A Cognitive Approach?
A lot of mathematical learning research, particularly in the UK, involves a cognitive approach to learning. A behavioural approach may be linked to alleviating maths anxiety (most of the time – a cognitive approach may be taken to adjust thought processes) but the process of conceptualisation is typically explained through a cognitive approach (i.e., understanding what is happening in a thought process and how pedagogy can influence it). Li et al. (2020) refers to cognitive activation as an instructional practice that encourages students engage in co-constructive and reflective higher-level thinking to develop an elaborated, content-related knowledge base. They cite a variety amount of literature that found cognitive activation is associated with students’ mathematical achievements.
What is Cognitive Activation?
Li et al. (2020) cites Lipowsky et al. (2009) who summarises cognitive activation into three elements:
- Conceptual Understanding
- Where a teacher emphasises the connections between facts or ideas which activates a pupil’s prior knowledge.
- Cognitive Level of Student’s Activities:
- These refer to the tasks and problems that place higher cognitive demands on students (i.e., challenges and reasoning opportunities).
- Quality of Interaction and Participation:
- A discourse (conversation) that involves argumentation (debate), explanation and defence – i.e., ‘prove it’ questions, ‘always, sometimes, never’, ‘true or false’ – all of the reasoning terms we have understood as maths teachers.
Essentially, Li et al. (2020) emphasises a need for challenge for pupil’s to engage in cognitive activation. However, this is where our teacher judgement comes in; the last thing we want is cognitive overload: something too challenging that overwhelms a child – this normally results in (if repeated over time and not consulted) maths anxiety.
What did they find?
They investigated the relationship between mathematics self-efficacy, cognitive activation and achievement along with socioeconomic status (SES). They found mathematics self-efficacy mediated the relationship between cognitive activation and mathematics achievement.
This means, if someone feels good about themselves with maths, they will approach a challenge and engage in cognitive activation, which leads to their achievement. Li et al. (2020) continue: the full mediating effect of mathematics self-efficacy implied that the frequent use of cognitive activation strategies in mathematics classrooms can be a positive predictor of students’ affect outcomes (their self-efficacy).
The study also highlighted the importance of filling the gap between low- and high-SES students and classes – this is typically done through formative assessment techniques in lessons and effective intervention strategies.
How does this help me in the classroom?
Li et al.’s (2020) implications for educational practice are as follows:
- Use cognitive activation instruction strategies:
- This could be through ‘what if’ questioning and reasoning starters (‘prove it’, ‘always, sometimes, never’, ‘true or false’ etc.)
- These should activate prior learning to help children make connections.
- Encourage content-related discourse
- Engage in a debate (argumentation) with the pupils, be the ‘devil’s advocate’ where you ask a child to prove your answer incorrect. Argue against them (as if you have the misconception)
- Teaching lower SES pupils with cognitive activation strategies
- The research shows that more cognitive activation instruction promotes their mathematical self-efficacy and achievement. This is necessary as the research suggests it is unlikely they receive this input type at home.
This shows that mathematical learning isn’t just through rote. It is developing a new mindset and promoting a new approach towards problem-solving. This can be applied to different conceptual areas of the curriculum.
Li, H., Liu, J., Zhang, D., & Liu, H. (2020). Examining the relationships between cognitive activation, self-efficacy, socioeconomic status, and achievement in mathematics: a multi-level analysis. British Journal of Educational Psychology. doi:10.1111/bjep.12351
NCETM Resources – https://www.ncetm.org.uk/resources/
NRich Resources – https://nrich.maths.org/
White Rose Resources – https://whiterosemaths.com/resources/
Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., … Tsai, Y.-M. (2010). Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress. American Educational Research Journal, 47(1), 133–180. https://doi.org/10.3102/0002831209345157
Faust, M.W. (1996). Mathematics anxiety effects in simple and complex addition. Mathematical Cognition, 2(1), 25-62. https://doi.org/10.1080/135467996387534