4.7: Molecular Structure and Polarity
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Learning Objectives
By the end of this section, you will be able to:
- Predict the structures of small molecules using valence shell electron pair repulsion (VSEPR) theory
- Explain the concepts of polar covalent bonds and molecular polarity
- Assess the polarity of a molecule based on its bonding and structure
Thus far, we have used two-dimensional Lewis structures to represent molecules. However, molecular structure is actually three-dimensional, and it is important to be able to describe molecular bonds in terms of their distances, angles, and relative arrangements in space (Figure \(\PageIndex{1}\)). A bond angle is the angle between any two bonds that include a common atom, usually measured in degrees. A bond distance (or bond length) is the distance between the nuclei of two bonded atoms along the straight line joining the nuclei. Bond distances are measured in Ångstroms (1 Å = 10 –10 m) or picometers (1 pm = 10 –12 m, 100 pm = 1 Å).
VSEPR Theory
Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular structure, including approximate bond angles around a central atom, of a molecule from an examination of the number of bonds and lone electron pairs in its Lewis structure. The VSEPR model assumes that electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between these electron pairs by maximizing the distance between them. The electrons in the valence shell of a central atom form either bonding pairs of electrons, located primarily between bonded atoms, or lone pairs. The electrostatic repulsion of these electrons is reduced when the various regions of high electron density assume positions as far from each other as possible.
VSEPR theory predicts the arrangement of electron pairs around each central atom and, usually, the correct arrangement of atoms in a molecule. We should understand, however, that the theory only considers electron-pair repulsions. Other interactions, such as nuclear-nuclear repulsions and nuclear-electron attractions, are also involved in the final arrangement that atoms adopt in a particular molecular structure.
As a simple example of VSEPR theory, let us predict the structure of a gaseous BeF 2 molecule. The Lewis structure of BeF 2 (Figure \(\PageIndex{2}\)) shows only two electron pairs around the central beryllium atom. With two bonds and no lone pairs of electrons on the central atom, the bonds are as far apart as possible, and the electrostatic repulsion between these regions of high electron density is reduced to a minimum when they are on opposite sides of the central atom. The bond angle is 180° (Figure \(\PageIndex{2}\)).
Figure \(\PageIndex{3}\) illustrates this and other electron-pair geometries that minimize the repulsions among regions of high electron density (bonds and/or lone pairs). Two regions of electron density around a central atom in a molecule form a linear geometry; three regions form a trigonal planar geometry; four regions form a tetrahedral geometry; five regions form a trigonal bipyramidal geometry; and six regions form an octahedral geometry.
Electron-pair Geometry versus Molecular Structure
It is important to note that electron-pair geometry around a central atom is not the same thing as its molecular structure. The electron-pair geometries shown in Figure \(\PageIndex{3}\) describe all regions where electrons are located, bonds as well as lone pairs. Molecular structure describes the location of the atoms , not the electrons.
We differentiate between these two situations by naming the geometry that includes all electron pairs the electron-pair geometry . The structure that includes only the placement of the atoms in the molecule is called the molecular structure . The electron-pair geometries will be the same as the molecular structures when there are no lone electron pairs around the central atom, but they will be different when there are lone pairs present on the central atom.
For example, the methane molecule, CH 4 , which is the major component of natural gas, has four bonding pairs of electrons around the central carbon atom; the electron-pair geometry is tetrahedral, as is the molecular structure (Figure \(\PageIndex{4}\)). On the other hand, the ammonia molecule, NH 3 , also has four electron pairs associated with the nitrogen atom, and thus has a tetrahedral electron-pair geometry. One of these regions, however, is a lone pair, which is not included in the molecular structure, and this lone pair influences the shape of the molecule (Figure \(\PageIndex{5}\)).
As seen in Figure \(\PageIndex{5}\), small distortions from the ideal angles in Figure \(\PageIndex{3}\) can result from differences in repulsion between various regions of electron density. VSEPR theory predicts these distortions by establishing an order of repulsions and an order of the amount of space occupied by different kinds of electron pairs. The order of electron-pair repulsions from greatest to least repulsion is:
\[\text { lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair } \nonumber \]
This order of repulsions determines the amount of space occupied by different regions of electrons. A lone pair of electrons occupies a larger region of space than the electrons in a triple bond; in turn, electrons in a triple bond occupy more space than those in a double bond, and so on. The order of sizes from largest to smallest is:
\[\text { lone pair }>\text { triple bond }>\text { double bond }>\text { single bond } \nonumber \]
Consider formaldehyde, H 2 CO, which is used as a preservative for biological and anatomical specimens (Figure \(\PageIndex{1}\)). This molecule has regions of high electron density that consist of two single bonds and one double bond. The basic geometry is trigonal planar with 120° bond angles, but we see that the double bond causes slightly larger angles (121°), and the angle between the single bonds is slightly smaller (118°).
In the ammonia molecule, the three hydrogen atoms attached to the central nitrogen are not arranged in a flat, trigonal planar molecular structure, but rather in a three-dimensional trigonal pyramid (Figure \(\PageIndex{5}\)) with the nitrogen atom at the apex and the three hydrogen atoms forming the base. The ideal bond angles in a trigonal pyramid are based on the tetrahedral electron pair geometry. Again, there are slight deviations from the ideal because lone pairs occupy larger regions of space than do bonding electrons. The H–N–H bond angles in NH 3 are slightly smaller than the 109.5° angle in a regular tetrahedron (Figure \(\PageIndex{3}\)) because the lone pair-bonding pair repulsion is greater than the bonding pair-bonding pair repulsion (Figure \(\PageIndex{5}\)). Figure \(\PageIndex{6}\) illustrates the ideal molecular structures, which are predicted based on the electron-pair geometries for various combinations of lone pairs and bonding pairs.
According to VSEPR theory, the terminal atom locations (Xs in Figure \(\PageIndex{6}\)) are equivalent within the linear, trigonal planar, and tetrahedral electron-pair geometries (the first three rows of the table). It does not matter which X is replaced with a lone pair because the molecules can be rotated to convert positions. For trigonal bipyramidal electron-pair geometries, however, there are two distinct X positions, as shown in Figure \(\PageIndex{7}\) an axial position (if we hold a model of a trigonal bipyramid by the two axial positions, we have an axis around which we can rotate the model) and an equatorial position (three positions form an equator around the middle of the molecule). As shown in Figure \(\PageIndex{6}\), the axial position is surrounded by bond angles of 90°, whereas the equatorial position has more space available because of the 120° bond angles. In a trigonal bipyramidal electron-pair geometry, lone pairs always occupy equatorial positions because these more spacious positions can more easily accommodate the larger lone pairs.
Theoretically, we can come up with three possible arrangements for the three bonds and two lone pairs for the ClF 3 molecule (Figure \(\PageIndex{7}\)). The stable structure is the one that puts the lone pairs in equatorial locations, giving a T-shaped molecular structure.
When a central atom has two lone electron pairs and four bonding regions, we have an octahedral electron-pair geometry. The two lone pairs are on opposite sides of the octahedron (180° apart), giving a square planar molecular structure that minimizes lone pair-lone pair repulsions (Figure \(\PageIndex{6}\)).
Predicting Electron Pair Geometry and Molecular Structure
The following procedure uses VSEPR theory to determine the electron pair geometries and the molecular structures:
- Write the Lewis structure of the molecule or polyatomic ion.
- Count the number of regions of electron density (lone pairs and bonds) around the central atom. A single, double, or triple bond counts as one region of electron density.
- Identify the electron-pair geometry based on the number of regions of electron density: linear, trigonal planar, tetrahedral, trigonal bipyramidal, or octahedral (Figure \(\PageIndex{6}\), first column).
- Use the number of lone pairs to determine the molecular structure (Figure \(\PageIndex{6}\)). If more than one arrangement of lone pairs and chemical bonds is possible, choose the one that will minimize repulsions, remembering that lone pairs occupy more space than multiple bonds, which occupy more space than single bonds. In trigonal bipyramidal arrangements, repulsion is minimized when every lone pair is in an equatorial position. In an octahedral arrangement with two lone pairs, repulsion is minimized when the lone pairs are on opposite sides of the central atom.
The following examples illustrate the use of VSEPR theory to predict the molecular structure of molecules or ions that have no lone pairs of electrons. In this case, the molecular structure is identical to the electron pair geometry.
Example \(\PageIndex{1}\): Predicting Electron-pair Geometry and Molecular Structure: CO 2 and BCl 3
Predict the electron-pair geometry and molecular structure for each of the following:
- carbon dioxide, CO 2 , a molecule produced by the combustion of fossil fuels
- boron trichloride, BCl 3 , an important industrial chemical
Solution
(a) We write the Lewis structure of CO 2 as:
This shows us two regions of high electron density around the carbon atom—each double bond counts as one region, and there are no lone pairs on the carbon atom. Using VSEPR theory, we predict that the two regions of electron density arrange themselves on opposite sides of the central atom with a bond angle of 180°. The electron-pair geometry and molecular structure are identical, and CO 2 molecules are linear.
(b) We write the Lewis structure of BCl 3 as:
Thus we see that BCl 3 contains three bonds, and there are no lone pairs of electrons on boron. The arrangement of three regions of high electron density gives a trigonal planar electron-pair geometry. The B–Cl bonds lie in a plane with 120° angles between them. BCl 3 also has a trigonal planar molecular structure (Figure \(\PageIndex{8}\)).
The electron-pair geometry and molecular structure of BCl 3 are both trigonal planar. Note that the VSEPR geometry indicates the correct bond angles (120°), unlike the Lewis structure shown above.
Exercise \(\PageIndex{1}\)
Carbonate, is a common polyatomic ion found in various materials from eggshells to antacids. What are the electron-pair geometry and molecular structure of this polyatomic ion?
