This 440-page report explores how students in pre-K through grade 8 learn mathematics, with a focus on number and operations, and recommends how teaching, curricula, and teacher education should change to improve mathematics learning. (A 39-page summary, Helping Children Learn Mathematics, is catalogued separately.) The authors identify five interdependent components of mathematical proficiency and describe how students develop this proficiency. The report presents a portrait of mathematics learning: research findings on what children know about numbers before they arrive in pre-K and the implications for instruction; details on the processes by which students acquire mathematical proficiency; what is known from research about teaching for mathematics proficiency and developing proficiency in teaching. Visitors to this website may read the full text online, download a copy (pdf), or purchase a hard copy.

This brief article discusses the importance of young children creating their own informal graphical representations of their mathematical thinking and problem solving. As distinguished from formal recording of a completed process, these early markings and symbols enable children to develop understanding and make meaning as well as communicate their thinking. The article includes a list of references, including the authors' research on which the article is based.

This eight-minute video explains the principles of convex lenses by blending video, animation, and still images. It segments the convex lens into pieces, much like one sees in an optical bench -- triangular prisms at top and bottom, trapezoidal prisms adjacent, and a rectangular prism in the precise middle. Animated ray diagrams show clearly how light refracts at both edges of the convex lens, and bend toward the principal axis. The animation depicts 3 fundamental actions of convex lenses: 1) A ray traveling parallel to the principal axis passes through the principal focus, 2) A ray traveling through the focus will emerge parallel to the principal axis, and 3) A ray traveling through the optical center will emerge undeviated. Designmate is a designer of eContent for K-12 education specializing in 3D and animation to simplify concepts. This particular video is one of a small collection offered for free download.

This blog entry by Keith Devlin highlights the discrepency between instruction and teaching/learning. Devlin points out several examples of instruction and details what teaching should look like. There are two videos embedded in the blog post, one is of a student response and subsequent interview, the second video is an example of online instruction.

This webpage contains the current and archived (UK) National Dyscalculia and Maths Learning Difficulties Conference Newsletters that are put out periodically throughout the year. Each newsletter contains an article by one of the keynote speakers, free resources, and information on further professional development. Additionally, this resource includes a link to subscribe to the newsletters.

This 47-page Practice Guide from the Institute of Education Sciences provides K-12 teachers with specific evidence-based recommendations that can be carried out in the classroom without requiring systemic change. To encourage girls to consider careers in math and science, the guide addresses girls' beliefs about their abilities, the development of their interests in these topics, and building associated skills. The document addresses potential roadblocks for each recommendation as well as possible solutions. Coaches, counselors, and principals may also find the guide useful. It includes an extensive list of references. This Guide supports a companion Doing What Works website, Encouraging Girls in Math and Science (cataloged separately).

In this activity, students study gas laws at a molecular level. They vary the volume of a container at constant temperature to see how pressure changes (Boyle's Law), change the temperature of a container at constant pressure to see how the volume changes with temperature (Charles’s Law), and experiment with heating a gas in a closed container to discover how pressure changes with temperature (Gay Lussac's Law). They also discover the relationship between the number of gas molecules and gas volume (Avogadro's Law). Finally, students use their knowledge of gas laws to model a heated soda can collapsing as it is plunged into ice water.

This article from New Zealand maths contains justifications for teaching geometry in the elementary grades and thoughts on how children learn geometry, including ideas from Piaget and the van Hieles. The article concludes with an example of how adults in a non-school setting would apply the van Hiele stages in an unfamiliar space.

This booklet provides information to guide the improvement of school mathematics from pre-K through grade 8, with a focus on the realm of number. The authors explain five strands of mathematical proficiency and discuss the major changes needed in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system. It answers some of the frequently asked questions regarding mathematics instruction and recommends actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance of working together to create a mathematically literate society. At this website visitors may read the book online, download a free copy (pdf) or purchase a hard copy. This is a 39-page summary of a comprehensive report, Adding It Up: Helping Children Learn Mathematics, which is cataloged separately.

The notion of students’ conceptual coherence is introduced in this thesis to clarify what is meant by conceptual understanding. Students’ conceptual coherence is divided into three aspects: contextual, representational, and conceptual framework coherence. The abilities required by the conceptual coherence are discussed as well as ways of evaluating it in the case of the force concept. A new research-based instructional approach to foster students’ conceptual coherence of the force concept and related kinematics is introduced and validated: it brings together interactive-engagement teaching methods and the research on students' difficulties with the target domain.

The microscopic world is full of phenomena very different from what we see in everyday life. Some of those phenomena can only be explained using quantum mechanics. This activity introduces basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology, especially nanotechnology. Start by exploring probability distribution, then discover the behavior of electrons with a series of simulations.

