The area model for multiplication can be used as a tool to help learners make connections between mathematical concepts that are included in mathematics curriculum across grade levels. We present ways the area model might be used in teaching about various concepts and explain how those ideas are connected.
Alyson E. Lischka and D. Christopher Stephens
Alyson E. Lischka, Kyle M. Prince and Samuel D. Reed
Encouraging students to persevere in problem solving can be accomplished using extended tasks where students solve a problem over an extended time. This article presents a structure for use of extended tasks and examples of student thinking that can emerge through such tasks. Considerations for implementation are provided.
Alyson E. Lischka, Natasha E. Gerstenschlager, D. Christopher Stephens, Jeremy F. Strayer and Angela T. Barlow
Select errors to discuss in class, and try these three alternative lesson ideas to leverage them and move students toward deeper understanding.
Angela T. Barlow, Alyson E. Lischka, James C. Willingham and Kristin S. Hartland
A well-crafted opening problem can provide preassessment of students' fraction knowledge and assist teachers in determining next steps for instruction.
Angela T. Barlow, Matthew Duncan, Alyson E. Lischka, Kristin S. Hartland and J. Christopher Willingham
Examine these three strategies, which offer scaffolds for enhancing students' understanding and lead toward more meaningful investigations.
Angela T. Barlow, Lucy A. Watson, Amdeberhan A. Tessema, Alyson E. Lischka and Jeremy F. Strayer
Carefully select and leverage student errors for whole-class discussions to benefit the learning of all.
James C. Willingham, Jeremy F. Strayer, Angela T. Barlow and Alyson E. Lischka
During a lesson on ratios involving percentages of paint, four research-based criteria are used to evaluate students' mistakes. The takeaway is that painting all mistakes with the same brush can also be a blunder.
Angela T. Barlow, Natasha E. Gerstenschlager, Jeremy F. Strayer, Alyson E. Lischka, D. Christopher Stephens, Kristin S. Hartland and J. Christopher Willingham
Examining two lessons using the same problem illuminates a way that scaffolding can support access to productive struggle.