- Answer
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The electron-pair geometry is trigonal planar and the molecular structure is trigonal planar. Due to resonance, all three C–O bonds are identical. Whether they are single, double, or an average of the two, each bond counts as one region of electron density.
Example \(\PageIndex{2}\): Predicting Electron-pair Geometry and Molecular Structure: Ammonium
Two of the top 50 chemicals produced in the United States, ammonium nitrate and ammonium sulfate, both used as fertilizers, contain the ammonium ion. Predict the electron-pair geometry and molecular structure of the cation.
Solution
We write the Lewis structure of as:
We can see that \(\ce{NH4^{+}}\) contains four bonds from the nitrogen atom to hydrogen atoms and no lone pairs. We expect the four regions of high electron density to arrange themselves so that they point to the corners of a tetrahedron with the central nitrogen atom in the middle (Figure \(\PageIndex{6}\)). Therefore, the electron pair geometry of Figure \(\PageIndex{9}\).
Exercise \(\PageIndex{2}\)
Identify a molecule with trigonal bipyramidal molecular structure.
- Answer
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Any molecule with five electron pairs around the central atoms including no lone pairs will be trigonal bipyramidal. PF 5 is a common example.
The next several examples illustrate the effect of lone pairs of electrons on molecular structure.
Example \(\PageIndex{3}\): Predicting Electron-pair Geometry and Molecular Structure: Lone Pairs on the Central Atom
Predict the electron-pair geometry and molecular structure of a water molecule.
Solution
The Lewis structure of H 2 O indicates that there are four regions of high electron density around the oxygen atom: two lone pairs and two chemical bonds:
We predict that these four regions are arranged in a tetrahedral fashion (Figure \(\PageIndex{10}\)), as indicated in Figure \(\PageIndex{6}\). Thus, the electron-pair geometry is tetrahedral and the molecular structure is bent with an angle slightly less than 109.5°. In fact, the bond angle is 104.5°.
Exercise \(\PageIndex{3}\)
The hydronium ion, H 3 O + , forms when acids are dissolved in water. Predict the electron-pair geometry and molecular structure of this cation.
- Answer
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electron pair geometry: tetrahedral; molecular structure: trigonal pyramidal
Example \(\PageIndex{4}\): Predicting Electron-pair Geometry and Molecular Structure: SF 4
Sulfur tetrafluoride, SF 4 , is extremely valuable for the preparation of fluorine-containing compounds used as herbicides (i.e., SF 4 is used as a fluorinating agent). Predict the electron-pair geometry and molecular structure of a SF 4 molecule.
Solution
The Lewis structure of SF 4 indicates five regions of electron density around the sulfur atom: one lone pair and four bonding pairs:
We expect these five regions to adopt a trigonal bipyramidal electron-pair geometry. To minimize lone pair repulsions, the lone pair occupies one of the equatorial positions. The molecular structure (Figure \(\PageIndex{11}\)) is that of a seesaw (Figure \(\PageIndex{6}\)).
Exercise \(\PageIndex{4}\)
Predict the electron pair geometry and molecular structure for molecules of XeF 2 .
- Answer
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The electron-pair geometry is trigonal bipyramidal. The molecular structure is linear.
Example \(\PageIndex{5}\): Predicting Electron-pair Geometry and Molecular Structure: XeF 4
Of all the noble gases, xenon is the most reactive, frequently reacting with elements such as oxygen and fluorine. Predict the electron-pair geometry and molecular structure of the XeF 4 molecule.
Solution
The Lewis structure of XeF 4 indicates six regions of high electron density around the xenon atom: two lone pairs and four bonds:
These six regions adopt an octahedral arrangement (Figure \(\PageIndex{6}\)), which is the electron-pair geometry. To minimize repulsions, the lone pairs should be on opposite sides of the central atom (Figure \(\PageIndex{12}\)). The five atoms are all in the same plane and have a square planar molecular structure.
Exercise \(\PageIndex{5}\)
In a certain molecule, the central atom has three lone pairs and two bonds. What will the electron pair geometry and molecular structure be?
- Answer
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electron pair geometry: trigonal bipyramidal; molecular structure: linear
Molecular Structure for Multicenter Molecules
When a molecule or polyatomic ion has only one central atom, the molecular structure completely describes the shape of the molecule. Larger molecules do not have a single central atom, but are connected by a chain of interior atoms that each possess a “local” geometry. The way these local structures are oriented with respect to each other also influences the molecular shape, but such considerations are largely beyond the scope of this introductory discussion. For our purposes, we will only focus on determining the local structures.
Example \(\PageIndex{6}\): Predicting Structure in Multicenter Molecules
The Lewis structure for the simplest amino acid, glycine, H 2 NCH 2 CO 2 H, is shown here. Predict the local geometry for the nitrogen atom, the two carbon atoms, and the oxygen atom with a hydrogen atom attached:
Solution
Consider each central atom independently. The electron-pair geometries:
- nitrogen––four regions of electron density; tetrahedral
- carbon ( C H 2 )––four regions of electron density; tetrahedral
- carbon ( C O 2 )—three regions of electron density; trigonal planar
- oxygen ( O H)—four regions of electron density; tetrahedral
The local structures:
- nitrogen––three bonds, one lone pair; trigonal pyramidal
- carbon ( C H 2 )—four bonds, no lone pairs; tetrahedral
- carbon ( C O 2 )—three bonds (double bond counts as one bond), no lone pairs; trigonal planar
- oxygen ( O H)—two bonds, two lone pairs; bent (109°)
Exercise \(\PageIndex{6}\)
Another amino acid is alanine, which has the Lewis structure shown here. Predict the electron-pair geometry and local structure of the nitrogen atom, the three carbon atoms, and the oxygen atom with hydrogen attached:
- Answer
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electron-pair geometries: nitrogen––tetrahedral; carbon ( C H)—tetrahedral; carbon ( C H 3 )—tetrahedral; carbon ( C O 2 )—trigonal planar; oxygen ( O H)—tetrahedral; local structures: nitrogen—trigonal pyramidal; carbon ( C H)—tetrahedral; carbon ( C H 3 )—tetrahedral; carbon ( C O 2 )—trigonal planar; oxygen ( O H)—bent (109°)
Link to Learning
The molecular shape simulator lets you build various molecules and practice naming their electron-pair geometries and molecular structures.
Example \(\PageIndex{7}\): Molecular Simulation
Using molecular shape simulator allows us to control whether bond angles and/or lone pairs are displayed by checking or unchecking the boxes under “Options” on the right. We can also use the “Name” checkboxes at bottom-left to display or hide the electron pair geometry (called “electron geometry” in the simulator) and/or molecular structure (called “molecular shape” in the simulator).
Build the molecule HCN in the simulator based on the following Lewis structure:
\[\ce{H-C#N} \nonumber \]
Click on each bond type or lone pair at right to add that group to the central atom. Once you have the complete molecule, rotate it to examine the predicted molecular structure. What molecular structure is this?
Solution
The molecular structure is linear.
Exercise \(\PageIndex{7}\)
Build a more complex molecule in the simulator. Identify the electron-group geometry, molecular structure, and bond angles. Then try to find a chemical formula that would match the structure you have drawn.
- Answer
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Answers will vary. For example, an atom with four single bonds, a double bond, and a lone pair has an octahedral electron-group geometry and a square pyramidal molecular structure. XeOF 4 is a molecule that adopts this structure.
Molecular Polarity and Dipole Moment
As discussed previously, polar covalent bonds connect two atoms with differing electronegativities, leaving one atom with a partial positive charge (δ+) and the other atom with a partial negative charge (δ–), as the electrons are pulled toward the more electronegative atom. This separation of charge gives rise to a bond dipole moment . The magnitude of a bond dipole moment is represented by the Greek letter mu ( µ ) and is given by the formula shown here, where Q is the magnitude of the partial charges (determined by the electronegativity difference) and r is the distance between the charges:
\[\mu= Qr \nonumber \]
This bond moment can be represented as a vector, a quantity having both direction and magnitude (Figure \(\PageIndex{13}\)). Dipole vectors are shown as arrows pointing along the bond from the less electronegative atom toward the more electronegative atom. A small plus sign is drawn on the less electronegative end to indicate the partially positive end of the bond. The length of the arrow is proportional to the magnitude of the electronegativity difference between the two atoms.
A whole molecule may also have a separation of charge, depending on its molecular structure and the polarity of each of its bonds. If such a charge separation exists, the molecule is said to be a polar molecule (or dipole); otherwise the molecule is said to be nonpolar. The dipole moment measures the extent of net charge separation in the molecule as a whole. We determine the dipole moment by adding the bond moments in three-dimensional space, taking into account the molecular structure.
For diatomic molecules, there is only one bond, so its bond dipole moment determines the molecular polarity. Homonuclear diatomic molecules such as Br 2 and N 2 have no difference in electronegativity, so their dipole moment is zero. For heteronuclear molecules such as CO, there is a small dipole moment. For HF, there is a larger dipole moment because there is a larger difference in electronegativity.
When a molecule contains more than one bond, the geometry must be taken into account. If the bonds in a molecule are arranged such that their bond moments cancel (vector sum equals zero), then the molecule is nonpolar. This is the situation in CO 2 (Figure \(\PageIndex{14}\)). Each of the bonds is polar, but the molecule as a whole is nonpolar. From the Lewis structure, and using VSEPR theory, we determine that the CO 2 molecule is linear with polar C=O bonds on opposite sides of the carbon atom. The bond moments cancel because they are pointed in opposite directions. In the case of the water molecule (Figure \(\PageIndex{14}\)), the Lewis structure again shows that there are two bonds to a central atom, and the electronegativity difference again shows that each of these bonds has a nonzero bond moment. In this case, however, the molecular structure is bent because of the lone pairs on O, and the two bond moments do not cancel. Therefore, water does have a net dipole moment and is a polar molecule (dipole).
