Chapter 1: Higher-Level Thinking and Applications to Physics Teaching

Professional and hidden physicists rely on cognitive abilities that emphasize constructing knowledge, evaluating arguments, and developing new models that can be applied and tested. While practitioners are steeped in the habits of mind of higher-level thinking, many students in physics courses have not yet mastered these kinds of thinking skills. With intentional practice and repetition, however, such skills can be developed quite effectively at all levels of the physics curriculum.

To produce materials for use in classrooms, a general understanding of cognitive thinking is needed. For our work here, the levels of cognitive thinking (and recent modifications), as specified in Bloom's taxonomy, are appropriate and are described. Later, various techniques, exercises, and examples are presented for use throughout the physics curriculum. Emphasis is given to the highest levels of thinking—analyzing, evaluating, and creating. Instructors are encouraged to incorporate higher-level thinking activities into their classrooms and laboratories to prepare students for a complex and ever-evolving world.

Building higher-level thinking skills has wide implications for students’ personal enrichment and their career development. In a world in which information (and misinformation) must be critically evaluated, the ability to apply higher-level thinking is crucial for citizens in the 21st century. In addition, employment in the 21st century demands that workers possess higher-level thinking skills to thrive in fast-paced and everchanging workplaces. Students who develop these skills as part of their educational background are in high demand as workers and are prepared to participate in society as informed citizens.

The development of higher-level thinking as proposed in these chapters will focus primarily on qualitative solutions to problems with some emphasis on building numerical arguments. Many other contributors have written quantitative problems for the physics education community; thus, these kinds of examples are already widely available. Besides improving higher-level thinking, the exercises discussed here are designed to expand students’ communication skills.

For reference, we will be using higher-level thinking and critical thinking interchangeably throughout the writing here.

In the late 1940s and early 1950s, several conferences were organized by educators to provide structural foundations to learning. From those meetings, several handbooks were written on educational goals and objectives. Along with these handbooks, a hierarchical model was developed to classify educational learning objectives. This model became known as Bloom's taxonomy after Benjamin Bloom who chaired the committee of educators who developed it. The original knowledge-based version of Bloom's taxonomy consists of the following levels: knowledge, comprehension, application, analysis, synthesis, and evaluation.

In the more traditional application of Bloom's taxonomy, learning progresses linearly from one level to another. Learners first master the knowledge and then use it at higher and higher levels until they are able to evaluate information. Evaluation typically refers to the ability to make judgments about information, the validity of ideas, or the quality of work. Over time, educators have come to embrace a more fluid style of learning and thinking in which learners move between the various kinds of thinking. A newer version of Bloom's taxonomy was established in 2001; the levels of cognitive thinking include: remembering, understanding, applying, analyzing, evaluating, and creating (Fig. 1.1).

One of the goals here is to encourage teachers to design learning activities that promote development of higher-level thinking in their courses. Assigning these kinds of questions and prompts ensures that students develop the skills necessary for success in the 21st century. Abilities to think broadly and to critique arguments are essential in a society characterized by change.

Following this chapter on background, general taxonomy, and examples, the remainder of the book addresses higher-level thinking throughout the undergraduate physics curriculum. Various chapters provide strategies for implementing higher-level thinking into the physics curriculum and suggest examples of assignments and projects. In some cases, critiques of student answers are discussed and grading rubrics are included.

The ability to recall information is referred to as remembering. Remembering in the physics curriculum often focuses on retaining information, such as physical concepts, theories, and laws. Once information is retained, it can be used to explain observations and phenomena and, ultimately, to create new models, experiments, or inventions. Thus, basic knowledge is often the foundation for developing higher-level thinking, such as understanding and applying.

In a more integrated approach to learning, the process of remembering is combined with other levels of thinking to solve problems. As knowledge of concepts, principles, and theories is gained, learners begin to use that knowledge even before it is completely retained. The act of applying knowledge before it is fully mastered reinforces remembrance.

Multiple levels of thinking can be combined to develop more sophisticated solutions to problems. For example, as knowledge is acquired, it is applied to familiar situations. As students gain experience in application, they begin to create new knowledge through developing new products or inventions.

The language of remembering typically uses the words: finding, naming, retrieving, describing, listing, and recognizing.

1. Describe Newton's laws of motion.

2. Name the fundamental element responsible for life on Earth.

3. List the three main methods of heat transfer.

4. What are the essential steps in charging a metal dome by electrical induction?

5. Name and describe the physics principle responsible for electric generators.

6. Describe acoustic resonance and give an example.

7. State the first law of thermodynamics.

8. Describe how total internal reflection occurs.

9. What is conservation of mechanical energy?

10. Name the conservation law that applies to all collisions.

The ability to explain ideas or concepts refers to understanding. At the understanding level, practitioners can relate information to others in meaningful ways and explain what is happening in various scenarios. Understanding often begins by learning how physics concepts and principles explain the blueness of the sky or how a telescope works. As students improve their skills, understanding principles can translate into applying, analyzing, evaluating, and creating.

