After improving enrolment rates significantly, many developing countries such as Peru are facing the challenge to increase learning levels among students. Over the past few years, many researchers have turned to teacher-related variables as a way to better understand classroom processes that may help increase learning levels among students. In this study we analyze one of these, that falls under what Shulman (1986) called Pedagogical Content Knowledge (PCK). Specifically, in this study we analyze one of the areas of PCK which is knowledge of content and students. This was measured through a test where teachers were asked to explain students' mistakes and predict responses in similar mathematics exercises. We explore if PCK is associated with the socioeconomic status of children and if it has an effect on children's achievement. Additionally we analyze which teacher characteristics are associated with higher scores in PCK. The analysis uses the Young Lives longitudinal survey for Peru. We found that students´ socioeconomic status at age one and maternal education were positively associated with their teachers´ PCK by the time students were enrolled in fourth grade, thus depicting a very unequal education system. Furthermore, teachers' PCK was positively associated with student achievement, but only when a threshold for the PCK test was established. For our sample, male teachers, who were younger, and Spanish -speakers had higher PCK scores.

The influential Common Core State Standards for Mathematics (CCSSM) expect students to start statistics learning during middle grades. Thus teacher education and professional development programs are advised to help preservice and in-service teachers increase their knowledge and confidence to teach statistics. Although existing self-efficacy instruments used in statistics education focus on students, the Self-Efficacy to Teach Statistics (SETS) instrument measures a teacher’s efficacy to teach key CCSSM statistical topics. Using the results from a sample of n = 309 participants enrolled in a mathematics education or introductory statistics course, SETS scores were validated for use with middle grades preservice teachers to differentiate levels of self-efficacy to teach statistics. Confirmatory factor analysis using the Multidimensional Random Coefficient Multinomial Logit Model supports the use of two dimensions, which exhibit adequate reliabilities and correspond to the first two levels of the Guidelines for Assessment and Instruction in Statistics Education adopted by the American Statistical Association. Item and rating scale analyses indicate that the items and the six-category scale perform as intended. These indicators suggest that the SETS instrument may be appropriate for measuring preservice teacher levels of self-efficacy to teach statistics.

With the increased use of standardised mathematics assessments at the classroom level, teachers are encouraged, and sometimes required, to use data from these assessments to inform their practice. As a consequence, teacher educators and researchers are starting to focus on the development of analytical tools that will help them determine how teachers interpret learners’ work, in particular learners’ errors in the context of standardised and other assessments. To detect variation and associations between and within the different aspects of teacher knowledge related to mathematical error analysis, we developed an instrument with six criteria based on aspects of teachers’ knowledge related to explaining and diagnosing learners’ errors. In this study we provide evidence of the usability of the criteria by coding 572 explanations given by groups of mathematics educators (teachers and district officials) in a professional development context. The findings consist of observable trends and associations between the different criteria that describe the nature of teachers’ explanations of learners’ errors.

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Summary The least squares method of fitting a line is not one that naturally occurs to students. We present three tasks to understand student views on how lines may be fit.

There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the Algebra for All movement. In light of this movement, there must be a clear consensus about what is taught in the name of algebra. Yet, researchers documented this is not the case. The present research proposes to unify the leading algebra standards and assessment framework documents to identify the key ideas of algebra. The analysis resulted in six key ideas: (a) Variables, (b) Functions, (c) Patterns, (d) Modeling, (e) Technology, and (f) Multiple Representations. Outlined is the research process and resulting unification of existing algebra framework documents, and consideration is given for its uses in educational policy regarding algebra and potential directions for future research.

There is a compelling need to develop an algebra teacher self‐efficacy instrument (ATSEI) as algebra continues to be considered a gatekeeper course for postsecondary educational and career opportunities, which is seen as a crucial piece in closing the achievement gap. This paper reports on the development and validation of the ATSEI, an instrument that measures two domains, Efficacy To Do School Algebra (Knowledge Efficacy, KE‐A) and Efficacy to Teach Algebra (Personal Teaching Efficacy, PTE‐A) along six categories. Four of the categories represented content standards (variables, functions, patterns, and modeling) and two of the categories represented process standards (technology and concrete models, and multiple representations). Through conducting an exploratory factor analysis across two phases, the instrument was reduced and refined from an initial 118 items developed from a curriculum analysis to 36 items that reflected two significant categories, Functions and Technology. The ATSEI measure is validated for in‐service mathematics teachers and thus provides an instrument to examine need and impact in professional development venues. The specificity of the ATSEI allows those working with teachers to be better able to support them in the field and in return positively influence the learning outcomes of the students they teach.