The emotional state and involvement of students will shape how well and how much they learn. Teaching and learning occur in dynamic environments. In these environments, teachers, students, materials, textbooks, technologies, and social structures are all related and interactive. Learning and teaching occurs across five basic dimensions:. These five elements are known as the dimensions of learning.

They cannot be treated individually; instead, they are dynamically interwoven. They describe the basic elements that must be part of every classroom learning and teaching experience. Attitudes and perceptions affect students' ability to learn. Learning occurs best when the development of positive attitudes and perceptions is made part of every learning task. Students learn to think positively about themselves, their peers, and the material they are learning. Establish a relationship with each student in the class. Practice positive classroom behavior. All rights reserved including the right of reproduction in whole or in part in any form.

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Students learn more easily when they have a desire to learn Discover the laws of learning and how students use the knowledge they acquire in the classroom. New teachers will find this advice particularly valuable, especially for back to school. Teaching Strategies:. Cooperative Learning Curriculum Planning Project Based Learning PBL is a teaching method in which students learn by actively engaging in real-world and personally meaningful projects. Students work on a project over an extended period of time — from a week up to a semester — that engages them in solving a real-world problem or answering a complex question.

They demonstrate their knowledge and skills by creating a public product or presentation for a real audience. As a result, students develop deep content knowledge as well as critical thinking, collaboration, creativity, and communication skills. Project Based Learning unleashes a contagious, creative energy among students and teachers.

Project Based Learning is a teaching method in which students gain knowledge and skills by working for an extended period of time to investigate and respond to an authentic, engaging, and complex question, problem, or challenge. And students will need multiple exposures to the same concept in different contexts before they begin to really understand it.

To foster conceptual change and increase student participation in a lecture course, Sokoloff and Ron Thornton, a physics professor at Tufts University, developed a curriculum built around Interactive Lecture Demonstrations ILDs —physical demonstrations of scientific phenomena that the instructor conducts in class. In the approach used by Sokoloff and Thornton, students first predict what will happen before the instructor does the demonstration. Students next discuss their predictions in small peer groups and explain their predictions to the whole class. Then the class observes the instructor conducting the demonstration.

In the final stage, students compare their observations to their predictions Sokoloff and Thornton, Sokoloff, Thornton, and Priscilla Laws at Dickinson College have also developed a related curriculum for active learning laboratories called Real Time Physics. In these labs, students do experiments supported by real-time, computer-based tools.

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But before conducting an experiment, students make predictions about the outcome and discuss their predictions in small groups. In both the ILDs and the lab activities, the prediction and discussion phases are essential to the process of conceptual change, says Sokoloff. Later demonstrations introduce more complex concepts Sokoloff and Thornton, See Box 3.

Scaffolding provides successive levels of temporary support that allow learners to accomplish a task and reach a level of understanding that they would otherwise be unable to achieve without assistance. The idea is that eventually the instructor will systematically remove the scaffolding supports so that students will use the newly acquired concepts and skills on their own.

For example, students in a physics class may realize that when they hold a book, both the book and their hands are exerting forces, and that the forces are balanced if the book does not move. But if a book is placed on a table, many students fail to understand that an upward force from the table is balancing the downward force of the book. To help students understand.

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## How Students Learn

The cart with very small friction is pulled with a constant force so that it moves away from the motion detector, speeding up at a steady rate. The cart with larger friction friction pad in contact with ramp is pulled with a constant force so that it still moves away from the motion detector, speeding up at a steady rate. Show that cart accelerates in either direction when only one fan unit is on as seen in previous demos.

With both fans on balanced , the cart does not move. Now push and release and observe velocity and acceleration. Cart with very small frictional force is given a brief pull away from the motion detector and released. The cart with very small friction is given a push toward the motion detector and released. A constant force acts in the direction away from the motion detector. The cart moves toward the motion detector, slowing down at a steady rate.

The cart moves toward the motion detector, slowing down at a steady rate, comes to rest momentarily, and then moves away from the motion detector. As part of this lesson about force, the instructor might show students a microscopic model of a rigid object like a table that is composed of atoms connected by spring-like bonds.

