Number Talks: 10-15 minute daily routine taking place during the beginning of lessons that focuses on the development of mental math. Number talks include student-student and student-educator discussions about solving a math problem mentally. These “talks” allow students to engage in discourse with each other, improve mental math strategies and fluency skills, and share with each other more than one strategy of solving a problem.
3-Act Tasks: Whole group student-centered mathematics activity consisting of three distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three. In order to complete a 3-Act Task, students must question, persevere, problem solve, and reason mathematically. 3-Act Tasks allow students to make sense of a problem in a variety of ways - Act 1 gives students an opportunity to generate questions and think critically about the picture or video they see, Act 2 adds to their thinking by providing a piece of information after they begin to ask for it through their noticings and wonderings, and Act 3 provides students with the solution.
Math Sketches: Intended to support students in learning abstract mathematical concepts, math sketches are visual representations of how to determine the solution to a problem. This “move” provides students with an alternate entry point in tackling a math problem through the use of diagrams, drawings, charts, number lines, etc.
Exploration: Student exploration in math gives young scholars the opportunity to make connections to concepts they already know, making way for critical thinking, questioning, and investigating. Teachers may encourage the use of different tools, such as manipulatives and technology, to solve problems. Rather than direct instruction, teachers serve as facilitators of discussion. After exploring concepts, students may come together as a whole or in small groups to discuss their findings.
Productive Discourse: Discourse in the classroom not only allows students to concentrate on sense-making, reasoning of math concepts, and critiquing ideas of others, it also gives teachers the opportunity to reflect on student understanding.
Math Talk Moves: Strategic discussion moves intended for teachers to facilitate classroom discussion that include
Prompt - prompting students to answer a question
Wait Time - providing adequate time for students to respond to a question
Revoice - repeating a student’s answer to emphasize and clarify what the student said
Restate - asking a student to restate what another student has said to ensure that students listen closely to each other
Apply Reasoning - asking students to evaluate, critique, and use each other’s responses and strategies
Here is a site that can be helpful guide for parents to understand the changes in mathematics and suggestions of ways to support their child's learning in math.
https://illuminations.nctm.org/uploadedFiles/Activities_Home/FamilyGuide_FullText.pdf
illuminations.nctm.org
Acknowledgements The National Council of Teachers of Mathematics wishes to acknowledge the extensive efforts of staff member Amy Mirra in gathering the information for and editing this guide.