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Sound Synthesis Theory/Oscillators and Wavetables

=Oscillators and Wavetables=

Oscillators

An oscillator is a repeating waveform with a fundamental frequency and peak amplitude and it forms the basis of most popular synthesis techniques today. Aside from the frequency or pitch of the oscillator and its amplitude, one of the most important features is the shape of its waveform. The time-domain waveforms in Fig. 5.1 show the four most commonly used oscillator waveforms. Although it is possible to use all kinds of unique shapes, these four each serve a range of functions that are suited to a range of different synthesis techniques; ranging from the smooth, plain sound of a sine wave, to the harmonically rich buzz of a sawtooth wave.

Oscillators are generally controlled by a keyboard synthesizer or MIDI protocol device. A key press will result in a MIDI note value which will be converted to a frequency value (Hz) that the oscillator will accept as its input, and the waveform period will repeat accordingly to the specified frequency. From here, the sound can be processed or manipulated in a variety of ways in the synthesizer or program to enrich or modify the sound further.

Generating oscillator waveforms
Note that the below diagrams have been incorrectly rendered. The x axis should be placed lower, every single signal should pass through y=0 at π radians.

Sine wave
As mentioned previously, the sine wave can be considered the most fundamental building block of sound. The best way to generate an oscillator which produces this waveform is to make use of an inbuilt library or function in the system concerned. Many programming languages have standard mathematics libraries with many of the trigonometric functions represented. A cycle of a sine wave is $$2 \pi$$ radians long and has a peak amplitude of $$+/-1$$, as shown in Fig. 5.2. In a digital system, the generated waves will be a series of equally-spaced values at the sample rate.

With a sample rate of 44100 cycles per second, and a required cycle length of 1 second, it will take 44100 samples to get from 0 to $$2\pi$$. In other words, we can determine the steps per cycle $$S$$ from cycle length $$T$$:

$$S = T \cdot F_{s} \,$$

Where $$F_{s}$$ is the sample rate. Each step will therefore take the following amount in radians:

$$\delta\phi = \frac{2\pi}{T \cdot F_{s}}$$ or $$\frac{2\pi f}{F_{s}}$$

Where $$f$$, in the second result, is the same result in terms of frequency. The importance of this is that it is possible to expand it into an algorithm that will be suitable for generating a sinusoidal wave of a user specified frequency and amplitude- effectively the simplest synthesizer possible! A sinusoidal wave can be generated by repeatedly incrementing a phase value by an amount required to reach a desired number of $$2\pi$$ length cycles a second, at the sample rate. This value can be passed to a sine function to create the output value, between the user specified peak amplitude.

Input: Peak amplitude (A), Frequency (f) Output: Amplitude value (y)

y = A * sin(phase)

phase = phase + ((2 * pi * f) / samplerate)

if phase > (2 * pi) then phase = phase - (2 * pi)

The most important thing to note about this algorithm is that when the phase value has exceeded $$2\pi$$ it will subtract by one whole period. This is to ensure that the function "wraps" round to the correct position instead of going straight back to 0; if a phase increment oversteps $$2\pi$$ and resets to 0, undesirable discontinuities would occur, causing harmonic distortion in the oscillatory sound.

Square wave
The square wave cannot be generated from a mathematical function library so easily but once again the algorithm is particularly straightforward since it is constructed from straight line segments. Unlike the sine wave, square waves have many harmonics above their fundamental frequency, and have a much brighter, sharper timbre. After examining a number of different waveforms it will start to become apparent that waveforms with steep edges and/or abrupt changes and discontinuities are usually harmonically rich.

(Note that the following square, sawtooth, and triangle functions are "naive"; they are equivalent to sampling the ideal mathematical functions without first bandlimiting them. In other words, all of the harmonics above the Nyquist frequency will be aliased back into the audible range.  This is most obvious when sweeping one of these waveforms into the high frequencies.  The aliased harmonics will move up and down the frequency spectrum, making "radio tuning" sounds in the background.  A better method to produce waveforms for audio would be additive synthesis, or something like MinBLEPs.  A properly-bandlimited waveform will have "jaggies" as you approach the discontinuities instead of piecewise straight lines.)

The square wave is constructed in a very similar fashion to the sine wave, and we use the same approach by cycling through a pattern with a phase variable, and resetting once we exceed $$2\pi$$ radians.

Input: Peak amplitude (A), Frequency (f) Output: Amplitude value (y)

if phase < pi then y = A else y = -A

phase = phase + ((2 * pi * f) / samplerate)

if phase > (2 * pi) then phase = phase - (2 * pi)

As is evident there is no reliance on an external function, the square wave can be defined by simple arithmetic, since it essentially switches between two values per cycle. One can expand on this by introducing a new variable which controls the point in the cycle the initial value switches to its signed value; this waveform is known as a pulse wave. Pulse waves are similar in character to square waves but the ability to modulate the switching point offers greater sonic potential.

Sawtooth wave

The sawtooth wave is more similar in sound to a square wave although it has harmonic decay and an appropriately "buzzy" timbre. It is constructed out of diagonal, sloping line segments and as such requires a line gradient equation in the algorithm. The mathematical form:

$$y = A - \frac{A}{\pi} \phi$$

Where $$A$$ represents amplitude and $$\phi$$ is the phase. This can be incorporated into the algorithmic form as follows:

Input: Peak amplitude (A), Frequency (f) Output: Amplitude value (y)

y = A - (A / pi * phase)

phase = phase + ((2 * pi * f) / samplerate)

if phase > (2 * pi) then phase = phase - (2 * pi)

Triangle wave

The triangle wave shares many geometric similarities with the sawtooth wave, except it has two sloping line segments. The algebra is slightly more complex and programmers may wish to consider consolidating the line generation into a new function for ease of reading. Triangle waves contain only odd-integer harmonics of the fundamental, and have a far softer timbre than square or saw waves, which is nearer to that of a sine wave. The mathematical form of the two lines segments are:

For $$0$$ to $$\pi$$ radians:

$$y = -A + \frac{2A}{\pi} \phi$$

For $$\pi$$ to $$2\pi$$ radians:

$$y = 3A - \frac{2A}{\pi} \phi$$

The algorithm then, is similar to the previous examples but with the gradient equations incorporated into it. In the example algorithms presented here it is evident that a range of different waveshapes can be designed, but there is the realisation that the shapes can only be described as mathematical functions. Complex shapes may become very demanding due to the increased processing power for more complicated mathematical statements.

Input: Peak amplitude (A), Frequency (f) Output: Amplitude value (y)

if phase < pi then y = -A + (2 * A / pi) * phase else y = 3A - (2 * A / pi) * phase

phase = phase + ((2 * pi * f) / samplerate)

if phase > (2 * pi) then phase = phase - (2 * pi)

Wavetables
There may be a situation or a desire to escape the limitations or complexity of defining an oscillatory waveform using mathematical formulae or line segments. As mentioned before, this could be a concern for processing power, or simply the fact that it would be easier to specify the shape through an intuitive graphical interface. In cases like these, musicians and engineers may use wavetables to be their source oscillator. Wavetables are popular in digital synthesis applications because accessing a block of memory is computationally faster than calculating values using mathematical operations.

The wavetable is in essence an array of N values, with values 1 through to N representing one whole cycle of the oscillator. Each value represents an amplitude at a certain point in the cycle. Wavetables are often displayed graphically with the option for the user to draw in the waveshape they require, and as such it represents a very powerful tool. There is also the possibility of loading a pre-recorded waveshape as well; but note that a wavetable oscillator is only a reference table for one cycle of a waveform; it is not the same as a sampler. The wavetable has associated with it a read pointer which cycles through the table at the required speed and outputs each amplitude value in sequence so as to recreate the waveform as a stream of digital values. When the pointer reaches the last value in the table array, it will reset to point one and begin a new cycle.

Using wavetables
The size of the wavetable and the sampling rate of the system determine what the fundamental frequency of the wavetable oscillator will be. If we have a wavetable with 1024 individual values and a sampling rate of 44.1 kHz, it will take:

$$\frac{1024}{44100} = 0.023 \,$$

seconds to complete one cycle. As previously shown, frequency can be determined from $$1 / t \,$$, giving us a fundamental frequency of:

$$\frac{1}{0.023} = 43.5$$ Hz.

It therefore becomes apparent that, in order to change the frequency of our oscillator we must change either the size of the wavetable or the sampling rate of the system. There are some real problems with both approaches:

 * Changing the wavetable size means switching to a different sized wavetable with the same, updated waveform. This would require dozens, hundreds, or even thousands of individual wavetables, one for each pitch, which is obviously totally inefficient and memory-consuming.

 * Digital systems, especially mixers that combine several synthesized or recorded signals, are designed to work at a fixed sampling rate and to make sudden changes to it is once again inefficient and extremely hard to program.

 * The sample rate required to play high frequencies with an acceptable level of precision becomes very high and puts high demand on the system.

One of the most practical and widely-used approaches to playing a wavetable oscillator at different frequencies is to change the size of the "steps" that the read pointer makes through the table. As with our previous example, our 1024-value wavetable had a fundamental frequency of 43.5 Hz when every point in the table was outputted. Now, if we stepped through the table every 5 values, we would have:

$$\frac{1024 / 5}{44100} = 0.0046 = 217.4$$ Hz.