The OCS molecule has a structure similar to CO 2 , but a sulfur atom has replaced one of the oxygen atoms. To determine if this molecule is polar, we draw the molecular structure. VSEPR theory predicts a linear molecule:
The C-O bond is considerably polar. Although C and S have very similar electronegativity values, S is slightly more electronegative than C, and so the C-S bond is just slightly polar. Because oxygen is more electronegative than sulfur, the oxygen end of the molecule is the negative end.
Chloromethane, CH 3 Cl, is a tetrahedral molecule with three slightly polar C-H bonds and a more polar C-Cl bond. The relative electronegativities of the bonded atoms is H < C < Cl, and so the bond moments all point toward the Cl end of the molecule and sum to yield a considerable dipole moment (the molecules are relatively polar).
For molecules of high symmetry such as BF 3 (trigonal planar), CH 4 (tetrahedral), PF 5 (trigonal bipyramidal), and SF 6 (octahedral), all the bonds are of identical polarity (same bond moment) and they are oriented in geometries that yield nonpolar molecules (dipole moment is zero). Molecules of less geometric symmetry, however, may be polar even when all bond moments are identical. For these molecules, the directions of the equal bond moments are such that they sum to give a nonzero dipole moment and a polar molecule. Examples of such molecules include hydrogen sulfide, H 2 S (nonlinear), and ammonia, NH 3 (trigonal pyramidal).
To summarize, to be polar, a molecule must:
- Contain at least one polar covalent bond.
- Have a molecular structure such that the sum of the vectors of each bond dipole moment does not cancel.
Properties of Polar Molecules
Polar molecules tend to align when placed in an electric field with the positive end of the molecule oriented toward the negative plate and the negative end toward the positive plate (Figure \(\PageIndex{15}\)). We can use an electrically charged object to attract polar molecules, but nonpolar molecules are not attracted. Also, polar solvents are better at dissolving polar substances, and nonpolar solvents are better at dissolving nonpolar substances.
Link to Learning
The molecule polarity simulation provides many ways to explore dipole moments of bonds and molecules.
Example \(\PageIndex{8}\): Polarity Simulations
Open the molecule polarity simulation and select the “Three Atoms” tab at the top. This should display a molecule ABC with three electronegativity adjustors. You can display or hide the bond moments, molecular dipoles, and partial charges at the right. Turning on the Electric Field will show whether the molecule moves when exposed to a field, similar to Figure \(\PageIndex{15}\).
Use the electronegativity controls to determine how the molecular dipole will look for the starting bent molecule if:
- A and C are very electronegative and B is in the middle of the range.
- A is very electronegative, and B and C are not.
Solution
- Molecular dipole moment points immediately between A and C.
- Molecular dipole moment points along the A–B bond, toward A.
Exercise \(\PageIndex{8}\)
Determine the partial charges that will give the largest possible bond dipoles.
- Answer
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The largest bond moments will occur with the largest partial charges. The two solutions above represent how unevenly the electrons are shared in the bond. The bond moments will be maximized when the electronegativity difference is greatest. The controls for A and C should be set to one extreme, and B should be set to the opposite extreme. Although the magnitude of the bond moment will not change based on whether B is the most electronegative or the least, the direction of the bond moment will.


12.1: Microbes and the Tools of Genetic Engineering
- Identify tools of molecular genetics that are derived from microorganisms
- Describe the methods used to create recombinant DNA molecules
- Describe methods used to introduce DNA into prokaryotic cells
- List the types of genomic libraries and describe their uses
- Describe the methods used to introduce DNA into eukaryotic cells
Kayla, a 24-year-old electrical engineer and running enthusiast, just moved from Arizona to New Hampshire to take a new job. On her weekends off, she loves to explore her new surroundings, going for long runs in the pine forests. In July she spent a week hiking through the mountains. In early August, Kayla developed a low fever, headache, and mild muscle aches, and she felt a bit fatigued. Not thinking much of it, she took some ibuprofen to combat her symptoms and vowed to get more rest.
What types of medical conditions might be responsible for Kayla’s symptoms?
The science of using living systems to benefit humankind is called biotechnology. Technically speaking, the domestication of plants and animals through farming and breeding practices is a type of biotechnology. However, in a contemporary sense, we associate biotechnology with the direct alteration of an organism’s genetics to achieve desirable traits through the process of genetic engineering. Genetic engineering involves the use of recombinant DNA technology, the process by which a DNA sequence is manipulated in vitro, thus creating recombinant DNA molecules that have new combinations of genetic material. The recombinant DNA is then introduced into a host organism. If the DNA that is introduced comes from a different species, the host organism is now considered to be transgenic.
One example of a transgenic microorganism is the bacterial strain that produces human insulin (Figure \(\PageIndex{1}\)). The insulin gene from humans was inserted into a plasmid. This recombinant DNA plasmid was then inserted into bacteria. As a result, these transgenic microbes are able to produce and secrete human insulin. Many prokaryotes are able to acquire foreign DNA and incorporate functional genes into their own genome through “mating” with other cells (conjugation), viral infection (transduction), and taking up DNA from the environment (transformation). Recall that these mechanisms are examples of horizontal gene transfer—the transfer of genetic material between cells of the same generation.
Molecular Cloning
Herbert Boyer and Stanley Cohen first demonstrated the complete molecular cloning process in 1973 when they successfully cloned genes from the African clawed frog ( Xenopus laevis ) into a bacterial plasmid that was then introduced into the bacterial host Escherichia coli . Molecular cloning is a set of methods used to construct recombinant DNA and incorporate it into a host organism; it makes use of a number of molecular tools that are derived from microorganisms.
Restriction Enzymes and Ligases
In recombinant DNA technology, DNA molecules are manipulated using naturally occurring enzymes derived mainly from bacteria and viruses. The creation of recombinant DNA molecules is possible due to the use of naturally occurring restriction endonucleases (restriction enzymes), bacterial enzymes produced as a protection mechanism to cut and destroy foreign cytoplasmic DNA that is most commonly a result of bacteriophage infection. Stewart Linn and Werner Arber discovered restriction enzymes in their 1960s studies of how E. coli limits bacteriophage replication on infection. Today, we use restriction enzymes extensively for cutting DNA fragments that can then be spliced into another DNA molecule to form recombinant molecules. Each restriction enzyme cuts DNA at a characteristic recognition site, a specific, usually palindromic, DNA sequence typically between four to six base pairs in length. A palindrome is a sequence of letters that reads the same forward as backward. (The word “level” is an example of a palindrome.) Palindromic DNA sequences contain the same base sequences in the 5ʹ to 3ʹ direction on one strand as in the 5ʹ to 3ʹ direction on the complementary strand. A restriction enzyme recognizes the DNA palindrome and cuts each backbone at identical positions in the palindrome. Some restriction enzymes cut to produce molecules that have complementary overhangs (sticky ends) while others cut without generating such overhangs, instead producing blunt ends (Figure \(\PageIndex{2}\)).
Molecules with complementary sticky ends can easily anneal, or form hydrogen bonds between complementary bases, at their sticky ends. The annealing step allows hybridization of the single-stranded overhangs. Hybridization refers to the joining together of two complementary single strands of DNA. Blunt ends can also attach together, but less efficiently than sticky ends due to the lack of complementary overhangs facilitating the process. In either case, ligationby DNA ligase can then rejoin the two sugar-phosphate backbones of the DNA through covalent bonding, making the molecule a continuous double strand. In 1972, Paul Berg, a Stanford biochemist, was the first to produce a recombinant DNA molecule using this technique, combining the SV40 monkey virus with E. coli bacteriophage lambda to create a hybrid.
Plasmids
After restriction digestion, genes of interest are commonly inserted into plasmids, small pieces of typically circular, double-stranded DNA that replicate independently of the bacterial chromosome (see Unique Characteristics of Prokaryotic Cells ). In recombinant DNA technology, plasmids are often used as vectors, DNA molecules that carry DNA fragments from one organism to another. Plasmids used as vectors can be genetically engineered by researchers and scientific supply companies to have specialized properties, as illustrated by the commonly used plasmid vector pUC19 (Figure \(\PageIndex{3}\)). Some plasmid vectors contain genes that confer antibiotic resistance; these resistance genes allow researchers to easily find plasmid-containing colonies by plating them on media containing the corresponding antibiotic. The antibiotic kills all host cells that do not harbor the desired plasmid vector, but those that contain the vector are able to survive and grow.
Plasmid vectors used for cloning typically have a polylinker site, or multiple cloning site (MCS). A polylinker site is a short sequence containing multiple unique restriction enzyme recognition sites that are used for inserting DNA into the plasmid after restriction digestion of both the DNA and the plasmid. Having these multiple restriction enzyme recognition sites within the polylinker site makes the plasmid vector versatile, so it can be used for many different cloning experiments involving different restriction enzymes.
This polylinker site is often found within a reporter gene, another gene sequence artificially engineered into the plasmid that encodes a protein that allows for visualization of DNA insertion. The reporter gene allows a researcher to distinguish host cells that contain recombinant plasmids with cloned DNA fragments from host cells that only contain the non-recombinant plasmid vector. The most common reporter gene used in plasmid vectors is the bacterial lacZ gene encoding beta-galactosidase, an enzyme that naturally degrades lactose but can also degrade a colorless synthetic analog X-gal, thereby producing blue colonies on X-gal–containing media. The lacZ reporter gene is disabled when the recombinant DNA is spliced into the plasmid. Because the LacZ protein is not produced when the gene is disabled, X-gal is not degraded and white colonies are produced, which can then be isolated. This blue-white screening method is described later and shown in Figure \(\PageIndex{4}\). In addition to these features, some plasmids come pre-digested and with an enzyme linked to the linearized plasmid to aid in ligation after the insertion of foreign DNA fragments.
