how to improve problem solving skills in physics

1.7 Solving Problems in Physics

Learning objectives.

By the end of this section, you will be able to:

• Describe the process for developing a problem-solving strategy.
• Explain how to find the numerical solution to a problem.
• Summarize the process for assessing the significance of the numerical solution to a problem.

Problem-solving skills are clearly essential to success in a quantitative course in physics. More important, the ability to apply broad physical principles—usually represented by equations—to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life.

As you are probably well aware, a certain amount of creativity and insight is required to solve problems. No rigid procedure works every time. Creativity and insight grow with experience. With practice, the basics of problem solving become almost automatic. One way to get practice is to work out the text’s examples for yourself as you read. Another is to work as many end-of-section problems as possible, starting with the easiest to build confidence and then progressing to the more difficult. After you become involved in physics, you will see it all around you, and you can begin to apply it to situations you encounter outside the classroom, just as is done in many of the applications in this text.

Although there is no simple step-by-step method that works for every problem, the following three-stage process facilitates problem solving and makes it more meaningful. The three stages are strategy, solution, and significance. This process is used in examples throughout the book. Here, we look at each stage of the process in turn.

Strategy is the beginning stage of solving a problem. The idea is to figure out exactly what the problem is and then develop a strategy for solving it. Some general advice for this stage is as follows:

• Examine the situation to determine which physical principles are involved . It often helps to draw a simple sketch at the outset. You often need to decide which direction is positive and note that on your sketch. When you have identified the physical principles, it is much easier to find and apply the equations representing those principles. Although finding the correct equation is essential, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities. Without a conceptual understanding of a problem, a numerical solution is meaningless.
• Make a list of what is given or can be inferred from the problem as stated (identify the “knowns”) . Many problems are stated very succinctly and require some inspection to determine what is known. Drawing a sketch can be very useful at this point as well. Formally identifying the knowns is of particular importance in applying physics to real-world situations. For example, the word stopped means the velocity is zero at that instant. Also, we can often take initial time and position as zero by the appropriate choice of coordinate system.
• Identify exactly what needs to be determined in the problem (identify the unknowns) . In complex problems, especially, it is not always obvious what needs to be found or in what sequence. Making a list can help identify the unknowns.
• Determine which physical principles can help you solve the problem . Since physical principles tend to be expressed in the form of mathematical equations, a list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all the other variables are known—so you can solve for the unknown easily. If the equation contains more than one unknown, then additional equations are needed to solve the problem. In some problems, several unknowns must be determined to get at the one needed most. In such problems it is especially important to keep physical principles in mind to avoid going astray in a sea of equations. You may have to use two (or more) different equations to get the final answer.

The solution stage is when you do the math. Substitute the knowns (along with their units) into the appropriate equation and obtain numerical solutions complete with units . That is, do the algebra, calculus, geometry, or arithmetic necessary to find the unknown from the knowns, being sure to carry the units through the calculations. This step is clearly important because it produces the numerical answer, along with its units. Notice, however, that this stage is only one-third of the overall problem-solving process.

Significance

After having done the math in the solution stage of problem solving, it is tempting to think you are done. But, always remember that physics is not math. Rather, in doing physics, we use mathematics as a tool to help us understand nature. So, after you obtain a numerical answer, you should always assess its significance:

• Check your units. If the units of the answer are incorrect, then an error has been made and you should go back over your previous steps to find it. One way to find the mistake is to check all the equations you derived for dimensional consistency. However, be warned that correct units do not guarantee the numerical part of the answer is also correct.
• Check the answer to see whether it is reasonable. Does it make sense? This step is extremely important: –the goal of physics is to describe nature accurately. To determine whether the answer is reasonable, check both its magnitude and its sign, in addition to its units. The magnitude should be consistent with a rough estimate of what it should be. It should also compare reasonably with magnitudes of other quantities of the same type. The sign usually tells you about direction and should be consistent with your prior expectations. Your judgment will improve as you solve more physics problems, and it will become possible for you to make finer judgments regarding whether nature is described adequately by the answer to a problem. This step brings the problem back to its conceptual meaning. If you can judge whether the answer is reasonable, you have a deeper understanding of physics than just being able to solve a problem mechanically.
• Check to see whether the answer tells you something interesting. What does it mean? This is the flip side of the question: Does it make sense? Ultimately, physics is about understanding nature, and we solve physics problems to learn a little something about how nature operates. Therefore, assuming the answer does make sense, you should always take a moment to see if it tells you something about the world that you find interesting. Even if the answer to this particular problem is not very interesting to you, what about the method you used to solve it? Could the method be adapted to answer a question that you do find interesting? In many ways, it is in answering questions such as these that science progresses.

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1 Units and Measurement

1.7 solving problems in physics, learning objectives.

By the end of this section, you will be able to:

• Describe the process for developing a problem-solving strategy.
• Explain how to find the numerical solution to a problem.
• Summarize the process for assessing the significance of the numerical solution to a problem.

Figure 1.13 Problem-solving skills are essential to your success in physics. (credit: “scui3asteveo”/Flickr)

Problem-solving skills are clearly essential to success in a quantitative course in physics. More important, the ability to apply broad physical principles—usually represented by equations—to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life.

As you are probably well aware, a certain amount of creativity and insight is required to solve problems. No rigid procedure works every time. Creativity and insight grow with experience. With practice, the basics of problem solving become almost automatic. One way to get practice is to work out the text’s examples for yourself as you read. Another is to work as many end-of-section problems as possible, starting with the easiest to build confidence and then progressing to the more difficult. After you become involved in physics, you will see it all around you, and you can begin to apply it to situations you encounter outside the classroom, just as is done in many of the applications in this text.

Although there is no simple step-by-step method that works for every problem, the following three-stage process facilitates problem solving and makes it more meaningful. The three stages are strategy, solution, and significance. This process is used in examples throughout the book. Here, we look at each stage of the process in turn.

