Test Design to Assess the Qualities of Science Students' Prior Knowledge

Prior knowledge is a complex variable that greatly determines the outcome of learning of science students. Prior knowledge inherent qualities facilitate or interfere in the process of learning; however it hasn´t always been possible to determine the extent and explicitness of these effects on learning. A test to measure these effects was developed with the intention to discern the specific influence of the inherent qualities of prior knowledge of incompleteness, correctness, misconceptions and the absence of declarative knowledge. This multiple choice test includes topics such as vectors, trigonometry, unit systems and prefix definitions, contents considered to be essential to learn Coulomb´s law for electricity and magnetism course in engineering major. The ultimate goal of this project was to design a test with content validity and determine the reliability of this test using Cronbach´s alpha coefficient with a minimum value of 0.7. Finally we present suggestions that can guide future research and the applicability of this test.

Assessing Authentic Intellectual Work in Mathematics Tasks

This paper reports an analysis of the tasks included in the Mathematical Challenges book. The analysis was based on the proposals of the Authentic Intellectual Work (AIW). The purpose of the study focuses on assessing the potential of the mathematical challenges to promote in-depth and meaningful learning through the connection with different contexts, and other features including purpose, multiple-solution pathways, construction of knowledge and higher order thinking. Participants in this study were 3 elementary school teachers, 2 mathematics specialists and the authors of this paper; they assessed the Mathematical Challenges through a questionnaire based on specific rubrics. The study used a mixed methods approach. The analysis produced two main findings. First, challenges vary in their connections to students' lives according to the context they come from. Second, almost all mathematical challenges are related to the highest levels of others AIW criteria.

Making Links Between Solutions to an Unstructured Problem

In the study described here, teaching resources have been developed to provide students with explicit opportunities to link invariant properties across a range of different solution strategies, and make comparative judgments about the same solutions. After tackling an unstructured problem, students complete, compare and critique pre-designed student responses to the same problem. The framework used to analyze the data focuses on the types of links students may make between responses. The findings indicate students made varied links when completing them. The outcome of these links appeared to be influenced by how students perceived the representation being completed. Students made further assorted links that focused on invariant properties and the comparative validity of the completed responses.

A Project-Based Learning Approach

Mathematical applications have a presence in an engineering environment; in the particular case of mathematical models. A pedagogic theoretical framework that supports various teaching-learning techniques is constructionism; one of these techniques is called Project Based Learning which provides several advantages. This chapter aims to show the experiences during the course of Mathematical Modeling in a context of project-based learning. It will show that students develop general skills of engineering which includes developing the faculties of memory, reasoning and problem solving, teamwork and initiative and of readiness to take risks. Also presents some of the advantages and issues for consideration in relation to its effectiveness as a teaching and learning method.

Financial Literacy

Financial literacy is a combination of financial knowledge, attitudes and behaviors, key for making informed decisions and for solving financial problems. This descriptive study explored the applied, conceptual and procedural financial knowledge of 243 Mexican students via three financial knowledge tests. In addition, these students were surveyed about their financial behavior, their attitudes towards money, and their experience with money using a self-report questionnaire. The study aims to identify financial-education needs and gaps between school levels and systems. Therefore, the analysis focuses on the differences and similarities between two subgroups: (1) students in public and in private education, and between (2) middle school (ages 12 to 15) and high school students (ages 15 to 18). Middle school and high school students differed significantly only in their conceptual knowledge and in their financial experience, while public and private students showed statistical significant differences on their financial knowledge, behavior, attitudes and experience.

Data Literacy and Citizenship

This chapter explores the challenges that emerge from a narrow understanding of the principles underpinning Big data, framed in the context of the teaching and learning of Science and Mathematics. This study considers the materiality of computerised data and examines how notions of data access, data sampling, data sense-making and data collection are nowadays contested by datafied public and private bodies, hindering the capacity of citizens to effectively understand and make better use of the data they generate or engage with. The study offers insights from secondary and documentary research and its results suggest that understanding data in less constraining terms, namely: a) as capable of secondary agency, b) as the vital fluid of societal institutions, c) as gathered or accessed by new data brokers and through new technologies and techniques, and d) as mediated by the constant interplay between public and corporate spheres and philosophies, could greatly enhance the teaching and learning of Science and Mathematics in the framework of current efforts to advance data literacy.

Teachers and Mathematical Modeling

Mathematics cannot be reduced to the use of algorithms. The main objective of teaching mathematics in school is their application in real world situations. Mathematical modeling was born as an answer of this concerned and implies the relation between mathematics and applications. Because of that, teachers need to be correctly training in the use of mathematical modeling in their daily lesson plans. The aim of this study is to propose a methodology for help teachers purchase mathematical modeling as a strategy to teach mathematics. Our methodology is based on the analysis of teachers' conceptions about learning and teaching mathematics and after that promote their evolution. The main characteristic is the collaborative work between teachers and the researcher in cycles of discussion and classes' implementation. The evidence showed that teachers can actually change their conceptions about what is needed for teaching mathematics and design lesson plans using mathematical modeling.

A Look into Students' Interpretation of Electric Field Lines

On Electricity & Magnetism (EM) courses at undergraduate level, the concept of electric field poses one of the most relevant and basic topics, along with the concept of magnetic field. Professors and students may use different diagrams as a tool to visualize the electric field, such as vectors or electric field lines. The present study aims to identify how students interpret and use electric field lines as a tool or resource to describe the electric field. Two versions of a test with open-ended questions were administered in Spanish in a private Mexican university to a random sample of students taking the EM course, and were analyzed with a qualitative approach. It was found that students do not interpret electric field lines diagrams correctly, which may lead to misconceptions. Many students based their answers on the concepts of superposition, force and repulsion.

Argumentation Schema to Analyze High School Students' Scientific Reasoning

This chapter describes how the explicit teaching of an argumentative schema Toulmin argumentative process (TAP) allows the exploration of students' scientific reasoning according to the cognitive model of science (CMS) when immersed in a kinematic activity called The walking man. A qualitative methodology was implemented to acquire, explore, and analyze two sources of data that were recollected from students discourse and a poster generated during the implementation of a kinematic activity. The results found show that it is possible to model students' scientific reasoning after the explicit teaching of TAP and that it also acts as a scaffolding resource for students to promote scientific reasoning cognitive abilities such as observation, data collection, use of representations (tabular, graphical and mathematical equation), creation, analysis and discussion of a kinematic model of the phenomena.

Using Modeling and Simulation to Learn Mathematics

In this chapter, we present a specific approach on how to teach math through mathematical modeling and simulation. The literature review is presented from the Math Education Community and the advantages for the students using this approach focuses on how to apply Math in their professional lives. We also introduce a framework of reference on using matching technology to help the students make some transitions in the modeling cycle. Several examples from a course in an undergraduate program are shown and we develop some conclusions for basic education and for high school level. Previous research studies developed from a qualitative point of view have helped to demonstrate the potential use of this approach for students to achieve better understanding of this science.