Molecular Cloning using Transformation
The most commonly used mechanism for introducing engineered plasmids into a bacterial cell is transformation, a process in which bacteria take up free DNA from their surroundings. In nature, free DNA typically comes from other lysed bacterial cells; in the laboratory, free DNA in the form of recombinant plasmids is introduced to the cell’s surroundings.
Some bacteria, such as Bacillus spp., are naturally competent, meaning they are able to take up foreign DNA. However, not all bacteria are naturally competent. In most cases, bacteria must be made artificially competent in the laboratory by increasing the permeability of the cell membrane. This can be achieved through chemical treatments that neutralize charges on the cell membrane or by exposing the bacteria to an electric field that creates microscopic pores in the cell membrane. These methods yield chemically competent or electrocompetent bacteria, respectively.
Following the transformation protocol, bacterial cells are plated onto an antibiotic-containing medium to inhibit the growth of the many host cells that were not transformed by the plasmid conferring antibiotic resistance. A technique called blue-white screening is then used for lacZ -encoding plasmid vectors such as pUC19. Blue colonies have a functional beta-galactosidase enzyme because the lacZ gene is uninterrupted, with no foreign DNA inserted into the polylinker site. These colonies typically result from the digested, linearized plasmid religating to itself. However, white colonies lack a functional beta-galactosidase enzyme, indicating the insertion of foreign DNA within the polylinker site of the plasmid vector, thus disrupting the lacZ gene. Thus, white colonies resulting from this blue-white screening contain plasmids with an insert and can be further screened to characterize the foreign DNA. To be sure the correct DNA was incorporated into the plasmid, the DNA insert can then be sequenced.
In blue-white screening, what does a blue colony mean and why is it blue?
Molecular Cloning Using Conjugation or Transduction
The bacterial process of conjugation (see How Asexual Prokaryotes Achieve Genetic Diversity ) can also be manipulated for molecular cloning. F plasmids, or fertility plasmids, are transferred between bacterial cells through the process of conjugation. Recombinant DNA can be transferred by conjugation when bacterial cells containing a recombinant F plasmid are mixed with compatible bacterial cells lacking the plasmid.  On contact, a cytoplasmic bridge forms between the two cells and the F-plasmid-containing cell replicates its plasmid, transferring a copy of the recombinant F plasmid to the recipient cell. Once it has received the recombinant F plasmid, the recipient cell can produce its own F pilus and facilitate transfer of the recombinant F plasmid to an additional cell. The use of conjugation to transfer recombinant F plasmids to recipient cells is another effective way to introduce recombinant DNA molecules into host cells.
Alternatively, bacteriophages can be used to introduce recombinant DNA into host bacterial cells through a manipulation of the transduction process (see How Asexual Prokaryotes Achieve Genetic Diversity ). In the laboratory, DNA fragments of interest can be engineered into phagemids, which are plasmids that have phage sequences that allow them to be packaged into bacteriophages. Bacterial cells can then be infected with these bacteriophages so that the recombinant phagemids can be introduced into the bacterial cells. Depending on the type of phage, the recombinant DNA may be integrated into the host bacterial genome (lysogeny), or it may exist as a plasmid in the host’s cytoplasm.
- What is the original function of a restriction enzyme?
- What two processes are exploited to get recombinant DNA into a bacterial host cell?
- Distinguish the uses of an antibiotic resistance gene and a reporter gene in a plasmid vector.
Creating a Genomic Library
Molecular cloning may also be used to generate a genomic library. The library is a complete (or nearly complete) copy of an organism’s genome contained as recombinant DNA plasmids engineered into unique clones of bacteria. Having such a library allows a researcher to create large quantities of each fragment by growing the bacterial host for that fragment. These fragments can be used to determine the sequence of the DNA and the function of any genes present.
One method for generating a genomic library is to ligate individual restriction enzyme-digested genomic fragments into plasmid vectors cut with the same restriction enzyme (Figure \(\PageIndex{5}\)). After transformation into a bacterial host, each transformed bacterial cell takes up a single recombinant plasmid and grows into a colony of cells. All of the cells in this colony are identical clones and carry the same recombinant plasmid. The resulting library is a collection of colonies, each of which contains a fragment of the original organism’s genome, that are each separate and distinct and can each be used for further study. This makes it possible for researchers to screen these different clones to discover the one containing a gene of interest from the original organism’s genome.
To construct a genomic library using larger fragments of genomic DNA, an E. coli bacteriophage, such as lambda, can be used as a host (Figure \(\PageIndex{6}\)). Genomic DNA can be sheared or enzymatically digested and ligated into a pre-digested bacteriophage lambda DNA vector. Then, these recombinant phage DNA molecules can be packaged into phage particles and used to infect E. coli host cells on a plate. During infection within each cell, each recombinant phage will make many copies of itself and lyse the E. coli lawn, forming a plaque. Thus, each plaque from a phage library represents a unique recombinant phage containing a distinct genomic DNA fragment. Plaques can then be screened further to look for genes of interest. One advantage to producing a library using phages instead of plasmids is that a phage particle holds a much larger insert of foreign DNA compared with a plasmid vector, thus requiring a much smaller number of cultures to fully represent the entire genome of the original organism.
To focus on the expressed genes in an organism or even a tissue, researchers construct libraries using the organism’s messenger RNA (mRNA) rather than its genomic DNA. Whereas all cells in a single organism will have the same genomic DNA, different tissues express different genes, producing different complements of mRNA. For example, all human cells’ genomic DNA contains the gene for insulin, but only cells in the pancreas express mRNA directing the production of insulin. Because mRNA cannot be cloned directly, in the laboratory mRNA must be used as a template by the retroviral enzyme reverse transcriptase to make complementary DNA (cDNA). A cell’s full complement of mRNA can be reverse-transcribed into cDNA molecules, which can be used as a template for DNA polymerase to make double-stranded DNA copies; these fragments can subsequently be ligated into either plasmid vectors or bacteriophage to produce a cDNA library. The benefit of a cDNA library is that it contains DNA from only the expressed genes in the cell. This means that the introns, control sequences such as promoters, and DNA not destined to be translated into proteins are not represented in the library. The focus on translated sequences means that the library cannot be used to study the sequence and structure of the genome in its entirety. The construction of a cDNA genomic library is shown in Figure \(\PageIndex{7}\).
- What are the hosts for the genomic libraries described?
- What is cDNA?
Introducing Recombinant Molecules into Eukaryotic Hosts
The use of bacterial hosts for genetic engineering laid the foundation for recombinant DNA technology; however, researchers have also had great interest in genetically engineering eukaryotic cells, particularly those of plants and animals. The introduction of recombinant DNA molecules into eukaryotic hosts is called transfection. Genetically engineered plants, called transgenic plants, are of significant interest for agricultural and pharmaceutical purposes. The first transgenic plant sold commercially was the Flavr Savr delayed-ripening tomato, which came to market in 1994. Genetically engineered livestock have also been successfully produced, resulting, for example, in pigs with increased nutritional value 1 and goats that secrete pharmaceutical products in their milk. 2
Electroporation
Compared to bacterial cells, eukaryotic cells tend to be less amenable as hosts for recombinant DNA molecules. Because eukaryotes are typically neither competent to take up foreign DNA nor able to maintain plasmids, transfection of eukaryotic hosts is far more challenging and requires more intrusive techniques for success. One method used for transfecting cells in cell culture is called electroporation. A brief electric pulse induces the formation of transient pores in the phospholipid bilayers of cells through which the gene can be introduced. At the same time, the electric pulse generates a short-lived positive charge on one side of the cell’s interior and a negative charge on the opposite side; the charge difference draws negatively charged DNA molecules into the cell (Figure \(\PageIndex{8}\)).
Microinjection
An alternative method of transfection is called microinjection. Because eukaryotic cells are typically larger than those of prokaryotes, DNA fragments can sometimes be directly injected into the cytoplasm using a glass micropipette, as shown in Figure \(\PageIndex{9}\).
Gene Guns
Transfecting plant cells can be even more difficult than animal cells because of their thick cell walls. One approach involves treating plant cells with enzymes to remove their cell walls, producing protoplasts. Then, a gene gun is used to shoot gold or tungsten particles coated with recombinant DNA molecules into the plant protoplasts at high speeds. Recipient protoplast cells can then recover and be used to generate new transgenic plants (Figure \(\PageIndex{10}\)).
Shuttle Vectors
Another method of transfecting plants involves shuttle vectors, plasmids that can move between bacterial and eukaryotic cells. The tumor-inducing (T i ) plasmids originating from the bacterium Agrobacterium tumefaciens are commonly used as shuttle vectors for incorporating genes into plants (Figure \(\PageIndex{11}\)). In nature, the T i plasmids of A. tumefaciens cause plants to develop tumors when they are transferred from bacterial cells to plant cells. Researchers have been able to manipulate these naturally occurring plasmids to remove their tumor-causing genes and insert desirable DNA fragments. The resulting recombinant T i plasmids can be transferred into the plant genome through the natural transfer of T i plasmids from the bacterium to the plant host. Once inside the plant host cell, the gene of interest recombines into the plant cell’s genome.
Viral Vectors
Viral vectors can also be used to transfect eukaryotic cells. In fact, this method is often used in gene therapy (see Gene Therapy ) to introduce healthy genes into human patients suffering from diseases that result from genetic mutations. Viral genes can be deleted and replaced with the gene to be delivered to the patient; 3 the virus then infects the host cell and delivers the foreign DNA into the genome of the targeted cell. Adenoviruses are often used for this purpose because they can be grown to high titer and can infect both nondividing and dividing host cells. However, use of viral vectors for gene therapy can pose some risks for patients, as discussed in Gene Therapy .