In a study conducted in modern physics courses, our investigation shows that inappropriate and an excessive number of demonstrations can lead to ineffective results. We carefully observed and recorded the activities done in all lectures in two modern physics classes throughout a quarter and analyzed students' responses to the end of the quarter questionnaires. We found a significant number of students did not recall many of the in-class demonstrations and were confused about the results of different demonstrations they had seen in lectures. In this paper, we will explore the possible reasons for this outcome and discuss implications for instructors who use demonstrations in lectures.

This thesis has three parts: development of theory, development of a learning environment that is consistent with theory, and the naturalistic trial of this environment. First, the focus is primarily on integrating some of the theoretical foundations of neuroscience, cognitive psychology and education. It is argued that, at a fundamental level, they all agree on the basic tenet of human learning: each individual constructs his or her own knowledge; there is no alternative. It is subsequently discussed how this informs teaching, arguing for stronger scaffolding for physics novices, emphasising the importance of prior knowledge with an explanation of why this is essential. Based on this theoretical understanding, a learning aid for first year physics students was developed: Link Maps. These resemble concept maps and knowledge maps, but were developed specifically for physics based on its characteristic integrated knowledge structure. To test the pedagogical effectiveness of Link Maps, they were implemented in Map Meetings - relatively scaffolding tutorials. First year students in four different physics courses were allocated to either Map Meetings or the standard inquiry based physics tutorials. Link Maps were developed for each course, which differed in levels of assumed prior knowledge. Data on students’ tutorial attendance, self-efficacy and examination performance were collected, and qualitative feedback was obtained through interviews and focus groups, short answer questions in questionnaires, tutorial observations by physics education experts and student-staff liaison committee meetings. Triangulation of results revealed that Map Meetings were considered more valuable by the students, both in terms of student attendance and qualitative feedback, had a more positive effect on students’ self-efficacy, and resulted in fewer students at risk of failing the course with the lowest assumed prior knowledge – a result that was borderline significant (p =0.056).

This article examines the reading comprehension strategy known as making connections. It involves linking what is being read (the text) to what is already known (schema, or background knowledge). The author provides links to four online resources that will help readers use the strategy in K-5 science and literacy classrooms. The article appears in the free, online magazine Beyond Weather and the Water Cycle, which integrates science and literacy instruction.

This paper describes the contents of Minds on Physics, an integrated curriculum material for high school physics developed by the Physics Education Research Group (PERG) with the University of Massachusetts and high school teachers. This curriculum is based on an action-oriented constructivist approach. There are six types of materials in the curriculum: (1) student activities; (2) student reader; (3) answers and instructional aids for teachers; (4) assessment items; (5) supplements; and (6) answer sheets. For sample activities or ordering materials from Minds on Physics visit: http://umperg.physics.umass.edu/resources/mop. Six volumes of activities have been published by Kendall/Hunt.

This collection of curriculum materials contains teacher notes, worksheets, and readings dealing with first-year physics concepts. Topic areas include mechanics, sound and waves, and electricity and magnetism. The materials were specifically aligned with teaching methodologies guided by Modeling Theory of Physics Instruction. This item is part of a larger collection of resources and pedagogic materials developed by the Modeling Instruction project at Arizona State University.

Teachers are trained to develop student abilities to make sense of physical experience, understand scientific claims, articulate coherent opinions of their own, and evaluate evidence in support of justified belief. For example, students analyze systems using graphical models, mathematical models, and pictorial diagrams called system schema.

This video-based experiment employs a pendulum to promote understanding of conservation of mechanical energy. Students explore qualitative ideas in the first video, then expand those ideas through analysis of a second, longer video of a stopped pendulum system. Each video includes learning goal and post-experiment questions. This material is from a collection of similar resources designed to have students mirror the activities of scientists to construct and apply knowledge.

This learning cycle features 32 videotaped experiments, organized sequentially for introducing electricity and magnetism. Each video includes learning goal, prior knowledge required, and post-activity questions. Topics include electrostatics, electric charge, conductance, charging by induction, electric field, electromagnetism and induced current, RC circuits, and more. The instructional method is based on cognitive apprenticeship, in which students focus on scientific process by observing, finding patterns, modeling, predicting, testing, and revising. The materials were designed to mirror the activities of scientists when they construct and apply knowledge. See Related Materials for links to the full collection by the same authors and for free access to an article explaining the theoretical basis for this instructional method.

This learning cycle features 12 videotaped experiments, organized sequentially for introducing fundamentals of fluid mechanics and Archimedes Principle. Each video includes learning goal, prior knowledge required, and post-activity questions. The instructional method is based on cognitive apprenticeship, in which students focus on scientific process by observing, finding patterns, modeling, predicting, testing, and revising. The materials were designed to mirror the activities of scientists when they construct and apply knowledge. See Related Materials for links to the full collection by the same authors and for free access to an article explaining the theoretical basis for this instructional method.