Providing diagnostic feedback about growth is crucial to formative decisions such as targeted remedial instructions or interventions. This article proposed a longitudinal higher-order diagnostic classification modeling approach for measuring growth. The new modeling approach is able to provide quantitative values of overall and individual growth…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

Most children, when presented with the option between two drink items, will choose the one with "more." But what exactly do children consider when they recognize one object as having more than another? Is it the perceived surface area or volume of an object? Depending on children's cognitive development, the aspect of measurement on…

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

More and more schools are acquiring advanced manufacturing equipment. Activities that incorporate the use of this equipment for the purpose of teaching some academic content can either be designed or redesigned for other educational purposes as well. This article describes how the authors extended an activity that was initially designed to help…

This document describes the model used to measure student growth for institutional accountability in New York State for the 2018/19 school year and how three years of student growth results were combined to generate a three-year growth measure called the Growth Index. The Growth Index was first used in 2017/18 to make accountability…

Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…

When the 2017 National Assessment of Educational Progress was released earlier this year, most states learned that their average scores in grades 4 and 8 reading and mathematics remained relatively flat since 2015. More troubling though, students performing at the lowest 10th and 25th percentiles saw a decline in their scores. To confront this…

"The root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25". Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives--epistemic and pedagogical--drawing on Toulmin's notion of…

This document describes the model used to measure student growth for institutional accountability in New York State for the 2017/18 school year and how three years of student growth results were combined to generate a three-year growth measure called the Growth Index. The Growth Index is new in 2017/18 and is used to make accountability…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

This essay articulates the benefits of teacher diversity by illustrating six themes: a) leading for social justice through local and global civic engagement; b) developing an inclusive school culture; c) culturally relevant pedagogy; d) cultural translators and transformers; e) role models; and (f) benefits accrued by White students. The authors…

Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…

This document describes the model used by the New York State Education Department (NYSED) to measure student growth for institutional accountability in New York State for the 2016/17 school year. In 2016/17, growth models were implemented for institutional accountability in Grades 4-8 ELA and mathematics. All models are based on assessing each…

This document describes the model used by the New York State Education Department (NYSED) to measure student growth for institutional accountability in New York State for the 2015/16 school year. In 2015/16, growth models were implemented for institutional accountability in Grades 4-8 ELA and mathematics. All models are based on assessing each…