- What are the methods used to introduce recombinant DNA vectors into animal cells?
- Compare and contrast shuttle vectors and viral vectors.
Key Concepts and Summary
- Biotechology is the science of utilizing living systems to benefit humankind. In recent years, the ability to directly alter an organism’s genome through genetic engineering has been made possible due to advances in recombinant DNA technology, which allows researchers to create recombinant DNA molecules with new combinations of genetic material.
- Molecular cloning involves methods used to construct recombinant DNA and facilitate their replication in host organisms. These methods include the use of restriction enzymes (to cut both foreign DNA and plasmid vectors) , ligation (to paste fragments of DNA together), and the introduction of recombinant DNA into a host organism (often bacteria).
- Blue-white screening allows selection of bacterial transformants that contain recombinant plasmids using the phenotype of a reporter gene that is disabled by insertion of the DNA fragment.
- Genomic libraries can be made by cloning genomic fragments from one organism into plasmid vectors or into bacteriophage.
- cDNA libraries can be generated to represent the mRNA molecules expressed in a cell at a given point.
- Transfection of eukaryotic hosts can be achieved through various methods using electroporation , gene guns , microinjection , shuttle vectors , and viral vectors .
Footnotes
- 1 Liangxue Lai, Jing X. Kang, Rongfeng Li, Jingdong Wang, William T. Witt, Hwan Yul Yong, Yanhong Hao et al. “Generation of Cloned Transgenic Pigs Rich in Omega-3 Fatty Acids.” Nature Biotechnology 24 no. 4 (2006): 435–436.
- 2 Raylene Ramos Moura, Luciana Magalhães Melo, and Vicente José de Figueirêdo Freitas. “Production of Recombinant Proteins in Milk of Transgenic and Non-Transgenic Goats.” Brazilian Archives of Biology and Technology 54 no. 5 (2011): 927–938.
- 3 William S.M. Wold and Karoly Toth. “Adenovirus Vectors for Gene Therapy, Vaccination and Cancer Gene Therapy.” Current Gene Therapy 13 no. 6 (2013): 421.


8.3: Putting It Together- Groups, Teams, and Teamwork
Do you remember our scenario to start this module? Lisa, with IT Solutions, has been given a major project and five individuals to get it done with. She has tight deadlines, and the project is for a major client—so the pressure is on. Lisa knows she needs to get the most out of this team, and she is familiar with the five stages of team development covered in this module. Let’s see how she manages through the stages.
Forming
Lisa brings everyone together for a face-to-face meeting on day one of the project. She knows that during this first stage of team development, everyone is getting to know each other. To facilitate this process, she opens the meeting with some icebreakers and a “getting to know you” time. As expected, they all try to find their particular place on the team given the skills and experiences of the others. As time passes, Lisa can see that they are starting to open up and share more about themselves. They are successfully transitioning to stage two.
Storming
Lisa has anxiously awaited this moment. From her study of management and team dynamics, she understands that the storming phase is critical to manage. She begins to see signs of friction between team members. Wendy and Antonio begin to jockey for position because both have strong project management backgrounds. Additionally, Raul begins to feel like the team is ignoring his opinions given that he has the least amount of experience.
It is important that Lisa exert influence at this crucial time in the team’s formation. She patiently waits for a little while to see if things resolve, but she acts when they don’t. She pulls everyone back together and reminds them of the project’s importance and each person’s agreed upon scope of responsibility. She also establishes a process for dealing with any differences of opinion going forward.
By stepping in and giving firm guidance, Lisa is able to bring the team together under her leadership. As a result, she begins to gain confidence in the outcome of the project.
Norming
The project is moving along now, and the team is working together very well. The disputes that arose in stage two are a thing of the past, and the team is becoming a cohesive unit. Each team member is sharing his or her knowledge, which serves to both bind the team and develop it. On a personal level, the team members are becoming good friends. They are socializing outside of work and truly enjoy one another’s company. Lisa is excited because she knows what’s coming next!
Performing
As the deadline nears, the team is performing at an amazingly high level. The work is being completed ahead of schedule and exceeds the requirements the customer established. Antonio told Lisa that in all his years of experience, he has never had so much fun while working so hard. Lisa’s boss is happy because all of this is being done well under budget, so IT Solutions is going to have a good year financially as a result.
Adjourning
Now that the project is over, Lisa gets everyone together again so that they can celebrate the win and say proper good-byes. Because the project was so successful, each member of the team has already been given their choice of next assignments in the organization. Similarly, Lisa has been identified as a rising star, and the executive team has big plans for her. They all exchange contact information and make plans to stay in touch as they move their separate ways. This has been an amazing experience for them all.
Learning to lead a team is important no matter what functional area of business you enter. A key role of management is to deliver results through others—and the strategies you have learned in this module will serve you well throughout your career.
Contributors and Attributions
- Putting It Together: Groups, Teams, and Teamwork. Authored by : Jeff Heflin and Lumen Learning. License : CC BY: Attribution
- No Name. Authored by : No Author. Located at : http://www.29palms.marines.mil/News/News-Article-Display/Article/699112/ctb-celebrates-anniversary/ . License : CC BY: Attribution


11.2: The Uniform Continuous Distribution
As mentioned in Week 9, there are certain processes which occurs more frequently than others and so we will attach "brand" names to the random variables which models these processes. In terms of discrete random variables, we studied the (discrete) Uniform Random Variable, The Bernoulli and Binomial Random Variables, The Geometric and Negative Binomial Random Variables, and the Poisson Random Variable.
For the class of continuous random variables, we will study the (continuous) Uniform Random Variable, the Exponential Random Variable, and the Normal Random Variable. We first begin with the (continuous) Uniform Random Variable.
Definition: Let \( a < b \) be real numbers. Suppose \( X \) is a random variable who has the following density:
\[
f(x) =
\begin{cases}
\frac{1}{b-a}, & \text{if} ~ a \leq x \leq b \ \\
0 , & \text{otherwise} \\
\end{cases}
\]
Then we say \( X \) has the uniform distribution on the interval \( [a,b] \) and we write \( X \sim \mathcal{U} [ a , b ] \).
Notice that the (continuous) Uniform Random Variable is something which is not totally new for us. Observe that we actually studied the \(\mathcal{U} [ 4, 200 ] \) random variable in the last section and so many of the proofs are left to the reader. Additionally, recall that the point of a random variable is to model some sort of quantity under certain assumptions and so we can ask, "what does the (continuous) Uniform random variable model?"
The (continuous) Uniform Random Variable models the outcome of an experiment where the experiment is choosing a number at random from the interval \( [a,b] \).
We end this section with a theorem concerning some of the properties of a discrete Uniform Random Variable. Their proofs are left as homework exercises.
Theorem: If \( X \sim \mathcal{U} [ a , b ] \) then:
\begin{align*} \mathbb{E}[X] &= \frac{a+b}{2} \\ \mathbb{V}ar[X] &= \frac{(b-a)^2}{12} \\ F(x) &= \begin{cases}
0, & \mbox{if } x < a \\ \frac{x-a}{b-a}, & \mbox{if } a \leq x < b \\ 1, & \mbox{if } x \geq b
\end{cases} \end{align*}


22.5: Force on a Moving Charge in a Magnetic Field- Examples and Applications
Learning Objectives
By the end of this section, you will be able to:
- Describe the effects of a magnetic field on a moving charge.
- Calculate the radius of curvature of the path of a charge that is moving in a magnetic field.
Magnetic force can cause a charged particle to move in a circular or spiral path. Cosmic rays are energetic charged particles in outer space, some of which approach the Earth. They can be forced into spiral paths by the Earth’s magnetic field. Protons in giant accelerators are kept in a circular path by magnetic force. The bubble chamber photograph in Figure \(\PageIndex{1}\) shows charged particles moving in such curved paths. The curved paths of charged particles in magnetic fields are the basis of a number of phenomena and can even be used analytically, such as in a mass spectrometer.
So does the magnetic force cause circular motion? Magnetic force is always perpendicular to velocity, so that it does no work on the charged particle. The particle’s kinetic energy and speed thus remain constant. The direction of motion is affected, but not the speed. This is typical of uniform circular motion. The simplest case occurs when a charged particle moves perpendicular to a uniform \(B\)-field, such as shown in Figure 2. (If this takes place in a vacuum, the magnetic field is the dominant factor determining the motion.) Here, the magnetic force supplies the centripetal force \(F_{c} = mv^{2}/r\). Noting that \(sin \theta = 1\), we see that \(F = qvB\).
Because the magnetic force \(F\) supplies the centripetal force \(F_{c}\), we have \[qvB = \frac{mv^{2}}{r}.\label{22.6.1}\] Solving for \(r\) yields \[r = \frac{mv}{qB}.\label{22.6.2}\] Here, \(r\) is the radius of curvature of the path of a charged particle with mass \(m\) and charge \(q\), moving at speed \(v\) perpendicular to a magnetic field of strength \(B\). If the velocity is not perpendicular to the magnetic field, then \(v\) is the component of the velocity perpendicular to the field. The component of the velocity parallel to the field is unaffected, since the magnetic force is zero for motion parallel to the field. This produces a spiral motion rather than a circular one.
Example \(\PageIndex{1}\): Calculating the Curvature of the Path of an Electron Moving in a Magnetic Field: A magnet on a TV Screen
A magnet brought near an old-fashioned TV screen such as in Figure 3 (TV sets with cathode ray tubes instead of LCD screens) severely distorts its picture by altering the path of the electrons that make its phosphors glow. (Don't try this at home, as it will permanently magnetize and ruin the TV.) To illustrate this, calculate the radius of curvature of the path of an electron having a velocity of \(6.00 \times 10^{7} m/s\) (corresponding to the accelerating voltage of about 10.0 kV used in some TVs) perpendicular to a magnetic field of strength \(B = 0.500 T\) (obtainable with permanent magnets).