Strategy is the beginning stage of solving a problem. The idea is to figure out exactly what the problem is and then develop a strategy for solving it. Some general advice for this stage is as follows:

• Examine the situation to determine which physical principles are involved . It often helps to draw a simple sketch at the outset. You often need to decide which direction is positive and note that on your sketch. When you have identified the physical principles, it is much easier to find and apply the equations representing those principles. Although finding the correct equation is essential, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities. Without a conceptual understanding of a problem, a numerical solution is meaningless.
• Make a list of what is given or can be inferred from the problem as stated (identify the “knowns”) . Many problems are stated very succinctly and require some inspection to determine what is known. Drawing a sketch can be very useful at this point as well. Formally identifying the knowns is of particular importance in applying physics to real-world situations. For example, the word stopped means the velocity is zero at that instant. Also, we can often take initial time and position as zero by the appropriate choice of coordinate system.
• Identify exactly what needs to be determined in the problem (identify the unknowns) . In complex problems, especially, it is not always obvious what needs to be found or in what sequence. Making a list can help identify the unknowns.
• Determine which physical principles can help you solve the problem . Since physical principles tend to be expressed in the form of mathematical equations, a list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all the other variables are known—so you can solve for the unknown easily. If the equation contains more than one unknown, then additional equations are needed to solve the problem. In some problems, several unknowns must be determined to get at the one needed most. In such problems it is especially important to keep physical principles in mind to avoid going astray in a sea of equations. You may have to use two (or more) different equations to get the final answer.

The solution stage is when you do the math. Substitute the knowns (along with their units) into the appropriate equation and obtain numerical solutions complete with units . That is, do the algebra, calculus, geometry, or arithmetic necessary to find the unknown from the knowns, being sure to carry the units through the calculations. This step is clearly important because it produces the numerical answer, along with its units. Notice, however, that this stage is only one-third of the overall problem-solving process.

Significance

After having done the math in the solution stage of problem solving, it is tempting to think you are done. But, always remember that physics is not math. Rather, in doing physics, we use mathematics as a tool to help us understand nature. So, after you obtain a numerical answer, you should always assess its significance:

• Check your units. If the units of the answer are incorrect, then an error has been made and you should go back over your previous steps to find it. One way to find the mistake is to check all the equations you derived for dimensional consistency. However, be warned that correct units do not guarantee the numerical part of the answer is also correct.
• Check the answer to see whether it is reasonable. Does it make sense? This step is extremely important: –the goal of physics is to describe nature accurately. To determine whether the answer is reasonable, check both its magnitude and its sign, in addition to its units. The magnitude should be consistent with a rough estimate of what it should be. It should also compare reasonably with magnitudes of other quantities of the same type. The sign usually tells you about direction and should be consistent with your prior expectations. Your judgment will improve as you solve more physics problems, and it will become possible for you to make finer judgments regarding whether nature is described adequately by the answer to a problem. This step brings the problem back to its conceptual meaning. If you can judge whether the answer is reasonable, you have a deeper understanding of physics than just being able to solve a problem mechanically.
• Check to see whether the answer tells you something interesting. What does it mean? This is the flip side of the question: Does it make sense? Ultimately, physics is about understanding nature, and we solve physics problems to learn a little something about how nature operates. Therefore, assuming the answer does make sense, you should always take a moment to see if it tells you something about the world that you find interesting. Even if the answer to this particular problem is not very interesting to you, what about the method you used to solve it? Could the method be adapted to answer a question that you do find interesting? In many ways, it is in answering questions such as these that science progresses.

The three stages of the process for solving physics problems used in this book are as follows:

• Strategy : Determine which physical principles are involved and develop a strategy for using them to solve the problem.
• Solution : Do the math necessary to obtain a numerical solution complete with units.
• Significance : Check the solution to make sure it makes sense (correct units, reasonable magnitude and sign) and assess its significance.

Conceptual Questions

What information do you need to choose which equation or equations to use to solve a problem?

What should you do after obtaining a numerical answer when solving a problem?

Check to make sure it makes sense and assess its significance.

Additional Problems

Consider the equation y = mt +b , where the dimension of y is length and the dimension of t is time, and m and b are constants. What are the dimensions and SI units of (a) m and (b) b ?

Consider the equation [latex] s={s}_{0}+{v}_{0}t+{a}_{0}{t}^{2}\text{/}2+{j}_{0}{t}^{3}\text{/}6+{S}_{0}{t}^{4}\text{/}24+c{t}^{5}\text{/}120, [/latex] where s is a length and t is a time. What are the dimensions and SI units of (a) [latex] {s}_{0}, [/latex] (b) [latex] {v}_{0}, [/latex] (c) [latex] {a}_{0}, [/latex] (d) [latex] {j}_{0}, [/latex] (e) [latex] {S}_{0}, [/latex] and (f) c ?

a. [latex] [{s}_{0}]=\text{L} [/latex] and units are meters (m); b. [latex] [{v}_{0}]={\text{LT}}^{-1} [/latex] and units are meters per second (m/s); c. [latex] [{a}_{0}]={\text{LT}}^{-2} [/latex] and units are meters per second squared (m/s 2 ); d. [latex] [{j}_{0}]={\text{LT}}^{-3} [/latex] and units are meters per second cubed (m/s 3 ); e. [latex] [{S}_{0}]={\text{LT}}^{-4} [/latex] and units are m/s 4 ; f. [latex] [c]={\text{LT}}^{-5} [/latex] and units are m/s 5 .

(a) A car speedometer has a 5% uncertainty. What is the range of possible speeds when it reads 90 km/h? (b) Convert this range to miles per hour. Note 1 km = 0.6214 mi.

A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12 s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the percent uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

a. 0.059%; b. 0.01%; c. 4.681 m/s; d. 0.07%, 0.003 m/s

The sides of a small rectangular box are measured to be 1.80 ± 0.1 cm, 2.05 ± 0.02 cm, and 3.1 ± 0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

When nonmetric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was used, where 1 lbm = 0.4539 kg. (a) If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

a. 0.02%; b. 1×10 4 lbm

The length and width of a rectangular room are measured to be 3.955 ± 0.005 m and 3.050 ± 0.005 m. Calculate the area of the room and its uncertainty in square meters.