It follows from this a general formulae for calculating the required step size, S for a given frequency, f:

$$S = N \frac{f}{F_{s}}$$

Where N is the size of the wavetable and $$F_{s}$$ is the sample rate. It is important to note that because the step size is being altered, the read pointer may not land exactly on the final table value N, and so it must "wrap around" in the same fashion as the functionally generated waveforms in the earlier section. This can be done by subtracting the size of the table from the current pointer value if it exceeds N; the algorithmic form of which can easily be gleaned from the examples above.

Frequency precision and interpolation
We must consider that some frequency values may generate a step size that has a fractional part; that is, it is not an integer but a rational number. In this case we find that the read pointer will be trying to step to locations in the wavetable array that do not exist, since each member of the array has an integer-valued index. There may be a value at position 50, but what about position 50.5? If we desire to play a frequency that uses a fractional step size, we must consider ways to accommodate it:

 * Truncation and rounding. By removing the fraction after the decimal point we reduce the step size to an integer—this is truncation. For instance, 1.3 becomes 1, and 4.98 becomes 4. Rounding is similar, but chooses the closest integer—3.49 becomes 3, and 8.67 becomes 9. For simple rounding, if the value after the decimal point is less than 5, we round down (truncate), otherwise we round up to the next integer. Rounding may be supported in the processor at no cost, or can be done by adding 0.5 to the original value and then truncating to an integer. For wavetable synthesis, the only difference between truncation and rounding is a constant 0.5 sample phase shift in the output. Since that is not detectable—and neither an improvement nor a detriment—a decision between truncation and rounding comes down to whichever is more convenient or quicker.

 * Linear interpolation. This is the method of drawing a straight line between the two integer values around the step location and using the values at both points to generate an amplitude value that interpolates between them. This is a more computationally demanding process but introduces greater precision.

 * Higher order interpolation. With linear interpolation considered first order interpolation (and truncation and rounding considered zero order interpolation) there are many higher-order forms that are commonly used—cubic Hermite, Lagrangian, and others. Just as linear interpolation requires two points for the calculation, higher orders require even more wavetable points to be used in the calculation, but produce a more accurate, lower distortion result. Sinc interpolation can be made arbitrarily close to perfect, at the expense of computation time.

By increasing the wavetable size, the precision of the above processes becomes greater and will result in a closer fit to the idealised, intended curve. Naturally, large wavetable sizes result in greater memory requirements. Some wavetable synthesizer hardware designs prefer table sizes that are powers of two (128, 256, 512, 1024, 2048, etc.), due to shortcuts that exploit the way in which digital memory is constructed (binary).


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Sound Synthesis Theory/Additive Synthesis

=Additive Synthesis=

Introduction
As previously discussed in Section 1, sine waves can be considered the building blocks of sound. In fact, it was shown in the 19th Century by the mathematician Joseph Fourier that any periodic function can be expressed as a series of sinusoids of varying frequencies and amplitudes. This concept of constructing a complex sound out of sinusoidal terms is the basis for additive synthesis, sometimes called Fourier synthesis for the aforementioned reason. In addition to this, the concepts of additive synthesis have also existed since the introduction of the organ, where different pipes of varying pitch are combined to create a sound or timbre.

A simple block diagram of the additive form may appear like in Fig. 6.1, which has a simplified mathematical form based on the Fourier series:

$$f(t) = a_0 + \sum_{n=1}^{\infty}a_n \sin(f_{n} t)$$

Where $$a_0$$ is an offset value for the whole function (typically 0), $$a_n$$ are the amplitude weightings for each sine term, and $$f_n$$ is the frequency multiplier value. With hundreds of terms each with their own individual frequency and amplitude weightings, we can design and specify some incredibly complex sounds, especially if we can modulate the parameters over time. One of the key features of natural sounds is that they have a dynamic frequency response that does not remain fixed. However, a popular approach to the additive synthesis system is to use frequencies that are integer multiples of the fundamental frequency, which is known as harmonic additive synthesis. For example, if the first oscillator's frequency, $$f_1$$ represents the fundamental frequency of the sound at 100 Hz, then the second oscillator's frequency would be $$f2 = 2f_1$$, and the third $$f3 = 3f_1$$ and so on. This series of sine waves produces an even "harmonic" sound that can be described as "musical". Oscillator frequency relationships that are not integer related, on the other hand, are called "inharmonic" and tend to be noisier and take on the characteristics of bells or other percussive sounds.

Constructing common harmonic waveforms in additive synthesis

If we know the amplitude weightings and frequency components of the first $$x$$ sinusoidal components or partials of a complex waveform, we can reconstruct that waveform using an additive system with $$x$$ oscillators. The popular waveforms square, sawtooth and triangle are harmonic waveforms because the constituent sinusoidal components all have frequencies that are integer multiples of the fundamental. The property that distinguishes them in this form is that they all have unique amplitude weightings for each sinusoid. Fig. 6.2 demonstrates the appearance of the time-domain waveform as a set of sines at unique amplitude weightings are added together; in this case the form begins to approximate a square wave, with the accuracy increasing with each added partial. Note that to construct a square wave we only include odd numbered harmonics- the amplitude weightings for $$a_2$$, $$a_4$$, $$a_6$$ etc. are 0. Below is a table that demonstrates the partial amplitude weightings of the common waveshapes:

A conclusion you may draw from Fig. 6.2 and the table is that it requires a large amount of frequency partials to create a waveform that closely approximates the idealised mathematical forms of the waveforms introduced in Section 5. For this reason, it should be apparent that additive synthesis techniques are perhaps not the best method for producing these forms. The strengths of additive synthesis lie in the fact that we can exert control over every partial component of our sound, which can produce some very intricate and wonderful results. With the constant modification of the frequency and amplitude values of each oscillator, the possibilities are endless. Some examples of ways to control the weightings and frequencies of each component oscillator are illustrated:

 * Manual control. The user controls a bank of oscillators with an external control device (typically MIDI), tweaking the values in real time. More than one person can join in and change / alter the timbre to their whims.

 * External data. Digital information from another source is taken and converted into appropriate frequency and amplitude values. The varying data source will then effectively be in 'control' of the timbral outcomes. Composers have been known to use data from natural sources or pieces derived from interesting geometric, aleatoric and mathematical models.

 * Recursive data. Given a source set of values and a set of algorithmic rules, the control parameters reference the previous value entered into the system to determine the result of the next one. Users may wish to "interfere" with the system to set the process on a new path. See Markov chains.

There is, however, the major consideration of computational power: complex sounds may require many oscillators all operating at once which will put major demand on the system in question.

Additive resynthesis
In Section 1 it was mentioned that just as it is possible to construct waveforms using additive techniques, we can analyse and deconstruct waveforms as well. It is possible to analyse the frequency partials of a recorded sound and then resynthesize a representation of the sound using a series of sinusoidal partials. By calculating the frequency and amplitude weighting of partials in the frequency domain (typically using a Fast Fourier transform), an additive resynthesis system can construct an equally weighted sinusoid at the same frequency for each partial. Older techniques rely on banks of filters to separate each sinusoid; their varying amplitudes are used as control functions for a new set of oscillators under the user's control. Because the sound is represented by a bank of oscillators inside the system, a user can make adjustments to the frequency and amplitude of any set of partials. The sound can be 'reshaped' - by alterations made to timbre or the overall amplitude envelope, for example. A harmonic sound could be restructured to sound inharmonic, and vice versa.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Sound Synthesis Theory/Subtractive Synthesis

=Subtractive Synthesis= Whereas additive synthesis is the process of combining individual sinusoidal partials to construct a complex sound, subtractive synthesis is essentially the reverse of this process. By starting with a harmonically (or partially) rich sound, a subtractive system will filter and modify the signal to reduce it to a desired form. By doing this, one can use one or two oscillators instead of a bank of 10 to achieve similar sonic results. Subtractive synthesis is an extremely popular method of synthesis that has been employed in hardware and software synthesizers since their popularity skyrocketed in the 1970s. This method of synthesis can be found traditionally in old modular or compact analogue synthesizers as well as modern virtual analogue models and software synthesizers. Fig. 7.1 illustrates a simple block diagram form of a subtractive system.

The oscillator will typically produce a waveform with a wide frequency spectrum (square wave, noise) at a frequency, $$f_1$$ and an amplitude $$a_1$$, although there can be two or perhaps even three oscillators in the design; any more begin to distract from the purpose of a subtractive synthesis technique although there are designs which exist. The filter block, which can be comprised out of many different types of filter (lowpass, bandpass), changes the character of the oscillator by controlling the balance of the frequency spectrum, before being modified further by additional effect modules built into the system. These elements can be user specified or automated using other oscillators or value envelopes. The subtractive approach is favoured by many musicians due to the fact that it is comparatively imprecise and therefore requires tweaking and experimentation of control parameters to get a desired sound.


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Sound Synthesis Theory/Modulation Synthesis

=Modulation Synthesis=

Introduction
When we talk about modulation from an audio synthesis point of view, we refer to a time-varying signal (the carrier) being affected in some way by another (the modulator). Modulation can be found in a range of different sound effects and synthesis techniques and some of these effects occur naturally and help us to identify certain types of sound; for instance the commonly found performance styles of tremolo (modulation of amplitude) and vibrato (modulation of frequency) that are used in many stringed instruments are examples of this. Modulation is typical in synthesis because it enriches the character of the sound and also adds to the variance in timbre / character over time which is so often found in nature.

