Proportional reasoning in the laboratory: an intervention study in vocational education

Abstract

Based on insights into the nature of vocational mathematical knowledge, we designed a computer tool with which students in laboratory schools at senior secondary vocational school level could develop a better proficiency in the proportional reasoning involved in dilution. We did so because we had identified computations of concentrations of chemical substances after dilution as a problematic area in the vocational education of laboratory technicians. Pre-and post-test results indeed show that 47 students aged 16-23 significantly improved their proportional reasoning in this domain with brief instruction time (50-90 min). Effect sizes were mostly large. The approach of using a visual tool that foregrounds mathematical aspects of laboratory work thus illustrates how vocational mathematical knowledge can be developed effectively and efficiently.

Which Techno-mathematical Literacies Are Essential for Future Engineers?

“…An example of an initiative regarding mathematics in context and use of technology is the design of a software tool to help students learning laboratory techniques in secondary vocational education develop a better understanding of proportional reasoning in dilution (Bakker, Groenveld, Wijers, Akkerman, & Gravemeijer, 2014). In engineering education, model-eliciting activities (MEAs) are increasingly used at the introductory course level.…”

El desarrollo de la competencia matemática en el aula de ciencias experimentales

“…Partiendo de una probeta y una pequeña balanza, los estudiantes pueden determinar las cantidades de agua o sal común necesarias para preparar una solución de, por ejemplo, el 10%. En este sentido podemos destacar una propuesta didáctica que intenta superar las dificultades con las que los alumnos se encuentran para calcular las concentraciones correctas de las soluciones químicas que se les plantean en los ejercicios, relacionando estrechamente conocimiento matemático y conocimiento químico (Baker et al, 2012).…”

Making abstract mathematics concrete in and out of school

“…Such approaches are then also seen as better preparation for the reality of the workplace (e.g., Bakker, Kent, Derry, Noss, & Hoyles, 2008). In addition, vocational education can design approaches and tools which more efficiently develop situated knowledge within the workplace (e.g., Bakker, Groenveld, Wijers, Akkerman, & Gravemeijer, 2012).…”