A car engine moves a piston with a circular cross-section of 7.500 ± 0.002 cm in diameter a distance of 3.250 ± 0.001 cm to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

a. 143.6 cm 3 ; b. 0.2 cm 3 or 0.14%

Challenge Problems

The first atomic bomb was detonated on July 16, 1945, at the Trinity test site about 200 mi south of Los Alamos. In 1947, the U.S. government declassified a film reel of the explosion. From this film reel, British physicist G. I. Taylor was able to determine the rate at which the radius of the fireball from the blast grew. Using dimensional analysis, he was then able to deduce the amount of energy released in the explosion, which was a closely guarded secret at the time. Because of this, Taylor did not publish his results until 1950. This problem challenges you to recreate this famous calculation. (a) Using keen physical insight developed from years of experience, Taylor decided the radius r of the fireball should depend only on time since the explosion, t , the density of the air, [latex] \rho , [/latex] and the energy of the initial explosion, E . Thus, he made the educated guess that [latex] r=k{E}^{a}{\rho }^{b}{t}^{c} [/latex] for some dimensionless constant k and some unknown exponents a , b , and c . Given that [E] = ML 2 T –2 , determine the values of the exponents necessary to make this equation dimensionally consistent. ( Hint : Notice the equation implies that [latex] k=r{E}^{\text{−}a}{\rho }^{\text{−}b}{t}^{\text{−}c} [/latex] and that [latex] [k]=1. [/latex]) (b) By analyzing data from high-energy conventional explosives, Taylor found the formula he derived seemed to be valid as long as the constant k had the value 1.03. From the film reel, he was able to determine many values of r and the corresponding values of t . For example, he found that after 25.0 ms, the fireball had a radius of 130.0 m. Use these values, along with an average air density of 1.25 kg/m 3 , to calculate the initial energy release of the Trinity detonation in joules (J). ( Hint : To get energy in joules, you need to make sure all the numbers you substitute in are expressed in terms of SI base units.) (c) The energy released in large explosions is often cited in units of “tons of TNT” (abbreviated “t TNT”), where 1 t TNT is about 4.2 GJ. Convert your answer to (b) into kilotons of TNT (that is, kt TNT). Compare your answer with the quick-and-dirty estimate of 10 kt TNT made by physicist Enrico Fermi shortly after witnessing the explosion from what was thought to be a safe distance. (Reportedly, Fermi made his estimate by dropping some shredded bits of paper right before the remnants of the shock wave hit him and looked to see how far they were carried by it.)

The purpose of this problem is to show the entire concept of dimensional consistency can be summarized by the old saying “You can’t add apples and oranges.” If you have studied power series expansions in a calculus course, you know the standard mathematical functions such as trigonometric functions, logarithms, and exponential functions can be expressed as infinite sums of the form [latex] \sum _{n=0}^{\infty }{a}_{n}{x}^{n}={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+{a}_{3}{x}^{3}+\cdots , [/latex] where the [latex] {a}_{n} [/latex] are dimensionless constants for all [latex] n=0,1,2,\cdots [/latex] and x is the argument of the function. (If you have not studied power series in calculus yet, just trust us.) Use this fact to explain why the requirement that all terms in an equation have the same dimensions is sufficient as a definition of dimensional consistency. That is, it actually implies the arguments of standard mathematical functions must be dimensionless, so it is not really necessary to make this latter condition a separate requirement of the definition of dimensional consistency as we have done in this section.

Since each term in the power series involves the argument raised to a different power, the only way that every term in the power series can have the same dimension is if the argument is dimensionless. To see this explicitly, suppose [x] = L a M b T c . Then, [x n ] = [x] n = L an M bn T cn . If we want [x] = [x n ], then an = a, bn = b, and cn = c for all n. The only way this can happen is if a = b = c = 0.

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Why Physics is Vital in Improving Problem-Solving Skills

Over the years, companies and organizations have started looking for holistic individuals. From academic, business and the job market, problem-solving is an incredibly vital skill. If you are looking for ways to improve your problem-solving skills, you should take a look at how physics equips us with the required skills we need for the real world (add title tag to hyperlink – “How Learning Physics Countributes To Real Life Situations”).

Identifying the problem.

When you read the description to a physics problem, you visualize the real situation and translate the written information into mathematical variables. You can start by constructing a mental image of the problem situation, done by drawing a rough, literal picture showing all essential objects. Then, you label all the known information and identify the approach you would use to solve the issue. The main challenge here is finding out all the ways you can utilize the approach to a variety of other situations.

Defining the main elements of the problem.

By having a description of your problem, you can translate the given information into an accurate picture of an idealized diagram. This helps you identify and define the variables and calculate their desired quantities. The biggest challenge physics student face is applying the law of physics before undertaking the quantitative analysis of the problem. By overcoming this temptation, you can be a much more effective problem solver. Another essential tip to define the principal elements is including each item's associated units to sharpen your problem-solving skills better.

Planning the solution.

Before calculating your answer, you need to have a plan. When physics laws are expressed in an equation, the solution changes to a conventional, general statement. The plan requires you to construct algebraic expressions, enabling you to calculate the target variable. Although this approach is common with expert solvers, you can begin with the target variable and work backwards in determining the path to the answer. In most cases, units help you identify the correct way. For example, if you are calculating volume, you know your final solution must be in m3.

Working on the plan.

Planning often includes, but not limited to, working through similar problems and by observing the solution processes. The known information from the solution process is substituted into the identified formula to solve the unknown quality. It is imperative to solve the problem algebraically before we insert in any numerical values. This is because some unknown quality may cancel out, leaving you without a proper numerical value. Paying attention to your plan can enable you to check on the reasonableness of your solution.

Evaluating the solution.

Now that you have arrived at your answer, it is imperative to do a final check to ensure it is correct. This is where you can utilize your analytical skills to evaluate how the real world works, as well as individual aspects of the physical world that you have learned in physics class. A good idea is to read through the solution carefully, multiple times if needed. Should your final evaluation suggest that your answer is indeed correct, you can write a statement that explains your reasoning.

Speaking on the subject of holistic individuals, someone who is currently pursuing a physics degree or going through physics tuition will no doubt find the use of physics well in society. The physics course not only enables you to have a solid grasp in problem-solving skills but analytical skills as well, both of which are necessary in the real world. The beauty of physics ensures that we can come up with approaches and solutions to any problem that may come our way!

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Habits of an Effective Problem Solver

One of the instructional goals of the Audio Help files is to assist students in becoming better and more confident problem-solvers. If all students who are good problem-solvers could be observed doing problems, then one would not necessarily observe that they use the same approaches to solving problems. Most good problem-solvers have unique little practices which make them different from other good problem-solvers. Nonetheless, there are several habits which they all share in common. While a good problem-solver may not religiously adhere to these habitual practices, they become more reliant upon them as the problems become more difficult.

The list below describes some of the habits which good problem-solvers share in common. The list is NOT an exhaustive list; it simply includes some commonly observed habits which good problem-solvers practice. Anyone can be a good problem-solver; because of personality and learning style differences, some will certainly be better than others. Nonetheless, anyone who puts effort into disciplining themselves to be successful at solving problems can learn how to be proficient at the task. A student who devotes some time and attention to the list below and makes an effort to personalize it into their own approach to problems will improve their problem-solving ability. The use of these Audio Help files and the problem-solving practices which they promote will not only assist you in completing your problem sets but will also make you a better and more confident problem-solver.

