidence and self-doubt, leading to low math self-efficacy. Researchers beginning to study how we develop high or low levels of math self-efficacy and how this translates to other aspects of our lives.

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

William Paul Thurston

Math Anxiety and Childhood

Emotions are inextricably linked to personal goals, according to today's emotional theories, and they play an important role in the development of coping and adapting skills. 

Because we may experience specific emotions as a result of our beliefs about ourselves, self-efficacy naturally includes our emotional health, and as the demand for science, technology, engineering, and mathematics (STEM) professionals grows, so do the emotional effects on today's students.

While many institutions have rushed to expand STEM educational programs, very few have prioritized the importance of addressing students' fear or apprehension of math, also known as Math Anxiety. Math anxiety, according to Pajares and Graham (1999), is related to constructs such as self-efficacy, implying that having a high level of math self-efficacy can help reduce math anxiety.

girl thinking about math with numbers around her

We can frequently trace the origins of the anxiety we carry into adolescence and adulthood back to our childhoods and the parenting styles we were exposed to as children. Researchers have discovered strong correlations between anxiety, parenting styles, and self-efficacy, as well as that parenting styles specifically affect math performance and a child's adaptability to their environment.

You may be familiar with the various parenting styles first investigated by Furnham and Cheng, such as authoritative, authoritarian, and permissive.

    Authoritarian

    Characterized by a high level of control and restraint, but also emphasizes punishment over rewards.

    Authoritarian parenting style comic

    Authoritative

    Distinguished by its controlling and restricting characteristics, and it teaches children through logic and rewards rather than punishments.

    Authoritative parenting style comic

    Permissive

    Relaxed with a fair amount of leeway for the children.

    Permissive Parenting Style Comic

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

    The findings of various studies looking into the relationships between math anxiety, self-efficacy, and parenting styles are both surprising and unsurprising. They discovered that children raised by unengaged parents (permissive) or authoritarian parents scored poorly in math resulting in increased math anxiety and lower math self-efficacy. 

     In contrast, the more authoritative the parenting, the higher the math self-efficacy, resulting in lower math anxiety levels in the child. In contrast, the more authoritative the parenting, the higher the math self-efficacy, resulting in lower math anxiety levels in the child.

    Researchers discovered that males and females with high self-efficacy did not differ in their math anxiety. Despite the long-held societal stereotype that females are inferior to males in STEM fields, this finding suggests that increasing female math self-efficacy may reduce math anxiety, resulting in increased confidence in excelling in mathematics and improving math scores.

    Self-Efficacy

    When delving deeper into how self-efficacy develops, it's critical to consider the various environments in which we learn. For example, we learn from our caregivers, in school, and at work. We form perceptions of ourselves in these environments as a result of various factors such as curiosity, validation, empowerment, and shame.

    Many of us have grown up learning within the traditional classroom model, where the teacher holds all of the knowledge before starting class. Before the class begins, students know very little about the subject. The student then learns the subject matter from the teacher and takes notes in class.

    While different learning models have pros and cons, this traditional model has its limitations, and different teaching environments have more effective ways of increasing students' self-efficacy. Currently, changes are being made to how we teach material to students, such as the Flipped Classroom Model (FCM). This teaching approach, indirectly inspired by Alison King in 1993, emphasizes 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 had 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 providing students with access to lectures prior to class to learn individually and bring their understanding and perspectives to class and engage with their peers in this manner, rather than making that a class activity. It has been demonstrated that students who use the FCM to rethink their classrooms may have higher self-efficacy and academic success.

    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 on personal projects.

    If you are an independent contractor, for example, you could practice spending the time required to gather all of your research or tools before devoting the time to sit down and work on your task. Using this method can assist you in preserving the time you've set aside for connecting and synthesizing your previous research.

    A monthly staff meeting, for example, could be used to demonstrate a similar approach in the workplace. A CEO could prepare discussion points for the meeting and allow enough time for staff to digest them. Because the staff has had time to form their own opinions and perspectives, the staff meeting will then be a forum for constructive discussion and the meeting can focus solely on problem solving and synthesizing.

    Feeling Down?

    While it's important to understand how we came to have the self-efficacy we do today, the belief we have about ourselves is fluid and malleable. If you have a high sense of self-efficacy and don't experience bouts of self-doubt, please disregard the following section.

    If you are human and experience high and low efficacy fluctuations, keep the following points in mind during times of low self-efficacy:

    Set simple objectives

    It may be easy to get carried away with the aspirations we have for our lives. Nonetheless, because self-efficacy is based on feelings of accomplishment, it's beneficial to break down our goals into smaller bite sizes. Some of the most impressive things are accomplished not through a single large effort, but through smaller and more tangible steps that can be taken.

