Soon, however, we will find that this is only possible where opposite bit states are adjacent to each other. For some people, describing a problem verbally is helpful in solving it. The first tag letter of each transmitter (AIT, FT) tells us its measurement function: chemical pH and flow, respectively. “Thought experiments” are useful in solving a wide variety of problems, because they allow us to test our understanding of a system’s behavior. Any problem becomes simpler to solve once we fully understand its rationale. One reason why students default to the “mental-only” approach when approaching new problems is that their educational experience has only presented annotation for specific types of problems. As a result, students tend to get “lost” when trying to solve new problems simply because they cannot readily reference of all their thoughts along the way. 10) Advanced Problem-Solving Strategies: Delegate and Separate Some of your team members work best on their own. Read the problem … Here, we see that FFC-23 must be reverse-acting, for if FT-23 reports a higher flow we will want FV-23 to close down. By imagining certain conditions or variables changing in a system and then asking ourselves what the effects will be, we probe our own understanding of that system, often times with the result being that we are able to predict its behavior under conditions that baffle us at first. A variety of problem-solving techniques have been presented for students over the years which are all helpful in tackling problems both in the classroom and in the real world. As problems never end, the need to solve them is also everlasting. Experience blocking progress. Here, ‘thought experiments’’ are useful as we imagine the process variable changing due to some load condition, and then determine how the controller must respond to bring that process variable back to setpoint. An application of this problem-solving strategy is found learning how to decode binary bits that have been encoded using the Manchester standard. Sometimes we may gain insight into the solution of a problem by assuming we already know the answer to a similar problem, then working “backward” to find the problem from that assumed solution. What made the difference between this problem as an elementary exercise and this same problem as a nearly impossible feat? Now we turn to the question of controller action, since we know the direction of each controller’s action (e.g. Thus, marking all the carry digits and subtotals is something they “only do” when performing multiplication by hand; marking calculated voltages and currents on a schematic diagram is something they “only do” when solving DC resistor circuits; taking notes when reading is something they “only do” when completing a book report. The freedom to write your steps on paper converts what would otherwise be a Herculean feat of arithmetic into a rather trivial exercise. General Problem Solving Strategies-Part 3. Download preview PDF. “What steps should I take to figure out where the data bits are?” they will ask. An example of this is the section explaining non-dispersive analyzers, which are instruments employing the absorption of light by certain species of chemicals in order to detect the presence and measure the quantities of those chemicals. pp 139-156 | Suddenly this elementary task becomes nearly impossible for anyone who isn’t a mathematical savant. Practice is the key to honing this skill. This service is more advanced with JavaScript available, Exploring Mathematics We know that all valves receive data, which means arrows must point toward the control valve. One particular example of this is the anecdote of Einstein observing a clock tower as he rode a trolley traveling away from the tower. Problem-Solving Strategies With 223 Figures 13 A-PDF Merger DEMO : Purchase from to remove the watermark. Following this reasoning, we see that AIC-28 should be direct-acting, calling for more nitric acid flow into the neutralizer as product pH becomes more alkaline (pH increases). What teachers should do is model and encourage annotation as a problem-solving technique for all types of problems, not just for some types of problems. In this case, we will write a short formula next to each controller denoting its action according to how the error is calculated (\(e = \hbox{PV} - \hbox{SP}\) for direct action and \(e = \hbox{SP} - \hbox{PV}\) for reverse action). Math problem solving strategies Some math problem solving strategies will be considered here. direct or reverse) is significant to how each controller will react to any given change in signal. If you are working in teams to solve a problem, a collaborative sketch goes a long way toward coordinating problem-solving efforts and ensuring everyone on the team has the same view of the problem. Annotating your intermediate steps as you solve a problem is actually an excellent general problem-solving strategy, applicable to far more than just arithmetic. What is the direction of action for each controller in the system. Learn all about general problem solving strategies. This reference may be referred to as often as necessary, without having to re-write the equations for each and every problem, thus eliminating unnecessary effort. If your brain tends to work like this – understanding concepts and situations better when they are cast into clear prose – then you may find it helpful to first draft an explanatory paragraph of the problem in your own words. Delegate a task (or a subset of a solution) to each of these people and watch them soar. This is a preview of subscription content, © Springer International Publishing AG, part of Springer Nature 2018,, Springer Undergraduate Mathematics Series. However, in the same ways that we teach strategies for other areas of maths, we can also teach strategies to solve maths problems. When we annotate the action of each controller, it is best to use symbols more descriptive than the words “direct” and “reverse,” especially due to the confusion this often causes when distinguishing the effects of a changing PV signal versus a changing SP signal. Over 10 million scientific documents at your fingertips. The discussion of problem solving strategies is extensive. “What would an observer see,” he wondered, “as he viewed the clock’s face while traveling away from it at the speed of light?” Concluding that the clock’s face would appear to be frozen in time was one of the surprising “experimental” results leading Einstein to a more rigorous examination of physical effects at extremely high velocities. This is also an exercise lending itself well to team-based problem solving, as the entire team can help each other describe the nature of the problem. Give them the opportunity to present their ideas verbally in an upcoming meeting. With Manchester encoding, binary bits are represented by the rising and falling edges of square-shaped waveforms rather than high and low states themselves. Read about General Problem-solving Techniques (Problem-solving and Diagnostic Strategies in Control System Analysis) in our free Automation Textbook Therefore, a helpful step in solving problems described to you in words is to translate those words into a picture to look at. While this technique is extremely useful, it might not always be practical or expedient. With Manchester encoding, binary bits are represented by the rising and falling edges of square-shaped waveforms rather than high and low states themselves. What does each instrument signal represent? This tells us the signal between AIC-28 and FFC-23 must be a cascade output-setpoint link, with AIC-28 as the master controller and FFC-23 as the slave controller. Create one now. Starting with the first two questions of where signals originate and terminate and what each signal represents, we may annotate this with arrows and text (shown in red): We know that all transmitters output data, and so all signal arrows should point away from all transmitters and toward all controllers. Angel Engel Institut f¨ur Didaktik der Mathematik Johann Wolfgang Goethe–Universit¨at Frankfurt am Main Senckenberganlage 9–11 60054 Frankfurt am Main 11 Germany Series Editor: Paul R. Halmos Department of Mathematics Santa Clara University Santa Clara, CA … This means the remote SP input must have a non-inverting effect on the output: a greater signal from AIC-28 will increase nitric acid flow into the neutralizer. Let’s face it: how soon would you give up on multiplying 3418 \(\times\) 572 without a calculator if you believed the only alternative was to manage all the arithmetic in your head? This strategy helps build your self-esteem at the same time it expands your mental energy for future problem-solving. Unable to display preview. Without this set-up, the task of analyzing the effects of FT-24 failing low would be much more difficult. General Problem Solving Strategies-Part 1 What does it take to solve any problem ? ... We usually don’t follow any fixed strategy for a new problem, as a new problem requires a different thinking to arrive at its solution. Suppose you were asked to solve this multiplication problem, without the use of a calculating machine of any kind, but with access to paper and a writing tool: Your primary school education should have prepared you to solve elementary arithmetic problems of this kind, by a process of digit-by-digit multiplication and addition, to arrive at an answer of 1,955,096.