Higher Order Thinking Skills
Questioning for HOTS
Suggestions for HOTS
These question stems from NCTM Professional Standards for Teaching Mathematics help promote students' higher order thinking while requiring students to engage in the standards for mathematical practice and probing for understanding.
Additional HOTS Questioning Resources
A discussion of the characteristics of questions that call on higher order thinking skills and how to infuse math class with open questions and activities targeting higher order thinking skills.
Students at all levels of mathematics should be expected to think about deep questions about the content, and they should be tasked to engage in positive collaborative problem solving activities regularly. This paper explores strategies for developing higher order thinking skills using open-ended tasks, questioning at the right level, "mathematizing" real world situations, requiring students to prove their answers, and engagaing students in mathematics discovery and discussions.
This article from the Mathematics Teacher publication of NCTM emphasizes that educationing students - for life, not for tests - requires the use of open-ended questions to develop higher-order thinking.
Use already-created or develop "Three-Act" tasks.
(Dan Meyer is credited with this idea.)
Incorporate PBL (problem-based learning).
Students meet an actual or simulated situation (based upon a real-world model) at the opening of a unit. The situation is the envelope containing a problem to be solved.
Students must solve real problems, not just learn procedures: teachers coach for growth in metacognition and critical thinking.
Resources for PBL
Use open-ended problems.
Resources for open-ended problems
Fermi questions emphasize estimation, numerical reasoning, communicating in mathematics, and questioning skills. Students often believe that word problems have one exact answer and that the answer is derived in a unique manner. Fermi questions encourage multiple approaches, emphasize process rather than the answer, and promote nontraditional problem-solving strategies. The Questions Library features classic Fermi questions with annotated solutions, a list of questions for use with students, questions with a Louisiana twist, and activities for the K-12 classroom.
Created for students in grades 6 to 8, the site offers math challenges that focus on everyday life, such as how fast your heart beats, what shape container holds the most popcorn, and how much of you shows in a small wall mirror.
Over 2,000 questions are archived. Online tools allow you to search the collection by content area, grade level, and difficulty. The site also shows what students at each achievement level are likely to know and how NAEP questions are scored.
Prepared by the Ohio Resource Center, this collection of problems includes not only test items on proportion but also access to performance data by subgroups of students, a scoring key, and discussion of the tested content.
The Ohio Resource Center collection of intriguing, inquiry-based problems for grades 3-12 can be browsed by topic and grade level.
This resource, available online for a small fee, provides more than 450 open-ended questions. All involve significant mathematics, are solvable in a variety of ways, elicit a range of responses, and enable students to reveal their reasoning processes. The site also offers samples of student answers, a scoring rubric, and additional narrative material that addresses the nature, construction, and reasons for using open-ended items.
The purpose of this site is to prepare middle school students for open-ended problem solving on the Philadelphia standardized tests. Many sample items are given.
Classroom practice questions for grades 4, 5, and 8 as well as algebra, geometry, probability and statistics. In addition to addressing content standards, the questions also address process standards and require students to explain or justify their answers and/or strategies.