Motivation, critical thinking, and productive struggle are three elements that shall be essential to focus on in the effort to assist a child with a challenge in mathematics to attain success in the subject. Motivation represents the force that encourages human beings to confront and overcome circumstances in life, including those that are or appear challenging and tough. Productive struggle is effort-filled learning that results in the development of grit and creative problem-solving, while critical thinking presents as objective analysis and evaluation of issues in order to form a judgment.
The element of critical thinking in learning describes an individual’s capacity to think rationally and clearly and to understand the logical connections that prevail between different ideas. It involves the individual’s ability to utilize reason actively in learning, rather than being a passive recipient of information. Critical thinking is essentially a disciplined process of the skillful and active application, conceptualization, analysis, synthesis, and evaluation of information that an individual gathers or generates from experience, observations, communications, reflections, and reasoning. One theory that supports and explains the role of critical thinking in learning is constructivism. This theory holds that the experiences of individuals in the environment are vital bases of knowledge. The basic premise of constructivism is the idea that people learn when they acquire experience from what they learn, such that individuals create their own meanings concerning phenomena through their experiences (Suhendi & Purwarno, 2018). The knowledge of learners is their own life, and their lives and styles are essentially their experiences. Constructivism regards learning as the “construction” of knowledge from experience, such that individuals have to apply their cognitive structures to interact with the reality in their environments to create knowledge. The cognitive structure, and hence an individual’s knowledge, alters and adapts according to the individual’s experience of the environment. Constructivism supports and explains the role of critical thinking in learning by emphasizing the role of an individual learner in the acquisition of knowledge. It holds that individuals have to adopt active positions and be responsible for the development of their knowledge (Pritchard & Woollard, 2013). In the case study of a child performing poorly in math, the problem could be a lack of liveliness and personal energy in the subject, which undermines his ability to take an active position and responsibility in the subject. The creativity and liveliness of individual learners is a critical determinant of their level of knowledge. The student’s passivity and lack of energy in math may undermine his capacity to adopt the role of experiential learning and continuous adaptation in the math learning environment.
Examples of research that demonstrates the roles of critical thinking in learning are those by Topolovcan and Matiljevic (2017) and Zain, Rasidi, and Abidin (2012). Topolovcan and Matiljevic (2017) utilized a sample of 703 final grade students in lower secondary education in Croatia to investigate the characteristics and frequency of constructivist learning and its dimensions, including critical thinking. The study illustrated that critical thinking was the most vital aspect of constructivist learning and that critical thinking was especially essential in empowering the students to participate and contribute actively in the learning process and yield personal and practical value of the learning process at an individual level. Zain et al. (2012) explored the impact that the student-centered learning approach had on the learning skills of Mathematics students and teachers at the pre-university level in Malaysia. The study yielded findings that this approach was vital in empowering the students to be analytical and hence in improving their responsiveness and ability to relate to and utilize their experiences in the learning process.
Productive struggle is effortful learning to develop creativity in problem-solving and grit. It leads to the understanding of the content at a deeper level among students and applications of learning to more complex and difficult problems. Productive struggle involves work that challenges students’ weaknesses, is not overwhelming, occurs in challenging assignments and activities, is productive and not frustrating, and influences students to apply metacognitive reflection to process their thinking. It influences students to think about how they learn, rather than only what they learn. In essence, productive struggle is the idea that failing initially while attempting to perform a task can improve learning. In the case study, the problem could be the student’s lack of perception of math as a challenge, or a tendency to give up after initial failure. The understanding that continuous attempts despite initial failure could improve learning and performance could present an attractive challenge for him, thereby improving his math performance. One theory that supports and explains the role of productive struggle in learning is Piaget’s theory of Cognitive Development. Piaget focused on the nature and development of intelligence in human beings, arguing that the commission of many different mistakes among children in the effort to solve problems was an important way of learning. The theory views cognitive development in terms of a progressive reorganization of processes of the mind and knowledge through experience of the environment and maturation (Carpendale et al., 2017). Discrepancies between the knowledge of individuals and their discoveries in their environment are vital influences on learning as they adjust their ideas accordingly. An example of research that demonstrates the role of productive struggle in learning is that by Moller (2016). The researcher used a 4-month experimental research project in children’s kindergartens to explore the relationship between creative imagination and the activities of children as they play with toys. The research indicated that children’s transgressions and negotiations through these transgressions in play activity transformed play and made it more mature and effective. As the children played with others, their transgressions influenced reevaluations of their own and others’ behaviors through reflections and negotiations (such as arguments), leading to learning and transformations in behavior.