Strategy:
We can find the radius of curvature \(r\) directly from the equation \(r = \frac{mv}{qB}\), since all other quantities in it are given or known.
Solution:
Using known values for the mass and charge of an electron, along with the given values of \(v\) and \(B\) gives us \[r = \frac{mv}{qB} = \frac{\left( 9.11 \times 10^{-31} kg \right) \left( 6.00 \times 10^{7} m/s \right) } { \left( 1.60 \times 10^{-19} C \right) \left( 0.500 T \right) } \] \[= 6.83 \times 10^{-4} m\] or \[r = 0.683 mm.\]
Discussion:
The small radius indicates a large effect. The electrons in the TV picture tube are made to move in very tight circles, greatly altering their paths and distorting the image.
Figure \(\PageIndex{4}\) shows how electrons not moving perpendicular to magnetic field lines follow the field lines. The component of velocity parallel to the lines is unaffected, and so the charges spiral along the field lines. If field strength increases in the direction of motion, the field will exert a force to slow the charges, forming a kind of magnetic mirror, as shown below.
The properties of charged particles in magnetic fields are related to such different things as the Aurora Australis or Aurora Borealis and particle accelerators. Charged particles approaching magnetic field lines may get trapped in spiral orbits about the lines rather than crossing them , as seen above. Some cosmic rays, for example, follow the Earth’s magnetic field lines, entering the atmosphere near the magnetic poles and causing the southern or northern lights through their ionization of molecules in the atmosphere. Those particles that approach middle latitudes must cross magnetic field lines, and many are prevented from penetrating the atmosphere.
Some incoming charged particles become trapped in the Earth’s magnetic field, forming two belts above the atmosphere known as the Van Allen radiation belts after the discoverer James A. Van Allen, an American astrophysicist (Figure \(\PageIndex{6}\)). Particles trapped in these belts form radiation fields (similar to nuclear radiation) so intense that manned space flights avoid them and satellites with sensitive electronics are kept out of them. In the few minutes it took lunar missions to cross the Van Allen radiation belts, astronauts received radiation doses more than twice the allowed annual exposure for radiation workers. Other planets have similar belts, especially those having strong magnetic fields like Jupiter.
Back on Earth, we have devices that employ magnetic fields to contain charged particles. Among them are the giant particle accelerators that have been used to explore the substructure of matter (Figure \(\PageIndex{7}\)). Magnetic fields not only control the direction of the charged particles, they also are used to focus particles into beams and overcome the repulsion of like charges in these beams.
Thermonuclear fusion (like that occurring in the Sun) is a hope for a future clean energy source. One of the most promising devices is the tokamak , which uses magnetic fields to contain (or trap) and direct the reactive charged particles (Figure \(\PageIndex{8}\)). Less exotic, but more immediately practical, amplifiers in microwave ovens use a magnetic field to contain oscillating electrons. These oscillating electrons generate the microwaves sent into the oven.
Mass spectrometers have a variety of designs, and many use magnetic fields to measure mass. The curvature of a charged particle’s path in the field is related to its mass and is measured to obtain mass information. Historically, such techniques were employed in the first direct observations of electron charge and mass. Today, mass spectrometers (sometimes coupled with gas chromatographs) are used to determine the make-up and sequencing of large biological molecules.
Summary
- Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius \[r = \frac{mv}{qB},\] where \(v\) is the component of the velocity perpendicular to \(B\) for a charged particle with mass \(m\) and charge \(q\).


14.4: Food Microbiology
Microorganisms have been used for centuries for food preservation and to improve or change its taste. Evidence exists that yogurt, which is milk fermented by bacteria, has been around for over 4000 years. Today, many of the foods we eat are the result of microorganisms acting on foods for a specific and desired effect. Examples of other fermented foods include wine/beer, sausage, sauerkraut/kimchee, bread, and cheese. The industrial use of microorganisms in food production began in earnest in the late 19th century, when pure cultures of bacteria were grown specifically for that purpose.
Bacteria and Health Hazards
While there are a wide number of foods that are produced with microorganisms, the introduction of harmful organisms to food presents a serious health hazard. Even bacteria that normally colonize the human digestive system (such as E. coli) can cause severe illness or even death if ingested. The most commonly encountered microbial pathogens are Listeria monocytogenes, Staphylococcus aureus, Bacillus cereus, Bacillus anthracis, Clostridium botulinum, Clostridium perfringens, members of the Salmonella and Campylobacter genus, Escherichia coli (especially type O157:H7), hepatitis and Rota viruses, prions, different species of tapeworms and roundworms, and protozoa. Food-borne illness can be limited to a single person who ingests the contaminated food, or can lead to a more widespread outbreak of the same illness when multiple people consumed the same contaminated product. Many outbreaks are local in nature, such as when food from a restaurant is not held at the proper temperature, allowing bacteria to grow to disease-causing levels. Increasingly there have been food-borne illness outbreaks that affect many geographical areas due to improper food handling. On May 23, 2019 5 lb
bags of Baker’s Corner All purpose flour was recalled due to potential E. Coli contamination. The CDC reported 17 infected individuals from 8 states.
https://www.cdc.gov/ecoli/2019/flour-05-19/index.html
Bacteria and Fermentation
Fermentation is important for the production of a variety of dairy products. Cheeses are typically made using lactic acid-producing bacteria that aid the coagulation of the milk protein casein in curd. The curd is then further treated with a different bacteria (depending on the desired final cheese) to produce distinctive tastes and aromas. The characteristic holes in Swiss cheese are produced by specific bacteria that generate carbon dioxide which create gas bubbles in the cheese.
Yogurt is made by the fermentation of lactose (milk sugar) by bacteria. Lactose is a disaccharide that consists of two simple sugars. During the making of yogurt, the lactose is broken down by the enzyme lactase into glucose and galactose. These sugars are then fermented generating lactic acid and acetaldehyde. These two products lower the pH of the milk giving it a sour tart taste. The lowered pH also effects the milk proteins (caseins) causing coagulation, precipitating the proteins into a solid curd that forms the yogurt. The left over watery liquid is the whey. There are a variety of bacteria that may be utilized in this process, the two most commonly used to are Lactobacillus bulgaris and Streptococcus thermophilus
In this experiment we will start with milk. To increase the shelf-life milk that is sold commercially is pasteurized. Pasteurization does not sterilize the milk, but will kill most of the microorganisms present. To manufacture yogurt these organisms must be destroyed so that they will not compete with the added organisms essential for the fermentation process. Commercially available yogurt containing live bacterial cultures will be used to inoculate the milk after heating.


6.7: How to Write a Formal Report
- Discuss how to write a formal report
Writing formal reports, like informal report, and that of any other writing task follows the same three steps. First is the planning. Second is the writing. Third is the revising.
Planning Your Formal Report
In all business writing, the first step is to check and see whether there is a prescribed structure for the document that is about to be created. If so, follow that. Many formal reports have specific formats that must be followed exactly. For example, some sales proposal requests and responses become part of a contract; therefore, you should ensure documents such as these have a legal review both in the planning of the document and as a part of the final review step.
Other steps in preparation of a formal report follow in the same way as those for an informal report. In an informal report, however, it is less likely there will be multiple writers. With a formal report, there may be many contributors. If so, it is important to meet as a group to divide the work, talk about style, and plan how the final document will be assembled and edited to ensure a common voice or tone throughout. You may wish to consider some of the strategies discussed in Module 12: Collaboration in and Across Teams.
Next you’ll complete any data gathering needed. A formal report likely requires extensive planning and data gathering: some proposals may require weeks or months in researching and preparing. For example, think about a proposal for the next three years of new store locations or construction. The author (likely a team of authors) will need primary and secondary research, which takes a great deal of time to gather and analyze.
You will use knowledge of that data to create the report’s outline. In constructing that outline, again consider the depth of understanding of the reader and the likelihood the reader’s views align with that of the report’s determination.
With group writing, there may be several coordination meetings at each stage of the document’s creation.
Writing Your Formal Report
Writing the formal report is a much easier task once you have created a detailed outline in the planning process. This outline is what helps the writing move along, as you already know exactly what is to be provided where and when. When writing a formal report as a team, a carefully constructed outline facilitates assigning sections of the report to different authors from the team. The writer or writers can then focus on paragraph structure, wording, and phrasing using the lessons found in Module 2: Writing in Business.
With a formal report, it is extremely rare to see the casual phrasing that might be found in a short message or informal report. Formal reports rarely use personal pronouns, contractions, or passive verb structures. However, this does not mean the language should be stilted or use excessively long words. You’ll continue to use the same clarity of wording as in all business communications.
Formatting Your Report
Formal reports implement many of the formatting skills you learned earlier. Usually formal reports are single spaced with double spaces between paragraphs. Usually paragraphs are not indented, but this may vary from organization to organization. The right hand side of paragraphs are left ragged.
Section headings are always provided in a formal report. It is acceptable to use labels to match the section’s purpose (e.g., Introduction, Findings, Research Methods). The headings may also use terms directly related to the report’s purpose such as “Fruit Spoilage Problem,” “Facts about Fruit Spoilage,” “Suggestions to Improve Fruit Freshness.” You may also have specific subheadings within more general section titles.
Formal reports of all types use page numbers.The pages may be numbered in a format such as 1–50, or they may be numbered by the section, such as Methods 1–Methods 50. The material in the front part of a report is generally numbered in lowercase roman numerals (i–ix).
Revising Your Formal Report
because of the length and possible subject complexity of formal reports, the final review takes more time than you might expect and involves more people. As mentioned in the start of this section, some reports may require additional legal review.
The most effective way to ensure a professional document is to have a team of individuals independently read the document, marking changes, corrections, and questions as they go. This team then meets as a group with one individual charged with collecting all corrections. This person ensures continuity across the entire document. If such a formal process cannot be completed, then you should work to ensure there are at least two reviewers who review work they themselves did not write.
