According to the National Assessment of Education Progress, “only 38% of America’s 8th graders could figure out a 15% tip on the cost of a restaurant bill.” This is indicative of a troubling trend in the disconnect students experience in confidently applying what is learned in math class to real-world situations.
Nationwide, 27% of students in major cities and urban centers have proficient scores on math standardized test in 2019. According to the Pennsylvania Department of Education, approximately 22% percent of Philadelphia students record proficient scores on the PSSAs and Keystones.
The WAC Clearinghouse defines WTL as: "short, impromptu or otherwise informal and low-stakes writing tasks that help students think through key concepts or ideas presented in a course. Often, these writing tasks are limited to less than five minutes of class time or are assigned as brief, out-of-class assignments."
Particularly in math class
Many students face math anxiety which is caused by the negative emotions associated with being tasked with solving a complicated math problem and can be as severe as the trauma seen in PTSD patients.
Students feel as if they cannot express themselves in math class as freely as they can in English and Social Studies classes. This perception is caused by the fact that there can be only one correct answer. Present are also false notions that there is only one way to solve a math problem. In this highly structured environment, creativity can be stifled.
Many math classes focus purely on procedural fluency and getting the correct answer. Without conceptual understanding, and real-world applications, students cannot fully understand what the math means and how it can be applied.
"I'm not a math person" is a phrase uttered by many students when describing their relationship with math. Low levels of self-efficacy can predict lower achievement and a predilection towards a fixed mindset.
According to Harvard researchers, writing, sharing, and listening to stories can increase levels of oxytocin in the brain, which can mitigate levels of anxiety. Writing interesting word problems or stories about the math may have the same effects.
...but not any kind of writing. Creative, expressive, and reflective writing have shown the best cognitive results. These types of writing exercises force students to integrate elements and ideas of the course materials into their work. Copying notes, filling-in-the-blanks and other low cognitive writing tasks do not show this benefit.
Increasing content knowledge on a topic has been shown to be associated with an increase in self-efficacy and so it follows that using WTL strategies that deepen understanding could also have positive impacts on student self-efficacy. As students successfully acquire knowledge, their mindsets may also change, moving closer the desired growth mindset.
The Self-Efficacy Questionnaire for Children (SEQ-C), is a tool that measures academic, social, and emotional self efficacy. All consenting student participants were given this questionnaire, then interviewed using probing questions (based on the SEQ-C) in order to explain students' self-efficacy levels due to WTL.
When reviewing student work, evidence of the three elements of a high-cognitive demand math tasks (mathematical rigor) were evaluated: procedural fluency, conceptual understanding, and real-world application, which became the codes during qualitative data analysis. A second round of magnitude coding was applied to determine the strength of each of these elements of rigor.
Data for each student was triangulated in order to better determine interrelationships between WTL strategies and self-efficacy levels and the corresponding impact on student work.
Every student in the study reported high academic self-efficacy in the SEQ-C and attributed this impact to WTL strategies during participant interviews. Academic self-efficacy however, did not predict student performance as the participants scoring the highest academic self-efficacy on the SEQ-C, did not have the highest scores in the student work samples. This could be explained by the Dunning-Kruger Effect, (cognitive bias), which could be a possible unintended side-effect of WTL. More study is needed in this area.
The study suggests a link between social self-efficacy and class climate. Most students reported valuing learning from each other as a part of the process in sharing their WTL work. During the study, students received frequent positive feedback from peers on their writing. This process of feedback created a low-stakes environment that encouraged participation, student expression, and hearing each others' ideas, and building upon each others' ideas.
All students reported higher levels of emotional self-efficacy on the SEQ-C which according to interview responses, mitigated math anxiety during the study period. According to interviews, students attributed this to their ability to express themselves and be creative in math class which has changed students' feelings and attitudes towards math as a subject. Students reported being better able to cope with anxiety.
In this study, students with the highest self-reported social self-efficacy on the SEQ-C, and in student interviews, also performed at the highest levels on their student work samples, outscoring students with lower self-efficacy, as a whole. The largest discrepancy in student work was found when looking for evidence of conceptual understanding which was highest among students with higher social self-efficacy.
[from my research paper]
“Given that social interaction is central to social cognitive theory, it is not surprising that students with higher levels of social self-efficacy performed at higher levels, and students with lower levels of social self-efficacy performed at lower levels, particularly when considering conceptual understanding - an understanding that could be strengthened by talking about math to others.”
This study suggests that the more students play with math, (by play I mean experiment with different ways to solve a problem, or how to apply mathematical concepts to a variety of situations), the more connected student will feel to the math. Students will also be more willing to take more risks in class.
By bringing social cognitive theory into the classroom, students will operate as providers and builders of their own education and cognitive development within an environment made up of a system of interactions and discussions. This process can be expedited by the teacher by virtue of the cognitive tasks assigned to students and allowing students to productively struggle through solutions, using each other as resources.
Student creations become the means by which their relationship with mathematics is shared with the class. One of the favorite WTL strategies used was creating stories that fit the mathematical concepts being studied. In an exercise I have since coined "flipped math" students create an elaborate, fun, word problem that shows conceptual understanding, create and solve the mathematical equation, represent the math graphically, and then create a visual representation of the problem. Students then share their work with the class, receive feedback, and answer questions about their work.
Writing-to-Learn strategies that deepen student understanding are often vehicles to extend mathematical thinking into other disciplines (Webb's DOK 4). Mathematical comprehension can take on a new level of meaning for students if it is associated with other subject areas which is easily attainable using writing.
[from my research paper]
"This could change the way math classrooms function in the future, leaving more room for creativity in a discipline that is built on structure. Students will be encouraged to discuss their answers, debate topics in mathematics, and explore how to use the math that they are learning into real life situations. Some may argue that the reason math is so structured is that there is only one correct answer. But what this study has shown is that students interact with math in different ways so that there may be more than one way to reach that answer. To keep students from finding their own process would suppress their creativity, retard their self-efficacy, and stifle their motivation."
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