In the two basic methods of modulation synthesis that occur, ring modulation and amplitude modulation, there are two unique types of signal that occur in each method: bipolar and unipolar signals. A bipolar signal is the type of signal we have been examining in previous chapters, it has both a negative and positive amplitude and the waveform generally "rests" around zero in a time-domain plot. A unipolar signal is a bipolar signal that has been constant-shifted, that is, a constant value added to the overall signal to shift it into a range above zero, typically between 0 and 1. The reason for these two different types of signal follows.

Ring Modulation
Ring modulation is the multiplication of two bipolar audio signals by each other. Each value of a carrier signal, C, is multiplied by a modulator signal, M, to create a new ring-modulated signal, R:

$$R(t) = C(t) \times M(t) \,$$

There are different ways to implement this; most likely it is suitable to simply multiply the two signals, but alternatively the amplitude input of a carrier module can be the output of a modulator module, as well. The frequency of the modulator signal also plays an important role in the characteristic of the RM signal. From this, we achieve the following important result:

When the frequency of M is in the audible range, that is, 20 Hz or more, there is an effect on the timbre of the signal. The variations in amplitude become fast enough that the modulator generates a set of frequency sidebands. With two sine waves as carrier and modulator, RM will generate a frequency spectrum containing two sidebands, which are the sum and difference of the carrier and modulator frequencies. When this occurs, the actual carrier frequency is removed from the spectrum, leaving two harmonic sidebands (if the frequency of C and M are an integer ratio to one another) or two inharmonic sidebands (if the ratio is otherwise). For instance, if the carrier is 900 Hz and the modulator is 500 Hz, we will get two sidebands; one at 400 Hz (900 - 500) and one at 1400 Hz (900 + 500).

If C and M are not sine waves (i.e. their waveforms are more complex) then the resultant signal will contain more than one or many different sidebands at different frequencies and amplitudes, indicating a more complex sound. Figure 8.2 illustrates two examples of ring modulation - the original example with frequencies C = 900 and M = 500 but also when C = 400 and M = 1000, which introduces negative frequencies into the spectrum. This results in a "wrapping" phenomenon where the difference sideband of C and M is -600 Hz! As a result, we find that a difference sideband occurs at 600 Hz, and that is true for any negative frequency; a sideband will occur at its the unsigned (positive) frequency.

Amplitude Modulation
In the ring modulation equation the frequency of the carrier signal is not present anymore in the resulting sound. In order to avoid this, the ring modulation equation can be modified. Amplitude modulation is mathematically expressed as:

$$A(t) = C(t) \times (M(t)+1) \,$$

Where C is the carrier signal and M is a unipolar modulator, typically set to vary between values of 0 and 1. Without mention of the unipolar modulator, this technique would appear to be identical to ring modulation. Like ring modulation, amplitude modulation produces a pair of sidebands for every sinusoidal component in the carrier and modulator, and these sidebands are generated at frequencies the sum and difference of the two signal frequencies. The difference between the two techniques is highlighted here:

One of the advantages of AM, like its cousin, RM, is that using just two signals or oscillators, we can create some partially rich signals. Using a harmonically dense signal such as a square wave oscillator can create a wealth of sidebands from a minimum of control parameters and computation. Control over these generated partials may not, however, be as detailed and straightforward as techniques such as additive synthesis. As a result, we find that AM and RM is used more often in signal processing than signal generation.

Expanding on amplitude modulation requires us to introduce more parameters and elements to the technique to give it some "weight" with other, more popular techniques. For instance, we can introduce into the system a unipolar low-frequency oscillator which is set to control the amplitude of the modulator; by changing the amplitude of the modulator we are modifying what is known as the modulation index; a factor which controls the strength of the AM sidebands. In addition to modifying the amplitude of the modulator, we can also modify the frequency of the modulator. As you may expect, this causes a shift in the frequencies of the sidebands generated through the AM process and can, carefully controlled, produce some interesting, dynamic sounds that are hard to produce with other techniques. Breaking away from sinusoidal oscillators in both cases of carrier and modulator, and even the modulation of the modulation index is one of the first steps to exploring this technique; try experimenting with the waveshapes introduced in the previous chapters.


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Sound Synthesis Theory/Synthesis Software and Tools

=Synthesis software / tools=

Analysis
Audacity - Wave editor with analysis and basic synthesis / modification tools. Free

Ardour - Digital audio workstation. Free

SPEAR - Spectrum analysis and resynthesis tool. Proprietary freeware

Hosts (VST, MIDI etc.)
VSTHost - Host for VST plugins. Windows. Free

Modular / environment
Pure Data (Pd) - Audio processing, synthesis and analysis environment. Free

OpenMusic - Visual programming language based on CommonLisp / CLOS. Free

Kyma - Sound design environment. Proprietary

Max / MSP - Audio processing, synthesis and analysis environment. Proprietary

Reaktor - Audio processing, synthesis and analysis environment. Proprietary

Synthedit - Modular synthesizer / VST plugin builder. Proprietary

Programming
SuperCollider - Object orientated audio programming language. Free

Overtone - Functional audio programming language written in Clojure, interfacing with SuperCollider. Free

CSound - Audio programming language. Free

Nyquist - Audio programming language. Free

ChucK - Strongly-timed, Concurrent, and On-the-fly Music Programming Language. Free

Synthesizers
SynFactory - Modular software synthesizer. Free

SynthEdit - Modular software synthesizers and effects units. <font style="color: orange">Proprietary


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Sound Synthesis Theory/Links and Bibliography

=Links and Bibliography=

Links
Sound On Sound Magazine - Many articles on synthesis available online to view.

The Theory and Techniques of Electronic Music - Electronic music manual written by Miller Puckette, inventor of Puredata.

Mathematics Of The Discrete Fourier Transform - Electronic manual on the application of mathematics to many areas of digital sound synthesis / processing by Julius O. Smith, inventor of digital waveguide synthesis.

Related / Useful Wikibooks
Control Systems - Inter-disciplinary engineering text that analyzes the effects and interactions of mathematical systems.


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Muggles' Guide to Harry Potter/Characters/Alecto Carrow

Overview
Alecto Carrow, sister of Amycus Carrow, is a Death Eater. When she is initially described, all Harry seems to notice about her is her repeated, almost-nervous giggle.

Goblet of Fire
Alecto and Amycus are two of the Death Eaters who were summoned after Lord Voldemort's rebirth. While their names are not mentioned by Voldemort, their membership in that group is strongly implied by Snape's comments in the early chapters of Harry Potter and the Half-Blood Prince.

Half-Blood Prince
Severus Snape mentions the Carrows when he is talking to Narcissa Malfoy and Bellatrix Lestrange.

The Carrows take part in the Battle of Lightning-Struck Tower. Both of them are at the top of the tower when Snape kills Albus Dumbledore. As Harry chases Snape through the battle and out the front door, he sees Alecto dueling with Minerva McGonagall before fleeing with Snape. We later see her on the grounds where she escapes along with her brother and Thorfinn Rowle.

Deathly Hallows
With Snape being appointed Headmaster of Hogwarts, and Charity Burbage having been killed by Voldemort, there are vacancies for Defence Against the Dark Arts and Muggle Studies teachers. Alecto Carrow is given the post of Muggle Studies teacher. Neville Longbottom tells Harry that, under Alecto, Muggle Studies seems to have become institutionalized hatred of Muggles, promulgating falsehoods about how Muggles are a lower order, dirty and stupid.

Alecto, told by Lord Voldemort to expect Harry to visit Ravenclaw Tower, has herself let into the Ravenclaw common room before Harry's arrival. When Harry steps out from under the Invisibility Cloak to examine the statue of Rowena Ravenclaw, Alecto sees him and summons Voldemort by touching her Dark Mark. She is then Stunned by Luna Lovegood, who was accompanying Harry, and had remained under the Invisibility Cloak. Bound by Professor McGonagall, she takes no further part in the story.

Strengths
Alecto compensates for her lack of intelligence by the use of unrestrained violence and Unforgivable Curses, most notably the Cruciatus curse. It is debatable whether this could be considered a strength. At the very least she seems more intelligent than Amycus.

Weaknesses
Alecto is not particularly intelligent. When her brother Amycus is unable to enter Ravenclaw tower, eventually he forces Professor McGonagall to open the door for him. Professor McGonagall at that time says that Professor Flitwick had earlier opened the door for Alecto, leading us to understand that she also was unable to answer the eagle's-head door knocker's query.

Relationships with Other Characters
While there is apparently some closeness between herself and her brother, Amycus Carrow, the only dealings we see her having with other people are situations in which she is operating from a position of power, or dueling. Her usual mode of interpersonal relationship seems to be taunting. Unlike other Death Eaters, Alecto trusted Snape immediately upon his return to the Death Eaters.

From her treatment of the students, as related by Neville, we can safely guess that Alecto disliked any sign of independent thought from the students. In this, she seems to be following Voldemort's lead with his own underlings.

Questions

 * 1) Why did Lord Voldemort select Alecto Carrow as a teacher at Hogwarts?
 * 2) Was Alecto Carrow a good choice? Explain.


