This systematic literature review was conducted to explore the effectiveness of problem-based and project-based learning (PBL) implemented with students in early elementary to grade 8 (ages 3–14) in mathematics and science classrooms. Nine studies met the following inclusion criteria: (a) focus on PBL, (b) experimental study, (c) kindergarten to grade 8 level, and (d) focus on mathematics or science content. For these studies, we examined: the definitions of PBL used, the components of PBL explicitly identified as salient to student learning, and the effectiveness of PBL. This review found that although there is no consistent definition of PBL, PBL is an effective method for improving K–8 students’ science academic achievement, including knowledge retention, conceptual development, and attitudes. Implications and limitations are discussed.

To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students participated in two 45-minute interviews and completed a written fractions assessment. Students operating with the second multiplicative concept had not constructed fractional numbers, but students operating with the third multiplicative concept had; students operating with the second multiplicative concept represented multiplicatively related unknowns in qualitatively different ways than students operating with the third multiplicative concept. A facilitative link is proposed between the construction of fractional numbers and how students represent multiplicatively related unknowns.

The purpose of the study was to investigate how Lesson Study influences pre-service teachers’ learning to professionally notice students’ mathematical thinking. The initial and last video-recorded discussions were analysed using a qualitative method. Findings suggest that Lesson Study can be useful means to improve pre-service teachers’ noticing expertise in reviewing and planning lessons. However, to maximise the effect of Lesson Study on developing pre-service teachers’ noticing expertise, several modifications need to be made to the Lesson Study protocol, which are discussed.