The lesson might conclude with an experiment in which a mirror is placed on the table and someone stands on the table; when a light beam is reflected off the mirror and onto the wall, the beam is deflected downward, indicating that the table has been compressed ever so slightly Clement, In geosciences, evidence on the effectiveness of instructional strategies in fostering conceptual change is derived mostly from studies of individual courses during brief periods.

One such study by Rebich and Gautier found large increases in knowledge and a decrease in misconceptions among students who had participated in a three-week mock summit on climate change; this approach used role-playing, debate, and discussion to heighten awareness of the concepts underlying climate change. Although students were able to identify more geological concepts after a sequence of instruction, they showed only small improvement in their ability to integrate those concepts into a framework of understanding.

Chapter 4 describes additional approaches in a variety of disciplines that hold promise for accomplishing this goal. Framing and Solving Problems with Greater Expertise. Learning how to solve problems is an important part of developing competency in science and engineering. Whether in an educational or a professional setting, the ability to solve problems is central to the practice of science and engineering.

Problem solving also comes into play in other areas of everyday life when one needs to reach a goal but is uncertain how to attain it. To solve problems effectively, students must not only have the types of conceptual understanding discussed above,. They must also bring to bear other sophisticated thinking skills that go beyond rote memory. Problem solving is a significant focus of DBER in physics, chemistry, and engineering, and it is an emerging area of study in biology and geosciences.

This line of research has found that students, as novices, tend to approach, organize, and go about solving problems differently than experts. DBER studies have identified the particular difficulties students experience with various aspects of problem solving. In addition, the research literature offers insights about instructional approaches that can help students develop greater expertise with problem solving.

When people set about solving a problem, they construct a model of how they might approach the problem—in their minds and sometimes in a tangible form like a drawing. These models, whether arrived at deliberately or with little forethought, will guide the steps people take to solve it. As novices, students approach problems in ways that are consistently and identifiably different from those used by experts.

Students typically focus unduly on the superficial features of a problem, such as the specific objects, terms, and phrasing used in a question. Experts, by contrast, look at the deeper structure of the problem—the underlying principles that are required to solve it. In one interview study, for example, undergraduate biology students grouped classical genetics problems according to their surface features, such as whether the problem concerned humans or fruit flies and how it was worded, whereas biology professors grouped them according to key underlying concepts, such as the mechanism of genetic inheritance Smith, Students, however, may assume the problems are distinctly different due to superficial variations and may construct very different models of the two problems.

Research from physics, and to a lesser extent from chemistry and biology, supports this finding. Novices relied much more on surface features, such as whether the problem mentions pulleys versus inclined planes versus springs de Jong and Ferguson-Hessler, The drawings of the less knowledgeable participants often more literally resembled the way chromosomes looked under a light microscope and included features like dimensionality and shape that were irrelevant to the solution.

The more knowledgeable participants included chromosome features that were biologically relevant to the problem. Research on human cognition see, for example, Bassok and Novick, has found that for some problems, getting the right mental model of the problem is a key to finding a solution.

Neither the model nor the process is fixed; each influences the other. However, students need to acquire sufficient expertise before they can recognize when they need to change their strategy instead of moving down the same dead ends, as novices tend to do. By focusing on superficial aspects, students miss the essence of a problem, which makes it much harder to solve. This approach is also less efficient. Because experts can recognize structural relationships and patterns, they can tap into their long-term memory about what to do when certain patterns are present and can readily see solutions.

A failure to recognize the most salient features of a problem also makes it difficult for students to apply what they have learned from one problem to new problems that are similar in structure but different in context. This type of knowledge transfer is crucial to becoming a more expert-like problem solver. Another difference between novices and experts relates to how much time they spend creating a model of the problem versus working to find a solution.

Novices often jump immediately to the end goal of a problem and start looking for an equation that might help them solve it. Then they must use another equation to calculate an unknown quantity in the first equation, and so on, until they find an equation that includes all the necessary quantities.