Reading and Visualizing

All good problem-solvers will read a problem carefully and make an effort to visualize the physical situation. Physics problems begin as word problems and terminate as mathematical exercises. Before the mathematics portion of a problem begins, a student must translate the written information into mathematical variables. Many errors (and perhaps even most) can be traced back to this translation process. These errors are usually the result of a failure to visualize the physical situation described in the verbal statement of the problem or of a failure in missing some strategic information during the reading process. A good problem-solver will often construct a diagram of some form to assist in this critical visualization task. The actual diagram will depend upon the topic which the problem pertains to. If the topic pertains to forces, a force diagram might be drawn. If the problem pertains to mirrors, a ray diagram or object-image diagram may be drawn. And if the problem pertains to vector addition, a vector addition diagram may be drawn. But regardless of the topic, a good problem-solver typically begins the translation of the written words into mathematical variables by an informative sketch or diagram which depicts the situation.

Organization of Known and Unknown Information

As mentioned earlier, physics problems begin as word problems and terminate as mathematical exercises. During the algebraic/mathematical part of the problem, the student must make substitution of known numerical information into a mathematical formula (and hopefully into the correct formula ). The mathematical formula is written in the form of symbols which represent some physical quantity such as focal length, distance, acceleration or force. Before performing such substitutions, the student must first equate the numerical information contained in the verbal statement with the appropriate physical quantity. It is the habit of a good problem-solver to carefully read the verbal statement and to combine the attention to units (meters, kilograms, Joules, etc.) with their understanding of the meaning of physical quantities in order to accurately extract the numerical information and equate it with the appropriate symbol. Furthermore, good problem-solvers will conduct this task by writing down the quantitative information with its unit and symbol in an organized fashion, often recording the values on their diagram. This task will also include observing strategic and meaningful phrases such as "a magnified and virtual image", "a diverging lens", "starting from rest", "with a constant velocity", and "in the absence of air resistance." While such phrases do not explicitly provide numerical information, they do go a long way towards offering information which implies a particular solution strategy. In addition to identifying the known information, good problem-solvers also practice the habit of identifying the quantity to be solved for, recording it in terms of its appropriate symbol.

Plotting a Strategy for Solving for the Unknown

Once the physical situation has been visualized and diagrammed and the numerical information has been extracted from the verbal statement, the strategy plotting stage begins. During this stage of a problem, the student ponders the question: "How can I use the known information - both explicit and implied - to determine the unknown quantity?" More than any other stage during the problem solution, it is during this stage that a student must think critically and apply their physics knowledge.

Difficult problems in physics (the kind which likely draw students to these audio help files) are multistep problems. The path from known information to the unknown quantity is often not immediately obvious. The problem becomes like a jigsaw puzzle; the assembly of all the pieces into the whole can only occur after careful inspection, thought, analysis, and perhaps some wrong turns. In such cases, the time taken to plot out a strategy will pay huge dividends, preventing the loss of several frustrating minutes of impulsive attempts at solving the problem. Good problem solvers use their background knowledge of physics and physics formulae to think about how the known information is related to each other and how it is related to the final unknown quantity. They know through practice and through observation of other expert problem-solvers (such as their teacher) that there are likely some intermediate unknown quantities which will have to be calculated before finding the final unknown quantity. By comparing the known information (which they have previously written down in an organized manner) to known mathematical formulae, they are able to determine the intermediate quantities which will allow them to subsequently determine the final quantity. They record their thoughts as they think through possible steps for solving the problem; they often sketch a schematic plan that depicts how to put the individual pieces together to solve the problem as a whole.

Often times, difficulties arising in the strategy plotting phase of a problem solution is the result of the lack of knowledge about the topic. A good problem-solver understands that if they know very little about the topic, there is no sense in attempting the problem. Rather than waste valuable time trying, they spend their time learning about the topic, looking for relevant mathematical formulae and studying pertinent concepts and principles. Good problem-solvers are resourceful enough to know where to look to find the formulae and other information which they need to know to solve the problem. They may look in their notes from class, in their instructional packets, in their textbooks or at online resources. Once a good problem-solver has filled their minds with information, they return to the problem to apply their new physics knowledge, asking once more "How can I use the known information - both explicit and implied - to determine the unknown quantity?"

Even with suitable understanding of the physics behind a problem, a student can still get stuck and become in need of help. Good problem-solvers are not typically caught off guard by such sticking points; they understand them to be natural to any strategy plotting process. In such instances, good problem-solvers will often take the time to look at previously done problems which are similar or identical to the one that they are trying to solve. They will compare the current problem to previous ones in terms of known and unknown quantities and observe the solution process to these similar problems, pondering if a similar strategy could be used. They may look at previous problems which they have done, sample problems from the textbook or from online resources, or problems done in class. Because they have taken careful notes from class and organized their own solutions to problems, good problem-solvers benefit tremendously from such comparisons. Often times, the current problem can use the same solution as a previous one. Often times, the mere practice of looking through previous solutions triggers a thought about how one can proceed with the current solution. Considerable learning occurs during this comparison process which allows a good problem-solver to not only solve the current problem but also internalize the mathematical relationships between quantities in physics. This effort makes good problem-solvers into even better problem-solvers, confident to approach any problem that subsequently arises.

Identification of Appropriate Formula(e)

Once a strategy has been plotted for solving a problem, a good problem-solver will list appropriate mathematical formulae on their paper. They may take the time to rearrange the formulae such that the unknown quantity appears by itself on the left side of the equation. They will take the time to inspect the units in which the given information was stated and make conversions to standard metric units if necessary. The process of identifying formula is simply the natural outcome of an effective strategy-plotting phase.

Algebraic Manipulations and Operations

Finally the mathematics begins, but only after the all-important thinking and physics has occurred. In the final step of the solution process, known information is substituted into the identified formulae in order to solve for the unknown quantity. Following the carefully plotted strategy, the good problem-solver takes the time to manipulate the equations and solve for the unknown. They record strategic algebra steps on paper in the event that their answer is wrong. If wrong, they can quickly inspect their algebra to determine if the error occurred during the mathematical phase of the problem or during the planning/thought/physics stage of the problem.

