This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times "something" (i.e., "2i" is an even number),…

To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…

A study of pre-service primary school teachers' content knowledge regarding real numbers related to infinity, i.e., division by zero and denseness of the real number line, was conducted at a Swedish university. Data were collected twice during the respondents' teacher education using questionnaires and interviews on both occasions. The data were…

Research Findings: The aim of this study was to investigate U.S. preschool teachers' math teaching knowledge in a specific content domain: counting and numbers. One hundred in-service and pre-service teachers participated in the study; they completed a questionnaire that is composed of learning scenarios and scenario-based math teaching questions.…

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition,…