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This burden leaves little room for them to learn general strategies for solving similar problems. It also makes it easy for them to forget crucial elements of the problem at hand. And when they get stuck, they lack strategies to proceed. Experts spend more time analyzing the nature of a problem from the outset and creating a coherent solution strategy. Experts go on to enrich their model of the problem with information from what they know and remember, such as procedures they have used to solve similar problems in the past.

Experts monitor their progress as they solve a problem and evaluate whether an answer is reasonable.

This difference between the working backward approach of novices and the working forward approach of experts has been documented in numerous studies. In physics, for example, research has shown that expert problem solvers typically begin by considering the qualitative aspects of a problem and using that information to decide on a solution strategy before taking the quantitative step of writing. Beginning physics students typically start by writing down equations that match the quantities provided in the problem statement and then work backward to find an equation for which the unknowns are supplied directly in the problem see, for example, Larkin et al.

Research in chemistry education has found that students tend to rely more on algorithms to solve problems—stuffing numbers into a formula that worked with a very similar problem or applying memorized chemical reactions—than on a logical problem-solving process Bhattacharyya and Bodner, Sometimes students can solve problems with these less skillful approaches, even though they have a shallow understanding of the underlying concept see, for example, Gabel and Bunce, In order to work forward, problem solvers must have an organized framework of disciplinary knowledge, as well as experience in solving problems in that discipline.

A command of basic facts and conceptual knowledge is a necessary part of this framework, but other elements are also critical. The framework should include discipline-specific models for approaching problems, as well as criteria for selecting the model appropriate to a context, determining which information in the problem is relevant and which is not, and evaluating whether an answer makes sense Mayer and Wittrock, Taken together, these findings suggest that it is important for science and engineering instructors to help students recognize the need for both a good mental model of a problem and a sound method to solve it.

When students run into difficulties in solving problems, they first need to consider alternate ways of representing the problem and then contemplate possible methods for figuring out an answer. Some instructors ask students to justify why their proposed procedures for solving a problem are reasonable. Toward this end, instructors might provide examples of how a good model can make it easier to find a solution, while a flawed one can make it harder. A body of research indicates that problem-solving skills can be taught and that carefully designed forms of scaffolding appear to benefit students.

The learning gains from any one type of support appear to be small and difficult to measure, however. Research has investigated a variety of strategies for moving students from novice toward expert problem-solving approaches.

### Tips on Fostering Student Achievement

Chapter 4 of this book discusses several broader instructional approaches aimed at improving problem solving and other aspects of science and engineering learning. Using Visual and Mathematical Representations. In every science or engineering discipline, visual, spatial, and mathematical representations are essential tools for communicating and remembering ideas and solving problems. Representations serve several purposes.

They enable people to communicate ideas within a discipline in a shorthand way. By storing information succinctly,. In some cases, representations can simplify the nature of a task. Consider, for example, how most people can estimate proportions more easily by looking at a pie chart than by studying a numerical table.

Representations also assist in problem solving and other types of critical thinking. Some representations are created to analyze a phenomenon in research; these may be quite complicated and targeted mainly at other researchers in the same field. Other representations are intended to convey information to someone else; these may omit the complexities in order to better communicate the central idea Dutrow, Each discipline has its own common ways of representing key concepts that are easily recognizable to experts.

For students to communicate conversantly in a. Just as importantly, they need to understand the concept a particular representation is intended to convey and know why both the representation and the underlying concept are important. Research suggests that when students construct their own representations, in addition to interpreting those produced by experts, they are often more engaged and learn better Ainsworth, Prain, and Tytler, When instructors observe how their students interpret, use, create, and translate among different types of.

When modeling—a pervasive but infrequently taught aspect of engineering—is taught explicitly, students gain a better understanding of how to use models and why they are important Carberry and McKenna, Representations that instructors and other experts can easily interpret may completely befuddle undergraduates, however. DBER studies and cognitive science research highlight the challenges students face in mastering representations. Across disciplines, students often have difficulty interpreting representations and constructing their own from existing information. In physics, a field with a strong research base on this topic, students struggle to interpret representations that are common in introductory courses Rosengrant, Etkina, and Van Heuvelen, Students often misunderstand the quantities and concepts being represented in diagrams, according to some research, and they shy away from using them because they have few opportunities to practice the skills needed to construct diagrams Van Heuvelen, A good example of the difficulties students confront in interpreting and creating representations comes from chemistry, another discipline with a considerable research base on representations.