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Contemporary Educational Psychology/Chapter 7: Classroom Management and the Learning Environment/Preventing Management Programs

Preventing Management Problems by Focusing Students on Learning
The easiest management problems to solve are ones that do not happen in the first place! You can help to prevent problems even before the first day of school by arranging classroom furniture and materials in ways that make learning as easy to focus on as possible. Later, during the first few days, you can establish procedures and rules that support a focus on learning even more.

Arranging Classroom Space
Viewed broadly, it may be tempting to think that classrooms are arranged in similar ways, but there are actually important alternative arrangements to consider. Variations happen because of grade level, the subjects taught, the teacher’s philosophy of education, and of course the size of the room and the furniture available. Whatever the arrangement that you choose, it should help students to focus on learning tasks as much as possible and minimize the chances of distractions. Beyond these basic principles, however, the “best” arrangement depends on what your students need and on the kind of teaching that you prefer and feel able to provide (Bothmer, 2003; Nations & Boyett, 2002). Here are some ideas to help choose among your options. In considering them (and before moving too much furniture around your room!), you might want to try experimenting with spatial arrangements “virtually” by using one of the computer programs available on the Internet (see, for example, http://teacher.scholastic.com/tools/class_setup/).

Displays and Wall Space
All classrooms have walls, of course, and how you fill or use them can affect the mood or feeling of a classroom. More displays make the room more interesting and can be used to reinforce curriculum goals and display (and hence recognize) students’ work. But too many displays can also make a room seem “busy” or distracting as well as physically smaller; and they can also be more work to maintain. If you are starting a new school year, then, there is usually a need to decorate some of the wall or bulletin board space, but no urgent need to fill it all. Leaving some open space can give flexibility to respond to curriculum or learning needs that emerge after the year is underway. The same advice applies for displays that are especially high maintenance, such as aquariums, pets, and plants. These can serve wonderfully as learning aids, but do not have to be in place on the first day of school. Not only the students, but also you yourself, may already have enough distractions to cope with at that time.

Computers in the Classroom
If you are like the majority of teachers, you will have only one computer in your room, or at most just a few, and their placement may be pre-determined by location of power and cable outlets. If so, you need to think about computer placement early in the process of setting up a room. Once the location of computers is set, locations for desks, high-usage shelves, and other moveable items can be chosen more sensibly—in general so as to minimize distractions to students and to avoid unnecessary traffic congestion.

Visibility of and Interactions with Students
Learning is facilitated if the furniture and space allow you to see all students and to interact with them from a comfortable distance. Usually this means that the main, central part of the room—where desks and tables are usually located—needs to be as open and as spacious as possible. While this idea may seem obvious, enacting it can sometimes be challenging in practice if the room itself is small or unusually shaped. In classrooms with young students (kindergarten), furthermore, open spaces tend to allow, if not invite, movement of children that is longer and faster—a feature that you may consider either constructive or annoying, depending on your educational goals and the actual level of activity that occurs.

Spatial Arrangements Unique To Grade Levels or Subjects
Some room arrangements depend significantly on the grade level or subject area of the class. If you teach in elementary school, for example, you may need to think about where students can keep their daily belongings, such as coats and lunches. In some schools, these can be kept outside the classroom—but not in all schools. Some subjects and grade levels, furthermore, lend themselves especially well to small group interaction, in which case you might prefer not to seat students in rows, but around several small-group tables or work areas. The latter arrangement is sometimes preferred by elementary teachers, but is also useful in high schools wherever students need lots of counter space, as in some shops courses, or wherever they need to interact, as in English as a Second Language courses (McCafferty, Jacobs, & Iddings, 2006). The key issue in deciding between tables and rows, however, is not grade level or subject as such, but the amount of small group interaction you want to encourage, compared to the amount of whole-group instruction. As a rule, tables make talking with peers easier, and rows make listening to the teacher more likely and group work slightly more awkward to arrange. Ironically, some teachers experience challenges about room arrangement without even having a room of their own, because they must “float” or move among other teachers’ rooms. “Floating” is especially likely among specialized teachers (e.g. music teachers in elementary schools, who move from class to class) and in schools that are short on classrooms overall. Floating can sometimes by annoying to the teacher, though it actually also has advantages, such as not having to take responsibility for how other teachers’ rooms are arranged). If you find yourself floating, it helps to consider a few key strategies, such as:
 * consider using a permanent cart to move crucial supplies from room to room;
 * make sure that every one of your rooms has an overhead projector (do not count on using chalkboards in other teachers’ rooms);
 * talk to the other teachers about having at least one shelf or corner in each room designated for your exclusive use.

Establishing Daily Procedures and Routines
Procedures or routines are specific ways of doing common, repeated classroom tasks or activities. Examples include checking daily attendance, dealing with students who arrive late, or allowing students to use the bathroom during class or go to their lockers to get materials which they forgot to bring. Procedures also include ways of turning in or retrieving daily homework (e.g. putting it on a designated shelf at a particular time), or of gaining the teacher’s attention during quiet seat work (e.g. raising your hand and waiting), or of choosing and starting a “free choice” activity after completing a classroom assignment.

Procedures serve the largely practical purpose of making activities and tasks flow smoothly and efficiently—a valuable and necessary purpose in classrooms, where the actions of many people have to be coordinated within limited amounts of time. As such procedures are more like social conventions than like moral expectations. They are not primarily about what is ethically right or ethically desirable to do (Turiel, 2006). Most procedures or routines can be accomplished in more than one way, with only minor differences in success at the outcomes. There is more than one way, for example, for the procedure of taking attendance: the teacher could call the role, delegate a student to call the role, or simply note students’ presence on a seating chart. Each variation accomplishes essentially the same task, and the choice among them may therefore be less important than the fact that the class coordinates its actions somehow, by committing to some sort of choice.

For teachers, of course, an initial task is to establish procedures and routines in the first place. Because of the conventional quality of procedures, some teachers find that it works well simply to announce and explain key procedures without inviting much discussion from students (“Here is how we will choose partners for the group work”). Other teachers, however, prefer to invite input from students when creating procedures (asking “What do you feel is the best way for students to get my attention during a quiet reading time?”). Both approaches have advantages as well as disadvantages. Simply announcing key procedures saves time and insures consistency in case you are teaching more than one class (as you would in high school). But it creates a bigger responsibility to choose procedures that are truly reasonable and practical. On the other hand, inviting students’ input can help students to become aware of and committed to procedures, but at the cost of taking more time to establish them, and at the risk of creating confusion if you teach multiple classes, each of which adopts different procedures. Whatever approach you choose, you and the students of course have to take into account the procedures or rules imposed by the school or school district as a whole. A school may have a uniform policy or expectation about how to record daily attendance, for example, and that policy may determine, either partly or completely, how you take attendance with your particular students.

Establishing Classroom Rules
Unlike procedures or routines, rules express standards of behavior for which individual students need to take responsibility. Although they may help in insuring the practical efficiency of classroom tasks, they are really about encouraging students to be personally responsible for learning, as well as for behaving decently and respectfully with each other. Table 7-X lists a typical set of classroom rules.

Note three things about the rules in Table 7-X. One is that they are not numerous; the table lists only five. Most educational experts recommend keeping the number of rules to a minimum in order to make them easier to remember (Thorson, 2003; Brophy, 2003). Another feature is that they are stated in positive terms (“Do X…”) rather than negative terms (“Do not do Y…”), a strategy that emphasizes and clarifies what students should do rather than what they should avoid. A third feature is that each rule actually covers a collection of more specific behaviors. The rule “Bring all materials to class,” for example, potentially covers bringing pencils, paper, textbooks, homework papers, and permission slips—depending on the situation. As a result of being stated somewhat generally, rules contain a degree of ambiguity that sometimes requires interpretation. Infractions may occur, that is, that are marginal or “in a grey area,” rather than clearcut. A student may bring a pen, for example, but the pen may not work properly, and you may therefore wonder whether this incident is really a failure to follow the rule, or just an unfortunate (and in this case minor) fault of the pen manufacturer.

As with classroom procedures, rules can be planned either by the teacher alone, or by the teacher with advice from students. The arguments for each approach are similar to the arguments for procedures: rules “laid on” by the teacher may be more efficient and consistent, and in this sense more fair, but rules influenced by the students may be supported more fully by the students. Because rules focus strongly on personal responsibility, however, there is a stronger case for involving students in making classroom rules than in making classroom procedures (Brookfield, 2006; Kohn, 2006). In any case the question of who plans classroom rules is not necessarily an either/or choice. It is possible in principle to impose certain rules on students (for example, “Always be polite to each other”) but let the students determine the consequences for violations of certain rules (for example, “If a student is discourteous to a classmate, he/she must apologize to the student in writing”). Some mixture of influences is probably inevitable, in fact, if only because of your own moral commitments as a teacher and because the school itself is likely to have rules of its own (like “No smoking in the school” or “Always walk in the hallways”). A classroom set of rules therefore might need to refer to and honor this broader source of rules somehow, if only by including a classroom rule stating something like “Obey all school rules.”

(back to Chapter 7...)


text:
Contemporary Educational Psychology/Chapter 7: Classroom Management and the Learning Environment/Pacing and Structuring

Pacing and Structuring Lessons and Activities
One of the best ways to prevent management problems is by pacing and structuring lessons or activities as smoothly and continuously as possible. Reaching this goal depends on three major strategies:
 * selecting tasks or activities at an appropriate level of difficulty for your students,
 * providing a moderate level of structure or clarity to students about what they are supposed to do, especially during transitions between activities, and
 * keeping alert to the flow and interplay of behaviors for the class as a whole and for individuals within it.