    Consider the big picture

    It is critical to practice the skill of looking beyond short-term losses in order to build self-efficacy. It allows us to keep the faith we have in ourselves that we will achieve our goals despite, not in spite of, setbacks.

    Reframe obstacles

    Our approach to obstacles has a huge impact on our self-efficacy. It's beneficial to practice identifying and reframing our barriers or thought blocks with positive interventions. Reconstructing how we view failures, such as the terminology we use to describe them, can help build resilience in the face of the unavoidable experience of making mistakes.

    Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence.

    Helen Keller

    Conclusion

    Our self-perceptions are among the most influential, if not the most important, thoughts we have. Reflecting on how we may have arrived at our current level of self-efficacy is the first step toward understanding how we can maintain or rebuild it from the ground up.

    Though we have examined the concept of self-efficacy in the context of Math Self-Efficacy, its principles are the same and apply to many areas of our lives that involve real or symbolic problem solving. When we are in the midst of our interpersonal battles, it can be difficult to distinguish between a loss and a personal shortcoming.

    Reaching our goals and succeeding is wonderful, but how we recover from the falls has far more impact and has the potential to ripple through our behavior for years to come.

    References

    Bandura A. The anatomy of stages of change.. (1997). The anatomy of stages of change. American journal of health promotion : AJHP, 12(1), 8–10.
    Cleary, F.. (2021). Understanding the Trivium and Quadrivium. Hillsdale College.
    Chowdhury, M.. (2021). 4 Ways To Improve And Increase Self-Efficacy. Positive Psychology.
    Eberhart, S. . (1982). Classical quadrivium and Kepler's Harmonice mundi. University of Montana .
    Foley, A., Herts, J., Borgonovi, F., Guerriero, S., Levine, S., & Beilock, S. . (2017). The Math Anxiety-Performance Link: A Global Phenomenon. Current Directions in Psychological Science.
    Jiang, R., Liu, R., Star, J., Zhen, R., Wang, J., & Hong, W. et al. . (2020). How mathematics anxiety affects students' inflexible perseverance in mathematics problem‐solving: Examining the mediating role of cognitive reflection. British Journal Of Educational Psychology, 91(1), 237-260.
    King, A. . (2010). From Sage on the Stage to Guide on the Side. College Teaching, 41:1, 30-35,.
    Lynch, P.. (2017). Quadrivium: the noble fourfold way to an understanding of the universe. . Irish Times.
    Margolis, H., & Mccabe, P. . (2006). Improving Self-Efficacy and Motivation: What to Do, What to Say. Intervention In School And Clinic, 41(4), 218-227.
    Macmull, M. S., & Ashkenazi, S. . (2019). Math Anxiety: The Relationship Between Parenting Style and Math Self-Efficacy. Frontiers in psychology, 10, 1721..
    Namaziandost, E., Çakmak, F.. (2020). An account of EFL learners’ self-efficacy and gender in the Flipped Classroom Model. . Education and Information Technologies 25, 4041–4055.
    Zhou, D., Du, X., Hau, K., Luo, H., Feng, P., & Liu, J. . (2019). Teacher-student relationship and mathematical problem-solving ability: mediating roles of self-efficacy and mathematical anxiety. Educational Psychology, 40(4), 473-489..

    This is where I would say the concept of unlearning would work, sometimes as we grow up we tend to hold certain beliefs as true. It may or may not be true, but if its detrimental to your overall growth then you should probably say it needs changing. Fail forward, grow forward, just keep moving. Life is a never ending journey of growth.

    As a personal finance expert, I truly love this article. I agree with all the major points, when we seem to be fighting a losing battle with an interpersonal conflict, we might wish for it all to just stop (and that's ok too!). But what matters, in the end, is not how hard we fought, but how well. This is because the way in which one comes back from a fall has an enormous effect on their behavior going forward and this is true for both individuals and groups.

     

    Let me just start by saying it would have been such a blessing to have been able to meet the great Albert Bandura. 

     I absolutely agree with the fact that learning math was a positive and empowering experience leading to confidence in solving math problems and, in turn, high Math Self-Efficacy. 

    You hit the nail directly on the head when you said the results from various studies investigating the relationships between math anxiety, self-efficacy, and parenting styles are surprisingly not surprising.

    Unfortunately children raised with unengaged parents or the Authoritarian style obtained low math scores.

        I loved this article, the comic illustrations were pleasing to the eye, amusing, and got the points across. I also agree with the point of view of how and where we learn affects our self-efficacy. Our environment and the process of understanding a concept are what help us learn. I am terrible at math and won't understand what you're teaching me unless you walk me through it. I could relate to this and I have never thought about things this way.

    Such an insightful article! As a low math self-efficacy person - I loved the simple explanation of why and how this may be.

    I didn't quite grasp how the parenting component plays into it - but certainly, the parenting we are given has a huge effect on most aspects of our personalities and life.

    Well done, Albert Bandura!