It should be observed in the above description of the habits of a good problem-solver that the majority of work on a problem is done prior to the actual mathematical operations are performed. Physics problems are more than exercises in mathematical manipulation of numerical data. Physics problems require careful reading, good visualization skills, some background physics knowledge, analytical thought and inspection and a lot of strategy-plotting.

How can problem solving skills be improved in physics?

• Focus on the Problem. Establish a clear mental image of the problem. A.
• Describe the Physics. Refine and quantify your mental image of the problem. A.
• Plan a Solution. Turn the concepts into math. A.
• Execute the Plan. This is the easiest step – it’s just the algebra/calculus/etc. A.
• Evaluate the Answer. Be skeptical.

How can students improve problem solving?

• Go Step-By-Step Through The Problem-Solving Sequence.
• Revisit Past Problems.
• Document What Doesn’t Work.
• “3 Before Me”
• Ask Open Ended Questions.
• Encourage Grappling.
• Emphasize Process Over Product.
• Model The Strategies Yourself!

What are the three parts of the problem solving strategy for solving physics problems?

The strategy we would like you to learn has five major steps: Focus the Problem, Physics Description, Plan a Solution, Execute the Plan, and Evaluate the Solution. Let’s take a detailed look at each of these steps and then do an sample problem following the strategy.

How important is problem solving in physics?

Problem-solving skills are clearly essential to success in a quantitative course in physics. More important, the ability to apply broad physical principles—usually represented by equations—to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts.

How do you solve hard physics problems?

What is the last thing you should do when solving a problem physics?

Answer and Explanation: The last thing that we do is rechecking of the answer, our answer should be correct and full fill all the requirements. Also, at last, recheck the unit and if there is not the unit, then provide the sign for the answer, checking all these things, at last, improve the accuracy of the answer.

Why is problem-solving important for students?

Problem-Solving Skills Build Confidence Typically, effective problem-solving skills result in “happier, more confident, and more independent” individuals. When children tackle problems on their own, or in a group, they become resilient. They learn to look at challenges from a fresh perspective.

How can a teacher help students become better problem solvers?

By giving children a variety of problems to solve and support while solving them. By giving tangible rewards for solving problems. By encouraging children to look for answers to the problems in the textbook. By providing correct solutions to all the problems they pose to students.

What can teachers do to encourage problem-solving techniques to students?

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear.
• Have students work through problems on their own.
• Don’t fear group work!

What are the general strategies for problem solving?

• Become aware of the problem.
• Define the problem.
• Choose the particular problem to be solved.
• Identify potential solutions.
• Evaluate the valid potential solutions to select the best one.
• Develop an action plan to implement the best solution.

Who is the father of problem solving method?

George Polya, known as the father of modern problem solving, did extensive studies and wrote numerous mathematical papers and three books about problem solving.

How do you think logically in physics?

The best way to deal with this is to “start with the basics” of any subject you are studying. In physics, go back to main principles. Acceleration is velocity/time because acceleration is the rate at which velocity changes. Just like that, take a basic principle that you do understand and move forward from there.

Is there an app that solves physics?

PhyWiz solves your physics homework for you. Get step by step solutions for questions in over 30 physics topics like Kinematics, Forces, Gravity, Quantum Physics and many more.

What should you do after obtaining a numerical answer when solving a problem?

So, after you obtain a numerical answer, you should always assess its significance: Check your units. If the units of the answer are incorrect, then an error has been made and you should go back over your previous steps to find it.

How do you solve NEET physics Numericals?

• Study and practice Physics every day.
• Don’t miss your classes and make class notes.
• Read/ Preview the topic before the class.
• Revise everything after the class.
• Follow NEET study material to understand concepts well.
• Solve problems from NCERT and coaching modules.

What topics are covered in physics?

• Linear motion.
• Interactions and Force.
• Motion in Two-Dimensions.
• Circular and Rotational Motion.

Why are physics Numericals so hard?

Why is Physics harder than Math? Answer: Physics demands problem-solving skills that can be developed only with practice. It also involves theoretical concepts, mathematical calculations and laboratory experiments that adds to the challenging concepts.

Is physics easy or hard?

Students and researchers alike have long understood that physics is challenging. But only now have scientists managed to prove it. It turns out that one of the most common goals in physics—finding an equation that describes how a system changes over time—is defined as “hard” by computer theory.

How can I study physics?

• Make use of the preview that you did prior to the class. Again,
• Read the homework problems first.
• Read actively with questions in mind.
• Stop periodically and pointedly recall the material that you have.
• During your reading you will notice sections, equations, or ideas that.

Which factors can help improve problem-solving abilities in children?

Allow your child to choose activities and games based on her interests. Free play provides plenty of opportunities to navigate and creatively solve problems. Children often learn best through play. Playing with items like blocks, simple puzzles, and dress-up clothes can teach your child the process of problem-solving.

What are the benefits of problem-solving?

Problem solving develops mathematical power. It gives students the tools to apply their mathematical knowledge to solve hypothetical and real world problems. Problem solving is enjoyable. It allows students to work at their own pace and make decisions about the way they explore the problem.

Why is it important to develop problem-solving skills?

Why is it important? Employers like to see good problem solving skills because it also helps to show them you have a range of other competencies such as logic, creativity, resilience, imagination, lateral thinking and determination. It is a vital skills for your professional and personal life.

What is problem-solving method in science?

A problem-solving method as the name suggests is a method where children learn by working on problems. This model enables the student to learn new knowledge by facing the problems to be solved, instead of burdened contents [1].

How would you assess problem-solving abilities of students?

Cognitive ability test: A pre-employment aptitude test assesses individuals’ abilities such as critical thinking, verbal reasoning, numerical ability, problem-solving, decision-making, etc., which are indicators of a person’s intelligence quotient (IQ). The test results provide data about on-the-job performance.

Which method is used for developing creative solution to problems?

Divergent thinking is the process of generating lots of potential solutions and possibilities, otherwise known as brainstorming. And convergent thinking involves evaluating those options and choosing the most promising one. Often, we use a combination of the two to develop new ideas or solutions.

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How To Enhance Your Problem-Solving Ability in Physics

Knowing how to solve physics problems is a process that can be learned..

Marcia Wendorf

Depositphotos

Albert Einstein once said: “The formulation of the problem is often more essential than its solution … “

RELATED: SOLVING THESE 6 MAJOR MATH PROBLEMS CAN EARN YOU $1 MILLION

Former Apple CEO Steve Jobs said, “When you start looking at a problem and it seems really simple, you don’t really understand the complexity of the problem. Then you get into the problem, and you see that it’s really complicated, and you come up with all these convoluted solutions. That’s sort of the middle, and that’s where most people stop… But the really great person will keep on going and find the key, the underlying principle of the problem — and come up with an elegant, really beautiful solution that works.”

