There has been an ongoing call in mathematics education for students to be engaging in problem solving and collaborative groupwork. \u00a0Although, many instructors find that when they put students in groups, some students seem disengaged and we may start to worry that groupwork is not nearly as motivating or interesting to students as we might expect. \u00a0A natural response at this point is to blame the student for their lack of engagement. \u00a0But, as Alfie Kohn, an author who writes extensively about education and student motivation, often states, \u201cWhen students are off task, our first response should be to ask: What\u2019s the task?\u201d \u00a0Indeed, this is one of the key elements to engaging students in the mathematics classroom; we need to design a good task.<\/p>\n
What makes for a good task? \u00a0Rachel Lotan, a teacher educator at Stanford, coined the term groupworthy task<\/i> to describe what we strive for in task design. \u00a0In a book review (link: http:\/\/ed-osprey.gsu.edu\/ojs\/index.php\/JUME\/article\/view\/240\/164<\/a> ) that I wrote of Mathematics for Equity, I describe groupworthy tasks as follows:<\/p>\n Let\u2019s take a closer look at interdependence, multiple abilities, and multiple representations:<\/p>\n Interdependence<\/b>:<\/strong> If we want students to work together, we need to create a task that actually requires working together to be able to solve it. Moreover, we need to convince<\/i> students that they need to work together. \u00a0If the task is not sufficiently complex and mathematically rich (See: What is a mathematically rich task<\/a>) then there will be no need to work together. \u00a0\u00a0The typical end of chapter exercises in most textbooks are not mathematically rich; merely teaching a skill and having students practice it (so-called \u201cdrill and practice\u201d or more derisively, sometimes called \u201cdrill and kill\u201d) is not sufficient to satisfy this criterion.<\/p>\n Multiple abilities and multiple representations:<\/b> A groupworthy mathematical task also requires students to use a lot of different academic abilities (verbal, written, spatial, visual) along with intra and interpersonal skills. \u00a0Going hand in hand with this, a good task also requires the use of multiple representations\u2014the so-called Rule of Four<\/a> suggests that we need to use graphical, numeric, linguistic, and symbolic ways of representing mathematics.<\/p>\nGroupworthy tasks facilitate students\u2019 interdependence by \r\nforegrounding <\/strong><\/em>multiple abilities and multiple representations, \r\nrequiring students to work <\/strong><\/em>together in solving complex \r\nmathematical problems. These tasks involve <\/strong><\/em>sufficient\r\ninterdependence and challenge; even those students who are <\/strong><\/em>\r\nperceived as \u201cadvanced learners\u201d often experience difficulty \r\ncompleting <\/strong><\/em>the tasks on their own.<\/strong><\/em><\/pre>\n