Research has established the importance of play-based experiences for young children's development and learning. Yet, facing the mounting pressure of accountability and standardized testing, some educators have turned to didactic methods of instruction. Guided play (Weisberg et al., 2016) provides a middle ground between play and instruction for…

Argues that mathematics education at the preschool and primary level should emphasize child-centered, hands-on, discovery learning, rather than paper-and-pencil tasks that may be too abstract for young children. Suggests that this holistic approach to mathematics fosters concept development and higher order thinking skills on a broad level. (MDM)

Discusses and provides sample lessons of learning by discovery and weekly problem sets, which are presented as alternative methods for teaching college calculus. Both approaches stress conceptual understanding and guide the students to explore the ideas of calculus in small groups in a computer laboratory setting. (JJK)

Chess experts remember meaningful knowledge in the form of networks or patterns. Applied to mathematics instruction, effective classroom approaches can use investigation to identify patterns or rules. Described are a class activity and a small-group activity to investigate addition of signed numbers and linear relationships. (MDH)

Describes the use and rationale of "Silent Teaching," a teaching technique in which the teacher remains silent as students generate and evaluate hypotheses while trying to understand an as-yet undiscovered concept. (MDH)