Reasoning in mathematics is the means by which students try to make sense (by thinking through ideas carefully, considering examples and alternatives, asking questions, hypothesizing, pondering, and so on) of mathematics so it is usable and useful (NCTM, 2000).
Faded Knowledge is knowledge that is forgotten by your students but can be restored through reasoning with the current content.
Collaborate and Reflect
Click on the button below to interact with your colleagues about this Mathematical Practice.
Weekly Checklist File
Download the checklist for this week by clicking the link below. Once complete, click on the submit button to upload your completed document.
Give a lesson, take a lesson...
Optional: Click the button below share ideas and lessons with your fellow edcuators!
Extend Your Understanding
Watch the video excerpt below to view an example of a teacher engaging students in sense-making and mathematical perseverance.
Fran Dickinson leads a lesson on numeric patterning, helping students to investigate a numeric pattern and to generalize what they see happening as the pattern grows. In this clip, Dickinson describes the importance of individual think time before he asks his students to discuss the relative strength of two different approaches to a patterning task. One pair discusses the numbers within the sample strategy, and Dickinson repeats back their conversation to the whole group, telling his students, “I’ve heard two really good questions about Learner B’s strategy. One was, what are all these 3’s? and Kelcey’s question was, what about this 4? Where’s the 4 coming from?”
This clip is also indicative of Mathematical Practice 1.