Identify different types of mistakes that students make and how they can inform your instruction.
Gina Gresham and Mary Little
Sit beside a fourth-grade teacher being trained to diagnose learning deficits and then develop and implement intervention strategies to help a struggling student become a successful learner.
Holland W. Banse, Natalia A. Palacios, Eileen G. Merritt and Sara E. Rimm-Kaufman
Eliminate obstacles to effective classroom communication with these research-tested suggestions.
Back Talk highlights the learning of one or two students and their approach to solving a math problem or prompt. Each article includes the prompt used to initiate the discussion, a portion of dialogue, samples of student work (when applicable), and teacher insights into the mathematical thinking of the students. This article describes how David used repeated addition to solve a multiplication problem. It reveals his processes of solving the problem mentally, of finding the repeated patterns in a problem context, and of representing the problem with a drawing.
Carolyn M. Jones
Connecting mathematical thinking to the natural world can be as simple as looking up to the sky. Volunteer bird watchers around the world help scientists gather data about bird populations. Counting all the birds in a large flock is impossible, so reasonable estimates are made using techniques such as those described in this problem scenario. Scientists draw on these estimates to describe trends in the populations of certain species and to identify areas for further research.
Patricia A. Sellers
The fourth graders were ready to learn long division; however, their teachers were hesitant to begin the unit—just as they are every year. In a grade-level meeting with the school's math consultant, the teachers voiced their typical concerns. The math consultant was a university mathematics education professor spending a semester of sabbatical working with teachers to find ways to help elementary-aged students get excited about doing math and about learning to make sense of math through problem-solving activities.
Students must actively engage in exploring math. That is why I am always looking for tasks that will allow my students to to explore problems using the Common Core's (CCSSI 2010) eight Standards for Mathematical Practice (SMP). These standards are vital for developing a deepening understanding of math. They allow students to cultivate skills and thought processes that aid in wiring their brains into being deep thinkers and problem solvers. These skills transcend the classroom and are needed to be successful in the world. I also want my students to revisit ideas that we have already touched on and continue to examine.
It is a “read”-letter day when storybooks, thinking strategies, and physical materials can use a splash of whimsy and fun to introduce multiplication facts to third graders.
Thomas E. Hodges, Terry D. Rose and April D. Hicks
A series of diagnostic questions helps this teacher better assess and comprehend the misconceptions of third graders who struggle with multiplication.
Cindy Jong and Robin Magruder
Build on teachers' and students' understanding of division by emphasizing partitive and measurement models and strategies for writing quality division story problems.