Each of these strategies presents its own special challenges to teachers, but also its own opportunities for helping students to learn.

Choosing Tasks at an Appropriate Level of Difficulty
As experienced teachers know and as research has confirmed, students are most likely to engage with learning when tasks are of moderate difficulty, neither too easy nor too hard and therefore neither boring nor frustrating (Britt, 2005). Finding the right level of difficulty, however, can sometimes be a challenge if you have little experience in teaching a particular grade level or curriculum, or even if a class is simply new to you and in this sense “unknown.” Whether familiar to you or not, members of any class are likely to have diverse abilities and readiness, and this fact alone makes it harder to determine what level of difficulty is appropriate. A common strategy for dealing with these ambiguities is to begin units, lessons, or projects with tasks or content that is relatively easy and familiar, and then gradually introduce more difficult material or tasks until students seem challenged, but not overwhelmed. Using this strategy gives the teacher a chance to observe and diagnose students’ learning needs before adjusting content, and gives students a chance to orient themselves to the teacher’s expectations and the topic of study without becoming stressed or frustrated prematurely. Later in a unit, lesson, or project, students are then in a better position to deal with more difficult tasks or content (Van Merrionboer, 2003). The principle seems to help even with “authentic” learning projects—ones that resemble real-world activities of students (such as learning to drive an automobile), and that present a variety of complex tasks simultaneously. Even in those cases it helps for the teacher to isolate and focus on the simplest subtasks first (such as “put the key in the ignition”) and only move to harder tasks later (such as parallel parking).

Sequencing instruction is only a partial solution to finding the best “level” of instruction, because it still does not deal with lasting differences among students as individuals. The core challenge to teachers is to fully individualize or differentiate instruction: to tailor instruction or activities not only to the class as a group, but to the differences among members of the class? One way to approach this problem is to plan different content or activities for different students or groups of students. While one group works on Task A, another group works on Task B; one group works on relatively easy math problems, for example, while another works on harder ones. Taken very far, managing multiple activities or tasks obviously complicates a teacher’s job, but it can and has been done by many teachers (and it also can make teaching more interesting!). (In Chapter 8, "Instructional Strategies", we describe some classroom management strategies that can help with the multi-tasking that differentiated instruction requires.

Providing Moderate Amounts of Structure and Detail
Chances are that at some point in your educational career you have asked, or at least wished, that a teacher would clarify or explain an assignment more fully, and thereby give it more structure or organization. Students’ need and desire for clarity is especially common with assignments that are by nature open-ended, such as long essays, large projects, or creative works. Simply being told to “write an essay critiquing the novel,” for example, leaves more room for uncertainty (and worry) than being given guidelines about what the essay should contain, what topics or parts it should have, and its appropriate length or style (Chesebro, 2003). Students’ need for structure and clarity varies, furthermore, not only among assignments, but among students as individuals. Some students desire it more than others, and perform especially well when provided with relatively more structure and clarity. Students with certain kinds of learning difficulties, in particular, often learn more effectively and stay on task more if provided with somewhat more explicit or detailed instructions about the specific tasks expected for assignments (Marks, 2003).

As a teacher, the challenge is to accommodate students’ need for clarity without making guidance so specific or detailed that students have little room to think for themselves. Carried to a (ridiculous) extreme, for example, a teacher can give “clear” instructions for an essay by announcing not only exactly which articles to read and cite in preparing for the essay and which topics or issues to cover, but even the wording of the key sentences in their essays. This much specificity may reduce students’ uncertainties and make the teacher’s task of evaluating the essays relatively straightforward and easy. But it also reduces or even eliminates the educational value of the assignment—assuming, of course, that its purpose is to get students to think for themselves.

Ideally, then, structure should be moderate rather than extreme. There should be just enough to give students some sense of direction and to stimulate more accomplishment than if they worked with less structure or guidance. This ideal is essentially Vygotsky’s idea of the zone of proximal development that we discussed in Chapter 2: a place (figuratively speaking) where students get more done with help than without it. The ideal amount of guidance—and the “location” of the zone of proximal development—may vary with the assignment and with the student, and it may (hopefully) decrease over time for all students. One student may need more guidance to do his or her best in math, but less guidance in order to write his best essay. Another student may need the reverse. Both students may need less at the end of the year than at the beginning.

Managing Transitions
The time between activities is often full of distractions and “lost” time, and is often when inappropriate behaviors are especially likely to occur. Part of the problem is intrinsic to transitions: students often have to wait before a new activity begins, and therefore get bored, at the same moment when the teacher may be preoccupied with locating and arranging materials for the new activity. From the point of view of students, therefore, transitions may seem essentially like unsupervised group time, when (seemingly) “anything goes.”

Minimizing such problems requires two strategies, one of which is easier to implement than the other. The easier strategy is for you, as teacher, to organize materials as well as possible ahead of time, so that you minimize the time needed to begin a new activity or class session. This advice sounds simple, and mostly is, but it can sometimes take a bit of practice to implement smoothly. When one of us (Kelvin) first began teaching university, for example, particular papers or overhead transparencies would sometimes move “magically” into the wrong folder in spite of his efforts to keep them where he would find them easily, and finding them caused delays at the last minute while students waited.

A second, more complex strategy is to teach students as many ways as possible to manage their own behavior during transitions (Marzano & Marzano, 2004). If students talk too loudly between activities, for example, then discuss with them what constitutes appropriate levels or amounts of talk during those times, as well as about the need for them to monitor their own sound level at that time. Or if students stop work early in anticipation of the end of an activity, then talk about—or even practice—using a signal from yourself to indicate the true ending point for an activity. If certain students continue working beyond the end of an activity, on the other hand, then try giving students advance warning of the impending end of the activity, and remind them about their taking the responsibility for actually finishing work once they hear the advance warning. And so on. The point of all of these tactics is to encourage students’ sense of responsibility for their behavior transitions, and thereby reduce your own need to monitor them at that crucial time.

None of these ideas, of course, mean that you, as teacher, can or should give up monitoring students’ behavior entirely. Chances are that you still will need to notice if and when someone talks too loudly, finishes too early, or continues too long, and you will still need to give those students appropriate reminders. But the amount of reminding will be less to the extent that students can remind and monitor themselves—a welcome trend at any time during the day, but especially during transitions.

Maintaining the Flow of Activities
A lot of classroom management is really about keeping activities flowing smoothly, both during individual lessons and across the school day. The trouble with this straightforward-sounding idea, however, is that there is never just “one” event happening at a time, even if only one activity has been formally planned and is supposed to be occurring. Even if, for example, everyone is supposed to be attending a single whole-class discussion on a topic, individual students will be having different experiences at any one moment. Several students may be listening and contributing comments, for example, but a few others may be planning what they want to say next and ignoring the current speakers, still others may ruminating about what a previous speaker said, and still others may be thinking about unrelated matters, like using the restroom, food, or sex. Things get even more complicated if the teacher deliberately plans multiple activities: in that case some students may interact with the teacher, for example, while others do work in an unsupervised group or work independently in a different part of the room. How is a teacher to keep activities flowing smoothly in the face of such variety?

A common mistake of beginning teachers in multi-faceted activity settings like these is to pay too much attention to any one activity, student, or small group, at the expense of noticing and responding to all the others. If you are helping a student on one side of the room but someone on the other side disturbs classmates with off-task conversation, it tends to be less effective either to finish with the student you are helping before attending to the disruption, or to interrupt your help for the student until you have solved the disruption on the other side of the room. Either approach is likely to allow the flow of activities to be disrupted somewhere; there is a risk that either the student’s chatting may spread to others, or the interrupted student may become bored with waiting to regain the teacher’s attention and get off-task herself.

A better solution, though at first it may seem tricky or challenging, is to attend to both events at once—a strategy that was named withitness in a series of now-classic research students several decades ago (Kounin, 1970). Withitness does not mean that you focus on all simultaneous activities with equal care, but only that you are aware multiple activities, behaviors, and events to some degree. At a particular moment, for example, you may be focusing on helping a student, but in some corner of your mind you also notice when chatting begins on the other side of the room. You have, as the saying goes, “eyes in the back of your head.” Research has found that experienced teachers are much more likely to show withitness than inexperienced teachers, and that these qualities are associated with their managing classrooms successfully (Emmer & Stough, 2001).

Simultaneous awareness—withitness—makes possible responses to the multiple events that are immediate and nearly simultaneous—what educators sometimes called overlapping. The teacher’s responses to each event or behavior need not take equal time, nor even be equally noticeable to all students. If you are helping one student with seat work at the precise moment when another student begins chatting off-task, for example, a quick glance to the second student may be enough to bring him back to the work at hand, and may scarcely interrupt your conversation with the first student, or be noticed by others who are not even involved. The result is a smoother flow to activities overall.

As a new teacher, you may find your initial skill at withitness and overlapping develops more easily in some situations than in others. It may be easier to keep an eye (and an ear) on the entire class during familiar routines, for example, like taking attendance, and harder to do the same during lessons or activities that are unfamiliar or complex, such as introducing a new topic or unit that you have never taught before. But skill at broadening your attention can and does increase with time and practice. So it helps to keep trying. Merely demonstrating to students that you are “withit,” in fact, even without making deliberate overlapping responses, can sometimes deter students from task behavior. Someone who is tempted to pass notes in class, for example, might not to do so because she decides that you will probably notice her doing it anyway.

