Five Ways to Elevate Students’ Self-Efficacy in Math

If I were to ask you what determines your self-worth: your family, your appearance, your happiness, your health, your friendships, I bet that ‘school grades’ would factor pretty low on your scale.

However, a study found that college students often base their self-worth on academic grades, which can have detrimental effects such as stress, aggression, and unhealthy behaviours. This reliance on external validation is influenced by an educational system that values outcomes more than the learning process. Interviews with students and parents revealed a negative perception of math, with limited positive associations and a lack of student empowerment. Addressing this issue requires transforming students’ mindsets and experiences in math education. Here are five ways to support their transformation.

At the end of this article, look for a PDF containing a comprehensive Transdisciplinary Maths Unit by my colleague and friend Brian Davidson.

1. Enhance math self-efficacy

During a discussion with a group of students about math, their responses were compiled into a wordle, visually representing their sentiments. The larger, more prominent words such as ‘difficult,’ ‘hate,’ ‘stupid,’ and ‘confusing’ outweighed the smaller words. Conversely, the smaller words like ‘smart’ or ‘interesting’ indicated that students had low self-confidence in math. In meetings, parents expressed concerns about their children “giving up” and feeling unheard.

To address these challenges, schools must establish a supportive environment that cultivates a positive attitude toward math. This involves encouraging students to view math as accessible, engaging, and relevant to their daily lives. By creating such an environment, schools can empower students to develop a growth mindset, enhance their self-efficacy, and foster a sense of agency and belonging in their math education.

An example of elevating efficacy.

2. Empower students’ voices

Traditional forms of assessing students in math were initially designed with the belief that grades would motivate students. However, contemporary practices recognize that grades are merely a snapshot and provide a simplistic indication of student understanding. Various factors can influence an assessment, such as the time of day, home environment, sleep, teacher-student relationship, or past traumas. Furthermore, students often perceive grades not as feedback on their learning progress but as a judgment of their overall identity, leading to self-identifications as “good” or “bad” students. Grades, therefore, act as blunt instruments that need a rework.

Teachers must emphasize actionable feedback to improve and adjust students' learning. Engaging in timely feedback conversations with teachers creates valuable opportunities for students to express their opinions, concerns, and ideas. These conversations foster a sense of ownership and agency, empowering students to actively participate in their learning and contribute to a collaborative and supportive educational environment.

Another way in which a damaging performance culture is cultivated is through frequent testing. Many teachers who have embraced the need for a growth mindset culture are frustrated by testing as they tell students that mistakes and struggles are essential for brain growth and then are forced to grade them down every time they make a mistake. Feedback sessions shift the focus from grades as the sole measure of success towards emphasizing the learning process, critical thinking, and problem-solving skills.

3. Supportive parental involvement: homework

A child’s primary responsibility is their education, spending approximately eight hours each day at school, where teachers expect their highest level of engagement. However, this expectation doesn’t end there. Students are often assigned additional work to be completed at home. While we would recognize and question a company that demands overtime or excessive time from their employees, we frequently ask students to devote hours of their evening to school-related tasks. This abundance of homework contributes to performance anxiety, especially when the assignments lack meaningful value and impede quality time for children and their families.

“Effective practice that stimulates the brain is not the repetition of similar questions over and over again; it is multi-dimensional and involves students representing ideas in many different ways, thinking creatively, and visually, and moving between words, visuals, numbers, and other mathematical forms.”

Boaler, 2016

Parents can engage in meaningful conversations about their child’s learning experiences throughout the day, regardless of age. To address this issue and overcome the typical response of “nothing” when asked about their day, a group of students has compiled a set of “homework” reflections for parents to facilitate discussions at home:

1. What was the central concept or idea you explored today?
2. Share any valuable ideas or insights that emerged during your learning.
3. What challenges or difficulties did you encounter today?
4. Can you think of practical situations where you could apply the knowledge you gained today?
5. Do you have any questions about the work or topics covered today?
6. Did today’s lesson spark any new ideas or thoughts in your mind?

Parents can use these prompts to foster a deeper understanding of their child’s learning journey and encourage thoughtful reflection, enabling meaningful conversations beyond surface-level responses.

4. Implement diverse teaching approaches.

Implement teaching strategies that accommodate diverse learning styles and abilities while integrating real-life applications, hands-on activities, and technology to enhance the engagement and accessibility of mathematics. While external pressures may contribute to an excessive focus on grades, educators have various methods to encourage students to shift their attention toward the learning process.

For instance, one practical approach is to assign “evolving assignments,” such as papers written in installments, providing descriptive feedback without assigning grades until the final submission. This assignment reinforces the notion that learning is an ongoing process and that continuous improvement is possible. Additionally, these projects prepare students for real-world scenarios where they may encounter long-term engineering projects or publishing contracts involving multiple drafts.

