Small-group assessment methods in mathematics

Abstract

Assessment of students' attainment in courses is often driven by the method of instruction. When mathematics is taught in the traditional style of lectures on theory coordinated with homework on standard problems, the testing is often oriented to reproducing the skills demonstrated by the instructor. If a more collaborative teaching method is used, how does one assess the students' acquisition of problem-solving and mathematical-thinking skills? The paper discusses a team-oriented formal testing method used in a mathematical modelling course taught during the Alma College intensive spring term.

Formative assessment in mathematics for engineering students

“…For example, the class could be divided into teams of three to four students, and one question be presented every five minutes for the duration of a normal lecture. A variation of this is to provide each team with a sheet of questions to work through and some group space to tackle the problems in a given time (separate rooms if practical, corners of rooms more likely) as described by Berry and Nyman (2002).…”

“…Students work either individually or in pairs to produce a short (five -ten minute) presentation on a mathematics topic that was covered earlier in the semester (Carr and Ní Fhloinn 2009). Alternatively, students may present their solution to a homework problem or prior examination question to the rest of the class (Berry and Nyman 2002;Kågesten and Engelbrecht 2007). Including such low-stakes oral mathematics assessments regularly in a student's degree programme may help to prepare them to undertake higher-stakes presentations at a later date (Iannone and Simpson 2015b, 984).…”

Requiring students to justify answer changes during collaborative testing may be necessary for improved academic performance*

“…Collaborative testing, in which students work together to discuss examination questions and arrive at consensus to test answers, is an extension of collaborative learning that has been reported to decrease test anxiety, and increase critical thinking, communication, and team building skills. 5,6 It also has been studied in a wide range of disciplines, including mathematics, 7 nursing, 8 and language training. 9 While examining the effects of collaborative testing on academic performance, 2 chiropractic education studies reported that students involved in collaborative testing achieved higher topical exam scores and course grades compared to noncollaborative testing.…”

Creencias y disposiciones de los formadores de profesores de matemáticas en Chile, respecto del enfoque de formación por competencias en el ámbito evaluativo

“…Por último, desde la mirada de los futuros profesores y de sus formadores, la evaluación se complejiza a partir de las concepciones previas que éstos tienen sobre lo que es la matemática, lo cual tiene incidencia en sus percepciones sobre la enseñanza, el aprendizaje y la evaluación de la misma (Berry & Sahlberg, 1996;Berry & Nyman, 2002, en Hernández et al, 2008.…”