As an example, suppose that someone were to give an explanation based on incorrect principles or maybe even non-scientific theories. A student skilled in remembering and understanding can dissect the argument (analyzing) and then critique its merits (evaluating). Once evaluated, the argument is either logical (and, therefore, valid) or faulty. If a fallacy is found, skilled learners are able to propose alternative arguments that are reasonable and valid.

The language of understanding typically uses the key words: explaining, classifying, interpreting, summarizing, and paraphrasing.

1. Summarize the law of conservation of angular momentum.

2. Explain how a simple heat engine works and how its efficiency is determined.

3. What method of heat transfer is most important for an outside wall on a house? Explain.

4. Explain the concept of inertia for a body moving in deep space with no forces acting on it.

5. An observer notices that when a diver tucks, their angular speed increases. What principle describes this observation? Justify your answer.

6. Classify the forces acting on a block being pulled along a tabletop as field or contact forces.

7. In your own words, summarize Archimedes principle.

8. Paraphrase the work-kinetic energy theorem.

9. Classify nuclear collisions as elastic or inelastic and explain your reasoning.

10. Distinguish between infrared and visible electromagnetic waves.

Applying is characterized by the ability to utilize information (concepts, principles, and theories) in other familiar scenarios. Those who are competent in applying knowledge recognize what principles and concepts are important and employ that information in appropriate ways.

In the study of physics, applying knowledge often refers to using scientific equations to solve numerical problems. Numerical problem solving generally requires identifying given and unknown quantities, identifying the physics principles and equations needed, and devising methods for solution. Students often struggle with knowing what the problems are asking and what physics to apply. With practice, however, they can greatly improve their skills in numerical problem solving.

In other contexts, applying refers to using or implementing physics principles in familiar situations to address problems. Activities here focus on developing solutions or responses by incorporating knowledge and understanding of physics.

The language of applying typically includes key words, such as implementing, using, executing, and solving.

1. Using laws of motion, what causes a basketball to bounce as it strikes the ground?

2. A car traveling at 25.0 m/s begins braking so that the magnitude of its acceleration is 1.30 m/s². Determine whether the car can come to a stop before striking a barrier 250.0 m directly in front of it.

3. The magnetic field at the center of a solenoid depends on the current as depicted by the data in Table 1.1. From these data, find the magnetic field when the current is 4.0 A.

4. A ball of mass 0.20 kg is released from rest at a height of 1.5 m above the floor. After colliding with the floor, the ball bounces to a height of 1.2 m. Compare numerical values of the momentum before and after the collision.

5. A tank of water open to the atmosphere is filled to a height of 18.0 m relative to the bottom of the tank. Determine the speed of water exiting a small hole near the bottom of the tank.

Analyzing refers to breaking information into parts and determining how those parts contribute to our understanding. Analyzing also examines how quantities are related to one another and how those relationships contribute to knowledge.

Laboratory work in physics often focuses on dissecting data and looking for relationships between physical quantities. As relationships are established, models (and ultimately theories) are confirmed, modified, or developed as experiments demand. This ongoing process of examining relationships is central to the enterprise of science.

The process of analyzing naturally leads to making hypotheses and critiquing arguments, proposals, and designs. This level of thinking is referred to as evaluating and is critical for discerning whether or not a claim is valid. Given our constant inundation with claims and counterclaims, evaluating information and data is essential for an informed citizenry—not to mention practicing scientists and technical workers.

The language of analyzing usually includes key words, such as comparing, organizing, deconstructing, and interrogating.

1. While tuning a flute, a professional player extends the length of the instrument by 0.5 cm. Was the instrument sharp or flat when the flutist began the tuning process? How do you know? Give your reasoning.

2. Two pouches with the same shape and volume contain slightly different concentrations of salt as saline solutions. Container A has a higher salt concentration and is hung from height h, while Container B is hung from the same height. Compare the pressures in the bottoms of the two containers.

3. A siren from an emergency vehicle produces a frequency of 1150 Hz. When at rest near the side of the road, an observer hears a frequency of 1200 Hz coming from the vehicle and 5.0 s later, the perceived frequency is 1100 Hz. What happened during the 5.0 s interval? Include your reasoning.

4. As part of a strength and fitness program, a gymnast adds several kg of muscular mass to her arms and legs. Assess how this change affects rotational motions of the gymnast in the floor exercise where rotations in the air are integral to outstanding performances.

5. In a passive solar house incident radiation from the Sun passes through a transparent medium (glass) and strikes an inner wall, known as a Trombe wall. The Trombe wall has holes (slits) near the top and bottom and is made of thick concrete. Discuss why thick concrete is used and why slits are placed in the walls.

6. A public statue with a broad base has just begun to lean without falling. City officials hire you as a consultant and task you with providing an assessment. Your assessment must include the kind of monitoring needed for public safety and your reasoning.

Evaluating refers to critiquing information to develop solutions, make decisions, or justify courses of action or decisions. Scientists constantly evaluate data and information as they engage in scientific methods that emphasize hypothesizing and experimenting. Likewise, informed and engaged citizens vet data and information quite regularly.