Communicating the Importance of Learning and of Positive Behavior
Taken together, arranging space, establishing procedures and rules, and developing withitness about multiple events set the stage for communicating an important message: that the classroom is a place where learning and positive social behavior are priorities. In addition, teachers can convey this message by giving feedback to students in a timely way, by keeping accurate records of their performance, and by deliberately communicating with parents or caregivers about their children and about activities in class.

Communicating effectively is so important for all aspects of teaching, in fact, that we discuss it more fully later in this book (see Chapter 12 about the nature and communication and about ways to facilitate it). Here we focus on only one of its important aspects: how communication contributes to a smoothly functioning classroom by conveying the importance of learning to students and their families.

Giving Timely Feedback
Feedback is a term often used by educators to refer to responses given to students about their behavior or performance. Feedback is essential for students if they are to learn or if they are to develop classroom behavior that is new or more subtle and “mature.” But feedback can only be fully effective if received as soon as possible, when it is still relevant to the task or activity at hand which is usually as soon as possible (Reynolds, 1992). A score on a test is more informative immediately after a test than after a six-month delay, when students may have forgotten much of the content of the test. A teacher’s comment to a student about an inappropriate, off-task behavior may not be especially welcome immediately after the behavior occurs, but it can be more influential and informative then; later, both teacher and student have trouble remembering the context of the off-task behavior, and in this sense may literally “not know what they are talking about.” The same is true for comments about a positive behavior by a student: hearing a compliment right away makes it easier to connect the comment with the behavior, and allows the compliment to influence the student more strongly. Even though there are of course practical limits to how fast feedback can be given, the general principle is clear: feedback tends to work better when it is timely.

The principle of timely feedback is consistent, incidentally, with one of the principles of operant conditioning discussed in Chapter 2: reinforcement works best when it follows a to-be-learned operant behavior closely. In this case think of a teacher’s feedback as a form of reinforcement. The analogy is easiest to understand when the feedback takes the form of praise for something a student did or performed; in operant conditioning terms, the reinforcing praise then functions like a “reward.” But the analogy to operant conditioning still holds when feedback is negative—when a teacher criticizes or reprimands a student. In those cases the criticism or reprimand sometimes functions like what Skinner call an “aversive stimulus” (or mild punishment), shutting down the behavior criticized. At other times, though, a teacher’s criticism functions in a more paradoxical and unexpected way: it acts less like an aversive stimulus than like a negative reinforcement. In these cases the criticism does not shut down a behavior (as true punishment might do), but leads to a less negative state for the student. This happens, for example, if a student misbehaves in order to gain attention from the teacher or classmates and to avoid being ignored. If the teacher in this case criticizes the student for the misbehavior, the student may experience the criticism as a reduction in isolation and as in increase in his importance in the class—in other words, as reinforcement for misbehavior. So the inappropriate behavior continues, and as teachers we might be tempted to say that “he is just misbehaving to get attention.” Figure 7-1 diagrams this sequence of events.

Maintaining Accurate Records
Although timeliness in responding to students can sometimes happen easily or spontaneously, there are also situations where promptness depends on having organized key information ahead of time. Obvious examples are the scores, marks, and grades returned to students for their work. With a short quiz (like, say, a weekly spelling test), it may be possible to return it quite soon after the quiz—especially if you or even your students themselves can mark it during class. More often, though, assignments and tests requiring longer processing times: you have to take significant time personally to read, score, or add constructive comments. The time needed for this work can reduce the usefulness of a teacher’s evaluations to students when she finally does return assignments (Black, et al., 2004). During the days or weeks while students wait for a test or assignment to be returned, they are left without information about quality or nature of their performance; at the extreme they may even have to complete a next test or assignment before getting any information from an earlier one. (Perhaps you have already experienced this problem during your years as a student!)

Delays in providing feedback about academic performance can never be eliminated entirely, but they can be reduced by keeping accurate, well-organized records of students’ work. We offer suggestions for organizing academic records in Chapter 10, but for now we simply emphasize that grading systems benefit students’ learning the most when they provide feedback as quickly and frequently as possible—precisely the circumstances which accurate, well-organized record-keeping can help the most. A number of computer programs are available to help with this challenge; if your school does not already have one in use, then there are several downloadable either free or at low cost from the Internet (e.g. http://dmoz.org/Computers/Software/Educational/Teachers_Help/Gradebooks/).

Accurate records are helpful not only for scores on tests, quizzes or assignments, but also for keeping descriptive information about the nature of students’ academic skills or progress. A common way to do so is the student portfolio, which is a compilation of the student’s work and on-going assessments of it added by the teacher or by the student (Moritz & Christie, 2005; White, 2005). To know of how a student’s science project evolved from its beginning, for example, a teacher and student can keep a portfolio of lab notes, logs, preliminary data, and the like. To know how a student’s writing skills are developing, on the other hand, they could keep a portfolio of early drafts on various writing assignments. As the work accumulates, the student can discuss it with the teacher, and either of them can write brief reflections on its strengths thus far and on the next steps needed to improve the work further. By providing a way to respond to work as it evolves, portfolios can respond to students’ work relatively promptly, and in any case sooner than if a teacher waited until the work was complete or final. (For more on portfolios, see [[Contemporary Educational Psychology/Chapter 10: Teacher-Made Assessments of Learning|Chapter 10).

Communicating with Parents and Caregivers
Since parents and caregivers in a sense “donate” children to schools (at least figuratively speaking), teachers are responsible for keeping parents informed and involved to whatever extent is practical. Virtually all parents understand and assume that schools are generally intended for learning, but communication can enrich their understanding of how this purpose is realized in their particular child’s classroom, and it can show them more precisely what their particular child is doing there. Such understanding in turn allows parents and caregivers to support their child’s learning more confidently and “intelligently,” and in this sense contributes, at least indirectly, to a positive learning environment in their child’s class.

There are various ways to communicate with parents, each with advantages and limitations. Here are three common examples:
 * A regular classroom newsletter: The advantage of a newsletter is that it establishes a link with all parents or caregivers with comparatively little effort on the part of the teacher. Since it is not likely to be concerned the problems of individual students, furthermore, it can be phrased in very positive terms. At the beginning of the year, for example, a newsletter can tell about special materials that students will need, important dates to remember (like professional development days when there is no school), or about curriculum plans for the next few weeks. But newsletters also have limitations. They can seem impersonal, for example, or they may get lost on the way home and never reach parents or caregivers. They can also be impractical for teachers with multiple classes, as in high school or in specialist subjects (like music or physical education), where each class may follow a different program or have a different purpose.
 * Telephone calls: The main advantage of phoning is its immediacy and individuality. Teacher and parent or caregiver can talk about a particular student, behavior, or concern, and it now. By the same token, however, phone calls are not an efficient way to inform parents about events or activities that affect everyone in common. The individuality of phoning may explain why teachers tend to use this method more often when a student has a problem that is urgent or unusual—as when he has failed a test or has misbehaved seriously. Rightly or wrongly, a student’s successes may not seem urgent enough to merit a call to the student’s home (though perhaps students are more likely to communicate their successes to parents themselves, than to communicate their failures).
 * Parent-teacher conferences: Most schools schedule regular times—often a day or an evening—when teachers meet briefly with any parents or caregivers who request a meeting. Under good conditions, the conferences can have the individuality of phone calls, but also the greater richness of communication possible in face-to-face meetings. Since conferences are available to all parents, they need not focus on behavior or academic problems, but often simply help to build rapport and understanding between parents or caregivers and the teacher. Sometimes too, particularly at younger grade levels, teachers organize conferences to be led by the student, who displays and explains his or her work using a portfolio or other archive of accumulated materials (Benson & Barnett, 2005; Stiggins & Chappuis, 2005). In spite of all of these advantages, though, parent-teacher conferences have limitations. Some parents have trouble getting to conferences, for example, because of their work schedules. Others may feel intimated by any school-sponsored event because they speak limited English or because they remember getting along poorly in school themselves as children.

Even if you make all of these efforts to communicate, some parents may remain out of contact. In these cases it is important to remember that the causes may not be parents’ indifference to their child or to the value of education. Other possibilities exist, as some of our comments above indicate: parents may have difficulties with child care, for example, have inconvenient work schedules, or feel self-conscious because of their own limited English skills (Stevens & Tollafield, 2003). Whatever the reasons, there are ways to encourage parents who may be shy, hesitant, or busy. One is to think of how they can assist the class or school even from home—for example, by making materials to be used in class or (if they are comfortable using English) phoning other parents about class events. A second way is to have a specific task for the parents in mind—one with clear structure, definite starting and ending points, and one that truly will benefit the class if someone can in fact complete it. A third is to encourage, support, and respect the parents’ presence and contributions when they do show up at school functions. Keep in mind, after all, that parents are experts about their own particular children, and without their efforts, you would have no students to teach!

