This article describes a learning trajectory on expressions and equations based on the sixth-grade Common Core State Standards for Mathematics (NGA/CCSSO, 2010). A classroom teaching experiment using design research (Lamberg & Middleton, 2009) was conducted. The data was analysed using Corbin and Strauss' (2014) Constant Comparative method and…

Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

To investigate student difficulties in solving word problems in algebra, we carried out a teaching experiment involving 51 Indonesian students (12/13 year-old) who used a digital mathematics environment. The findings were backed up by an interview study, in which eighteen students (13/14 year-old) were involved. The perspective of mathematization,…

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly…

Our paper is an analytical review of the design, development and reporting of learning progressions and teaching sequences. Research questions are: (1) what criteria are being used to propose a "hypothetical learning progression/trajectory" and (2) what measurements/evidence are being used to empirically define and refine a "hypothetical learning…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

This document is an English-language abstract (approximately 1,500 words) of a book containing the results of many years of experimental research aimed at ascertaining the intellectual ability of students in the junior grades to assimilate theoretical knowledge. Chapter one analyzes the problem of the age peculiarities of children. The author…

The faculty learning community project at Howard University involved a diverse group of men and women, tenured, tenure-track, and future faculty across science, technology, engineering, and mathematics (STEM) disciplines. The purpose of the group was to engage in the scholarship of teaching and learning by learning about teaching, reflecting on…