Different types of open tasks can be used as a tool to promote rigorous student mathematical discourse and considerations for facilitation.
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Let’s Give Them Something to Talk About
Nicola M. Hodkowski and Carolyn Carhart-Quezada
Problems to Ponder
Chris Harrow and Justin Johns
Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.
Reconsidering Mathematical Authority
Michael D. Hicks, Jessica Pierson Bishop, Christina Koehne, and Mai Bui
Who has mathematical authority in your classroom, and what does authority look like? Find out different ways you can help students gain authority.
Build It! The Rectangle Game
Theresa Wills, Jennifer Suh, Kate Roscioli, Amanda Guzman, Jennifer Everdale, and Sandra Lee
Discover technology-enhanced, game-based tasks and student generalizations.
Construct It! Intersecting Language and Mathematics with Interlocking Cubes
Basil Conway IV and Marjorie Mitchell
Students learn to build their own numbering system by recognizing and identifying patterns with interlocking cubes in different place values.
Developing Multilingual Learners’ Mathematics Reasoning and Register
Richard Kitchen, Libni B. Castellón, and Karla Matute
By examining some of Ms. Hill’s instructional moves, we demonstrate how a fifth-grade teacher simultaneously developed her multilingual learners’ mathematical reasoning and mathematics register.
Exploring Prospective Teachers’ Development of the Cartesian Form of Complex Numbers
Gülseren Karagöz Akar, Merve Saraç, and Mervenur Belin
In this study, we investigated prospective secondary mathematics teachers’ development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written artifacts from these teaching sessions, and their answers to pre-and-post written assessment questions. Results point toward prospective teachers’ improved meanings regarding the definition of complex numbers and the algebraic and geometrical meanings of the Cartesian form of complex numbers. Implications for mathematics teacher education include providing specific tasks and strategies for strengthening the knowledge of prospective and in-service teachers.
Let’s Be Flexible
Clayton Edwards and Rebecca Robichaux-Davis
Problems to Ponder
Chris Harrow and Justin Gregory Johns
Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.
Advancing Agency Through Conjecturing
Kristin Doherty
Support students in conjecturing in ways that can promote their agency in the learning process.
