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Observing the Pattern: How to Develop Mathematical Thinking with Young Children[^1^]



Typically, the observer pattern is implemented so that the subject being observed is part of the object for which state changes are being observed (and communicated to the observers). This type of implementation is considered tightly coupled, forcing both the observers and the subject to be aware of each other and have access to their internal parts, creating possible issues of scalability, speed, message recovery and maintenance (also called event or notification loss), the lack of flexibility in conditional dispersion and possible hindrance to desired security measures. In some (non-polling) implementations of the publish-subscribe pattern, this is solved by creating a dedicated message queue server (and sometimes an extra message handler object) as an extra stage between the observer and the object being observed, thus decoupling the components. In these cases, the message queue server is accessed by the observers with the observer pattern, subscribing to certain messages and knowing (or not knowing, in some cases) about only the expected message, while knowing nothing about the message sender itself; the sender may also know nothing about the observers. Other implementations of the publish-subscribe pattern, which achieve a similar effect of notification and communication to interested parties, do not use the observer pattern.[3][4]




Observing the Pattern.




In early implementations of multi-window operating systems such as OS/2 and Windows, the terms "publish-subscribe pattern" and "event-driven software development" were used as synonyms for the observer pattern.[5]


JavaScript has a deprecated Object.observe function that was a more accurate implementation of the observer pattern.[7] This would fire events upon change to the observed object. Without the deprecated Object.observe function, the pattern may be implemented with more explicit code:[8]


In Fig. 4a, we show the experimentally observed steady-state patterns and the RMS amplitude \(\sqrt\sum _\bfrA_\bfr^2/N\) as a function of the drive frequency Ω. The amplitude response peaks at certain frequencies, as opposed to observing an uninterrupted band extending over all the eigenfrequencies of the array. This is because only eigenmodes with predominantly long-wavelength contributions couple constructively to the spatially uniform drive such that only the lower end of the frequency band and hence its first few modes are experimentally accessible. In other words, if we would have a spatially non-uniform drive, then we should see a much larger frequency band than what we observe. In addition, the two strongest peaks feature elliptical pillar motions (see insets of Fig. 4a), hence according to our earlier analysis there must exist at least two (linearly polarized) array eigenmodes within the bandwidth of these peaks. A well-established useful quantity in polarization physics is the complex Stokes field \(\sigma =A^2\cos (2\zeta )e^2i\theta \) (Fig. 2a, b). By studying its average across all pillars, \(\sum _\bfr\sigma _\bfr/\sum _\bfrA_\bfr^2\), we can extract both the mean orientation (via the phase) and its fluctuations (via the magnitude). In Fig. 4a, these quantities have been color-coded to illustrate the evolution with frequency.


Encouraging careful observation usually leads your students to ask questions. This is the beginning of a scientific investigation! Also, scientists need to be able to repeat the experiments of other scientists exactly to check the conclusions and findings. This means observing systematically and recording observations carefully. It may also involve deciding what to look for, feel or hear before starting so that everyone observes in the same way. This allows the data gathered to be compared across groups. This activity is one way to help your students to develop the necessary skills and understanding about the importance of the rigorous nature of science investigations.


Because most of the Indian festivals are based on the lunar calendar, I asked the students to interview their family elder about the festivals or rituals observed by them and mark these on the drawings they made while observing the phases of the Moon. Some of them recorded the talk on their phones and we were able to listen to some in groups in class.


After one complete lunar cycle (28 days), we looked at the drawings and I asked the students if they could see a pattern. They noticed the change in the shape of the Moon in the sky and that in one month the shapes showed a regular change until they again became a full moon. The students really enjoyed this activity and asked lots of questions about the Moon. I was really pleased with the displays that gradually went up on the walls. It was very satisfying to see the students enjoy their learning. I thought in the next lesson I would use a model to explain the phases of the Moon and relate this to their displays.


With younger students, learning about objects in the sky should be entirely observational and qualitative in nature. This is to develop their skills in observing and help them to become more accurate and competent at gathering data. The Sun, Moon, stars, clouds, birds and aircraft all have properties, locations and movements that can be observed and described over time. Observations and patterns are also an important part of learning about living things in the environment. For example, looking at where and how plants grow.


Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.


The key difference then is at what point the photon is observed / interacted with and therefore localised - either close enough to the slits to reveal which slit it passed through, or far enough such that it remains uncertain. The former will produce the two bar pattern, the latter the interference pattern.


Now, when the photon interacts with the screen this does happen at a point, and indeed the interaction creates a spot on the photographic film/CCD/whatever at the point where the interaction happened. We can't say in advance where the interaction will occur, only that the probability of it happening is given by the wavefunction. So any one photon interacts at a point, but when we take many photons the points where they interact with the screen are distributed according to the wavefunction and together they build up the interference pattern.


Note the randomness of the pattern. Extrapolating the dots on the screen back to the two slits, either slit could be the source, there can be no unique track identification unless a detector(i.e an interaction as John explains) intervenes close to the slits after the particle passes through, and this would change the wavefunction.


The following exercises take us through nine ways of observing. They are inspired by Bill Mollison, one of the founders of permaculture, and by the lessons I've learned from the Wilderness Awareness School.... Taken together, they are the beginning of learning to read a landscape.


Simple inspection of the respiratory cycle, observing rate, rhythm, inspiratory volume, and effort of breathing, is all that is necessary. The rate is noted by observing the frequency of the inspiratory phase, since this phase is active and easy to count. Record the number of breaths per minute; this is the respiratory rate. While observing the rate, note the inspiratory expansion of the chest cage. This expansion should be the same during each cycle.


To maintain accurate control the respiratory system has a central respiratory pacemaker located within the medulla of the brainstem. Neural output travels from this center through the spinal cord to the muscles of respiration. The changes are effected through two groups of muscles, inspiratory and expiratory, which contract and relax to produce a rhythmic respiratory rate and pattern. In most individuals with unchanging metabolic demand, the rate and pattern are surprisingly constant, only interrupted every several minutes by a larger inspiratory effort or sigh. Ventilation at rest in most individuals requires only the inspiratory muscles. Expiration is usually passive and is secondary to the respiratory system returning to its resting state. Therefore, with quiet breathing the inspiratory time is the period of active respiratory pacemaker output. Adjusting the rate, length, and intensity of neural output from the pacemaker will lead to changes in the breaths per minute and the volume of each inspiration or tidal volume. These final outputs of the respiratory pacemaker, the rate and tidal volume, are the two components of ventilation. The expiratory muscles begin to play a role with disease or increased ventilatory demands. When this occurs, the length of time it takes to empty the lungs adequately will also lead to changes in rate and tidal volume.


A final modulator of the central respiratory drive is input from higher centers. For example, the state of being awake is associated with important neural inputs to the respiratory center that will play a large role in determining an individual's respiratory rate and pattern. When an individual falls asleep, the cortical input decreases, as does the respiratory center output. During nondreaming or non-rapid-eye-movement sleep, the input from the chemical receptors becomes increasingly important. If absent, apnea may result. During sleep associated with rapid eye movements or dreaming, the breathing patterns may be related to the contents of the dreams and again reflect input from higher cortical centers. Higher center input also accounts for hyperventilation associated with anxiety and other behavioral factors. 2ff7e9595c


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