As an initial step toward understanding the relationships between the molecular structure of a material and its properties, chemistry students are often taught to draw and manipulate diagrams called Lewis structures. Many students struggle with this task see Box 3. In a related vein, many students have difficulty extracting the most salient information from representations.

As in problem solving, novices often have trouble seeing beyond superficial but irrelevant features of a representation to grasp the abstract idea being represented Hegarty, Even when students know the conventions for how a diagram is meant to represent reality, they tend to miss important patterns that experts pick up. Students also have difficulty processing diagrams that violate familiar conventions.

In diagrams where this left-to-right processing makes it difficult to interpret relationships, simply shifting the diagram degrees above the vertical axis can improve comprehension Novick, Stull, and Catley, Similarly, circles and. To understand chemistry, students must understand that matter is made up of atoms bonded together into molecules and that the properties of a material can be predicted from its molecular structure and vice versa.

As an initial step toward comprehending the relationships between molecular structure and properties, students are often taught to draw and manipulate Lewis structures. These diagrams, which are common in chemistry, use atomic symbols, lines, and dots to show the arrangement of atoms and electrons in a molecule and the bonds between atoms. While concise in design, Lewis structures are packed with important information that can be used to predict and explain the physical and chemical structure of a substance Cooper et al.

Knowing how to construct them is an essential skill in chemistry. For chemists, drawing a Lewis structure is second nature. Rules for how to do this are found in most chemistry textbooks. Cooper and her colleagues tracked the processes used by undergraduate students in general and organic chemistry, as well as by graduate students and faculty members, as they drew Lewis structures. Many students, and even a few faculty members, were confused about how to draw valid Lewis structures.

As the number of atoms in the diagram increased from six to seven or more, the percentage of students who drew accurate representations plummeted. The increase from six to seven atoms represents a shift to a molecular structure with more than one carbon atom. Indeed, students had difficulty drawing even one-carbon compounds if they were not given structural clues. But this misconception about symmetry may lead students to produce incorrect structures, such as the one for methanethiol on the right in the figure in this box Cooper et al. The rules for drawing.

Examples of symmetrical Lewis structures produced by students. The rules also include numerous exceptions, but students are not given meaningful criteria for deciding when they apply. Interviews conducted for the study revealed that most students did not understand the kinds of chemical information that can be inferred from Lewis structures.

Based on this research, Cooper and colleagues have developed and evaluated a chemistry curriculum that emphasizes the critical connection between energy changes and atomic interactions as a core concept. Within this curriculum, students learn about key concepts, such as the properties of materials and the different models of bonding, before they are asked to draw Lewis structures. To gain familiarity with the structures involved, students work with physical and computer-based three-dimensional models of simple molecules. After students have practiced going back and forth between two- and three-dimensional representations, more complex structures are introduced.

Once students are able to draw simple structures from a given molecular formula, they move on to the task of decoding the information contained in the formula. Students taught with this curriculum show marked improvements in their ability to create structures, compared with a control group of students Cooper et al. They also do significantly better at decoding the information contained in these structures.

When diagrammatic representations are consistent with these conventions, college students are able to make appropriate inferences more quickly and accurately Hurley and Novick, Undergraduates also struggle to see similarities among different representations that describe the same phenomenon.

In chemistry, for example, students have difficulty translating among alternative ways of representing the same set of relationships, such as videos, graphs, animations, equations, and verbal descriptions Kozma and Russell, Take, for example, the diagrams used in biology to represent the evolutionary relationships among groups of organisms. These diagrams, called cladograms, typically take the form of a tree or a ladder, or in some cases circles nested within larger circles. Biology students have trouble understanding these diagrams and translating among alternative formats that show the same set of relationships see, for example, Novick, Stull, and Catley, A study by Novick and Catley asked students who had taken at least one semester of an introductory biology class for majors to transfer a hierarchy of relationships from the nested circles format to the tree and ladder formats, and from the tree format to the ladder format and vice versa.