Our research includes undergraduate students who major in primary school education. Their academic background is prevailingly in the humanities. This poses specific demands on their mathematics instruction at university. To attract them to their mathematics course and raise its effectiveness, we use a series of activities. Writing assignments…

A first application of multilevel latent class analysis (MLCA) to educational large-scale assessment data is demonstrated. This statistical technique addresses several of the challenges that assessment data offers. Importantly, MLCA allows modeling of the often ignored teacher effects and of the joint influence of teacher and student variables.…

This article describes a type of professional development focused on students' thinking that occurs in middle school mathematics classrooms. This type of professional development is called "Classroom Embedded" and occurs over one or two days in a classroom with middle school students and their teacher. Teachers actively participate in…

Several studies on analogical transfer to algebra word problems have demonstrated that adapting solutions learned from worked examples to nonisomorphic problems of the same type is challenging and that most instructional aids do not alleviate this difficulty. At the same time, various authors have suggested that transfer difficulties sometimes…

We consider designs for conceptual learning where students first engage in pre-symbolic problem solving and then articulate their solutions formally. An enduring problem in these designs has been to support students in accessing their pre-conceptual situated process, so that they can reflect on it and couch it in mathematical form. Contemplative…

This paper analyzes the thought process involved in problem solving and its categorization as creative thinking as defined by psychologist R. Weisberg (2006). Additionally, the notion of insight, sometimes present in unconscious creative thinking and often leading to creative ideas, is discussed in the context of geometry problem solving. In…

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…

Two studies were conducted to examine and compare the construct validity of scores on the Junior Metacognition Awareness Inventory (JMAI) and problem-solving interview protocols. Participants consisted of 183 middle and high school students attending a university summer program for academically talented youth. Study 1 results indicated that JMAI…

The Better Math Teaching Network (BMTN) is organized as a networked improvement community, which is a structured network of researchers and practitioners working together to address a common problem of practice, in this case, how to improve opportunities to increase student engagement in high school mathematics. During the 2017-18 school year, 41…

Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

We tested a method for solving Bayesian reasoning problems in terms of spatial relations as opposed to mathematical equations. Participants completed Bayesian problems in which they were given a prior probability and two conditional probabilities and were asked to report the posterior odds. After a pretraining phase in which participants completed…

One of the subjects that constitute a problem for adult students of mathematics is the understanding of fractions and proportions. These notions are interrelated with proportional reasoning which was the focal point of our study. Using a mixed methods approach, we tried to assess the proportional reasoning of adult students during problem solving.…

In this article, the authors emphasise the importance of purposeful mathematical discussion and using sequences of connected, cumulative, and challenging tasks in advancing students' spatial reasoning in the early years of schooling.

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

This study reports on a way to address twenty-first-century skills in mathematics education by organizing one-day mathematics challenges in the Netherlands. During such a day, students work in teams in school on an open-ended problem which aims to elicit skills like problem-solving, modeling, collaboration, and communication. The framework and the…