Authentic Choice in Mathematical Assessments

Ear to the Ground features voices from various corners of the mathematics education world.

Attitudinal and Mathematical Assessments as Measures of Student Success in a College General Chemistry II Course

This study reports results from administering unannounced attitudinal and mathematical assessments to 118 students, at the beginning of the term, in second-semester general chemistry classes (designed for science majors) at Eastern Michigan University. Testing was conducted during the 2010-2011 school year. The question to be answered was: which is more important in determining student course grades, attitudes toward chemistry and mathematics, or mathematical skill? The hypothesis was that attitudes and mathematical skill equally affect final course grade. A modified Wiebe instrument was selected to evaluate student attitudes toward chemistry and mathematics. To evaluate student mathematical skills, this study employed a mathematics assessment developed and performed at the University of Minnesota, and hence will be called the Minnesota Mathematics Assessment or MMA—a 20-question, multiple choice quiz designed for second-semester general chemistry students. Results were inter-correlated to determine what factors influenced student success. This study found a strong correlation between mathematics attitudes and chemistry attitudes, with a Pearson product-moment correlation coefficient (r) of 0.50. Between course grade vs. either chemical attitudes or mathematics attitudes, the r values were 0.25 and 0.23 respectively, showing weak correlations. The correlation of course grade versus total MMA score gave an r value of 0.35, a moderate correlation. Comparison of the current study's MMA results with those of a previous Minnesota study demonstrates that the MMA is reproducible. The correlation coefficient found for course grade vs. total MMA score was comparable to that found in the Minnesota study. Analysis of the 20-question MMA data resulted in a 10-question subgroup whose r = 0.41. Although some gender attitude differences were found, these did not correlate with course grade.

Not all Equals are Equal: Decoupling Thinking Processes and Results in Mathematical Assessments

One of the greatest challenges in mathematics education is in fostering an understanding of what mathematicians would recognise as “mathematical thought.” We seek to encourage students to develop the transferable skills of abstraction, problem generalization and scalability as opposed to simply answering the specific question posed. This difference is perhaps best illustrated by the famous – but likely apocryphal – tale of Gauss’s school days and his approach to summing all positive integers up to and including 100, rather than just summing each sequentially. Especially with the rise of technology-enabled marking and results-focussed tutoring services, the onus is on the educator to develop new types of question which encourage and reward the development of mathematical processes and deprioritise results alone. Some initial work in this area is presented here.

Young Children Representing Numbers: What Does the Literature Say?

Children are exposed to written numerals from a very young age, and the practice of using written numerals is encouraged in early childhood educational settings. Further, many mathematical assessments are based on young children’s understanding of conventional numerals. Supported by socio-constructivist ideas, this review summarizes a body of research in the areas of symbolic and numeric development in young children, providing a synthesis for early childhood educators and teachers. This work is an invitation to reflect on both the pedagogical principles that underline “pencil-pushing practices” and the conceptual frameworks that support current early childhood mathematics education.