M. Alejandra Sorto

Validation of Scores From a New Measure of Preservice Teachers’ Self-efficacy to Teach Statistics in the Middle Grades

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.

Unifying the Algebra for All Movement.

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.

Statistical Training of Central American Teachers

The statistical preparation and training of primary and secondary teachers in two Central American countries, Panama and Costa Rica, are described and compared. Teachers in both countries that graduate with a college degree have several courses in statistics, but the purpose of the courses is to prepare the prospective teachers to do a senior research project and not necessarily to teach the subject. Primary teachers that graduate from a Normal School in Panama have no preparation in statistics.

The Gumball Machine: Linking Research and Practice about the Concept of Variability.

Inspired by the research of Reading and Shaughnessy (2004), we modified an existing lesson from the National Council of Teachers of Mathematics. This lesson, a variation on the “Gumball Task”, gives students the opportunity to explore and discuss the variation which occurs in sampling. This paper describes our experience using this lesson as an enrichment activity in a fifth grade classroom.

Teacher Knowledge and Teaching Practices in Linguistically Diverse Classrooms

This study sought to empirically estimate teachers’ mathematical knowledge and knowledge of teaching linguistically diverse learners, and to shed light on the links that may exist between mathematical and teaching knowledge and classroom practices. Correlational analysis showed that there were strong associations between teachers’ mathematical knowledge and knowledge of teaching linguistically diverse learners. These in turn were strongly associated with rich mathematics and attention to students as learners during instruction.

Validation of Scores From the High School Version of the Self-Efficacy to Teach Statistics Instrument Using Preservice Mathematics Teachers

Recently adopted state standards for middle grades and high school mathematics content have an increased emphasis on statistical topics. With this change, teacher education programs may need to adapt how they prepare preservice secondary mathematics teachers (PSMTs) to teach statistics and require measures related to statistics teaching to assess the impact of programmatic changes and track teacher growth. Using responses from a sample of 290 PSMTs from 20 institutions across the United States, this study presents validity and reliability evidence for the high school version of the Self-Efficacy to Teach Statistics (SETS-HS), which could be used to assess statistics teaching efficacy. Confirmatory factor analysis results via Rasch modeling support the use of three subscales, which exhibit adequate reliabilities and correspond to the three levels in the Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education endorsed by the American Statistical Association. Item and rating scale analyses indicate that the 46 items and the six-category scale employed in the SETS-HS perform as intended.