The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics--to be called TSM--that is predominant in almost all the school textbooks. By analyzing how the long…

Project Mathematics and English Language Development (MELD) is a sixth-grade mathematics intervention aimed at supporting English learners' (ELs) development of academic language and mathematical knowledge. This article describes the MELD scaffolds and strategies for ELs with multiple examples, as well as survey and focus group data on the…

This article explains the process behind estimating a National Education Cost Model (NECM) and generating from that model projections of per-pupil costs to achieve 2016 national average outcomes (reading and math grades 3 to 8) across all districts in the United States, from 2019-20 to 2020-21. This article is a follow-up to a preliminary report…

Given the important role played by students' spatial reasoning skills, in this paper we analyse how students use these skills to solve problems involving 2D representations of 3D geometrical shapes. Using data from in total 1357 grades 4 to 9 students, we examine how they visualise shapes in the given diagrams and make use of properties of shapes…

Do GCSE and A-level questions that purport to be about consequences actually reward reasoning about historical consequences at all? Molly-Ann Navey concluded that they do not and that they fail to encourage the kind of argument that academic historians engage in when reaching judgements about consequences. Navey decided that it was important to…

The focus of this special edition is students' literacy development over the school years. Drawing on data that includes classroom interactions, analyses of texts, and interviews with students, this edition builds on the seminal treatment of the question of literacy transitions provided in Christie and Derewianka (2008). This paper aims to…

Introduction: Further inquiry into constructs such as creativity, intelligence and scholastic abilities, and understanding how they relate to each other, can promote better understanding of the variables involved in academic achievement. Consequently, the objective of the present study was to examine the predictive value of creativity and multiple…

Research has demonstrated strong relations between spatial skill and mathematics across ages and in both typical and atypical populations, suggesting that a significant proportion of variance in mathematics performance can be explained by variance in spatial skill. Why do these relations exist and how do they develop? Studies of dimensionality in…

Why is the use of letters in algebraic expressions and equations--variables--the source of such uncertainty for students and teachers? The authors studied a sixth-grade classroom and observed that students hold many misconceptions about variables. Some students hold an algebraic view of the equal sign. For them, it indicates an equation and…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

Fully articulating validation arguments in the context of classroom assessment requires connecting evidence from multiple sources and addressing multiple types of validity in a coherent chain of reasoning. This type of validation argument is particularly complex for assessments that function in close proximity to instruction, address the fine…

Mechanistic reasoning, or reasoning systematically through underlying factors and relationships that give rise to phenomena, is a powerful thinking strategy that allows one to explain and make predictions about phenomena. This article synthesizes and builds on existing frameworks to identify essential characteristics of students' mechanistic…

The Common Core State Standards for Mathematics have a widespread impact on children's statistical learning opportunities. The Grade 6 standards are particularly ambitious in the goals they set. In this critique, experiences helping children work toward the Grade 6 Common Core statistics expectations are used in conjunction with previous research…

In this article we examine the profiling of human rights and children's rights in religious education (RE) and its secular alternative in Finland. We use the term 'worldview education' to describe the combination of these subjects. We analyse what kinds of human rights and ethical issues are raised in Finnish worldview education. One specific…

We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely,…