by Dr Ragnar Purje
Transforming negative attitudes towards mathematics through Responsibility Theory. How often do we hear students declare, “I hate maths”? Equally, how frequently do we hear enthusiastic expressions such as: “I love maths” being announced? Throughout my teaching career, I have rarely encountered students eagerly proclaiming their love for maths. I dare say that this observation and experience are not unique.
There could be numerous reasons for students disliking or even “hating” maths. As Glasser (1986, 1999) explains, individuals have control over their choices, including their attitudes toward learning. Purje (2014) similarly asserts that taking responsibility for learning is an internal process, with students possessing the cognitive ability to shift their perceptions and engagement. This aligns with Dweck’s (2006) findings on growth mindset, which highlight that students’ attitudes toward any subject or task can be transformed through effort and belief in their capacity to improve.
In light of this, I will share the research and the applied empirical application into how Responsibility Theory was applied, which changed students’ negative perceptions of mathematics and personally inspired them to change their thinking and behaviour to embrace the study of maths with joyful enthusiasm, self-motivation and great confidence.
The role of intrinsic motivation in learning
Glasser (1986), in “Control Theory,” asserts that personal attitude and intrinsic motivation are the most significant factors influencing learning outcomes. His research demonstrates that unless students are personally driven to learn, external efforts to motivate them yield limited success. While teachers can offer guidance and encouragement, ultimately, students are responsible for their learning.
If a student has decided that they do not want to work, all one can do is offer ongoing support and encouragement. It is the student who must want to “pick up the pencil and write,” “throw the basketball,” “play the piano,” “open the book and read,” and “want to learn.” The spark of action – and the results that follow – can only be ignited by the student. As Glasser (1986) declares: “We can force…students to stay in school…but we can no more make those students work than we can make the proverbial horse drink even though we tether him to the water trough.”
Great teacher = great results? Wrong
Marwood (2015), writing in the “Guardian) under the title: “Great teacher = great results? Wrong,” reinforces Glasser’s viewpoint. Marwood acknowledges that while teachers are responsible for creating optimal learning environments, the effectiveness of these efforts depends on students’ willingness to learn. He emphasises that learning is challenging and requires substantial effort, repetition, and practice on the part of the student. The fact is that unless the student wants to learn and wants to do the work, the immutable reality is that learning will not take place. Adding to this, Woolfolk (1998) points out that it is the student who must engage in the learning process to benefit from the information being presented. This indicates that students are not only responsible for their learning; they are also the masters of their education and personal destiny. Therefore, according to Woolfolk, the “responsibility and the ability to learn [remains] within the student; [no one can actually] learn for someone else.”
Shifting the mindset and applied motivation to “I love maths”
An unexpected opportunity arose when I became a permanent relieving primary teacher, allowing me to work with various classrooms, from Prep to Grade 6. When I entered the Prep and Grade 1 classes, the teachers asked me to specifically enhance the students’ numeracy skills and knowledge, hoping that this would also lead to greater enthusiasm for the subject. I was happy to oblige, and my experience and success in presenting Responsibility Theory became the conduit for these mathematics classes for the Prep and Grade 1 students.
Crafting success through explicit teaching
My approach aligns with Glasser’s Control Theory (1986), Glasser’s Choice Theory (1999), the work of Woolfolk (1998), plus Fynes-Clinton (2010), citing Masters (2009) who points out that highly effective teachers are the ones who are able to facilitate and manage the learning process for all of the students, and one of the better ways of achieving this goal is through explicit teaching. According to Fynes-Clinton, “[e]xplicit teaching is essential if students are to develop the thinking, reasoning and reflective skills and habits of mind that will enable them to manipulate information and ideas in order to solve problems, make informed decisions and form new understandings.”
Crafting success through sequence learning
Then, there is the research dealing with sequence learning. Starzyk and He (2007) point out that in terms of advancing cognitive, scholarship and skill acquisition potential, “sequence learning is one of the most critical components for human intelligence.” Adding to and further amplifying the importance of sequence learning. Citing Anderson (1995), Sun and Giles (2001), Schneider and Logan (2006), He (2011) emphasises that “sequence learning is presumably among one of the most important components of human intelligence” that is because “most human behaviours are in the sequential format.”
In fact, according to Curran and Keele (1993, p. 189), “humans excel [in] the learning of sequential patterns of behaviour.” This includes but is not limited to, language development, reasoning and planning, speech recognition, the development of writing, the acquisition of all skills, and the advancement of knowledge and creativity in sports, the sciences, the humanities, music and the arts. Sequence learning process should be thought of as being a significant pedagogical instrument in all fields and disciplines where the passing of knowledge and the advancement of skills is taking place (Curran & Keele, 1993).
Crafting success through repetition
Plus, there is the research of Coyle (2009), the author of “The Talent Code,” who refers to the work conducted by UCLA neurologist Dr. George Bartzokis. Coyle, citing Bartzokis, explains that all skills (whether in music, mathematics, or movement- develop through repeated practice, which strengthens neural circuits. This concept, for me, enters the realm of what could be described as neuroeducation. Bartzokis's research, as cited by Coyle, regarding repeated practice confirmed and reaffirmed the value and immense power of repetition and rote learning to me.