Differentiation example: open-ended problems

Open-ended problems, often called “ill-structured” problems, are characterized by a higher level of ambiguity and the potential for multiple correct solutions. These problems mirror real-life mathematical scenarios or investigations, such as determining the amount of water our school can save over four months or designing an improved gym room within a specified budget. Open-ended problems empower students to make their own mathematical decisions, fostering mathematical thinking and providing space for their reasoning and communication skills to develop.

Differentiation example: Harkness table

Mathematics education can be effectively delivered through the Harkness Tradition, a student-centred approach where teachers prioritize creating a supportive classroom environment where students feel comfortable collaborating and asking questions. This model celebrates mistakes as they provide valuable learning opportunities and foster increased student collaboration. Students collectively contribute to growth and mastery in mathematics through active exploration, discussion, and explanation of ideas. In contemporary math instruction, students are encouraged to assume responsibility for their comprehensive engagement with the subject. This includes understanding theorems, accurately employing formulas and techniques, critically assessing results for reasonability, and effectively utilizing technology when appropriate. By emphasizing these aspects, students develop a well-rounded mathematical proficiency and the ability to think critically and apply their knowledge in various contexts.

An example of differentiation through Harkness.

Instead of traditional textbooks, students engage with faculty-developed problems that foster rigour and require careful reading to extract essential information. Teachers expect active participation from students, encouraging them to contribute solutions to homework problems, ask relevant questions, and share insights that enlighten their classmates.

Teachers use tools like Equity Maps to map students’ contributions and insights to facilitate this. By assuming the role of the primary drivers in daily investigations, students perceive themselves as the creators of mathematical knowledge, recognizing their agency over the subject matter rather than relying solely on teachers, textbooks, or the internet.

Differentiation example: flipped learning

Flipped learning is an educational approach that flips the traditional classroom model. In this method, students are exposed to instructional content outside the classroom, typically through pre-recorded videos or online materials, allowing them to learn at their own pace and convenience. Classroom time is then dedicated to interactive activities, discussions, and problem-solving, where teachers act as facilitators and provide individualized support. Flipped learning promotes active engagement, critical thinking, and collaboration among students. It enables personalized learning experiences, as students can revisit and review content as needed. By flipping the learning process, educators can create dynamic and student-centred classrooms that foster more profound understanding and higher levels of achievement. In 2016, I had the opportunity to collaborate with other members of TEDEd to create an animated math lesson. Can you spot me?

“Parts per million” is a scientific unit of measurement that counts the number of units of one substance per one million units of another. But because it’s hard to conceptualize huge numbers, it can be challenging to wrap our brains around what “one part per million” means. Kim Preshoff (with help from 100+ animators from the TED-Ed Community) created a video with nine helpful ways to visualize it. This lesson has been customized 162 times, bringing real-life math to the classroom. That’s a lot of flipping!

5. Promote a holistic understanding of self-worth.

To cultivate a holistic understanding of self-worth, students can shift their focus from solely deriving it from academic performance to internal sources. Emphasizing personal growth, values, and accomplishments beyond grades fosters a healthier sense of self. Encouraging self-reflection, setting personal goals, and engaging in transdisciplinary learning that aligns with their passions and values nurture a sense of fulfillment. Valuing qualities like resilience, empathy, creativity, and integrity helps students recognize that their worth extends beyond academic achievements, leading to greater self-confidence and a more balanced outlook on their overall value.

Transdisciplinary learning provides a holistic approach that nurtures a sense of fulfillment in students. Students engage in real-world contexts by integrating knowledge and skills across multiple disciplines, fostering curiosity and deep understanding. This approach promotes critical thinking, problem-solving, collaboration, and creativity, empowering students to make meaningful connections and develop a broader perspective, ultimately fulfilling their educational journey.

An example of Transdisciplinary Learning by Brian Davidson

If you are interested in presenting these ideas to your community, here is the PDF of the presentation with robust examples and a complete Grade 7 MYP unit of inquiry, including the criterion and rubrics for assessment.

This article delves into the transformative power of inquiry-based learning in mathematics, focusing on enhancing math efficacy and empowering students' voices. It highlights the importance of effective feedback and the role of supportive parents in fostering a positive math learning environment. By implementing these approaches, educators can create engaging and inclusive classrooms that empower students, ultimately leading to improved math outcomes and a greater sense of mathematical self-confidence.

Citation:

Crocker, J. (2002), The Costs of Seeking Self–Esteem. Journal of Social Issues, 58: 597–615. https://doi.org/10.1111/1540-4560.00279