Mathematisation and Irish students: The ability of Irish second-level students to transfer mathematics from the classroom to solve authentic, real life problems.
Lynch, Peggy Ellen (2011) Mathematisation and Irish students: The ability of Irish second-level students to transfer mathematics from the classroom to solve authentic, real life problems. PhD thesis, National University of Ireland Maynooth.
This research considers the mathematical performance of Irish second-level students. The author considers the ability of Irish students to utilise the mathematics learned in a classroom situation to solve authentic, real-life problems. It is a mixed methods study involving testing, structured observations and semi-structured interviews. The research participants are Irish second-year, second-level mathematics students and grade 8 students from a school in the state of Massachusetts (both groups share a mean age of 13.5 years). The students from Massachusetts were involved solely at the testing stage of the data collection process in order to consider Irish performance with regard to mathematical performance from students in a different education system. The observed mathematics lessons provide a valuable insight into the teaching and learning practices used at second-level. The quantitative analysis of the classroom observations highlight patterns and learning theories used in the mathematics lessons observed with interesting results. Two tests were implemented: one traditional in format and based on the Irish Junior Certificate examination; the second consisting of an authentic scenario where students are asked to demonstrate their mathematical comprehension when faced with questions posed in an unfamiliar manner. Statistical analysis of both tests, using a two-sample t-test and a one-way ANOVA, provide the comparison techniques required to consider students performance and highlight various similarities and differences between the test results. The final stage in the data collection process involved semi-structured interviews with the mathematics teachers which provide qualitative data to enrich the findings from the quantitative aspects of the study. The findings provide an interesting insight into the ability of Irish students to solve mathematics when presented in a traditional, familiar context consisting of closed-ended questions compared with their ability to solve mathematical questions that are unfamiliar in style and consist of realistic, open-ended, messy questions. This study suggests that an ability to perform well in a traditional examination does not necessarily illustrate an ability to utilise the mathematics learned for examination success when faced with unfamiliar scenarios. The Irish students involved in this research performed at a significantly higher standard in the traditional test given compared with a lack-luster performance in the realistic test. The same pattern held true for the Massachusetts’ cohort; however the gap in performance between the two test types was considerably smaller for these students. An inability to utilise school-learned mathematics when solving real-life problems is a worrying phenomenon and the author hopes that this body of work will engage educators and policy makers in discussion, thus contributing to progress in this field.
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