This article is about utilizing the process of building and exploiting models as a framework for inquiry in mathematics education research. We introduce and discuss a model of such a process and compare this model with key methodological features of design research in mathematics education. We argue that despite several communalities, educational…

Given the challenges of scaling up content-related professional development (PD), the PD facilitators have gained increasing attention in PD research. In this mainly programmatic and structural article, we try to systematize existing research strategies which take into account the multifaceted and multi-level structure of PD research. We discuss…

Excluded-volume interactions are ubiquitous to modeling the average size of polymers in solution. This paper shows how simulations can be used by students to explore the emergence of mathematical scaling relations from excluded-volume interactions. Simulations provide robust visual representations of the system, and can be used to investigate a…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

The teaching of mathematical modeling to undergraduate students requires that students are given ample opportunity to develop their own models and experience first-hand the process of model building. Finding an appropriate context within which modeling can be undertaken is not a simple task as it needs to be readily understandable and seen as…

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of…

This package contains four FORTRAN 77 programs for Markov Model based learning experiments. One program estimates the likelihood of a one-stage learning model, another delivers estimates for a two-stage learning model. The third and fourth were designed for hypothesis testing the parameter differences between and within experimental conditions,…

This paper describes a PASCAL program that computes both different types of transitions and learning statistics suitable for learning experiments in which a two-stage Markov model is used. The frequency counts of the different transitions are used for estimating the parameters of the two-stage Markov model. (Author/LMO)

Autonomously developing organisms face several challenges when learning reaching movements. First, motor control is learned unsupervised or self-supervised. Second, knowledge of sensorimotor contingencies is acquired in contexts in which action consequences unfold in time. Third, motor redundancies must be resolved. To solve all 3 of these…

Describes similarities and differences between modeling cycles and stages of development. Includes examples of relevant constructs underlying children's developing ways of thinking about fractions, ratios, rates, proportions, or other mathematical ideas. Concludes that modeling cycles appear to be local or situated versions of the general stages…

To examine how conceptual knowledge about fraction magnitudes changes as students' learning progresses, 5th and 7th-grade students were asked to solve fraction magnitude problems that entailed finding a fraction between two given fractions and then to evaluate solutions for similar problems that were modeled for them. When the given fractions…

Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

Describes and evaluates a learning model for information filtering and selective dissemination of information which is an adaptation of the generalized probabilistic model of information retrieval. The model is based on the concept of uncertainty sampling that allows for relevance feedback both on relevant and nonrelevant documents. (Author/LRW)

Building Blocks is a National Science Foundation-funded project designed to enable all young children to build a solid foundation for mathematics. To ensure this, we used a design and development model that drew from theory and research in each phase. Our design process is based on the assumption that curriculum and software design can and should…