The value and immense power of repetition and rote learning
Rote learning, often criticised for its perceived lack of critical engagement, serves as an essential component of foundational education. Research indicates that memorisation provides the necessary groundwork upon which critical thinking and higher-order thinking skills can be developed (Ausubel, 2000).
Establishing complex neural pathways
Without the neurologically established complex neural pathways that develop and consolidate during repeated deep practice (such as rote learning), the cognitive and intellectual capacity for automatic cognitive retrieval of fundamental knowledge, or memory retrieval, is hindered. This increase in cognitive load then impedes complex cognitive problem-solving and the potential for enhancing creative thinking potential (Sweller, 2011). This research indicates that rote learning is not an impediment to deeper learning, understanding, and information retrieval; instead, it could be considered a prerequisite for advancing skills, knowledge, and learning potential (Sweller, 2011).
Essential
Additionally, in fields such as mathematics, language acquisition, and music, rote learning has proven essential. Memorising multiplication tables, vocabulary, and musical scales reshapes the brain in terms of connections and neurological complexities, which contribute to the development of fluency and enable the application of these foundational elements in more complex contexts (Geary, 2005). Furthermore, research by Ericsson, Krampe, and Tesch-Römer (1993) in the area of ‘deliberate practice’ affirms the necessity of explicit teaching, repetition, and structured rehearsal, all of which are crucial for achieving any level of success in all disciplines. This aligns with Bartzokis’s (2004) findings, which also emphasise that repetition and continuous deep practice enhance myelin formation, improving neural transmission efficiency and aiding in the eventual mastery of skills over time.
Neuroscience perspective
Neuroeducational perspectives emphasise that rote learning not only develops myelin but also strengthens synaptic connections, both of which play crucial roles in knowledge retention and retrieval (Coyle, 2009; Sousa, 2017). Encoding information through repetition enables learners to access knowledge swiftly and accurately, reducing cognitive load and enhancing overall academic performance (Paas & Sweller, 2014). The importance of rote learning across all disciplines further enhances its enduring educational value (Ericsson et al., 1993).
Significant benefit of explicit teaching and rote learning
Integrating rote learning with lessons on conceptual understanding creates a balanced educational approach, where rote learning and memorisation act as a foundation for developing, progressing, and enhancing analytical thinking and problem-solving skills (Kirschner, Sweller, & Clark, 2006). Further to this Kirschner, Sweller, and Clark, 2006, with their research titled: “Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching,” inform that while constructivist methods tend to emphasise discovery learning, the reality is that cognitive load theory indicates that novice learners tend to benefit significantly from explicit instruction, structured repetition, and rote learning before tackling complex reasoning tasks (Sweller, Ayres, & Kalyuga, 2011).
Implementing Responsibility Theory and NeuroNumeracy
With the support of classroom teachers, I introduced the Responsibility Theory NeuroNumeracy program, integrating explicit teaching and rote learning and the impact these activities have on changing the brain and behaviours in maths lessons. The methodology involved the following:
• Hands-on Learning: Students worked in small groups using LEGO blocks to move the blocks for the mathematical operations that were presented on the board and then explicitly presented as worked examples for the purpose of understanding the numbers and maths symbols (plus, minus, multiplication and division) that were written on the board.
• Peer teaching also took place. Students who completed tasks early assisted their peers, reinforcing their understanding through the teaching and the learning they were applying.
• All of the lessons involved repetitive engagement, rote learning, question-and-answer classroom processes
Transformation
The program ran for ten weeks, featuring 40 minute sessions in each classroom. Over time, students transitioned from sequential counting to rapid problem-solving, showcasing a remarkable shift in their cognitive processing. A defining moment occurred when students began instinctively calling out the correct answers. When asked how they knew the answer, their response was illuminating: “I don’t know; I just know the answer is” (followed by the correct numerical answer). This indicated a transformation in their neural wiring, which enhanced the brain, mind, and consciousness to provide the insights. This reinforced the principles of brain plasticity, as well as the value of explicit teaching, worked examples, and rote learning.
Declarative and procedural knowledge
Woolfolk (1998), differentiates between declarative knowledge (knowing that something is true) and procedural knowledge (knowing how to do something). Through the Responsibility Theory NeuroNumeracy program, the students developed both forms of knowledge, leading to increased confidence and enthusiasm for mathematics. Within a few weeks, the students were voluntarily regularly shouting the following mantras with glee: “I love maths,” “I am working hard,” and “I’m an excellent student.” These mantras were part of the lessons that were taking place.
The power of self-empowerment
The success of the Responsibility Theory NeuroNumeracy program highlighted a crucial truth: self-empowerment is the key to learning. When students recognise that they have control over their learning processes, they become active participants in their education. By shifting the narrative from “I hate maths” to “I love maths,” we can cultivate a generation of confident and motivated learners. Through the integration of cognitive neuroscience, the Responsibility Theory, explicit teaching, worked examples, repeated practice, rote learning, and the NeuroNumeracy program, the empirical evidence supports the hypothesis presented here: we can transform mathematics education, ensuring that students develop not only numerical proficiency but also a self-empowering mindset and the enthusiasm for a self-motivated scholarship necessary for lifelong learning and success.
Dr Ragnar Purje is an Adjunct Senior Lecturer in the School of Education at CQUniversity, and the author of Responsibility Theory. With the support of Professor Ken Purnell (Head of Neuroscience at CQU), Dr Purje presents lectures to preservice graduate teachers about Responsibility Theory.