Solving problems, whether in physics or other disciplines, can be learned. Rafis Abazov on the TopUniversities website promotes the IDEAL methodology for his students: Identify, Define, Examine, Act and Look.

1. Identify the problem – identify the nature of the problem by visualizing the physical situation, and translating the written information in the problem into mathematical variables. Draw a diagram showing the objects, and their motions or interactions. For example, an interaction can be two objects connected by a rope.

2. Define the main elements of the problem – on the diagram, label all the known and unknown information. This allows you to translate between verbal, visual, and mathematical modes and their concrete manifestations of words, pictures, and equations. Be sure to include each item’s associated units, this will help you identify what is being solved for.

3. Examine possible solutions – once the physical situation has been visualized and diagrammed, and the numerical information has been extracted from the problem statement, students can either use their background knowledge of physics and physics formulae or else they can seek out that information in class notes, instructional packets, textbooks or online resources.

It sometimes helps to work backward by saying, “I want the answer to Z, but if I knew Y, I could find Z, and if I knew X … and so forth until you get back to something you are given in the original problem statement.

4. Act on resolving the problem – this often includes working through previous problems that are similar, and observing the solution process. Then, the known information is substituted into the identified formulae to solve for the unknown quantity. Always solve symbolically first before putting in the actual quantities. This allows you to make sure your answer makes sense in the physical world.

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5. Look for lessons to be learned – by evaluating the solution process, you can formulate the lessons you’ve learned so that the next problem-solving project will be more effective.

A Solution in a Dream

Sometimes, other hands are at work in the solving of problems. Take chemist August Kekule’s solution to the structure of the benzene molecule, and hence the structure of all aromatic compounds. After long struggling with the problem, Kekule took a nap. He dreamed of a snake that was swallowing its own tail, and he awoke with the realization that the shape of the benzene molecule was a ring.

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ABOUT THE EDITOR

Marcia Wendorf <p>Marcia is a former high school math teacher, technical writer, author, and programmer. In much the same way as high school students in the U.S. are taught "defensive driving", Marcia practices "defensive living": staying on top of worldwide news about science, government policies, finance, infrastructure, and medical issues. An outlier, Marcia is always "sniffing the wind" for the latest trends and directions, and keeping her readers abreast of these developments.</p>

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Learning Objectives

• Describe the process for developing a problem-solving strategy.
• Explain how to find the numerical solution to a problem.
• Summarize the process for assessing the significance of the numerical solution to a problem.

Problem-solving skills are clearly essential to success in a quantitative course in physics. More important, the ability to apply broad physical principles—usually represented by equations—to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life.

As you are probably well aware, a certain amount of creativity and insight is required to solve problems. No rigid procedure works every time. Creativity and insight grow with experience. With practice, the basics of problem solving become almost automatic. One way to get practice is to work out the text’s examples for yourself as you read. Another is to work as many end-of-section problems as possible, starting with the easiest to build confidence and then progressing to the more difficult. After you become involved in physics, you will see it all around you, and you can begin to apply it to situations you encounter outside the classroom, just as is done in many of the applications in this text.

Although there is no simple step-by-step method that works for every problem, the following three-stage process facilitates problem solving and makes it more meaningful. The three stages are strategy, solution, and significance. This process is used in examples throughout the book. Here, we look at each stage of the process in turn.

Strategy is the beginning stage of solving a problem. The idea is to figure out exactly what the problem is and then develop a strategy for solving it. Some general advice for this stage is as follows:

• Examine the situation to determine which physical principles are involved . It often helps to draw a simple sketch at the outset. You often need to decide which direction is positive and note that on your sketch. When you have identified the physical principles, it is much easier to find and apply the equations representing those principles. Although finding the correct equation is essential, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities. Without a conceptual understanding of a problem, a numerical solution is meaningless.
• Make a list of what is given or can be inferred from the problem as stated (identify the “knowns”) . Many problems are stated very succinctly and require some inspection to determine what is known. Drawing a sketch be very useful at this point as well. Formally identifying the knowns is of particular importance in applying physics to real-world situations. For example, the word stopped means the velocity is zero at that instant. Also, we can often take initial time and position as zero by the appropriate choice of coordinate system.
• Identify exactly what needs to be determined in the problem (identify the unknowns). In complex problems, especially, it is not always obvious what needs to be found or in what sequence. Making a list can help identify the unknowns.
• Determine which physical principles can help you solve the problem . Since physical principles tend to be expressed in the form of mathematical equations, a list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all the other variables are known—so you can solve for the unknown easily. If the equation contains more than one unknown, then additional equations are needed to solve the problem. In some problems, several unknowns must be determined to get at the one needed most. In such problems it is especially important to keep physical principles in mind to avoid going astray in a sea of equations. You may have to use two (or more) different equations to get the final answer.

The solution stage is when you do the math. Substitute the knowns (along with their units) into the appropriate equation and obtain numerical solutions complete with units . That is, do the algebra, calculus, geometry, or arithmetic necessary to find the unknown from the knowns, being sure to carry the units through the calculations. This step is clearly important because it produces the numerical answer, along with its units. Notice, however, that this stage is only one-third of the overall problem-solving process.

Significance

After having done the math in the solution stage of problem solving, it is tempting to think you are done. But, always remember that physics is not math. Rather, in doing physics, we use mathematics as a tool to help us understand nature. So, after you obtain a numerical answer, you should always assess its significance:

• Check your units . If the units of the answer are incorrect, then an error has been made and you should go back over your previous steps to find it. One way to find the mistake is to check all the equations you derived for dimensional consistency. However, be warned that correct units do not guarantee the numerical part of the answer is also correct.
• Check the answer to see whether it is reasonable. Does it make sense? This step is extremely important: –the goal of physics is to describe nature accurately. To determine whether the answer is reasonable, check both its magnitude and its sign, in addition to its units. The magnitude should be consistent with a rough estimate of what it should be. It should also compare reasonably with magnitudes of other quantities of the same type. The sign usually tells you about direction and should be consistent with your prior expectations. Your judgment will improve as you solve more physics problems, and it will become possible for you to make finer judgments regarding whether nature is described adequately by the answer to a problem. This step brings the problem back to its conceptual meaning. If you can judge whether the answer is reasonable, you have a deeper understanding of physics than just being able to solve a problem mechanically.
• Check to see whether the answer tells you something interesting. What does it mean? This is the flip side of the question: Does it make sense? Ultimately, physics is about understanding nature, and we solve physics problems to learn a little something about how nature operates. Therefore, assuming the answer does make sense, you should always take a moment to see if it tells you something about the world that you find interesting. Even if the answer to this particular problem is not very interesting to you, what about the method you used to solve it? Could the method be adapted to answer a question that you do find interesting? In many ways, it is in answering questions such as these science that progresses.