Role of Motivation in Learning
Motivation describes the drive for a behavior, such that it stimulates an individual’s behavior towards a model that can facilitate success in the achievement of a goal. It refers to a desire to perform an action and achieve a goal. Motivation involves both the directional (stimulant) and seeking (activity) aspects. It involves the cycle of thoughts influencing behavior and performance drive affecting the thoughts, such that there is continuous stimulation of desire and action towards the achievement of a goal and higher success. In the case study, part of the problem could be the student’s lack of inner satisfaction from performance in math and/or external sources of drive, such as the absence of rewards, praise, or promises of gifts to stimulate engagement in the subject. One theory that supports and explains the role of motivation in learning is behaviorism, which holds that behavior is the outcome of stimuli in the environment or reinforcement/punishment factors. In particular, Skinner’s theory of Operant Conditioning illustrates the influence that stimuli in the environment have on individuals’ behavior (Schreiber, 2016). In this context, reinforcement in the environment (such as rewards, verbal praise, or personal satisfaction in performance) has the potential to strengthen the desired response (Robins, 2012). The lack of these reinforcements in the environment would consequently undermine the individual’s responses. Examples of research that demonstrates the role of motivation in learning are those by Davis et al. (2006) and Tokan and Imakulata (2019). Davis et al. (2006) examined the perceptions of extrinsic rewards from teachers and parents for academic performance among 136 college students. The study indicated that a history of rewards (gifts, TV time, desserts, outings, etc.) from parents related significantly with high motivation and performance in college among the respondents. In a study of 54 students, Tokan and Imakulata (2019) observed that both intrinsic and extrinsic motivation had a significant effect on learning achievements, and that intrinsic motivation had a higher and more sustainable impact on learning behavior and achievement.
This discussion illustrates the importance of focus on critical thinking, productive struggle, and motivation in the effort to help the student with low performance in math. Encouragement of the student’s liveliness in math activities and consideration of math as a positive and fulfilling challenge is important in this effort, while the offer of external stimulants for motivation, such as praise and gifts, would serve to strengthen his desire to perform better in the subject.
Carpendale, J., Lewis, C., & Muller, U. (2017). The development of children’s thinking: Its social and communicative foundations. New York, US: Sage Publishing.
Davis, K., Winsler, A., & Middleton, M. (2006). Students’ perceptions of rewards for academic performance by parents and teachers: Relations with achievement and motivation in college. The Journal of Genetic Psychology 167(2): 211-220.
Moller, S. (2016). Playfulness, imagination, and creativity in play with toys: A cultural-historical approach. International Research in Early Childhood Education, 7(2): 111-128.
Pritchard, A., & Woollard, J. (2013). Psychology for the Classroom. London, UK: Routledge.
Robins, G. (2012). Praise, motivation, and the child. London, UK: Routledge.
Schreiber, J. (2016). Motivation 101. New York, US: Springer Publishing.
Suhendi, A., & Purwano, A. (2018). Constructivist learning theory: The contribution to foreign language learning and teaching. In the 1st Annual International Conference on Language and Literature, KNE Social Sciences and Humanities (pp.87-95).
Tokan, M., & Imakulata, M. (2019). The effect of motivation and learning behavior on student achievement. South African Journal of Education 39(1): 1-8.
Topolovcan, T., & Matijevic, M. (2017). Critical thinking as a dimension of constructivist learning: Some of the characteristics of students of lower secondary education in Croatia. CEPS Journal 7(3): 47-66.
Zain, S., Rasidi, F., & Abidin, I. (2012). Student-centered learning in mathematics – constructivism in the classroom. Journal of International Education Research 8(4): 310-328.