(back to Chapter 7...)


text:
Contemporary Educational Psychology/Chapter 7: Classroom Management and the Learning Environment/Responding to Misbehavior

Responding to Student Misbehavior
So far we have focused on preventing behaviors that are off-task, inappropriate, or annoying. Our advice has all been pro-active or forward-looking: plan the classroom space thoughtfully, create reasonable procedures and rules, pace lessons and activities appropriately, and communicate the importance of learning clearly. Although we consider these ideas to be important, it would be naïve to imply they are enough to prevent all behavior problems. For various reasons, students sometimes still do things that disrupt other students or interrupt the flow of activities. At such moments the challenge is not about long-term planning but about making appropriate, but prompt responses. Misbehaviors left alone can be contagious, a process educators sometimes call the ripple effect (Kounin, 1970). Chatting between two students, for example, can gradually become chatting among six students; rudeness by one can eventually become rudeness by several; and so on. Because of this tendency, delaying a response to inappropriate behavior can make the job of getting students back on track harder than responding to it as immediately as possible.

There are many ways to respond to inappropriate behaviors, of course, and they vary in how much they focus on the immediate behavior of a student rather than on longer-term patterns of behavior. There are so many ways to respond, in fact, that we can only describe a sampling of the possibilities here. None are effective all of the time, though all do work at least some of the time. We start with a response that may not seem on the surface like a remedy at all—simply ignoring misbehaviors.

Ignoring Misbehaviors
A lot of misbehaviors are not important enough or frequent enough to deserve any response from the teacher at all. They are likely to disappear (or extinguish, in behaviorist terms) if simply left alone. If a student who is usually quiet during class happens to whisper to a neighbor once in awhile, it is probably simpler, less disruptive, and just as effective to ignore this rare infraction of a classroom rule. And some misbehaviors may not be worth a response even if they are frequent, as long as they do not seem to bother others. Suppose, for example, that a certain student has a habit of choosing quiet seat work times to sharpen her pencil. Yet this behavior is not really noticed by others. Is it then really a problem, however unnecessary or ill-timed it may be? In both examples ignoring the behavior may be wise because there is little danger of the behavior spreading to other students or of become even more frequent. Interrupting your activities—or the students’—might cause more disruption than simply ignoring the problem.

That said, there can sometimes still be problems in deciding whether a particular misbehavior is indeed minor, infrequent, or unnoticed by others. Unlike in our example above, a student may whisper more than “rarely” but less than “often”: in that case, when do you decide that the whispering is in fact too frequent and needs a more active response from you? Or that student who taps her pencil, whom we mentioned above, may not bother most others, but she may nonetheless bother a few. In that case how many bothered classmates are “too many”—five, three, just one, or…? In these grey, ambiguous cases, you may need a more active way of dealing with an inappropriate behavior, like the ones described in the next sections.

Gesturing Nonverbally
Sometimes it works to communicate using gestures, eye contact, or “body language” that involve little or no speaking. Nonverbal cues are often appropriate if a misbehavior is just a bit too serious or frequent to ignore, but not serious or frequent enough to merit taking the time deliberately to speak to or talk with the student. If two students are chatting off-task for a relatively extended time, for example, sometimes a glance in their direction, a frown, or even just moving closer to the students is enough of a reminder to get them back on task. And even if these responses prove not to be enough, they may help to keep the off-task behavior from spreading to other students.

A risk of relying on nonverbal cues, however, is that some students may not understand their meaning, or even notice them. If the two chatting students mentioned above are too engrossed in their talking, for example, they may not see you glance or frown at them. Or they might notice but not interpret your cue as a reminder to get back on task. Misinterpretation of nonverbal gestures and cues is a little more likely with young children, who are still learning the subtleties of adults’ nonverbal “language” (Guerrero & Floyd, 2005; Heimann, et al., 2006). It can also be more likely with students who speak limited English and whose cultural background differs significantly different from yours, because the students may be used to communicating nonverbally in ways that literally “look different” from the ways familiar to you (Marsh, Elfenbein, & Ambady, 2003).

Natural and Logical Consequences
Consequences are the outcomes or results of an action. When managing a classroom, two kinds of consequences are especially effective, at least when the conditions are appropriate: natural consequences and logical consequences. Natural consequences are ones that happen “naturally” or without any deliberate intention by anyone. If a student is late for class, for example, a natural consequence is that he may miss information or material that he needs to do an assignment. Logical consequences are ones that happen because of the responses of others, but that also have an obvious or “logical” relationship to the original action. If one student steals another’s lunch, for example, a logical consequence might be for the thief to reimburse the victim for the cost of the lunch. Natural and logical consequences are often woven together and thus hard to distinguish: if one student picks a fight with another student, a natural consequence might be injury to the aggressor (a natural risk of fighting), but a logical consequence might to lose friends (the response of others to fighting). In practice both may occur.

In general research has found that natural and logical consequences can be effective for minimizing undesirable behaviors, provided they are applied in appropriate situations (Weinstein, Tomlinson-Clarke, & Curran, 2004). Take, for example, a student who runs impulsively down school hallways. By the very nature of this action, he or she is especially likely to have “traffic accidents,” and thus (hopefully) to see that running is not safe and to reduce the frequency of running. Or think of a student who chronically talks during class instead of working on a class-time assignment. A logical outcome of this choice is to require the student to make up the assignment later, possibly as homework. Because the behavior and the consequence are connected directly, the student is relatively likely to see the drawback of choosing to talk, and to reduce how much he or she talks on subsequent occasions. In both cases, the key features that make natural and logical consequences work is
 * 1) that they are appropriate to the misbehavior and
 * 2) that the student sees or understands the connection between the consequences and the original behavior.

Notice, though, that natural and logical consequences do not work for every problem behavior; if they did, there would be no further need for management strategies! One limitation is that misbehaviors can sometimes be so serious that no natural or logical consequence seems sufficient or appropriate. Suppose, for example, that one student deliberately breaks another student’s eyeglasses. There may be a natural consequence for the victim (he or she will not be able to see easily), but not for student who broke the glasses. There may also be no logical consequences for the aggressor that are fully satisfactory: the misbehaving student will not be able to repair the broken glasses and may not even be able to pay for new glasses for the victim.

Another limitation of natural and logical consequences is that their success depends on the motives of the misbehaving student. If the student is seeking attention or acceptance by others, then the consequences often work well. Bullying in order to impress others, for example, is more likely to lose friends than to win them—so this sort of bullying is to some extent self-limiting. If a student is seeking power over others, on the other hand, then consequences may not work well. Bullying in order to control others’ actions, for example, may actually achieve its own goal, and its “natural” results (losing friends) would not affect it. And of course, students may sometimes act from combinations of motives, with the result that natural and logical consequences may succeed, but only partially.

A third problem with natural and logical consequences is that they can easily be confused with deliberate punishment (Kohn, 2006). The difference is important. Consequences are focused on repairing damage and restoring relationships, and in this sense consequences focus on the future. Punishments, in contrast, highlight the mistake or wrongdoing and in this sense focus on the past. Consequences tend to be more solution focused; punishments tend to highlight the person who committed the action and to shame or humiliate the wrong doer. (Table 7-2 summarizes these and other differences.)

Classroom examples of the differences are plentiful. If a student is late for class, then a consequence may be that he or she misses important information, but a punishment may be that the teacher scolds or reprimands the student. If a student speaks rudely to the teacher, a consequence may be that the teacher does not respond to the comment, or simply reminds the student to speak courteously. A punishment may be that the teacher scolds the student in the presence of other students, or even imposes a detention (“Stay after school for 15 minutes”).

Conflict Resolution and Problem Solving
When a student misbehaves persistently and disruptively, you will need strategies that are more active and assertive than the ones discussed so far, and that lead to conflict resolution—the reduction of disagreements that persist over time. The conflict resolution strategies that educators and teachers advocate and use usually have two parts (Jones, 2004). First, the strategies involve a way of identifying precisely what “the” problem is. Once this is done, they require reminding the student of classroom expectations and rules without apology or harshness, but with simple clarity and assertiveness. When used together, the clarification and assertion can not only reduce conflicts between a teacher and an individual student, but also provide a model for other students to consider when they have disagreements of their own.

 * Step 1: Clarifying and Focusing Problem Ownership: Classrooms can be emotional places even when its primary purpose is to promote “thinking” rather than the expression of feelings as such. The emotional quality can be quite desirable: it can give teachers and students “passion” for learning and respect or even good feelings for each other. But it can also cause trouble if students misbehave: at those moments negative feelings—annoyance, anger, discomfort—can interfere with understanding exactly what went wrong and how to set things right again. But gaining a bit of distance from the negative feelings is exactly those moments need, especially by the teacher, the person with (presumably) the greatest maturity.

 * In one widely cited and used approach to conflict resolution called Teacher Effectiveness Training, the educator Thomas Gordon discusses this challenge as a matter of identifying problem ownership: deciding whose problem a behavior or conflict really is (Gordon, 2003). The “owner” of the problem is the primary person who is troubled or bothered by it. The owner can be the student committing the behavior, or the teacher, or another student who merely happens to see the behavior. Since the owner of a problem needs to take responsibility for solving it, ownership makes a difference in how to deal with the behavior or problem effectively.