How to Improve Your Problem-Solving Skills for JEE

• Active page

May 11, 2023, 16:45 IST

IIT JEE is one of the toughest engineering entrance exams in our country. This exam is conducted after the 12th board's exam, which not only tests students' conceptual knowledge of core subjects like Physics, Chemistry, and Mathematics but also tests problem-solving skills and logical, analytical, and critical thinking skills.

To secure a good rank in the IIT JEE exam, you must tighten your seatbelts and study very hard, it is not an easy game, but surely not impossible. You can easily secure good grades and top rank, But how can one do that?

Well, apart from the main subjects, problem-solving skills for IIT JEE are very crucial to work on as it is key to succeeding in the IIT-JEE exam . Problem-solving skills are not a skill that one is born with, instead, they can be cultivated, can be learned, and improved with practice and consistent efforts.

If we talk about questions in JEE exam, they can be solved by using numerous approaches, but you have to select the one which is best suitable for the problem, which saves time and results in the correct answer.

Below are given some of the best problem-solving tips for JEE which might be helpful in preparing for the IIT-JEE exam-

Tips for Effective Problem-Solving Skills

• Be Clear with the Theory

Firstly, be very clear with all the concepts and formulations of the subjects. Acquire all the necessary knowledge regarding the subjects and their important topics.

As building a base is very important in any exam, otherwise, you will face problems later. So, before solving questions, try to grab all the detailed knowledge of concepts and key areas.

• Read the Data carefully

The key is to thoroughly read the problem and keep an eye on the data given in the problem. Note down all the crucial data given in the problem, it will make it easier to understand and organize the problem.

When you read a problem, read the data in numeric form, and you will automatically fit in the key pieces in your brain, and related formulae will come to your mind easily and effectively.

• Mental Math

Focusing on mental math is one of the greatest ways to enhance your problem-solving abilities for the IIT JEE exam . Mental math is the fastest way to solve any question, and it also gives you a direction to work on fast calculations.

Some tricks like vedic maths concepts, heuristics, and tips can really cut your calculation time. If you choose the long traditional way of solving answers, you will not be able to complete your paper on time.

• Don't panic with larger problems

There are times, when the problem is lengthy in language form, don't panic, just grab the important data parts and try to assemble them into easy-to-grab information pieces.

There is always a simpler expression to the problem, sometimes even the lengthy-looking problems end up being very simple and easy to solve.

• Make Mind Maps

Try to develop a mind map while reading the question, it will save time and will surely help in selecting the best solving strategy.

Mind mapping opens up potential possibilities for solving the question, you also gain clarity and keep yourself calm in a stressful situation.

Using Mind maps is mostly about creativity and spontaneity, which uses heuristics and mnemonic techniques to help solve questions easily.

For beginners, you can make use of flowcharts and can depict the central idea behind the problem.

• Theorems and Formulae on Tips

Before solving any question, you must be thorough with all the important formulae and algorithms in each subject. You can write down all the formulae and reactions in chemistry and revise them regularly on time.

As you should spend the least amount of time remembering the formulae, it must be on your tips always. This will save enough time to solve and do the calculation part. This way, you can solve questions in less time and in an effective way.

• Quality Practise

When you practice the question, make sure you set a daily goal to solve this much of questions. For example, you can set a daily goal of 50 questions daily, and slowly you can increase this when you feel you are grabbing the core of the topic.

In addition to this, make sure the sums you are solving are of standard quality according to the syllabus of the exam. Solve previous years IIT JEE question papers for added benefit.

It will greatly enhance your speed and accuracy.

• Always Use a Stopwatch

You must record the time taken to solve a problem with a stopwatch. During practice, always use a stopwatch it will be of great help for JEE aspirants. For example, it will take less time for you to solve a sum on day 10 of practice, as compared to that on day 1, so it will help you in taking note of how much have you improved and thereby reduces the time.

Setting a time limit also helps in keeping a track of questions solved and will prepare you for performing best in the final exam.

Problem-solving skills are very crucial in any exam, in an exam like IIT JEE, where most of the questions are in numerical form,which directly tests your arithmetic and logical ability,you must develop your critical thinking skills,which will surely help you in solving questions faster, and in an effective way.

JEE Exam FAQ

Q1. Why problem solving is so important?

Ans. Problem-solving is very crucial as it makes us use our logic, creativity, take a new path/ approach, imagination, and resilience while solving paper, it is also very important in daily life.

Q2. What are the challenges in problem-solving?

Ans. There come a lot of challenges, such as - assumption, which can hinder the mindset which helps in solving a question using a different approach.

Second, it is the functional fixedness that comes in the way it restricts us from solving using a new technique and makes it difficult to proceed with the answer.

Q3. How can I be confident in the JEE Examination?

Ans. You must be determined enough for the IITJEE goal, if you have a clear vision and great willpower, nobody can stop you from clearing the exam. Just consistently prepare for the exam with daily practice, and you can easily crack it.

Don't listen to any negative talk, stay away from negative people, and focus on your goal.

Do not compare yourself with others, everyone is different.

Make a proper schedule and try to stick with it.

Q4. Is coaching necessary for the IIT-JEE exam?

Ans. No, you can easily clear the exam without any coaching, however, it is not an easy thing, you must work very hard as it is an entrance exam with a lot of fo competition, so make sure you study daily and consistently.

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Intervention based on science of reading and math boosts comprehension and word problem-solving skills

by University of Kansas

New research from the University of Kansas has found that an intervention based on the science of reading and math effectively helped English learners boost their comprehension, visualize and synthesize information, and make connections that significantly improved their math performance.

The intervention , performed for 30 minutes twice a week for 10 weeks with 66 third-grade English language learners who displayed math learning difficulties, improved students' performance when compared to students who received general instruction. This indicates that emphasizing cognitive concepts involved in the science of reading and math are key to helping students improve, according to researchers.

