Tasks, Questions, and Practices
by Chandra Howley Orrill, Associate Professor and department chairperson in STEM Education and Teacher Development at the University of Massachusetts–Dartmouth
The 1st CCSSM Standard is make sense of problems and persevere in solving them. Many teachers will create their own problems for students to solve, and it is important to recognize and monitor three items while doing this. Chandra Howley Orrill writes that tasks, questions, and practices are three very important things to take note of when creating problems.
Tasks are described as the actual problem, and require a certain level of competency in order to solve the problem. There are lower-demand tasks and higher demand tasks. Orrill explains that lower demand tasks are problems that require simple memorization to solve. On the other hand, higher-demand tasks are problems that require students to think outside of the actual question and connect it to other areas of mathematics in order to solve.
Questions are another important component in creating problems. Lower-demand questions are those that can be answered with one-word or short answers. Orrill gives examples of these questions being similar to, "What is your answer?" Higher-demand questions require students to explain their process for finding their answer. Higher-demand questions are more effective in allowing students to make sense of the problems that they are handed.
When using these higher-demand tasks and questions, the processes that students use to solve problems, in turn, become more higher-demand practices. Students must be able to pull sense from the problem, while identifying meaning and determining how to solve the problem. All of these higher-demand practices allow students to make better sense of problems and persevere to solve them.
Additionally, this article provided two tasks, or problem solving examples questions, that could be asked to a group of students. One was considered a lower-demand task, while the other was a higher-demand task. It was interesting to see the difference and how the higher-demand task required much more thinking and cognitive abilities to be used on a student's part.
Reasoning and Sense Making - Expanding our NCTM Initiative
by J. Michael Shaughnessy, NCTM President
The 2nd CCSSM Standard is reason abstractly and quantitatively. To the surprise of many educators, reasoning is not a new concept in education. In fact, books published in the last two hundred years have made mentions to student reasoning, and the importance of young learners actually thinking about their thinking and processes. Even in these dated publications, reasoning was a student-centered activity. In today's classrooms, reasoning is still just as important and useful to students' understanding in mathematics. However, it has grown and created a more insightful and in depth type of reasoning.
Current reasoning practices include the use of student metacognition, discourse, and ample opportunities for students to share and explain their reasoning to peers (Shaughnessy, 2011). All of these are examples that can be used in a classroom to promote reasoning among students during mathematics. Reasoning in mathematics has become so well-known and discussed that half of the CCSSM Standards deal with reasoning in some way. This is a clear indication that reasoning in mathematics is a very important concept, and teachers need to encourage students to practice it.
References:
Orrill, C.H. (n.d.) Tasks, questions, and practices. National Council of Teachers of Mathematics. Retrieved from http://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/Tasks,-Questions,-and-Practices/
Shaughnessy, J.M. (2011). Reasoning and making sense - expanding our NCTM initiative. NCTM Summing Up. Retrieved from http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/J_-Michael-Shaughnessy/Reasoning-and-Sense-Making%E2%80%94Expanding-Our-NCTM-Initiative/
Thanks Kaitlin:)
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