 * Suppose, for example, that a student makes a remark that the teacher finds offensive (like “Fats kids are stupid”). This could be primarily the teacher’s problem because it is mostly the teacher who is bothered by the remark. The student may not believe that anything serious is wrong with the remark. On the other hand, suppose that a different student complains repeatedly that classmates refuse to let him into group projects. This is less likely to be the teacher’s problem than the student’s: the student’s difficulty may affect the student’s ability to do his work, but not really affect the teacher’s ability to do her work. Then again (on the “third” hand?!), a problem may affect several people at once. That student who criticizes “fat kids” may discover that he is offending not only the teacher, but also classmates, who therefore avoid working with him. At that point everyone shares in some aspect of “the” problem: the criticizing student is prevented from doing his group work, and many classmates and the teacher are offended.

 * Step 2: Active, Empathetic Listening: Diagnosing accurately who really has a problem with a behavior—who owns it—is helped by a number of strategies. One is active listening—attending carefully to all aspects of what a student says and attempting to understand or empathize with it as fully as possible, even if you do not agree with what is being said (Cooper & Simonds, 2003). Active listening involves asking a lot of questions in order continually to check your understanding. It also involves encouraging the student to elaborate or expand on his or her remarks, and paraphrasing and summarizing what the student has said in order to check your perceptions of what is being said. It is important not to move too fast toward “solving” the problem with advice, instructions, or scolding, even if these are responses that you might, as a teacher, feel responsible for making. Responding too soon in these ways can shut down communication prematurely, and leave you with an inaccurate impression of the source of the problem.

 * Step 3: Assertive Discipline and I-Messages: Once you have listened well enough to understand the student’s point of view, it helps to frame your responses and comments in terms of how the student’s behavior affects you as a teacher. The comments should have several features:

 * They should be assertive—neither passive and apologetic, nor unnecessarily hostile or aggressive. State what the problem is, as matter-of-factly as possible: “Joe, you are talking while I’m explaining something,” instead of either “Joe, do you think you could be quiet now?” or “Joe, be quiet!”

 * The comments should emphasize I-messages, which are comments that focus on how the problem behavior is affecting the teacher’s ability to teach, as well as how the behavior makes the teacher feel. They are distinct from you-messages, which focus on evaluating the mistake or problem which the student has created. An I-message might be, “Your talking is making it hard for me to remember what I’m trying to say.” A you-message might be, “Your talking is rude.”

 * The comments should encourage the student to think about the effects of his or her actions on others—a strategy that in effect encourages the student to consider the ethical implications of the actions (Gibbs, 2003). Instead of simply saying, “When you cut in line ahead of the other kids, that was not fair to them,” you can try saying, “How do you think the other kids feel when you cut in line ahead of them?”

 * Step 4: Negotiation: The steps so far describe ways of interacting that are desirable, but also fairly specific in scope and limited in duration. In themselves they may not be enough when conflict persists over time and develops a number of complications or confusing features. A student may persist, for example, in being late for class, in spite of diverse efforts by the teacher to modify this behavior. Two students may persist in speaking rudely to each other, even though the teacher has mediated this conflict in the past. Or a student may fail to complete homework, time after time. Because these problems develop over time, and because they may involve repeated disagreements between teacher and student, they can eventually become stressful for the teacher, for the student, and for any classmates who may be affected. Their persistence can tempt a teacher simply to announce or dictate a resolution—a decision that may simply leave everyone feeling defeated, including the teacher.

 * Often in these situations it is better to negotiate a solution, which means systematically discussing options and compromising on one if possible. Negotiation always requires time and effort, though usually not as much as continuing to cope with the original problem, and the results can be beneficial to everyone. A number of experts on conflict resolution have suggested strategies for negotiating with students about persistent problems (Davidson & Wood, 2004). The suggestions vary in detail, but usually include some combination of the steps we have already discussed above, along with a few others.

 * Decide as accurately as possible what the problem is—Usually this step involves a lot of the active listening described above.

 * Brainstorm possible solutions, and then consider their effectiveness—Remember to include students in this step; otherwise you are simply imposing a solution on others, which is not what negotiation is supposed to achieve.

 * Choose a solution, if possible by consensus—Complete agreement on the choice may not be possible, but strive for it as best you can. Remember that taking a vote may be a democratic, acceptable way to settle differences in many situations. If feelings are running high, however, voting has an ironic by-product: it simply allows individuals to “announce” their differences to each other and therefore maintain the conflict.

 * Pay attention later to how well the solution works—For many reasons, things may not work out the way you or the students hope or expect, and you may need to renegotiate the solution at a later time.

(back to Chapter 7...)


text:
Contemporary Educational Psychology/Chapter 6: Student Motivation/Motives as Interests

Motives as Interests
In addition to holding different kinds of goals—with consequent differences in academic motivation—students show obvious differences in level of interest in the topics and tasks of the classroom. Suppose that two high school classmates, Frank and Jason, both are taking chemistry, and specifically learning how to balance chemical equations. Frank finds the material boring and has to force himself to study it; as a result he spends only the time needed to learn the basic material and to complete the assignments at a basic level. Jason, on the other hand, enjoys the challenges of balancing chemical equations. He thinks of the task as an intriguing puzzle; he not only solves each of them, but also compares the problems to each other as he goes through them.

Frank’s learning is based on effort compared to Jason’s, whose learning is based more fully on interest. As the example implies, when students learn from interest they tend to devote more attention to the topic than if they learn from effort (Hidi & Renninger, 2006). The finding is not surprising since interest is another aspect of intrinsic motivation—energy or drive that comes from within. A distinction between effort and interest is often artificial, however, because the two motives often get blended or combined in students’ personal experiences. Most of us can remember times when we worked at a skill that we enjoyed and found interesting, but that also required effort to learn. The challenge for teachers is therefore to draw on and encourage students’ interest as much as possible, and thus keep the required effort within reasonable bounds—neither too hard nor too easy.

Situational Interest versus Personal Interest
Students’ interests vary in how deeply or permanently they are located within students. Situational interests are ones that are triggered temporarily by features of the immediate situation. Unusual sights, sounds, or words can stimulate situational interest. A teacher might show an interesting image on the overhead projector, or play a brief bit of music, or make a surprising comment in passing. At a more abstract level, unusual or surprising topics of discussion can also arouse interest when they are first introduced. Personal interests are relatively permanent preferences of the student, and are usually expressed in a variety of situations. In the classroom, a student may (or may not) have a personal interest in particular topics, activities, or subject matter. Outside class, though, he or she usually has additional personal interests in particular non-academic activities (e.g. sports, music) or even in particular people (a celebrity, a friend who lives nearby). The non-academic personal interests may sometimes conflict with academic interest; it may be more interesting to go to the shopping mall with a friend than to study even your most favorite subject.

Benefits of Personal Interest
In general personal interest in an academic topic or activity tends to correlate with achievement related to the topic or activity. As you might suppose, a student who is truly interested is more likely to focus on the topic or activity more fully, to work at it for longer periods, to use more thoughtful strategies in learning—and to enjoy doing so (Hidi & Renninger, 2006). Small wonder that the student achieves more! Note, though, a persistent ambiguity about this benefit: it is often not clear whether personal interest leads to higher achievement, or higher achievement leads to stronger interest. Either possibility seems plausible. Research to sort them out, however, has suggested that at least some of the influence goes in the direction from interest to achievement; when elementary students were given books from which to learn about a new topic, for example, they tended to learn more from books which they chose themselves than from books that were simply assigned (Reynolds & Symons, 2001). So interest seemed to lead to learning. But this conclusion does not rule out its converse, that achievement may stimulate interest as well. As Joe learns more about history, he steadily finds history more interesting; as McKenzie learns more about biology, she gradually wants to learn more of it.

Stimulating Situational Interests
If a student has little prior personal interest in a topic or activity, the teacher is faced with stimulating initial, situational interest, in hopes that the initial interest will gradually become a more permanent and personal. There are a number of strategies for meeting this challenge:

 * It helps to include surprises in your comments and in classroom activities from time to time: tell students facts that are true but counter-intuitive, for example, or demonstrate a science experiment that turns out differently than students expect (Guthrie, Wigfield, & Humenick, 2006).

 * It also helps to relate new material to students’ prior experiences even if their experiences are not related to academics or to school directly. The concepts of gravitation and acceleration, for example, operate every time a ball is hit or thrown in a softball game. If this connection is pointed out to a student who enjoys playing a lot of softball, the concepts can make concepts more interesting.

 * And it helps to encourage students to respond to new material actively. By having students talk about the material together, for example, student can begin making their own connections to prior personal interests, and the social interaction itself helps to link the material to their personal, social interests as well.

A Caution: Seductive Details
Even though it is important to stimulate interest in new material somehow, it is also possible to mislead or distract students accidentally by adding inappropriate, but stimulating features to new material (Garner, et al., 1992; Harp & Mayer, 1998). Distractions happen a number of ways, such as any of these among others:

 * deliberately telling jokes in class,
 * using colorful illustrations or pictures,
 * adding interesting bits of information to a written or verbal explanation.

When well chosen, all of these moves can indeed arouse students’ interest in a new topic. But if they do not really relate to the topic at hand, they may simply create misunderstandings or prevent students from focusing on key material. As with most other learning processes, however, there are individual differences among students in distractability, with students who are struggling more prone to distraction and misunderstanding than students who are already learning more successfully (Sanchez & Wiley, 2006). On balance the best advice is probably therefore to use strategies to arouse situational interest, but to assess students’ responses to them continually and as honestly as possible. The key issue is whether students seem to learn because of stimulating strategies that you provide, or in spite of them.

(back to Chapter 6...)