So...what is a task? You've heard me talk about tasks, you will be analyzing them, creating them, teaching them. What even is a task?
So Stein et al. says that "A STEM task has been defined as a single problem or a set of problems that focuses student attention on a mathematical or scientific idea (Stein et al., 1996)."
Ok...clearer? As mud?
I'm going to even add another layer of complication. What is a meaningful/worthwhile task?
I have a list of thoughts. However, I'd like you to build your own list in your blog.
- Are based on sound and significant science and/or math
- Use knowledge of students’ understandings, interests, and experiences
- Develop students’ scientific/mathematical understandings and skills
- Stimulate students to make connections and develop a coherent framework for scientific/mathematical ideas
- Promote communication about science and mathematics
- Promote the development of all students’ dispositions to do science and mathematics.
In effective teaching, worthwhile mathematical tasks are used to introduce important mathematical ideas and to engage and challenge students intellectually. Well-chosen tasks can pique students’ curiosity and draw them into mathematics … worthwhile tasks should be intriguing, with a level of challenge that invites speculation and hard work. Such tasks often can be approached in more than one way … Teachers must also decide what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask to challenge those with varied levels of expertise, and how to support students without taking over the process of thinking for them and thus eliminating the challenge.
… When challenged with appropriately chosen tasks, students become confident in their ability to tackle difficult problems, eager to figure things out on their own, flexible in exploring scientific/mathematical ideas and trying alternative solution paths, and willing to persevere … When students work hard to solve a difficult problem or to understand a complex idea, they experience a very special feeling of accomplishment, which in turn leads to a willingness to continue and extend their engagement with mathematics.
(PSSM, 2000, p. 18)
Here is a game we will play when we take a look at tasks.
If you want to play with some tasks, here is another blog completely around the game PrimeClimb
To do this week:
This week I want you to write about what you think a worthwhile task would be in your own content area of interest?
Share an example of a task. Talk about why you think it is worthwhile.
Our tag for this week is #module-3-worthwhile-tasks
References
NCTM, Professional Standards for Teaching Mathematics, 1991, p. 25
Stein MK, Grover BW, Henningsen MA (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. Am. Educ. Res. J. 33:455-488