The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…

Optimization is a component critical to method development. Mathematical modeling of physical phenomena enables an efficient search for the parameters and conditions that optimize methods and systems. Here, optimization of methods in sonoelectrochemistry, electrochemical separations, electrochemical education, and assessment of diabetic status are…

Blocked designs in functional magnetic resonance imaging (fMRI) are useful to localize functional brain areas. A blocked design consists of different blocks of trials of the same stimulus type and is characterized by three factors: the length of blocks, i.e., number of trials per blocks, the ordering of task and rest blocks, and the time between…

A key issue of cognitive diagnostic models (CDMs) is the correct identification of Q-matrix which indicates the relationship between attributes and test items. Previous CDMs typically assumed a known Q-matrix provided by domain experts such as those who developed the questions. However, misspecifications of Q-matrix had been discovered in the past…

In this paper, we examine the development of pre-service mathematics teachers' use of multiple representations during teaching in technology-rich environments. The pre-service teachers took part in a preparation program aimed at integration of technology into teaching mathematics. The program was designed on the basis of Technological Pedagogical…

Refined item digraph analysis (RIDA) is a way of studying diagnostic and prescriptive testing. It permits assessment of a test item's diagnostic value by examining the extent to which the item has properties of ideal items. RIDA is illustrated with the Orange Juice Test, which assesses the proportionality concept. (TJH)

A latent class model for handling the items in Birenbaum and Tatsuoka's study is described. A method to derive the optimal scoring rule when multiple choice test items are used is illustrated. Remedial training begins after a determination is made as to which of several erroneous algorithms is being used. (Author/DWH)

The importance of regression diagnostics in detecting influential data points is discussed, and five statistics are recommended for the applied researcher. The suggested diagnostics were used on a dataset of 24 subjects, and effects were analyzed. Colinearity-based diagnostics and diagnostics for a variety of procedures are discussed. (SLD)

This study developed a hybrid of item response theory (IRT) models and latent class models, which combined the strengths of each type of model. The primary motivation for developing the new model is to describe characteristics of examinees' knowledge at the time of the examination. Hence, the application of the model lies mainly in so-called…

Diagnostic testing confronts several challenges at once, among which are issues of test interpretation and immediate modification of the test itself in response to the interpretation. Several methods are available for administering and evaluating a test in real-time, towards optimizing the examiner's chances of isolating a persistent pattern of…

A newly introduced approach, rule space, can represent large numbers of erroneous rules of arithmetic operations quantitatively and can predict the likelihood of each erroneous rule. The new model challenges the credibility of the traditional right-or-wrong scoring procedure. (Author/PN)

Results of cognitive diagnoses were validated using the rule-space model, and the usefulness of cognitive diagnosis for instruction was demonstrated. Through preliminary studies, 33 stages of knowledge were defined as cognitive diagnoses to be applied to results from a test of knowledge about fractions of seventh and eighth graders (initial test…

Computer-based, criterion-referenced testing can be a humanizing process if it is used for diagnostic and remedial purposes in helping individual students to attain their maximum levels of achievement. The procedure is based upon the proposition that certain classroom situations involving cognitive acquisition, when tested at equally spaced time…

This paper introduces a probabilistic model that is capable of diagnosing and classifying cognitive errors in a general problem-solving domain. Item response theory is used to deal with the variability of response errors. Responses from a 38 item fraction addition test given to 595 junior high school students are used to illustrate the model.…

This paper reports on a project which has developed the general latent class model as a framework for representation of item responses. This framework can be used to represent data in applications such as mastery tests and other kinds of achievement tests, where there is reason to believe that current foundations are deficient. Methods of…