One of the hallmarks of evaluating is the ability to examine arguments for flaws and/or gaps in logic. Flaws in arguments often lead to faulty designs and, in worst cases, disastrous effects. In my hometown of Kansas City, MO, a skywalk collapsed in 1981 due to changes in design that were not critiqued properly to discover their basic flaws. Evaluating also includes the validation of arguments to advance scientific and technical progress.

Evaluating data and information often leads thinkers to develop designs, models, and knowledge. In these cases, evaluating contributes to the highest level of thinking known as creating. Thus, multiple levels of thinking are pursued together in order to solve complex and demanding problems.

The language of evaluating typically uses the key words: checking, hypothesizing, critiquing, and experimenting.

1. Shipping experts responsible for operating a large ship realize that the waters in which they will be sailing are saltier than usual. To maintain the same water level on the side of the ship, these experts suggest decreasing the load of the ship. Evaluate whether or not their proposal is reasonable, starting with arguments that the waters in which they will be sailing are saltier than usual. Also, propose an alternative solution if the one suggested is flawed.

2. According to designers, a large inductive load in a circuit is causing significant impedance so that currents do not reach their desired values. Engineers propose to add an inductor in series with the rest of the circuit to solve the problem. Critique the engineers’ proposal and suggest an alternative solution if their solution is untenable.

3. When certain trucks pass over potholes in a road just before entering a bridge structure, the bridge is observed to bounce up and down more than usual. Hypothesize what is happening when these trucks pass over the potholes and move onto the bridge and give your reasoning.

4. An advocacy group for the oil industry claims that we cannot rely on solar energy because there is not enough solar energy reaching the Earth to satisfy humankind's demands. Critique their claims by making some basic assumptions about U.S. energy usage and comparing that to the amount of energy that we could expect to capture at the Earth's surface. Clearly state your conclusion.

5. A power supply (with variable voltage and current settings) is used to operate a red LED. However, when the power supply is used with green or blue LEDs, the devices do not operate (are not illuminated). Hypothesize why this occurs and discuss your reasoning.

6. Two superconducting circuits are arranged so that each has a straight section of wire that is parallel to a straight section in the other circuit. Propose two experimental ways to reduce forces between the parallel wires while keeping currents the same and estimate numerically how much these forces will be reduced in each of your scenarios.

7. An observer notices that a section of a train track buckled during the last heatwave. Propose a hypothesis to explain this effect and give your reasoning.

8. In the morning following a cold night, workers discover that a gas (fuel) storage tank has collapsed. Develop a hypothesis to explain the collapse and suggest an experiment to test your hypothesis.

Creating in the sciences usually refers to developing new models to describe nature or to devising new inventions or designs. Other distinguishing factors of creating may include designing novel experiments or advancing new theories.

One example of creating is proposing new models to explain nature or phenomena more accurately. Here, investigators might look at experimental data and propose several models. As more and more data are collected, working models are developed over time.

This highest level of thinking often is reserved for professionals working in the field, but not all work must be done within the academy. Novices can imagine new models, propose novel conceptual designs, and conceive of improvements that lead to inventions.

The language of creating typically uses the key words: designing, constructing, planning, producing, and inventing.

1. Propose a new product to add to new home construction to mitigate increasing temperatures due to climate change. What is unique about your solution? How would it help to lower temperatures? Discuss scientifically how your solution works.

2. One energy storage design consists of a rotating flywheel. Rotational energy in the form of 0.5 Iω² is developed for later use when devices, such as solar panels and wind turbines, are not producing due to intermittent sunshine or wind. After testing an original design, engineers find that a rotating disk needs to be re-designed due to space limitations. Propose a re-design of the disk so that it has the same moment of inertia but with a radius that is 50% of the original design.

3. A fence surrounding a farm field has a gate at one end. The gate is attached to a vertical post that, over time, has started to lean to one side due to the weight (and torque) produced by the gate. Propose a modification to the current design that helps prevent the problem described. Be sure to describe the modification and explain how your design addresses the problem.

4. A city has limited funds but wants to modify its street lights to prevent so much light from being projected upward. Their goals are to reduce light pollution and to re-direct as much light as possible so that most of the light shines on sidewalks and streets below. Propose a design that uses the current lights but addresses the problem of light pollution and re-directs light to traffic areas below. Be sure to describe the design and how it works.

5. During a natural disaster, 100 ml of medicine must be kept cold during transport from one city to another, about 150 km away. Design an insulated container from materials you might find in your home. Be sure to maximize the insulating properties of the vessel by considering convection, conduction, and radiation.

The human mind has evolved to engage in multiple kinds of thinking, but, broadly speaking, the brain makes decisions based on survival thinking and the more complex and nuanced evaluative thinking. Survival thinking refers to reacting to stimuli without carefully considering alternative actions. Decisions made using survival thinking are automatic with no time for reflection.

Critical (evaluative) thinking, by contrast, requires reflecting on what is known and what can be determined and then building arguments to formulate decisions or responses. Critical-thinking skills are much needed in a world where monumental problems threaten our way of life and existence. With intentional practice, critical-thinking skills can be developed throughout the physics curriculum. The physics classroom is an ideal learning ground for critical thinking given that physics as a discipline is steeped in rigorous critique of data and models.