As part of the STEAM in Times project, we are convinced that manipulatives are an effective way of teaching mathematics, but what are the benefits and how should they be incorporated into our STEAM lessons?
Some of the leading educationalists specialising in developmental theories, such as Montessori (1964), Bruner (1964) and Piaget (1962), agree that the use of manipulatives supports the development of abstract reasoning (Carbonneau et al., 2016).
Another advantage of manipulatives is that they facilitate connections between abstract mathematical concepts and everyday life (Brown et al. Cited in Carbonneau et al., 2016; Brown, Collins, & Duguid in Belenky et all., 2009; Hawkins, Boggan, Harper and Whitmire cited in Cockett, & Kilgour, 2015). Indeed, by providing manipulatives, teachers create an experience that is more meaningful to students (Stein and Bavolino cited in Cockett, & Kilgour, 2015).
Another benefit of manipulatives that follows from the previous one is that they enable greater engagement on the part of learners and allow them to be more focused on the task (Florence, 2012 cited in Cockett, & Kilgour, 2015). Presenting learners with a task whose usefulness they understand and in which they are active will enable them to be more engaged, motivated and focused (Swirling, Moyer, cited in Cockett, & Kilgour, 2015).
Manipulations also make it possible to present several means of representation and therefore enable better retrieval of stored information (Sweller, Merrienboer, & Paas cited in Belenky et all., 2009) since encoding was able to take place via two channels; the verbal channel and the non-verbal channel (the motor channel) (Clark & Paivio cited in Carbonneau et al., 2016).
Manipulatives are useful ways of meeting the different learning styles of learners. Indeed, they are particularly appropriate for students who primarily have a visual and/or kinesthetic learning style (Sundstorm cited in Cockett, & Kilgour, 2015).
Conditions for implementation:
Smith (cited in Cockett, & Kilgour, 2015, p. 4) states, “There are probably as many bad ways of teaching with manipulatives as there are without”.
Thierry Dias in his book “Manipuler et expérimenter en mathématiques” (cited in Gracom, 2021), details 4 phases for setting up manipulatives in a way that is relevant and effective for learning.
Phase 1: give the pupils time to get to grips with the material freely.
Phase 2 : verbalisation phase. At this stage, all ideas are accepted, and the teacher provides a supportive framework and can stimulate discussion with questions if necessary.
Phase 3: Sorting out the approaches formulated earlier. This phase gives rise to debate, argumentation and validation. The teacher’s role is to lead the debate.
Phase 4: Institutionalising the concepts discovered. This phase aims is to provide all the pupils with an official record of what they have learned.
Dias concludes by making three recommendations to ensure that manipulative activities enable pupils to achieve abstraction.
The manipulation must :
– Raise questions ;
– Create a challenge = manipulation becomes the only way of solving the problem;
– Be part of a complete sequence that ends with a verbalisation of the mathematical concepts learned.
So, are you convinced of the value of manipulations? To help you get started with STEAM manipulations, the STEAM in Times project has provided ready-to-use materials. You will find construction plans and teaching materials to help you incorporate the manipulations into your lessons. You will find them throughout the year on our website. Keep up to date by visiting our website or following our partners on their social networks!
Belenky, D. M., & Nokes, T. J. (2009). Examining the Role of Manipulatives and Metacognition on Engagement, Learning, and Transfer. The Journal of Problem Solving, 2(2). https://doi.org/10.7771/1932-6246.1061
Carbonneau, K., Marley, S., & Selig, J. (2013). A Meta-Analysis of the Efficacy of Teaching Mathematics With Concrete Manipulatives. Journal of Educational Psychology, 105. https://doi.org/10.1037/a0031084
Cockett, A., & Kilgour, P. W. (2015). Mathematical Manipulatives : Creating an Environment for Understanding, Efficiency, Engagement, and Enjoyment. 1(1), 47 54.
GRACOM. (2021). GRACOM : Manipuler pour travailler les notions mathématiques | Portail pédagogique académique. https://pedagogie.ac-montpellier.fr/gracom-manipuler-pour-travailler-les-notions-mathematiques