As mentioned before, the final revision must consider both grammar and style issues as well as revisiting the primary purpose of the document.
Contributors and Attributions
- Plan, Write, Revise Formal Report. Authored by : Susan Kendall. License : CC BY: Attribution


6.3.4: Immunological Memory, Primary, and Secondary Adaptive Response
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Learning Objectives
- Describe the role of memory B and T cells in immunological memory
The adaptive immune system has a memory component that allows for a rapid and large response upon re-invasion of the same pathogen. During the adaptive immune response to a pathogen that has not been encountered before, known as the primary immune response, plasma cells secreting antibodies and differentiated T cells increase, then plateau over time. As B cells and T cells mature into effector cells, a subset of the naïve populations differentiates into B and T memory cells with the same antigen specificities. A memory cell is an antigen-specific B or T lymphocyte that does not differentiate into an effector cell during the primary immune response, but that can immediately become an effector cell on re-exposure to the same pathogen. As the infection is cleared and pathogenic stimuli subside, the effector cells are no longer needed; they undergo apoptosis. In contrast, the memory cells persist in circulation.
If the pathogen is not encountered again during the individual’s lifetime, B and T memory cells will circulate for a few years or even several decades, gradually dying off, having never functioned as effector cells. However, if the host is re-exposed to the same pathogen type, circulating memory cells will immediately differentiate into plasma cells and T C cells without input from APCs or T H cells. This is known as the secondary immune response. One reason why the adaptive immune response is delayed is that it takes time for naïve B and T cells with the appropriate antigen specificities to be identified, activated, and proliferate. On reinfection, this step is skipped. The result is a more rapid production of immune defenses. Memory B cells that differentiate into plasma cells output ten to hundred-fold greater antibody amounts than were secreted during the primary response. This rapid and dramatic antibody response may stop the infection before it can even become established. Individuals may not realize they had been exposed.
Vaccination is based on the knowledge that exposure to noninfectious antigens, derived from known pathogens, generates a mild primary immune response. The immune response to vaccination may not be perceived by the host as illness, but still confers immune memory. When exposed to the corresponding pathogen to which an individual was vaccinated, the reaction is similar to a secondary exposure. Because each reinfection generates more memory cells and increased resistance to the pathogen, some vaccine courses involve one or more booster vaccinations to mimic repeat exposures.
Key Points
- During the adaptive immune response to a pathogen that the body has not previously encountered (the primary immune response), the level of plasma cells that secrete antibodies to the new pathogen and T cells that recognize the pathogen will increase at a modest pace.
- If a pathogen is re-encountered, memory B and T cells can immediately differentiate into plasma cells and cytotoxic T cells without input from APCs or T H cells; this secondary immune response occurs much more rapidly than the primary immune response.
- Vaccination can be used to generate a mild, primary immune response against an inactivated pathogen, which will allow the secondary immune response to function the first time the immune system encounters the actual pathogen.
Key Terms
- vaccination : inoculation in order to protect against a particular disease or strain of disease; causes a primary immune response without illness, allowing the secondary response to destroy subsequent infection
- effector cell : a plasma B cell or cytotoxic T cell, which are the main types of cells responsible for the humoral and cellular immune responses, respectively


10.14: Distribution of Sample Means (2 of 4)
Learning Objectives
- Describe the sampling distribution of sample means.
Our next goal is to determine how the size of the sample affects the variability we see in sample means.
Example
Sample Size Affects Variability of Sample Means
We assumed that the population of individual babies has a mean of µ = 3,500 grams and a standard deviation of σ = 500 grams. We selected a random sample of babies to test our assumptions about the population.
We saw previously that for this population of babies, it was not surprising to see a random sample of 9 babies with a mean birth weight of 3,400 grams. So a sample with a mean of 3,400 does not suggest that the town’s mean birth weight is less than 3,500 grams this year.
What if we increase the sample size? Will our conclusion change? That is, if the mean birth weight of 3,400 grams comes from a larger sample of babies, does the sample provide stronger evidence that the town’s mean birth weight is less than 3,500 grams?
To investigate this question, we ran the simulation for different sample sizes. For each sample size, we collected 1,000 random samples and recorded the sample means.
When we compare the histograms of sample means, we notice the following:
- Center: The center is not affected by sample size. The mean of the sample means is always approximately the same as the population mean µ = 3,500.
- Spread: The spread is smaller for larger samples, so the standard deviation of the sample means decreases as sample size increases. This is not surprising because we observed a similar trend with sample proportions.
- Shape: The sampling distributions all appear approximately normal. This is not surprising because the distribution of birth weights in the population has a normal shape.
Based on the histograms, it appears that sample size will change our conclusion about the population’s mean birth weight this year. Suppose our sample mean of 3,400 grams came from a random sample of 100 babies. Means from samples this large did not vary much. We marked this sample result in a histogram for samples of size 100.
For n = 100, a sample mean of 3,400 grams is an unlikely result. It gives fairly strong evidence that the population’s mean birth weight is less than 3,500 grams.
From advanced probability theory, we have a probability model for the sampling distribution of sample means. The model reinforces what we have already observed about the center and gives more precise information about the relationship between sample size and spread.
Theoretical Probability Model for the Sampling Distribution of Sample Means
Suppose a population has a mean µ and a standard deviation of σ. The distribution of all possible sample means from this population will have a mean of µ and a standard deviation of .
Let’s compare and contrast what we know about the sampling distributions for sample means and sample proportions.
| Sampling Distribution | |||||
|---|---|---|---|---|---|
| Variable | Parameter | Statistic | Center | Spread | Shape |
| Categorical (example: left-handed or not) | p = population proportion | = sample proportion | p | Normal when np ≥ 10 and n (1 – p ) ≥ 10 | |
| Quantitative (example: age) | μ = population mean, σ = population standard deviation | = sample mean | μ | When will the distribution of sample means be approximately normal? |
We investigate the conditions that guarantee a normal sampling distribution for sample means on the next page.
Contributors and Attributions
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


13.7: Greatness and Genre
The preceding discussion about the Pulitzer Prize for Music has essentially been a discussion about “greatness” and genre. For most of the twentieth century, the Pulitzer committee restricted their concept of “greatness” to classical music. In the late twentieth century they expanded it to include jazz, and in the twenty-first century that have expanded still further to include hip-hop. What will come next? We can only wait and see. However, it is clear that the committee has historically perceived some genres as superior to others, and continues to see “greatness” only in specific realms.
Some of the best performing artists, however, clearly do not place these same limitations on music. In this section, we will explore the work of individual artists and performing ensembles that have excelled in the realm of classical music, but have put as much (or more) energy into other genres. All of these artists would disagree that any one musical genre is superior to another. Instead, they hear good music everywhere and are inspired by a variety of styles and approaches.


7.2.17: Drag and Drop (Usable with Workarounds)
Query \(\PageIndex{1}\)
Overall Usability
Usable with Workarounds
- The activity requires significant adjustments by content authors.
Important Reminders
H5P does not provide an option to include a correctly structured heading or separate instructions for the activity. The activity may be usable if an accessible list of the labels associated with each drop zone is included for users of screen reading software. If the activity uses only one (1) drop zone, in the Drag and Drop text overrides and translations, change the Dropzone prefix to describe the drop zone (for example, "Milkshake glass to drop items").
Use workarounds and best practices for content authoring, including:
- Add a unique label for the activity on the page outside of the H5P content
- Add instructions for questions on the page outside of the H5P content
- Add alt-text descriptions up to 150 characters for meaningful images
- Use good color contrast for meaningful visual information in images.
Users who require magnification up to 400% may require a alternative version of the content. Users of screen reading software may require an alternative version of the activity.
Visible Indication of Focus
The activity buttons, draggable items, and drop zones have a visible indication of focus.
Color Contrast
The visible indication of focus has good contrast. The visible indication of focus is a thin black line. Users who require a visible indication of focus with more contrast may use assistive technology.
Keyboard Usability
The activity is usable with the keyboard.
No Keyboard Traps
There are no keyboard traps.
Magnification
Content magnifies up to 200% using browser settings without loss of content or functionality. The draggable elements may not magnify up to 400%.
An alternative version of the activity should be included that supports magnification up to 400% without requiring horizontal scrolling to view content and interact with content.
Usability with Screen Reading Software
The activity is not usable with screen reading software. H5P does not include the label for each drop zone as part of the information announced with screen reading software when users review the location of dropped items.


4.1: Curriculum Models
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- Jennifer Paris, Kristin Beeve, & Clint Springer
- College of the Canyons
Curriculum Models provide a framework to organize planning experiences for children. In previous chapters, the planning cycle has been introduced and in accordance with best practices, the models identified in this chapter represent a variety of ways to use the planning cycle within these models.
Bank Street Model
Lucy Sprague Mitchell founded Bank Street, an Integrated Approach also referred to as the Developmental-Interactionist Approach.
In this model, the environment is arranged into learning centers and planning is organized by the use of materials within the learning areas (centers).
- Art
- Science
- Sensory/Cooking
- Dramatic Play
- Language/Literacy
- Math/Manipulative/Blocks
- Technology
- Outdoors: Water and Sand Play
The Bank Street Model of curriculum represents the ideology of Freud, Erikson, Dewey, Vygotsky, and Piaget. This model draws upon the relationship between psychology and education. By understanding developmental domains and creating interest centers with materials that promote specific areas of development, children’s individual preferences and paces of learning are the focus.