"Word problem-solving is influenced by both the science of reading and the science of math. Key components include number sense, decoding, language comprehension and working memory. Utilizing direct and explicit teaching methods enhances understanding and enables students to effectively connect these skills to solve math problems . This integrated approach ensures that students are equipped with necessary tools to navigate both the linguistic and numerical demands of word problems," said Michael Orosco, professor of educational psychology at KU and lead author of the study.

The intervention incorporates comprehension strategy instruction in both reading and math, focusing and decoding, phonological awareness, vocabulary development, inferential thinking, contextualized learning and numeracy.

"It is proving to be one of the most effective evidence-based practices available for this growing population," Orosco said.

The study, co-written with Deborah Reed of the University of Tennessee, was published in the journal Learning Disabilities Research and Practice .

For the research, trained tutors implemented the intervention, developed by Orosco and colleagues based on cognitive and culturally responsive research conducted over a span of 20 years. One example of an intervention session tested in the study included a script in which a tutor examined a word problem explaining that a person made a quesadilla for his friend Mario and gave him one-fourth of it, then asked students to determine how much remained.

The tutor first asked students if they remembered a class session in which they made quesadillas and what shape they were, and demonstrated concepts by drawing a circle on the board, dividing it into four equal pieces, having students repeat terms like numerator and denominator. The tutor explains that when a question asks how much is left, subtraction is required. The students also collaborated with peers to practice using important vocabulary in sentences. The approach both helps students learn and understand mathematical concepts while being culturally responsive.

"Word problems are complex because they require translating words into mathematical equations, and this involves integrating the science of reading and math through language concepts and differentiated instruction," Orosco said. "We have not extensively tested these approaches with this group of children. However, we are establishing an evidence-based framework that aids them in developing background knowledge and connecting it to their cultural contexts."

Orosco, director of KU's Center for Culturally Responsive Educational Neuroscience, emphasized the critical role of language in word problems, highlighting the importance of using culturally familiar terms. For instance, substituting "pastry" for "quesadilla" could significantly affect comprehension for students from diverse backgrounds. Failure to grasp the initial scenario could impede subsequent problem-solving efforts.

The study proved effective in improving students' problem-solving abilities, despite covariates including an individual's basic calculation skills, fluid intelligence and reading comprehension scores. That finding is key, as while ideally all students would begin on equal footing and there would be few variations in a classroom, in reality, covariates exist and are commonplace.

The study had trained tutors deliver the intervention, and its effectiveness should be further tested with working teachers, the authors wrote. Orosco said professional development to help teachers gain the skills is necessary, and it is vital for teacher preparation programs to train future teachers with such skills as well. And helping students at the elementary level is necessary to help ensure success in future higher-level math classes such as algebra.

The research builds on Orosco and colleagues' work in understanding and improving math instruction for English learners. Future work will continue to examine the role of cognitive functions such as working memory and brain science, as well as potential integration of artificial intelligence in teaching math.

"Comprehension strategy instruction helps students make connections, ask questions, visualize, synthesize and monitor their thinking about word problems," Orosco and Reed wrote. "Finally, applying comprehension strategy instruction supports ELs in integrating their reading, language and math cognition…. Focusing on relevant language in word problems and providing collaborative support significantly improved students' solution accuracy."

Provided by University of Kansas

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2024 DNA Internship (Domestic)

Location Taiwan Job Type Others Employment Type Intern Posted Jan 05, 2024

TSMC Summer Intern Program provides an unique experience for students to learn about the semiconductor industry and have a first-hand experience of career life in TSMC. You will not only join a series of training sessions related to your major, but also be part of the team and expected to provide solutions and create valuable impacts to our company.

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Implementation of Problem Based Learning to Train Physics Students' Problem Solving Skills

H N Hidaayatullaah 1 , Dwikoranto 1 , N Suprapto 1 , H Mubarok 1 and D Wulandari 1

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1491 , Seminar Nasional Fisika (SNF) Unesa 2019 19 October 2019, Surabaya, Indonesia Citation H N Hidaayatullaah et al 2020 J. Phys.: Conf. Ser. 1491 012053 DOI 10.1088/1742-6596/1491/1/012053

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1 Department of Physics, Faculty of Mathematics and Natural Science, Universitas Negeri Surabaya, Jl. Ketintang, Surabaya 60231, Indonesia

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Problem solving skills (PSS) are the skills needed to face the challenges of the industrial revolution 4.0, which need to be developed through the learning process, and are still a challenge for teachers today. This study aims to determine the effect of the implementation of problem-based learning (PBL) in practicing students' problem solving abilities on material momentum and impulses. The research utilised a pre-experimental design with one-group pretest-posttest paradigm. The sample in this study consisted of 3 groups: one experimental group and two replication groups. The results showed that the implementation of PBL affected the problem solving abilities of students in the experimental and replication groups. The three groups experienced a different increase of PSS due to several factors, namely the implementation of learning, the existence of different student intelligence and student activities during learning.

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My Journey of Learning Problem-Solving Skills through Coding Contests

I still remember the day I gave my first coding contest because I learned many things afterwards. when I was in my first year I didn’t know how to strengthen my problem-solving skills so I went to my seniors and ask a solution for it and then they gave a solution if you want to test your problem-solving skills you should participate in weekly coding contests. but firstly you should have learned some basic patterns of DSA . it will enhance your problem-solving skills and your speed will gradually increase do not overthink if you are not able to solve the problem you can see the solution after the contest and learn how the problem will solved. I took this advice seriously.

My first coding contest

when I was in my first year I knew that Geeksforgeeks conducted a weekly coding contest and it also provided amazing goodies who scored a good rank in the contest so I registered for the contest there were 4 questions in the contest and I solved the first question easily because it is related to a prime number which I recently learned but the second question seems tough to me I find the right approach but not able to implement it during the contest. After all, it is related to an array and at that time did not know the concept of prefix sum . but was not demotivated by this because it was the first time I had given such kind of contest and remembered what my senior said to me after the contest ended I saw the solution and learned the concept of prefix sum and the next time I gave the contest this approach helped a lot of times.

Tips I want to give from my learnings

• Participate in weekly contests will give you different benefits
• Your timing and problem-solving speed will be increased by giving weekly contest
• And never demotivated when a new question comes and you are not able to solve it just see the solution after the contest ends and learn how the question solved
• Whenever you learn a new concept like binary search, sliding window or two pointers solve different questions using these concepts and you never forget these concepts
• Remember you can not become a proficient problem solver in a day it takes time so trust the process and believe in consistency.

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