“A teacher’s knowledge and understanding of child development is crucial to this approach. Educational goals are set in terms of developmental processes and include the development of competence, a sense of autonomy and individuality, social relatedness and connectedness, creativity and integration of different ways of experiencing the world” (Gordon). [1]
Creative Curriculum Model (Diane Trister Dodge)
In the Creative Curriculum model, the focus is primarily on children’s play and self-selected activities. The Environment is arranged into learning areas and large blocks of time are given for self-selected play. This model focuses on project-based investigations as a means for children to apply skills and addresses four areas of development: social/emotional, physical, cognitive, and language.
The curriculum is designed to foster development of the whole child through teacher-led, small and large group activities centered around 11 interest areas:
- blocks
- dramatic play
- toys and games
- art
- library
- discovery
- sand and water
- music and movement
- cooking
- computers
- outdoors.
The commercial curriculum provides teachers with details on child development, classroom organization, teaching strategies, and engaging families in the learning process. Child assessments are an important part of the curriculum, but must be purchased separately. Online record-keeping tools assist teachers with the maintenance and organization of child portfolios, individualized planning, and report production. [2]
High Scope Model (David Weikert)
The High Scope Model focuses on developing learning centers similar to the Bank Street Model and emphasizes key experiences for tracking development. The key experiences are assessed using a Child Observation Record for tracking development and include areas of:
- Creative Representation
- Initiative
- Social Relations
- Language and Literacy
- Math (Classification, Seriation, Number, Space, Time)
- Music and Movement
The High Scope Model also includes a “Plan-Do-Review” Sequence in which children begin their day planning for activities they will participate in, followed by participation in the activities and engaging in a review session at the end of the day. Teachers can use this sequence format to help children learn how to organize choices of activities and to reflect upon what they liked or would do different at the end of the day. The High Scope Model reflects the theories of Piaget, Vygotsky and Reggio Emilia by way of emphasis on construction of knowledge through hands-on experiences with reflection techniques.
Montessori Approach (Dr. Maria Montessori)
The Montessori Approach refers to children’s activity as work (not play); children are given long periods of time to work and a strong emphasis on individual learning and individual pace is valued. Central to Montessori’s method of education is the dynamic triad of child, teacher and environment. One of the teacher’s roles is to guide the child through what Montessori termed the 'prepared environment, i.e., a classroom and a way of learning that are designed to support the child’s intellectual, physical, emotional and social development through active exploration, choice and independent learning.
The educational materials have a self-correcting focus and areas of the curriculum consist of art, music, movement, practical life (example; pouring, dressing, cleaning). In the Montessori method, the goal of education is to allow the child’s optimal development (intellectual, physical, emotional and social) to unfold.
A typical Montessori program will have mixed-age grouping. Children are given the freedom to choose what they work on, where they work, with whom they work, and for how long they work on any particular activity, all within the limits of the class rules. No competition is set up between children, and there is no system of extrinsic rewards or punishments. [3]
Waldorf Approach (Rudolf Steiner)
The Waldorf Approach, founded by Rudolf Steiner, features connections to nature, sensory learning, and imagination. The understanding of the child’s soul, of his or her development and individual needs, stands at the center of Steiner’s educational world view.
The Waldorf approach is child centered. [4] It emerges from a deep understanding of child development and seeks to support the particular developmental tasks (physical, emotional and intellectual) children face at any given stage. Children aged 3–5, for example, are developing a keen interest in the world, supported to a large extent by freedom of movement and must be supported to follow and deepen their curiosity through the encouragement of their sometimes endless asking of questions (Van Alphen & Van Alphen 1997 ). This approach to supporting children’s naturally blossoming curiosity, rather than answering the teachers’ questions. At this stage, children’s play becomes increasingly complex, with children spontaneously engaging in role plays, as they construct and act upon imaginative situations based on their own experiences and stories they have heard. Thus, in Waldorf schools, ample time is given for free imaginative play as a cornerstone of children’s early learning. [5]
The environment should protect children from negative influences and curriculum should include exploring nature through gardening, but also developing in practical skills, such as cooking, sewing, cleaning, etc. Relationships are important so groupings last for several years, by way of looping.
Reggio Emilia Approach (Loris Malaguzzi)
The Reggio Emilia approach to early childhood education is based on over forty years of experience in the Reggio Emilia Municipal Infant/toddler and Preschool Centers in Italy. Central to this approach is the view that children are competent and capable.
It places emphasis on children’s symbolic languages in the context of a project-oriented curriculum. Learning is viewed as a journey and education as building relationships with people (both children and adults) and creating connections between ideas and the environment. Through this approach, adults help children understand the meaning of their experience more completely through documentation of children’s work, observations, and continuous teacher-child dialogue. The Reggio approach guides children’s ideas with provocations—not predetermined curricula. There is collaboration on many levels: parent participation, teacher discussions, and community.
Within the Reggio Emilia schools, great attention is given to the look and feel of the classroom. Environment is considered the “third teacher.” Teachers carefully organize space for small and large group projects and small intimate spaces for one, two, or three children. Documentation of children’s work, plants, and collections that children have made from former outings are displayed both at the children’s and adult’s eye level. Common space available to all children in the school includes dramatic play areas and worktables.
There is a center for gathering called the atelier (art studio) where children and children from different classrooms can come together. The intent of the atelier in these schools is to provide children with the opportunity to explore and connect with a variety of media and materials. The studios are designed to give children time, information, inspiration, and materials so that they can effectively express their understanding through the “inborn inheritance of our universal language, the language that speaks with the sounds of the lips and of the heart, the children’s learning with their actions, their signs, and their eyes: those “hundred languages” that we know to be universal. There is an atelierista (artist) to support this process and instruct children in arts. [6]
Webbing
The Reggio Emilia Approach is an emergent curriculum. One method that many Early Childhood Educators use when planning emergent curriculum is curriculum webbing based on observed skills or interests. This method uses brainstorming to create ideas and connections from children’s interests to enhance developmental skills. Webbing can look like a “Spider’s Web” or it can be organized in list format.
Example:
Webbing can be completed by:
- An individual teacher
- A team of teachers
- Teachers and Children
- Teachers, Children and Families
Webbing provides endless planning opportunities as extensions continue from observing the activities and following the skills and interests exhibited. As example demonstrates a web can begin from a skill to develop, but it can also be used in a Theme/Unit Approach such as transportation; friendships; animals, nature, etc…
Project Approach
The project approach is an in-depth exploration of a topic that may be child-or teacher-initiated and involve an individual, a group of children, or the whole class. A project may be short-term or long-term depending on the level of children’s interests. What differentiates the project approach from an inquiry one is that within the project approach there is an emphasis on the creation of a specific outcome that might take the form of a spoken report, a multimedia presentation, a poster, a demonstration or a display. The project approach provides opportunities for children to take agency of their own learning and represent this learning through the construction of personally meaningful artefacts. If utilized effectively, possible characteristics may include: active, agentic, collaborative, explicit, learner-focused, responsive, scaffolded, playful, language-rich and dialogic. [10]
In the project approach, adults and children investigate topics of discovery using six steps: Observation, Planning, Research, Exploration, Documentation, Evaluation.
- Observation: A teacher observes children engaging with each other or with materials and highlights ideas from the observations to further explore.
- Planning : Teachers talk with children about the observation and brainstorm ideas about the topic and what to explore
- Research: Teachers find resources related to the topic
- Explore: Children engage with experiences set around the topic to create hypotheses and make predictions and formulate questions
- Documentation : Teachers write notes, create charts and children draw observations and fill in charts as they explore topics/questions
- Evaluate: Teachers and children can reflect on the hypotheses originally developed and compare their experiences to predictions. Evaluation is key in determining skills enhanced and what worked or what didn’t work and why.
The benefits of a project approach are that young learners are directly involved in making decisions about the topic focus and research questions, the processes of investigation and in the selection of the culminating activities. When young learners take an active role in decision making, agency and engagement is promoted.
As young learners take ownership of their learning they, ‘feel increasingly competent and sense their own potential for learning so they develop feelings of confidence and self-esteem’ (Chard, 2001). [11]
Culturally Appropriate Approach
The Cultural Appropriate Approach has evolved over the years and the practice of valuing children’s culture is imperative for children to feel a sense of belonging in ECE programs. Sensitivity to the variety of cultures within a community can create a welcoming atmosphere and teach children about differences and similarities among their peers. Consider meeting with families prior to starting the program to share about cultural beliefs, languages and or traditions. Classroom areas can reflect the cultures in many ways:
- Library Area: Select books that represent cultures in the classroom
- Dramatic Area: Ask families to donate empty boxes of foods they commonly use, bring costumes or clothes representative of culture
- Language: In writing center include a variety of language dictionaries;
- Science: Encourage families to come and share a traditional meal [12]
References
[1] Gordon, A. M. & Browne, K. W. (2001) Beginnings and Beyond, 8th edition . Wadsworth, Cengage Learning. (pg. 364)
[2] The Creative Curriculum for Preschool, Fourth Edition by the U.S. Department of Education is in the public domain
[3] Montessori education: a review of the evidence base by Chloë Marshall is licensed under CC BY 4.0
[4] On the Unique Place of Art in Waldorf Education by Gilad Goldshmidt is licensed under CC BY 4.0
[5] Imagination, Waldorf, and critical literacies: Possibilities for transformative education in mainstream schools by Monica Shank is licensed under CC BY 2.0
[6] Reggio Emilia Theory and Application by One Community is licensed under CC BY 3.0
[7] Image by Ian Joslin is licensed under CC BY 4.0
[8] Image by Ian Joslin is licensed under CC BY 4.0
[9] Image by Ian Joslin is licensed under CC BY 4.0
[10] Age Appropriate Pedagogies Project by Hanstweb is licensed under CC BY
[11] Age Appropriate Pedagogies Project by Hanstweb is licensed under CC BY
[12] Child Growth and Development by Jennifer Paris, Antoinette Ricardo, and Dawn Rymond is licensed under CC BY 4.0